Documentation for the TIMES Model PART II

Transcription

1 Eegy Techology Syem Aalyi Pogamme h:// Documeaio fo he TIMES Model PART II Ail 2005 Auho: Richad Loulou Ai Lehilä Ami Kaudia Uwe Reme Gay Goldei 1

2 Geeal Ioducio Thi documeaio i comoed of hee Pa. Pa I comie eigh chae coiuig a geeal deciio of he TIMES aadigm wih emhai o he model geeal ucue ad i ecoomic igificace. Pa I alo iclude a imlified mahemaical fomulaio of TIMES a chae comaig i o he MARKAL model oiig o imilaiie ad diffeece ad chae decibig ew model oio. Pa II comie 7 chae ad coiue a comeheive efeece maual ieded fo he echically mided modele o ogamme lookig fo a i-deh udeadig of he comlee model deail i aicula he elaiohi bewee he iu daa ad he model mahemaic o coemlaig makig chage o he model equaio. Pa II iclude a full deciio of he e aibue vaiable ad equaio of he TIMES model. Pa III decibe he GAMS cool aeme equied o u he TIMES model. GAMS i a modelig laguage ha alae a TIMES daabae io he Liea Pogammig maix ad he ubmi hi LP o a oimize ad geeae he eul file. I addiio o he GAMS ogam wo model ieface (VEDA-FE ad VEDA-BE) ae ued o ceae bowe ad modify he iu daa ad o exloe ad fuhe oce he model eul. The wo VEDA ieface ae decibed i deail i hei ow ue guide. 2

3 PART II: REFERENCE MANUAL 3

4 TABLE OF CONTENTS FOR PART II 1 INTRODUCTION Baic oaio ad coveio GAMS modellig laguage ad TIMES imlemeaio SETS Idexe (Oe-dimeioal e) Ue iu e Defiiio of he Refeece Eegy Syem (RES) Pocee Commodiie Defiiio of he ime ucue Time hoizo Timelice Muli-egioal model Oveview of all ue iu e Defiiio of ieal e PARAMETERS Ue iu aamee Ie- ad exaolaio of ue iu aamee Iheiace ad aggegaio of imeliced iu aamee Oveview of ue iu aamee Ieal aamee Reo aamee VARIABLES VARACT(v) VARBLND(bleo) VARCAP() VARCOMNET(c) VARCOMPRD(c) VARDNCAP(u) VARELAST(cjl) VARFLO(vc) VARIRE(vcie) VARNCAP(v) VAROBJ(y 0 ) ad elaed vaiable VAROBJR( y 0 ) INVCOST(y) INVTAXSUB(y) INVDECOM(y) FIXCOST(y) FIXTAXSUB(y) VARCOST(y)

5 ELASTCOST(y) LATEREVENUES(y) SALVAGE(y 0 ) VARSIN/SOUT(vc) Vaiable ued i Ue Coai VARUC(uc) VARUCR(uc) VARUCT(uc) VARUCRT(uc) VARUCTS(uc) VARUCRTS(uc) VARUCSU(uc) VARUCSUS(uc) VARUCRSUS(uc) VARUCRSU(uc) EQUATIONS Noaioal coveio Noaio fo ummaio Noaio fo logical codiio Uig Idicao fucio i aihmeic exeio Objecive fucio EQOBJ Ioducio ad oaio Noaio elaive o ime Ohe oaio Remide of ome echology aibue ame (each i idexed by ) Dicouig oio Comoe of he Objecive fucio Iveme co: INVCOST(y) Taxe ad ubidie o iveme Decommiioig (dimalig) caial co: COSTDECOM(y) Fixed aual co: FIXCOST(y) SURVCOST(y) Aual axe/ubidie o caaciy: FIXTAXSUB(Y) Vaiable aual co VARCOST(y) y EOH Co of demad educio ELASTCOST(y) Salvage value: SALVAGE (EOH1) Lae eveue fom edogeou commodiy ecyclig afe EOH LATEREVENUE(y) The wo dicouig mehod fo aual ayme Coai Equaio: EQACTFLO Equaio EQ(l)ACTBND Equaio: EQ(l)BLND Boud: BNDELAST Equaio: EQ(l)BNDNET/PRD Equaio: EQ(l)CAPACT Equaio: EQ(l)CPT Equaio: EQ(l)COMBAL Equaio: EQECOMPRD Equaio: EQ(l)CUMNET/PRD Equaio EQDSCNCAP Equaio: EQDSCONE Equaio: EQ(l)FLMRK Equaio: EQ(l)FLOBND Equaio: EQ(l)FLOFR Equaio elaed o exchage (EQIRE EQIREBND EQXBND) Equaio EQIRE Equaio: EQ(l)IREBND Equaio: EQ(l)XBND

6 Equaio: EQ(l)INSHR EQ(l)OUTSHR Equaio: EQPEAK Equaio: EQPTRANS Equaio: EQSTGTSS/IPS EQSRGTSS: Soage bewee imelice (icludig igh-oage device): EQSTGIPS: Soage bewee eiod Equaio: EQ(l)STGIN / EQ(l)STGOUT Ue Coai Equaio: EQ(l)UC / EQEUC Equaio: EQ(l)UCR / EQEUCR Equaio: EQ(l)UCT / EQEUCT Equaio: EQ(l)UCRT / EQEUCRT Equaio: EQ(l)UCRTS / EQEUCRTS Equaio: EQ(l)UCTS / EQEUCTS Equaio: EQ(l)UCSU / EQEUCSU Equaio: EQ(l)UCRSU / EQEUCRSU Equaio: EQ(l)UCRSUS / EQEUCRSU Equaio: EQ(l)UCSUS / EQEUCSUS Equaio: EQ(l)UCSU / EQEUCSU Equaio: EQ(l)UCRSU / EQEUCRSU Equaio: EQ(l)UCRSUS / EQEUCRSU Equaio: EQ(l)UCSUS / EQEUCSUS THE ENDOGENOUS TECHNOLOGICAL LEARNING (ETL) OPTION Se Swiche ad Paamee Vaiable VARCCAP() VARCCOST() VARDELTA(k) VARIC() VARLAMBD(k) Equaio EQCC() EQCLU() EQCOS() EQCUINV() EQDEL() EQEXPE1(k) EQEXPE2(k) EQIC1() EQIC2() EQLA1(k) EQLA2(k) EQOBJSAL(cu) EQOBJINV(cu) THE TIMES CLIMATE MODULE Fomulaio of he TIMES Climae Module Aoach ake Coceaio (accumulaio of CO2) Radiaive focig Temeaue iceae Iu aamee of he Climae Module Climae elaed Vaiable VARCO2TOT() VARCO2ATM() VARCO2UP() VARCO2LOW()

7 7.4 Climae Equaio Equaio: EQCO2TOT Equaio: EQCO2ATM Equaio: EQCO2UP Equaio: EQCO2LOW Equaio: EQMXCONC Reoig Paamee DTFORC DTATM DTLOW Defaul value of he climae aamee GAMS imlemeaio Secificaio of aamee Climae elaed Vaiable Equaio Examle of ue Exoig eul o VEDA Refeece fo chae

8 1 Ioducio The uoe of he Refeece Maual i o lay ou he full deail of he TIMES model icludig daa ecificaio ieal daa ucue ad mahemaical fomulaio of he model Liea Pogam (LP) fomulaio a well a he Mixed Iege Pogammig (MIP) fomulaio equied by ome of i oio. A uch i ovide he TIMES modelle/ogamme wih ufficiely deailed ifomaio o fully udead he aue ad uoe of he daa comoe model equaio ad vaiable. A olid udeadig of he maeial i hi Maual i a eceay eequiie fo ayoe coideig makig ogammig chage i he TIMES ouce code. The Refeece Maual i ogaized a follow: Chae 1 Baic oaio ad coveio: lay he goudwok fo udeadig he e of he maeial i he Refeece Maual; Chae 2 Se: exlai he meaig ad ole of vaiou e ha ideify how he model comoe ae goued accodig o hei aue (e.g. demad device owe la eegy caie ec.) i a TIMES model; Chae 3 Paamee: elaboae he deail elaed o he ue-ovided umeical daa a well a he ieally couced daa ucue ued by he model geeao (ad eo wie) o deive he coefficie of he LP maix (ad eae he eul fo aalyi); Chae 4 Vaiable: defie each vaiable ha may aea i he maix boh exlaiig i aue ad idicaig how if fi io he maix ucue; Chae 5 Equaio: ae each equaio i he model boh exlaiig i ole ad ovidig i exlici mahemaical fomulaio; Chae 6 The Ue Coai: exlai he famewok ha may be emloyed by modelle o fomulae addiioal liea coai which ae o a of he geeic coai e of TIMES wihou havig o bohe wih ay GAMS ogammig; Chae 7 The Lumy Iveme faciliy ad Chae 8 The Edogeou Techological Leaig caabiliy. 1.1 Baic oaio ad coveio To ai he eade he followig coveio ae emloyed coiely houghou hi chae: Se ad hei aociaed idex ame ae i lowe ad bold cae e.g. com i he e of all commodiie; Lieal exlicily defied i he code ae i ue cae wihi igle quoe e.g. UP fo ue boud; Paamee ad cala (coa i.e. u-idexed aamee) ae i ue cae e.g. NCAPAF fo he availabiliy faco of a echology; Vaiable ae i ue cae wih a efix of VAR e.g. VARACT coeod o he aciviy level of a echology. Equaio ae i ue cae wih a efix of EQ o EQ(l) wih he laceholde (l) deoig he equaio ye (l=e fo a ic equaliy l=l fo a iequaliy wih he lef 8

9 had ide em beig malle o equal he igh had ide em ad l=g fo a iequaliy wih he lef had ide em beig geae o equal he igh had ide em)e.g. EQCOMBAL i he commodiy balace coai ad 1.2 GAMS modellig laguage ad TIMES imlemeaio TIMES coi of geeic vaiable ad equaio couced fom he ecificaio of e ad aamee value deicig a eegy yem fo each diic egio i a model. To couc a TIMES model a eoceo fi alae all daa defied by he modelle io ecial ieal daa ucue eeeig he coefficie of he TIMES maix alied o each vaiable of Chae 4 fo each equaio of Chae 5 i which he vaiable may aea. Thi e i called Maix Geeaio. Oce he model i olved (oimied) a Reo Wie aemble he eul of he u fo aalyi by he modelle. The maix geeaio eo wie ad cool file ae wie i GAMS 1 (he Geeal Algebaic Modellig Syem) a oweful high-level laguage ecifically deiged o faciliae he oce of buildig lagecale oimiaio model. GAMS accomlihe hi by elyig heavily o he coce of e comoud idexed aamee dyamic looig ad codiioal cool vaiable ad equaio. Thu hee i vey a og yegy bewee he hiloohy of GAMS ad he oveall coce of he RES ecificaio embodied i TIMES makig GAMS vey well uied o he TIMES aadigm. Fuhemoe by aue of i udelyig deig hiloohy he GAMS code i vey imila o he mahemaical deciio of he equaio ovided i Chae 5. Thu he aoach ake o imleme a TIMES model i o maage he iu daa by mea of a (ahe comlex) eoceo ha hadle he eceay exceio ha eed o be ake io coideaio o oely couc he maix coefficie i a fom eady o be alied o he aoiae vaiable i he eecive equaio. GAMS alo iegae eamlely wih a wide age of commecially available oimie ha ae chaged wih he ak of olvig he acual TIMES liea (LP) o mixed iege (MIP) oblem ha eee he deied model. Thi e i called he Solve o Oimiaio e. CPLEX o XPRESS ae he oimie mo ofe emloyed o olve he TIMES LP ad MIP fomulaio. The adad TIMES fomulaio ha oioal feaue uch a lumy iveme ad edogeou echology leaig. I addiio a modelle exeieced i GAMS ogammig ad he deail of he TIMES imlemeaio ca defie addiioal equaio module o eo ouie module baed o a exeio mechaim which allow he likage of hee module o he adad TIMES code i a flexible way (ee PART III chae 3) To build u ad aalye a TIMES model eveal ofwae ool have bee develoed i he a o ae cuely ude develome o ha he modelle doe o eed o ovide he iu ifomaio eeded o build a TIMES model diecly i GAMS. Thee ool ae he model ieface VEDA-FE ANSWER-TIMES a well a he eoig ad aalyig ool VEDA-BE. 1 GAMS A Ue Guide A. Booke D. Kedick A. Meeau R. Rama GAMS Develome Cooaio Decembe

10 2 Se Se ae ued i TIMES o gou eleme o combiaio of eleme wih he uoe of ecifyig qualiaive chaaceiic of he eegy yem. Oe ca diiguih bewee oedimeioal ad muli-dimeioal e. The fome e coai igle eleme e.g. he e c coai all ocee of he model while he eleme of muli-dimeioal e ae a combiaio of oe-dimeioal e. A examle fo a muli-dimeioal e i he e o which ecifie fo a oce he commodiie eeig ad leavig ha oce. Two ye of e ae emloyed i he TIMES famewok: ue iu e ad ieal e. Ue iu e ae ceaed by he ue ad ued o decibe qualiaive ifomaio ad chaaceiic of he deiced eegy yem. Oe ca diiguih he followig fucio aociaed wih ue iu e: defiiio of he eleme o buildig block of he eegy yem model (i.e. egio ocee commodiie) defiiio of he ime hoizo ad he ub-aual ime eoluio defiiio of ecial chaaceiic of he eleme of he eegy yem. I addiio o hee ue e TIMES alo geeae i ow ieal e. Ieal e eve o boh eue oe exceio hadlig (e.g. fom wha dae i a echology available o i which ime-lice i a echology emied o oeae) a well a omeime ju o imove he efomace o mooh he comlexiy of he acual model code. I he followig ecio he ue iu e ad he ieal e will be eeed. A ecial ye of e i a oe-dimeioal e alo called idex which i eeded o build mulidimeioal e o aamee. A he highe level of he oe-dimeioal e ae he mae o domai e ha defie he comeheive li of eleme (e.g. he mai buildig block of he efeece eegy yem uch a he ocee ad commodiie i all egio) emied a all ohe level wih which GAMS efom comlee domai checkig helig o auomaically eue he coece of e defiiio (fo iace if he oce ame ued i a aamee i o elled coecly GAMS will iue a waig). Theefoe befoe elaboaig o he vaiou e he idexe ued i TIMES ae dicued. 2.1 Idexe (Oe-dimeioal e) Idexe (alo called oe-dimeioal e) coai i mo cae he diffee eleme of he eegy model. A li of all idexe ued i TIMES i give i Table 2. Examle of idexe ae he e c coaiig all ocee he e c coaiig all commodiie o he e alleg coaiig all egio of he model. Some of he oe-dimeioal e ae ube of aohe oe-dimeioal e e.g. he e comiig he o-called ieal model egio i a ube of he e alleg which i addiio alo coai he o-called exeal model egio 2. To exe ha he e deed o he e alleg he mae e alleg i u i backe afe he e ame : (all). The e cg comie all commodiy gou 3. Each commodiy c i coideed a a commodiy gou wih oly oe eleme he commodiy ielf. Thu he commodiy e c i a ube of he commodiy gou e cg. Aa fom idexe ha ae ude ue cool ome idexe have fixed eleme o eve a idicao wihi e ad aamee ad hould o be modified by he ue (Table 1). The oly exceio o hi ule i he e cg: while he oce gou IRE NST PRV 2 The meaig ad he ole of ieal ad exeal egio i dicued i Secio See Secio fo a moe i-deh eame of commodiy gou. 10

11 PRW STG ad STK ae ued wihi he code ad mu o be deleed he ohe oce gou may be modified by he ue. Table 1: Se wih fixed eleme Se/Idex ame Deciio bd(lim) Idex of boud ye; ube of he e lim havig he ieally fixed eleme LO UP FX. comye Idicao of commodiy ye; iiialized o he eleme DEM (demad) NRG (eegy) MAT (maeial) ENV (eviome) FIN (fiacial) bu he ue ca defie ay li fo comye i MAPLIST.DEF wih he exceio of he edefied eleme DEM ENV FIN MAT NRG. lim Idex of limi ye; ieally fixed o he eleme LO UP FX N. ie Exo/imo exchage idex; ieally fixed o he wo eleme: IMP adig fo imo ad EXP adig fo exo. io Iu/Ouu idex; ieally fixed eleme: IN OUT ; ued i combiaio wih ocee ad commodiie a idicao whehe a commodiy ee o leave a oce. cg Li of oce gou; ieally eablihed i MAPLIST:DEF a: CHP: combied hea ad owe la DISTR: diibuio oce DMD: demad device ELE: eleciciy oducig echology excludig CHP HPL: hea la MISC: micellaeou PRE: echology wih eegy ouu o fallig i he gou of he ohe eegy echologie REF: efiey oce RENEW: eewable eegy echology XTRACT: exacio oce. The ue may adju hi li o ay dijoi gou deied. The followig gou ae equied by he model heefoe mu o be deleed by he ue: IRE: ie-egioal exchage oce PRV: echology wih maeial ouu meaued i volume ui PRW: echology wih maeial ouu meaued i weigh ui NST: igh (off-eak) oage oce STG: oage oce STK: ockilig oce. lvl Idex of imelice level; ieally fixed o he eleme ANNUAL SEASON WEEKLY DAYNITE. ucgye Idex of ieally fixed key ye of vaiable: = ACT CAP COMPRD COMCON FLO IRE NCAP ued i aociaio wih he ue coai. ucame Li of ieally fixed idicao fo aibue able o be efeeced a coefficie i ue coai (e.g. he flow vaiable may be mulilied by he aibue FLOCOST i a ue coai if deied): = ACTCOST ACTBNDUP ACTBNDLO ACTBNDFX CAPBNDUP CAPBNDLO CAPBNDFX GROWTH FLOCOST FLODELIV FLOSUB FLOTAX NCAPCOST NCAPITAX NCAPISUB. 11

12 Table 2: Idexe i TIMES Idex 4 Aliae 5 Relaed Idexe 6 age Deciio Idex fo age (umbe of yea ice iallaio) io a aamee haig cuve; defaul eleme all alleg All ieal ad exeal egio. bd bdye lim Idex of boud ye; ube of lim havig he ieally fixed eleme LO UP FX. c cg comy e com com1 com2 com3 comg cg1 cg2 cg3 cg4 cg c Ue defied 7 li of all commodiie i all egio; ube of cg. Ue defied li of all commodiie ad commodiy gou i all egio 8 ; each commodiy ielf i coideed a commodiy gou; iiial eleme ae he membe of comye. Idicao of commodiy ye; iiialized o he eleme DEM (demad) NRG (eegy) MAT (maeial) ENV (eviome) FIN (fiacial) bu he ue ca defie ay li fo comye i MAPLIST.DEF wih he exceio of he edefied eleme DEM ENV FIN MAT NRG. cu cu Ue defied li of cuecy ui. daayea y Yea fo which model iu daa ae ecified. ie imex Exo/imo exchage idicao; ieally fixed = EXP fo exo ad IMP fo imo. io iou Iu/Ouu idicao fo defiig whehe a commodiy flow ee o leave a oce; ieally fixed = IN fo ee ad OUT fo leave. j k Idicao fo elaic demad e ad equece umbe of he hae/muli cuve; defaul eleme Idex fo kik oi i ETL fomulaio; cuely limied o 1-6 {ca be exeded i <cae>.u file by icludig SET KP / 1* /; fo -kik oi. lim limye l bd Idex of limi ye; ieally fixed = LO UP ll FX ad N. c Ue defied li of all ocee i all egio 9. 4 Thi colum coai he ame of he idexe a ued i hi docume. 5 Fo ogammig eao aleaive ame (aliae) may exi fo ome idexe. Thi ifomaio i oly eleva fo hoe ue who ae ieeed i gaiig a udeadig of he udelyig GAMS code. 6 Thi colum efe o oible elaed idexe e.g. he idex c i a ube of he idex cg. 7 VEDA comile he comlee li fom he uio of he commodiie defied i each egio. 8 VEDA comlie he comlee li fom he uio of he commodiy gou defied i each egio. 9 VEDA comlie he comlee li fom he uio of he ocee defied i each egio. 12

13 Idex 4 Aliae 5 Relaed Idexe 6 Deciio ayea y modlyeay Yea fo which a iveme ae ecified; ayea mu be befoe he begiig of he fi eiod. cg Li of oce gou; ieally eablihed i MAPLIST:DEF a: CHP: DISTR: DMD: ELE: HPL: MISC: PRE: combied hea ad owe la diibuio oce demad device eleciciy oducig echology excludig CHP hea la micellaeou echology wih eegy ouu o fallig i he gou of he ohe eegy echologie efiey oce REF: RENEW: eewable eegy echology XTRACT: exacio oce. The ue may adju hi li o ay dijoi gou deied. The followig gou ae equied by he model ad heefoe mu o be deleed by he ue: IRE: ie-egioal exchage oce PRV: echology wih maeial ouu meaued i volume ui PRW: echology wih maeial ouu meaued i weigh ui NST: igh (off-eak) oage oce STG: oage oce STK: ockilig oce. eg all Exlici egio wihi he aea of udy. all Timelice diviio of a yea a ay of he lvl level. 2 l mileoy y Reeeaive yea fo he model eiod. eg Techologie modelled wih edogeou echology leaig. lvl Timelice level idicao; ieally fixed = ANNUAL SEASON WEEKLY DAYNITE. u ui uicom uica Li of all ui; maiaied i he file UNITS.DEF. ucgy e uc uiac Fixed ieal li of he key ye of vaiable: fixed = ACT CAP COMPRD COMCON FLO IRE NCAP. Ue ecified uique idicao fo a ue coai. 13

14 Idex 4 Aliae 5 Relaed Idexe 6 ucame ui Deciio The li of idicao aociaed wih vaiou aibue ha ca be efeeced i ue coai o be alied whe deivig a coefficie (e.g. he flow vaiable may be mulilied by he aibue FLOCOST o eee exediue aociaed wih aid flow i a ue coai if deied): = ACTCOST ACTBNDUP ACTBNDLO ACTBNDFX CAPBNDUP CAPBNDLO CAPBNDFX GROWTH FLOCOST FLODELIV FLOSUB FLOTAX NCAPCOST NCAPITAX NCAPISUB. Li of caaciy block ha ca be added i lumy iveme oio; defaul eleme 0-100; he eleme 0 decibe he cae whe o caaciy i added. uiac u Li of aciviy ui; maiaied i he file UNITS.DEF. uica u Li of caaciy ui; maiaied i he file UNITS.DEF. uico m u Li of commodiy ui; maiaied i he file UNITS.DEF. v modlyea ayea Uio of he e ayea ad coeodig o all modellig eiod. y allyea k ll daayea ayea modlyea mileoy Yea ha ca be ued i he model; defaul age ; ude ue cool by he dolla cool aamee $SET BOTIME yyyy ad $SET EOTIME i he <cae>.run file. 14

15 2.2 Ue iu e The ue iu e coai he fudameal ifomaio egadig he ucue ad he chaaceiic of he udelyig eegy yem model. The ue iu e ca be goued accodig o he ye of ifomaio elaed o hem: Oe dimeioal e defiig he comoe of he eegy yem: egio commodiie ocee; Se defiig he Refeece Eegy Syem (RES) wihi each egio; Se defiig he ie-coecio (ade) bewee egio; Se defiig he ime ucue of he model; Se defiig vaiou oeie of ocee o commodiie. The fomulaio of ue coai alo ue e o ecify he ye ad he feaue of a coai. The ucue ad he iu ifomaio equied o couc a ue coai i coveed i deail i Chae 5 ad heefoe will o be eeed hee. I he followig ubecio fi he e elaed o he defiiio of he RES will be decibed (ubecio 2.2.1) he he e elaed o he ime hoizo ad he ub-aual eeeaio of he eegy yem will be eeed (ubecio 2.2.2). The mechaim of defiig ade bewee egio of a muli-egioal model i dicued i ubecio Fially a oveview of all oible ue iu e i give i ubecio Defiiio of he Refeece Eegy Syem (RES) A TIMES model i ucued by egio (all). Oe ca diiguih bewee exeal egio ad ieal egio. The ieal egio () coeod o egio wihi he aea of udy ad fo which a RES ha bee defied by he ue. Each ieal egio may coai ocee ad commodiie o deic a eegy yem wheea exeal egio eve oly a oigi of commodiie (e.g. fo imo of imay eegy eouce o fo he imo of eegy caie) o a deiaio fo he exo of commodiie. A egio i defied a a ieal egio by uig i i he ieal egio e () which i a ube of he e of all egio all. A exeal egio eed o exlici defiiio all egio ha ae membe of he e all bu o membe of ae exeal egio. A TIMES model mu coi of a lea oe ieal egio he umbe of exeal egio i abiay. The mai buildig block of he RES ae ocee () ad commodiie (c) which ae coeced by commodiy flow o fom a ewok. A examle of a RES wih oe ieal egio (UTOPIA) ad wo exeal egio (IMPEXP MINRNW) i give i Figue 1. All comoe of he eegy yem a well a ealy he eie iu ifomaio ae ideified by a egio idex. I i heefoe oible o ue he ame oce ame i diffee egio wih diffee umeical daa (ad deciio if deied) o eve comleely diffee commodiie aociaed wih he oce. 15

16 Exeal egio Ieal egio UTOPIA IMPEXP OIL HYD URN FEQ HCO GSL DSL ELC RH RL TX NOX E01 E51 RHE E21 SRE E31 E70 RL1 RHO TXD MINRNW TXE TXG Figue 1: Examle of ieal ad exeal egio i TIMES Pocee A oce may eee a idividual la e.g. a ecific exiig uclea owe la o a geeic echology e.g. he coal-fied IGCC echology. TIMES diiguihe hee mai ye of ocee: Sadad ocee; Ie-egioal exchage ocee ad Soage ocee Sadad ocee The o-called adad ocee ca be ued o model he majoiy of he eegy echologie e.g. codeig owe la hea la CHP la demad device uch a boile coal exacio ocee ec. Sadad ocee ca be claified io he followig gou: PRE fo geeic eegy ocee; PRW fo maeial oceig echologie (by weigh); PRV fo maeial oceig echologie (by volume); REF fo efiey ocee; ELE fo eleciciy geeaio echologie; HPL fo hea geeaio echologie; CHP fo combied hea ad owe la; DMD fo demad device; DISTR fo diibuio yem; MISC fo micellaeou ocee 16

17 via he e cma(cg). Thi gouig doe o affec he oeie of he adad ocee 10 o he maix bu i ieded fo eoig uoe. The e i maiaied i he MAPLIST.DEF file ad may be adjued by ue io ay li of dijoi echology gou of iee wih ome eicio a oed i Table 1. The oology of a adad oce i ecified by he e o(cio) of all quadule uch ha he oce i egio i coumig (io = IN ) o oducig (io = OUT ) commodiy c. Uually fo each ey of he oology e o a flow vaiable (ee VARFLO i Chae 4) will be ceaed. Whe he o-called educio algoihm i acivaed ome flow vaiable may be elimiaed ad elaced by ohe vaiable (ee PART III chae 4). The aciviy vaiable (VARACT) of a adad oce i equal o he um of oe o eveal commodiy flow o eihe he iu o he ouu ide of a oce. The aciviy of a oce i limied by he available caaciy o ha he aciviy vaiable eablihe a lik bewee he ialled caaciy of a oce ad he maximum oible commodiy flow eeig o leavig he oce duig a yea o a ubdiviio of a yea. The commodiy flow ha defie he oce aciviy ae ecified by he e cacu(cgu) whee he commodiy idex cg may be a igle commodiy o a ue-defied commodiy gou. The commodiy gou defiig he aciviy of a oce i alo called Pimay Commodiy Gou (PCG). Oil OIL Aciviy i PJ Dieel Commodiy gou CGSRE DSL GSL Gaolie Refiey SRE All commodiie i PJ Defiiio of commodiy gou Defiiio of oce aciviy COMGMAP(cgc) = {UTOPIA.CGSRE.DSL UTOPIA.CGSRE.GSL} PRCCG(cg) = {UTOPIA.SRE.CGSRE} PRCACTUNT(cgu) = {UTOPIA.SRE.CGSRE.PJ} Figue 2: Examle of he defiiio of a commodiy gou ad of he aciviy of a oce Ue-defied commodiy gou ae ecified by mea of he e comgma(cgc) which idicae he commodiie (c) belogig o he gou (cg). I ode o aly a uedefied commodiy gou i coecio wih a oce (o oly fo he defiiio of he oce aciviy bu alo fo ohe uoe e.g. i he afomaio equaio EQPTRANS) oe ha o aig he commodiy gou cg o he oce by ecifyig he ccg(cg). Thu i i oible o ue he ame commodiy gou ame fo diffee ocee. A examle fo he defiiio of he aciviy of a oce i how i Figue 2. I ode o defie he aciviy of he oce SRE a he um of he wo ouu flow of gaolie (GSL) ad dieel (DSL) oe ha o defie a commodiy gou called CGSRE coaiig hee wo commodiie. The ame of he commodiy gou ca be abiaily choe by he modelle. 10 The oly exceio ae maeial oceig echologie of ye PRW o PRV whee he gouig may affec he ceaio of he ieal e cg (ee Table 4). 17

18 I addiio o he aciviy of a oce oe ha o defie he caaciy ui of he oce. Thi i doe by mea of he e ccau(cgu) whee he idex cg deoe he imay commodiy gou. I he examle i Figue 3 he caaciy of he efiey oce i defied i moe/a (megaoe oil equivale). Sice he caaciy ad aciviy ui ae diffee (moe fo he caaciy ad PJ fo he aciviy) he ue ha o uly he coveio faco fom he eegy ui embedded i he caaciy ui o he aciviy ui. Thi i doe by ecifyig he aamee ccaac(). I he examle ccaac ha he value Oil OIL Aciviy i PJ Dieel Commodiy gou CGSRE DSL GSL Gaolie Refiey SRE All commodiie i PJ Caaciy i moe/a Defiiio of caaciy ui Coveio faco fom caaciy o aciviy ui PRCCAPUNT(cgu) = {UTOPIA.SRE.CGSRE.MTOE} PRCCAPACT UTOPIASRE = Figue 3: Examle of he defiiio of he caaciy ui I migh occu ha he ui i which he commodiy(ie) of he imay commodiy gou ae meaued i diffee fom he aciviy ui. A examle i how i Figue 4. The aciviy of he ao echology CAR i defied by commodiy TX1 which i meaued i aege kilomee PKM. The aciviy of he oce i howeve defied i vehicle kilomee VKM while he caaciy of he oce CAR i defied a umbe of ca NOC. DSL Aciviy i vehicle kilomee VKM Ca CAR TX1 Commodiy ui Paege kilomee PKM Caaciy i # of ca NOC Defiiio of oce aciviy PRCACTUNT(cgu) = {UTOPIA.CAR.TX1.PKM} Defiiio of caaciy ui PRCCAPUNT(cgu) = {UTOPIA.CAR.TX1.NOC} Coveio faco fom caaciy o aciviy ui PRCCAPACT UTOPIA CAR = Coveio faco fom aciviy ui o commodiy ui PRCACTFLO UTOPIA 2000CARTX1 = 1.5 Figue 4: Examle of diffee aciviy ad commodiy ui 18

19 The coveio faco fom caaciy o aciviy ui ccaac decibe he aveage mileage of a ca e yea. The oce aamee cacflo(ycg) coai he coveio faco fom he aciviy ui o he commodiy ui of he imay commodiy gou. I he examle hi faco coeod o he aveage umbe of eo e ca (1.5) Ie-egioal exchage ocee Ie-egioal exchage (IRE) ocee ae ued fo adig commodiie bewee egio. They ae eeded fo likig ieal egio wih exeal egio a well a fo modellig ade bewee ieal egio. A oce i ecified a a ie-egioal exchage oce by ecifyig i a a membe of he e cma( IRE ). If he exchage oce i coecig ieal egio hi e ey i equied fo each of he ieal egio adig wih egio. The oology of a ie-egioal exchage oce i defied by he e oie(allegcomallc) aig ha he commodiy com i egio alleg i exoed o he egio all (he aded commodiy may have a diffee ame c i egio all ha i egio alleg). Fo examle he oology of he exo of he commodiy eleciciy (ELCF) fom Face (FRA) o Gemay (GER) whee he commodiy i called ELCG via he exchage oce (HVGRID) i modelled by he oie ey: oie( FRA ELCF GER ELCG HVGRID ). The fi ai of egio ad commodiy ( FRA ELCF ) deoe he oigi ad he ame of he aded commodiy while he ecod ai ( GER ELCG ) deoe he deiaio. The ame of he aded commodiy ca be diffee i boh egio hee ELCF i Face ad ELCG i Gemay deedig o he choe commodiy ame i boh egio. A wih adad ocee he aciviy defiiio e cacu(cgu) ha o be ecified fo a exchage oce belogig o each ieal egio. The ecial feaue elaed o ieegioal exchage ocee ae decibed i ubecio Soage ocee Soage ocee ae ued o oe a commodiy eihe bewee eiod o bewee imelice. A oce () i ecified o be a ie-eiod oage (IPS) oce fo commodiy ( c ) by icludig i a a membe of he e cgi(c). I a imila way a oce i chaaceied a a geeal imelice oage (TSS) by icluio i he e cg(c). A ecial cae of imelice oage i a o-called igh-oage device (NST) whee he commodiy fo chagig ad he oe fo dichagig he oage ae diffee. A examle fo a igh oage device i a elecic heaig echology which i chaged duig he igh uig eleciciy ad oduce hea duig he day. Icludig a oce i he e c() idicae ha i i a igh oage device which i chaged i imelice(). Moe ha oe imelice ca be ecified a chagig imelice he oecified imelice ae aumed o be dichagig imelice. The chagig ad dichagig commodiy of a igh oage device ae ecified by he oology e (o). I hould be oed ha fo ie-eiod oage ad geeal imelice oage ocee he commodiy eeig ad leavig he oage i ecified by he e cgi(c) ad cg(c) eecively. Ohe commodiy flow ae o emied i combiaio wih hee wo oage ye ad hece he oology e o i o alicable o hee oage. A fo adad ocee he flow ha defie he aciviy of a oage oce ae ideified by ovidig he e cacu(c) ey. I coa o adad ocee he aciviy of a oage oce i howeve ieeed a he amou of he commodiy beig oed i he oage oce. Accodigly he caaciy of a oage oce decibe he maximum commodiy amou ha ca be ke i oage. 19

20 Baed o he oage chaaceizaio give by cgi cg o c fo a oce ieally a cma( STG ) ey i geeaed o u he oce i he gou of he oage ocee. A fuhe cma ey i ceaed o ecify he ye of oage ( STK fo ie-oeiod oage STS fo ime-lice oage ad NST fo a igh-oage device) Commodiie A meioed befoe he e of commodiie ( c ) i a ube of he commodiy gou e (cg). A commodiy i TIMES i chaaceied by i ye which may be a eegy caie ( NRG ) a maeial ( MAT ) a emiio --o eviomeal imac ( ENV ) a demad commodiy ( DEM ) o a fiacial eouce ( FIN ). The commodiy ye i idicaed by membehi i he commodiy ye maig e (comma(comyec)). The commodiy ye affec he defaul ee of he commodiy balace equaio. Fo NRG ENV ad DEM he commodiy oducio i omally geae ha o equal o coumio while fo MAT ad FIN he defaul commodiy balace coai i geeaed a a equaliy. The ye of he commodiy balace ca be modified by he ue fo idividual commodiie by mea of he commodiy limi e (comlim(clim)). The ui i which a commodiy i meaued i idicaed by he commodiy ui e (comui(cuicom)). The ue hould oe ha wihi he GAMS code of TIMES o ui coveio e.g. of imo ice ake lace whe he commodiy ui i chaged fom oe ui o aohe oe. Theefoe he oe hadlig of he ui i eiely he eoibiliy of he ue (o he ue ieface) Defiiio of he ime ucue Time hoizo The ime hoizo fo which he eegy yem i aalyed may age fom oe yea o may decade. The ime hoizo i uually li io eveal eiod which ae eeeed by ocalled mileoe yea ((allyea) o mileoy(allyea) ee Figue 5). Each mileoe yea eee a oi i ime whee deciio may be ake by he model e.g. iallaio of ew caaciy o chage i he eegy flow. The aciviy ad flow vaiable ued i TIMES may heefoe be coideed a aveage value ove a eiod. The hoe oible duaio of a eiod i oe yea. Howeve i ode o kee he umbe of vaiable ad equaio a a ize ha ca be oceed by he cue oluio ad eoig ofwae a well a comue hadwae a eiod uually comie eveal yea. The duaio of he eiod do o have o be equal o ha i i oible ha he fi eiod which uually eee he a ad i ued o calibae he model o hioic daa ha a legh of oe yea while he followig eiod may have loge duaio. Thu i TIMES boh he umbe of eiod ad he duaio of each eiod ae fully ude ue cool. The begiig yea of a eiod B(allyea) i edig yea E(allyea) i middle yea M(allyea) ad i duaio D(allyea) have o be ecified a iu aamee by he ue (ee Table 12 i ubecio 3.1.3) exce fo a yea whee B=E=mileoy. To decibe caaciy iallaio ha ook lace befoe he begiig of he model hoizo ad ill exi duig he modelig hoizo TIMES ue addiioal yea he ocalled a yea (ayea(allyea)) which ideify he coucio comleio yea of he aleady exiig echologie. The amou of caaciy ha ha bee ialled i a ayea i ecified by he aamee NCAPPASTI(allyea) alo called a iveme. Fo a oce a abiay umbe of a iveme may be ecified o eflec he age ucue i he exiig caaciy ock. The uio of he e mileoy ad ayea i called modelyea (o v). The yea fo which iu daa i ovided by he ue ae called daayea (daayea(allyea)). The daayea do o have o coicide wih modelyea ice he eoceo will ieolae o exaolae he daa ieally o he modelyea. All 20

21 ayea ae by defaul icluded i daayea bu a a geeal ule ay ohe yea fo which iu daa i ovided hould be exlicily icluded i he e daayea o ha ifomaio will o be ee by he model. Aa fom a few exceio (ee Table 3) all aamee value defied fo yea ohe ha daayea (o ayea) ae igoed by he model geeao. Due o he diicio bewee of modelyea ad daayea he defiiio of he model hoizo e.g. he duaio ad umbe of he eiod may be chaged wihou havig o adju he iu daa o he ew eiod. The ule ad oio of he ie- ad exaolaio ouie ae decibed i moe deail i ubecio Model hoizo 1 eiod 2 d eiod 3 d eiod 4 h eiod 5 h eiod Payea Mileoeyea Modelyea Daayea Figue 5: Defiiio of he ime hoizo ad he diffee yea ye Oe hould oe ha i i oible o defie a iveme (NCAPPASTI) o oly fo ayea bu alo fo mileoeyea. Sice he fi eiod() of a model may cove hioical daa i i ueful o oe he aleady kow caaciy iallaio made duig hi ime-a a a iveme ad o a a boud o ew iveme i he model daabae. If oe lae chage he begiig of he model hoizo o a moe ece yea he caaciy daa of he fi eiod() do o have o be chaged ice hey ae aleady oed a a iveme. Thi feaue heefoe uo he decoulig of he daayea fo which iu ifomaio i ovided ad he defiiio of he model hoizo fo which he model i u makig i elaively eay o chage he defiiio of he modelig hoizo. The ue of a iveme fo mileoeyea i alo ueful o ideify aleady laed (alhough o ye couced) caaciy exaio i he ea fuue I hi cae he model may ill decide o add addiioal ew caaciy if hi i ecoomical ad o ihibied by ay iveme boud. 21

22 Table 3: Paamee ha ca have value defied fo ay yea ieecive of daayea 12 Aibue ame GDRATE GCHNGMONY MULTI COMCUMPRD COMCUMNET CMHISTORY Deciio Geeal dicou ae fo cuecy i a aicula yea Exchage ae fo cuecy i a aicula yea Paamee mulilie able wih value by yea Cumulaive limi o go oducio of a commodiy fo a block of yea Cumulaive limi o e oducio of a commodiy fo a block of yea Climae module calibaio value; o a of he adad TIMES code bu icluded i he climae module exeio (ee chae 7 fo a deciio of he climae module) Timelice The mileoeyea ca be fuhe divided i ub-aual imelice i ode o decibe fo he chagig eleciciy load wihi a yea which may affec he equied eleciciy geeaio caaciy o ohe commodiy flow ha eed o be acked a a fie ha aual eoluio. Timelice may be ogaied io fou hieachy level oly: ANNUAL SEASON WEEKLY ad DAYNITE defied by he ieal e lvl. The level ANNUAL coi of oly oe membe he edefied imelice ANNUAL while he ohe level may iclude a abiay umbe of diviio. The deied imelice level ae acivaed by he ue ovidig eie i e gou(lvl) whee alo he idividual ue-ovided imelice () ae aiged o each level. A addiioal ue iu e ma(12) i eeded o deemie he ucue of a imelice ee whee imelice 1 i defied a he ae ode of 2. Figue 6 illuae a imelice ee i which a yea i divided io fou eao coiig of wokig day ad weeked ad each day i fuhe divided io day ad igh imelice. The ame of each imelice ha o be uique i ode o be ued lae a a idex i ohe e ad aamee. No all imelice level have o be uilized whe buildig a imelice ee fo examle oe ca ki he WEEKLY level ad diecly coec he eaoal imelice wih he dayie imelice. The duaio of each imelice i exeed a a facio of he yea by he aamee GYRFR(). The ue i eoible fo euig ha each lowe level gou um u oely o i ae imelice a hi i o veified by he e-oceo. The defiiio of a imelice ee i egio-ecific. Whe diffee imelice ame ad duaio ae ued i wo egio which ae coeced by a exchage oce he maig aamee IRECCVT(cegcom) fo commodiie ad IRETSCVT(eg) fo imelice have o be ovided by he ue o ma he diffee imelice defiiio. Whe he ame imelice defiiio ae ued hee maig able do o eed o be ecified by he ue. 12 The uoe of hi able i o li hoe aamee whoe yea value ae ideede of he iu daayea aociaed wih mo of he egula aamee ad heefoe hould o be ecified fo daayea. Fo examle a value fo MULTI(j2012) would o iclude 2012 i daayea if 2012 wee o eleva o he ohe iu aamee. 22

23 Figue 6: Examle of a imelice ee Commodiie may be acked ad oce oeaio coolled a a aicula imelice level by uig he e coml(clvl) ad cl(lvl) eecively. Povidig a commodiy imelice level deemie fo which imelice he commodiy balace will be geeaed whee he defaul i ANNUAL. Fo ocee he e cl deemie he imelice level of he aciviy vaiable. Thu fo iace codeig owe la may be foced o oeae o a eaoal level o ha he aciviy duig a eao i uifom while hydoowe oducio may vay bewee day ad igh if he DAYNITE level i ecified fo hydo owe la. Iead of ecifyig a imelice level he ue ca alo ideify idividual imelice fo which a commodiy o a oce i available by he e com(c) ad c() eecively. Noe ha whe ecifyig idividual imelice fo a ecific commodiy o oce by mea of com o c hey have o be o he ame imelice level. The imelice level of he commodiy flow eeig ad leavig a oce ae deemied ieally by he eoceo. The imelice level of a flow vaiable equal he imelice level of he oce whe he flow vaiable i a of he commodiy gou defiig he aciviy of he oce. Ohewie he imelice level of a flow vaiable i e o whicheve level i fie ha of he commodiy o he oce Muli-egioal model If a TIMES model coi of eveal ieal egio i i called a muli-egioal model. Each of he ieal egio coai a uique RES o eee he aiculaiie of he egio. A aleady meioed he egio ca be coeced by ie-egioal exchage ocee o eable ade of commodiie bewee he egio. Two ye of ade aciviie ca be deiced i TIMES: bi-laeal ade bewee wo egio ad mulilaeal ade bewee eveal uly ad demad egio. Bi-laeal ade ake lace bewee ecific ai of egio. A ai of egio ogehe wih a exchage oce ad he diecio of he commodiy flow i fi ideified whee he model eue ha ade hough he exchage oce i balaced bewee hee wo egio (whaeve amou i exoed fom egio A o egio B mu be imoed by egio 23

24 B fom egio A oibly adjued fo aoaio loe). The baic ucue i how i Figue 7. Bi-laeal adig may be fully decibed i TIMES by defiig a ie-egioal exchage oce ad by ecifyig he wo ai-wie coecio by idicaig he egio ad commodiie be aded via he e oie(cegcom). If ade hould occu oly i oe diecio he oly ha diecio i ovided i he e oie (exo fom egio io egio eg). The oce caaciy ad he oce elaed co (e.g. aciviy co iveme co) of he exchage oce ca be decibed idividually fo boh egio by ecifyig he coeodig aamee i each egio. If fo examle he iveme co fo a eleciciy lie bewee wo egio A ad B ae 1000 moeay ui (MU) e MW ad 60 % of hee iveme co hould be allocaed o egio A ad he emaiig 40 % o egio B he iveme co fo he exchage oce have o be e o 600 MU/MW i egio A ad o 400 MU/MW i egio B. Regio A com com Regio B Ie-egioal exchage oce Figue 7: Bilaeal ade i TIMES Bi-laeal ade i he mo deailed way o ecify ade bewee egio. Howeve hee ae cae whe i i o imoa o fully ecify he ai of adig egio. I uch cae he o-called muli-laeal ade oio deceae he ize of he model while eevig eough flexibiliy. Muli-laeal ade i baed o he idea ha a commo makelace exi fo a aded commodiy wih eveal ulyig ad eveal coumig egio fo he commodiy e.g. fo cude oil o GHG emiio emi. To faciliae he modellig of hi kid of ade cheme he coce of makelace ha bee ioduced i TIMES. To model a makelace fi he ue ha o ideify oe ieal egio ha aiciae boh i he oducio ad coumio of he aded commodiy. The oly oe exchage oce i ued o lik he uly ad demad egio wih he makelace egio uig he e oie. 13 The followig examle illuae he modellig of a makelace i TIMES. Aume ha we wa o e u a make-baed adig whee he commodiy CRUD ca be exoed by egio A B C ad D ad ha i ca be imoed by egio C D E ad F (Figue 8). 13 Noe howeve ha ome flexibiliy i lo whe uig mulilaeal ade. Fo iace i i o oible o exe aoaio co i a fully accuae mae if uch co deed uo he ecie ai of adig egio i a ecific way 24

25 Suly egio Demad egio Regio A Regio D Regio B Makelace Regio C Regio E Regio D The ame egio may occu o he uly ad demad ide. Regio F Figue 8: Examle of muli-laeal ade i TIMES Fi he exchage oce ad makelace hould be defied. Fo examle we could chooe he egio C a he makelace egio. The exchage oce ha he ame XP. The ade oibiliie ca he be defied imly by he followig ix oie eie: SET PRC / XP /; SET TOPIRE / A.CRUD.C.CRUD.XP B.CRUD.C.CRUD.XP D.CRUD.C.CRUD.XP C.CRUD.D.CRUD.XP C.CRUD.E.CRUD.XP C.CRUD.F.CRUD.XP /; To comlee he RES defiiio of he exchage oce oly he e cacu(cu) i eeded o defie he ui fo he exchage oce XP i all egio: SET PRCACTUNT / A.XP.CRUD.PJ B.XP.CRUD.PJ C.XP.CRUD.PJ D.XP.CRUD.PJ E.XP.CRUD.PJ F.XP.CRUD.PJ /; Thee defiiio ae ufficie fo eig u of he make-baed ade. Addiioally he ue ca of coue ecify vaiou ohe daa fo he exchage ocee fo examle iveme ad diibuio co ad efficiecie. 25

26 2.2.4 Oveview of all ue iu e All he iu e which ae ude ue cool i TIMES ae lied i Table 4. Fo a few e defaul eig exi ha ae alied if o ue iu ifomaio i give. Se ame aig wih he efix com ae aociaed wih commodiie he efix c deoe oce ifomaio ad he efix uc i eeved fo e elaed o ue coai. Colum 3 of Table 3 i a deciio of each e. I ome cae (eecially fo comlex e) wo (equivale) deciio may be give he fi i geeal em followed by a moe ecie deciio wihi quae backe give i em of -ule of idice. Remak Se ae ued i baically wo way: - a he domai ove which ummaio mu be effeced i ome mahemaical exeio o - a he domai ove which a aicula exeio o coai mu be eumeaed (elicaed) I he cae of -dimeioal e ome idexe may be ued fo eumeaio ad ohe fo ummaio. I each uch iuaio he diicio bewee he wo ue of he idexe i made clea by he way each idex i ued i he exeio. A examle will illuae hi imoa oi: coide he 4-dimeioal e o havig idexe cio (ee able 3 fo i ecie deciio). If ome quaiy A(cio) mu be eumeaed fo all value of he hid idex (c=commodiy) ad of he la idex (io=oieaio) bu ummed ove all ocee () ad egio () hi will be mahemaically deoed: EXPRESSION1 c io = A( c io) c io o I i hu udeood fom he idexe lied i he ame of he exeio (cio) ha hee wo idexe ae beig eumeaed ad hu by deducio oly ad ae beig ummed uo. Thu he exeio calculae he oal of A fo each commodiy c i each diecio io ( IN ad OUT ) ummed ove all ocee ad egio. Aohe examle illuae he cae of eed ummaio whee idex i eumeaed i he ie ummaio bu i ummed uo i he oue ummaio. Agai hee he exeio i made uambiguou by obevig he oiio of he diffee idexe (fo iace he oue ummaio i doe o he idex) EXPRESSION2 = B A c io ( ) ( ) c io o 26

27 Table 4: Ue iu e i TIMES Se ID/Idexe 14 Alia 15 Deciio alleg all Se of all egio ieal a well a exeal ; a egio i defied a ieal by uig i i he ieal egio e () egio ha ae o membe of he ieal egio e ae e defiiio exeal. c com com1 Ue defied li of all commodiie i all egio; ube of com2 com3 cg. cg comg cg1 cg2 Ue defied li of all commodiie ad commodiy gou (ee Figue 2) i all egio. cg3 cg4 clu Se of clue echologie i edogeou echology () clue (egc) comgma (cgc) comlim (clim) comoff (cy1y2) comeak (cg) leaig. Idicao ha echology eg i a leaig comoe ha may be a of eveal echologie c; eg i alo called key comoe [e of ile {egc} uch ha leaig comoe eg i a of echology c i egio ]. 16 Maig of commodiy c o ue-defied commodiy gou cg icludig ielf [e of ile {cgc} uch ha commodiy c i i gou cg i egio ]. Defiiio of commodiy balace equaio ye [e of ile {clim}uch ha commodiy c ha a balace of ye lim (lim= UP LO EQ ) i egio ]; Defaul: fo commodiie of ye NRG DM ad ENV oducio i geae o equal coumio while fo MAT ad FIN commodiie he balace i a ic equaliy. Secifyig ha he commodiy c i egio i o available bewee he yea y1 ad y2 [e of quadule {cy1y2} uch ha commodiy c i uavailable fom yea y1 o y1 i egio ] ; oe ha y1 may be BOH fo he fi yea of he fi eiod ad y2 may be EOH fo he la yea of he la eiod. e of ai {cg} uch ha a eakig coai i o be geeaed fo commodiy cg i egio ; oe ha he eakig equaio ca be geeaed fo a igle commodiy (cg alo coai igle commodiie c) o fo a gou of commodiie e.g. eleciciy commodiie diffeeiaed by volage level. 14 The fi ow coai he e ame. If he e i a oe-dimeioal ube of aohe e he ecod ow coai he ae e i backe. If he e i a muli-dimeioal e he ecod ow coai he idex domai i backe. 15 Fo ogammig eao aleaive ame (aliae) may exi fo ome idexe. Thi ifomaio i oly eleva fo hoe ue who ae ieeed i gaiig a udeadig of he udelyig GAMS code. 16 Fo mulidimeioal e uch a hi oe wo defiiyio ae omeime give oe a a idicao fucio o maig he ohe (i quae backe) a a e of -ule. 27

28 Se ID/Idexe 14 Alia 15 Deciio comk (cg) Se of ile {cg} uch ha a eakig coai fo a igle commodiy o a gou of commodiie cg (e.g. if he model diffeeiae bewee hee eleciciy commodiie: eleciciy o high middle ad low volage ) i o be geeaed fo he imelice ; Defaul: all imelice of com; oe ha he eakig coai will be bidig comma (comyec) com (c) coml (clvl) comui (cuicom) cu daayea oly fo he imelice wih he highe load. Maig of commodiie o he mai commodiy ye (ee comye); [e of ile {comyec} uch ha commodiy c ha ye comye]; Se of ile {c}uch ha commodiy c i available i imelice i egio ; commodiy balace will be geeaed fo he give imelice; Defaul: all imelice of imelice level ecified by coml. Se of ile {clvl} uch ha commodiy c i modelled o he imelice level lvl i egio ; Defaul: ANNUAL imelice level. Se of ile {cuicom} uch ha commodiy c i exeed i ui uicom i egio. Ue defied li of cuecy ui. Yea fo which model iu daa ae o be ake; No defaul. c Ue defied li of all ocee i all egio ayea y Yea fo which a iveme ae ecified; ayea have o lie befoe he begiig of he fi eiod; No defaul. cacu (cguiac) caoff (y1y2) ccau (cguica) ccg (cg) cdcca () Defiiio of aciviy [Se of quadule uch ha he commodiy gou cg i ued o defie he aciviy of he oce wih ui uiac i egio ]. Se of quadule {y1y2} uch ha oce cao oeae (aciviy i zeo) bewee he yea y1 ad y2 i egio ; oe ha y1 may be BOH fo fi yea of fi eiod ad y2 may be EOH fo la yea of la eiod. Defiiio of caaciy ui of oce [e of quadule {cguica}uch ha oce ue commodiy gou cg ad ui uica o defie i caaciy i egio ]. Ue defied commodiy gou (cg) aociaed wih a oce [e of ile {cg} uch ha commodiy gou cg ha bee defied fo oce i egio ]; oe: he ame commodiy gou ca be ued fo eveal ocee. Se of ocee o be modelled uig he lumy iveme fomulaio i egio ; Defaul: emy e. If i o i hi e he ay lumy iveme aamee ovided fo ae igoed. 28

29 Se ID/Idexe 14 Alia 15 Deciio cfoff (cy1y2) Se of exule ecifyig ha he flow of commodiy c a oce ad imelice i o available bewee he yea y1 ad y2 i egio ; oe ha y1 may be BOH fo fi yea of fi eiod ad y2 may be EOH fo la yea of la eiod. cg Li of oce gou ued icly fo eoig uoe; Defaul li of gou (defied i MAPLIST.DEF) i how i ecio cma (cg) coff (y1y2) c () ckaf (all) cko (all) cgi (c) cg (c) c (all) cl (lvl) cvi () c2 Gouig of ocee io oce gou (cg) [e of ile {cg} uch ha oce belog o gou cg i egio ]. Noe: ued icly fo eoig uoe. Se of quadule {y1y2} uch ha ew caaciy of oce cao be ialled bewee he yea y1 ad y2 i egio ; oe ha y1 may be BOH fo fi yea of fi eiod ad y2 may be EOH fo la yea of la eiod. Se of ile {} uch ha oce i a igh oage device wih chagig imelice i egio ; oe ha fo igh oage device he commodiy eeig ad he commodiy leavig he oage may be diffee a defied via he e o. Se of ai {all} uch ha he availabiliy faco (caaf) i o be ued a value fo he facio of caaciy of oce ha ca coibue o he eakig coai (cakc) i egio. Se of ai {all}uch ha oce cao be ued i he eakig coai i egio. Se of ile {c}uch ha oce i a ie-eiod oage fo he commodiy c i egio ; oe ha he commodiy c eeig ad leavig he oage i he ame o he e o i o ued fo hi ye of oce. Se of ile {c}uch ha oce i a oage oce bewee imelice (e.g. eaoal hydo eevoi day/igh umed oage) fo commodiy c i egio ; oe ha he oage oce oeae fo he imelice ecified by c; he ame commodiy c ee ad leave he oage o he e o i o ued fo hi ye of oce. Se of ile {all} uch ha oce ca oeae a imelice i egio ; Defaul: all imelice o he imelice level ecified by cl.. Se of ile {llvl} uch ha oce ca oeae a imelice level lvl i egio ; Defaul: ANNUAL imelice level. Se of ocee ha ae viaged echologie i egio i.e. echical chaaceiic ae ied o whe he caaciy wa ialled o he cue eiod; Defaul: oce i o viaged; oe ha viagig iceae he model ize. eg Se of ieal egio; Sube of all. 29

30 Se ID/Idexe 14 Alia 15 Deciio all 2 Se of all imelice (defie he ub-aual diviio of a l eiod). Timelice effecively defied fo ecific ocee eg o (cio) oie (allegcom allc) gou (alllvl) ma (all) uca (ucide ucgye ucame) mileoy ad echologie ae ube of hi e. Se of eeeaive yea (middle yea) fo he model eiod wihi he modellig hoizo. Se of echologie eleced fo edogeou echology leaig; Sube of e ; if o i eg he ay ETL iveme aamee ovided ae igoed. RES oology defiiio idicaig ha commodiy c ee (io= IN ) o leave (io= OUT ) he oce [e of quadule {cio} uch ha oce ha a flow of commodiy c wih oieaio io i egio ]. RES oology defiiio fo ade bewee egio [Se of quiule idicaig ha commodiy com fom egio alleg i aded (exoed) via exchage oce (whee i i imoed) io egio all a commodiy c]; oe: he ame of he aded commodiy may be diffee i he wo egio. Se of ile {alllvl} uch ha imelice belog o he imelice level lvl i egio ; eeded fo he defiiio of he imelice ee; oly defaul i ha he ANNUAL imelice belog o he ANNUAL imelice level. Se of ile {all} uch ha i a iemediae ode of he imelice ee (eihe ANNUAL o he lowe level) ad i a ode diecly ude i egio ; he e i fuhe exeded by allowig = (ee figue 1). Se of quiule uch ha he TIMES aibue ecified by he ucame (e.g. caaciy flow ec.) will be ued a coefficie fo he vaiable ideified by ucgye i he ue coai uc fo he ide ide ( LHS o RHS ) i egio ; if ucame= GROWTH he ue coai eee a gowh coai. ucgye Fixed ieal li of he key ye of vaiable: fixed = ACT CAP COMPRD COMCON FLO IRE NCAP. uc ucame uceach (alluc) Li of ue ecified uique idicao of he ue coai. The li of idicao aociaed wih vaiou aibue ha ca be efeeced i ue coai o be alied whe deivig a coefficie (e.g. he flow vaiable may be mulilied by he aibue FLOCOST o eee exediue aociaed wih aid flow i a ue coai if deied): = ACTCOST ACTBNDUP ACTBNDLO ACTBNDFX CAPBNDUP CAPBNDLO CAPBNDFX GROWTH FLOCOST FLODELIV FLOSUB FLOTAX NCAPCOST NCAPITAX NCAPISUB. Se of ai {alluc} uch ha he ue coai uc i o be geeaed fo each ecified egio all. 30

31 Se ID/Idexe 14 Alia 15 Deciio ucum (alluc) Se of ai {alluc}idicaig ha he ue coai uc i ummig ove all ecified egio all (ha i hee coai do o have a egio idex). Noe ha deedig o he ecified egio i uum he ummaio may be doe oly ove a ube of all model egio. Fo examle if he model coai he egio FRA GER ESP ad oe wa o ceae a ue coai called GHG ummig ove he egio FRA ad GER bu o ESP he e ucum coai ha he wo eie { FRA GHG } ad { GER GHG }. uceach (uc) Idicao ha he ue coai uc i o be geeaed fo each ecified eiod. ucucc (uc) Idicao ha he ue coai uc i o be geeaed bewee he wo ucceive eiod ad 1. ucum (uc) Idicao ha he ue coai uc i o be geeaed ummig ove he eiod. uceach (uc) Idicao ha he ue coai uc will be geeaed fo each ecified imelice. ucum (uc) Idicao ha he ue coai uc i o be geeaed ummig ove he ecified imelice. v modlyea Uio of he e ayea ad coeodig o all he yea (eiod) of a model u. 31

32 2.3 Defiiio of ieal e The e ieally deived by he TIMES model geeao ae give i Table 5. The li of ieal e eeed hee coceae o he oe fequely ued i he model geeao ad he oe ued i he deciio of he model equaio i Chae 5. Some ieal e ae omied fom Table 5 a hey ae icly auxiliay e of he eoceo whoe mai uoe i he educio of he comuaio ime fo eoceo oeaio. Table 5: Ieal e i TIMES Se ID 17 Idexe 18 af (bd) Deciio Idicao ha he ieal aamee COEFAF which i ued a coefficie of he caaciy (ew iveme vaiablevarncap lu a iveme NCAPPASTI) i he caaciy uilizaio coai EQ(l)CAPACT exi. bohyea Se allyea lu eleme BOH (Begiig Of Hoizo). (*) 19 dmyea Uio of e daayea ad modlyea (y) eachyea (y) eohyea (*) eohyea (y) fie () femi (cgccom) miy1 () oac () oca () ov (v) obj1a (v) Se of all yea bewee cala MINYR (fi yea eeded fo co calculaio i objecive fucio) ad MIYRVL DURMAX (eimaio of la yea oible co em may occu). Se allyea lu eleme EOH (Edig OF Hoizo) Se of all yea bewee cala MINYR (fi yea eeded fo co calculaio i objecive fucio) ad MIYRVL (la yea of model hoizo). Se of fie imelice ued i egio. Idicao ha he flow vaiable (VARFLO) aociaed wih emiio com ca be elaced by he flow vaiable of c mulilied by he emiio faco FLOSUM which i ued i he afomaio equaio (EQPTRANS) bewee he commodiy gou cg ad he commodiy com; ued i he educio algoihm (ee Pa III). Fi mileoy. Li of ocee i egio o equiig he aciviy vaiable; ued i educio algoihm Li of ocee i egio o havig ay caaciy elaed iu aamee; ued i educio algoihm. New iveme i oce i egio i o oible i eiod v ad eviouly ialled caaciy doe o exi aymoe. Iveme cae mall iveme (NCAPILED/D(v) <= GILEDNO) ad o eeiio of iveme (NCAPTLIFE NCAPILED >= D(v)) fo oce i egio ad viage eiod v. 17 Name of he ieal e a ued i hi documeaio ad he GAMS code. 18 Idex domai of he ieal e i give i backe. 19 The aeik deoe i he modelig yem GAMS a wildcad o ha domai checkig i diabled ad ay idex may be ued. 32

33 Se ID 17 Idexe 18 obj1b (v) obj2a (v) obj2b (v) objumi (yvk) objumiii (yvk) objumiv (yvk) objumiv (ykv) objum (v) objum3 (v) objumi (vk) eiody (vy) cac () cca () Deciio Iveme cae mall iveme (NCAPILED/D(v) <= GILEDNO) ad eeiio of iveme (NCAPTLIFE NCAPILED < D(v)) fo oce i egio ad viage eiod v. Iveme cae lage iveme (NCAPILED/D(v) > GILEDNO) ad o eeiio of iveme (NCAPTLIFE NCAPILED >= D(v)) fo oce i egio ad viage eiod v. Iveme cae lage iveme (NCAPILED/D(v) > GILEDNO) ad eeiio of iveme (NCAPTLIFE NCAPILED < D(v)) fo oce i egio ad viage eiod v. Summaio cool fo iveme ad caaciy elaed axe ad ubidie wih uig yea idex y of aual objecive fucio viage eiod v ad commiioig yea k (e.g. i cae of eadig iveme ove coucio ime). Summaio cool fo decommiioig co wih fo he uig yea idex y of aual objecive fucio viage eiod v ad commiioig yea k (e.g. fo eadig decommiioig co ove decommiioig ime). Summaio cool fo fixed co wih uig yea idex y of aual objecive fucio viage eiod v ad commiioig yea k. Summaio cool fo decommiioig uveillace co wih uig yea idex y of aual objecive fucio viage eiod v ad commiioig yea k. Idicao ha oce i egio wih viage eiod v ha a alvage value fo iveme wih a (echical) lifeime ha exed a he model hoizo. Idicao ha oce i egio wih viage eiod v ha a alvage value aociaed wih he decommiioig o uveillace co. Idicao ha fo commiioig yea k oce i egio wih viage eiod v ha a alvage value due o iveme decommiioig o uveillace co aig fom he echical lifeime exedig a he model hoizo. Maig of idividual yea y o he modlyea (mileoy o ayea; v) eiod hey belog o; if v i a ayea oly he ayea ielf belog o he eiod; fo he la eiod of he model hoizo alo he yea uil he vey ed of he model accouig hoizo (MIYRVL DURMAX) ae eleme of eiody. Idicao ha a oce i egio eed a aciviy vaiable (ued i educio algoihm). Idicao ha a oce i egio eed a caaciy vaiable (ued i educio algoihm). 33

34 Se ID 17 Idexe 18 cg (cg) c (c) cj (cjbd) ccombal (cbd) ccomd (cbd) ccom (c) hcombal (c) hcomd (c) () 11 () 1 () flo () iou (io) ie (all) g (cg) Deciio Shadow imay gou (SPG) of a oce ; all commodiie o he ooie oce ide of he imay commodiy gou (PCG) which have he ame commodiy ye a he PCG uually ieally deemied (hough i may be ecified by he ue ude ecial cicumace (e.g. whe o all he commodiie o he ooie ide of he oce which hould be i he SPG ae of he ame commodiy ye comye); if o commodiy of he ame ye i foud: if PCG i of ye DEM ad oce i a maeial oceig oce (PRV o PRW) he he SPG coai all maeial commodiie; if o he SPG coai all eegy commodiie. Li of all commodiie c foud i egio. Se j ued i diecio bd fo he elaic demad fomulaio of commodiy c. Idicao of which imelice () aociae wih commodiy c i egio fo ime eiod he commodiy balace equaio (EQ(l)COMBAL) i o be geeaed wih a coai ye coeodig o bd. Idicao of which imelice () aociae wih commodiy c i egio fo ime eiod he commodiy oducio equaio (EQ(l)COMBAL) i o be geeaed wih a coai ye accodig o bd whe a coeodig hcomd idicao exi. All imelice beig a o above imelice level (coml) of commodiy c i egio. Idicao ha he commodiy e vaiable (VARCOMNET) i equied i commodiy balace (EQECOMBAL) owig o a limi/co imoed o he e. Idicao ha he commodiy oducio vaiable (VARCOMPRD) i equied i commodiy balace (EQECOMPRD) owig o a limi/co imoed o he oducio. Li of ocee () i each egio (). Idicao of ocee () i egio () wih exacly oe iu ad oe ouu flow (exludig emiio commodiy of (comye= ENV )); ued i educio algoihm. Idicao of ocee () i egio () wih oe iu flow ad a abiay umbe of ouu flow; ued i educio algoihm. Li of all ocee i egio exce ie-egioal exchage ocee (ie). Idicao a o whehe a oce () i a egio () i iu o ouu (io = IN / OUT ) omalized wih eec o i aciviy. Li of ie-egioal exchage ocee () foud i each egio (all). The imay commodiy gou (cg) of each oce () i a egio (). 34

35 Se ID 17 Idexe 18 gye (comye) c (c) cac (c) caie (iec) ccaflo (vc) ccoly (vc) cemi (cg) ceqie (c) ccffuc (c) cie (allcie) cmake (allc) cg (cgc) cg (c) cga (c1c2cg1cg2) cva (c) c () Deciio The commodiy ye (comye) of imay commodiy gou of a oce () i a egio (). Li of commodiie ( c ) aocaied wih a oce i egio (by o o oie). Idicao ha he imay commodiy gou of a oce ( exce exchage ocee ee caie) coi of oly oe commodiy (c) eablig he coeodig flow vaiable o be elaced by he aciviy vaiable (ued i educio algoihm). Idicao ha he imay commodiy gou of a exchage oce (ie) coi of oly oe commodiy (c) eablig he coeodig flow vaiable o be elaced by he aciviy vaiable (ued i educio algoihm). Idicao ha a commodiy flow c i egio i aociaed wih he caaciy of a oce ( due o NCAPICOM NCAPOCOM o NCAPCOM beig ovided). A ube of ccaflo idicaig hoe ocee () i a egio () whee a commodiy (c) i oly coumed o oduced hough caaciy baed flow. Idicao ha he flow vaiable of a emiio commodiy (cg) aociaed wih oce () i a egio () ca be elaced by he fuel flow cauig he emiio mulilied by he emiio faco (ued i educio algoihm). Idicao of he commodiie (c) aociaed wih ie-egioal exchage ocee () i egio () fo which a ie-egio exchage equaio (EQIRE) i o be geeaed; he e doe o coai he makelace egio (cmake). Flow vaiable of a commodiy (c) aociaed wih a oce () ha ca be elaced by aohe flow vaiable of he oce due o a diec FLOFUNC o FLOSUM elaiohi. Commodiie (c) imoed o exoed (ie= IMP / EXP ) via oce i a egio (all). The li of make lace egio (ube of all) ha ade a commodiy (c) hough a oce (). The make ucue i ue defied hough he e oie. cmake i ieally deived baed o he ucue of oie bu may alo be exlicily ecified by he ue. The maig of he commodiie (c) i a egio () ha belog o he imay commodiy gou (cg) aociaed wih oce. The li of commodiie (c) i a egio () belogig o he hadow imay gou of oce (). Idicao of he afomaio equaio (EQPTRANS) ha ca be elimiaed by he educio algoihm. The li of valid imelice fo he flow vaiable (VARFLO) of commodiy c aociaed wih oce i egio ; flow vaiable of commodiie which ae a of he imay commodiy gou have he imelice eoluio of he oce (cl) while all ohe flow vaiable ae ceaed accodig o he 1 imelice. All (emied) imelice () a o above he oce () imelice level (cl) i a egio (). 35

36 Se ID 17 Idexe 18 1 () 2 () eg (allegall) below (all) below1 (all) ee (all) ccume (c) ccumd (c) cig (cio) cvac (c) = v (v) cy (v) off () qac () vaa () va () viy (v) c (vc) Deciio All (emied) imelice () belogig o he fie imelice level of he oce ( cl) ad he commodiy imelice level (coml) of he hadow imay commodiy gou. All (emied) imelice () a o above he fie imelice level of he oce () imelice level cl) ad he commodiy imelice level (coml) of he hadow imay commodiy gou. Idicao ha ade exi fom egio alleg o egio all. All imelice () icly below he highe imelice () i he imelice ee. All imelice () immediaely (oe level) below he highe imelice () i he imelice ee. Fo a imelice () all imelice () ha ae o he ame ah wihi he imelice ee e.g. if =SP WD i Fig. 6 valid imelice ae: ANNUAL SP SPWD SPWDD SPWDN Idicao ha he commodiy e vaiable (VARCOMNET) fo commodiy c i egio fo eiod ha a cumulaive boud alied. Idicao ha he commodiy oducio vaiable (VARCOMPRD) fo commodiy c i egio fo eiod ha a cumulaive boud alied. Idicao ha a commodiy c i o available i a ecific eiod ad imelice ice he oly ocee oducig (io = OUT ) o coumig he oce (io = IN ) ae ued-off.. I he cae of io = OUT he commodiy i o available meaig ha ocee which have oly hi commodiy a iu cao oeae. Simila eaoig alie o he cae io = IN. Fo commodiy (c) i egio () idicao fo he imelice () ad he eiod () he commodiy i available. Idicaio of he eiod ad ayea fo which oce () i egio ( ) i available; all ohe RTP* cool e ae baed o hi e. Fo each viage eiod (v) a idicaio of he eiod () fo which ewly ialled caaciy of oce () i a egio ()i available akig io accou coucio lead-ime (NCAPILED) ad echical lifeime (NCAPTLIFE). Idicaio of he eiod () i which o ew iveme i emied fo a oce () i a egio (). Idicao ha a boud o oce aciviy (ACTBND) of a oce i a egio ca be alied diecly o he aciviy vaiable (VARACT); ued i educio algoihm. Idicaio of he eiod () fo which a oce () i a egio () i available. Idicao ha he caaciy vaiable (VARCAP) will be geeaed fo oce () i a egio () i eiod (). A idicaio of fo which eiod () a oce () i a egio () i available ice i wa fi ialled (v); fo viaged ocee (cvi) ideical o cy fo o-viaged ocee he v idex i he cy eie i igoed by eig i o (v = ). Fo a oce () i a egio () he combiaio of he eiod i i available () ad commodiie aociaed wih i (c). 36

37 Se ID 17 Idexe 18 off () cvaf (c) ucdydi (ucide) ucgmac (ucucgyec) ucgma (ucucgye) ucmaflo (ucc) ucmaie (ucc) Deciio A idicaio fo oce () of he imelice () fo which he oce i ued-off (ued i educio algoihm). The li of valid imelice () ad eiod () fo he flow vaiable (VARFLO) of oce () ad commodiy (c); akig io accou he aciviy caaciy ad flow availabiliy (vaa cva ad cfoff). The imelice level of a flow vaiable equal he imelice level of he oce (cl) whe he flow vaiable i a of he commodiy gou defiig he aciviy of he oce. Ohewie he imelice level of a flow vaiable i e o whicheve level i fie ha of he commodiy o he oce. If ide = RHS idicao fo gowh coai o be geeaed bewee he eiod -1 ad ; if ide = LHS he e i igoed. Idicao ha a commodiy vaiable (VARCOMCON o VARCOMPRD) fo commodiy (c) i a egio () aea i a ue coai (uc). Idicao ha a vaiable (VARACT VARNCAP o VARCAP) aociaed wih a oce () i a egio () aea i a ue coai (uc). Idicao ha he flow vaiable (VARFLO) fo egio oce ad commodiy c i ivolved i ue coai uc. Idicao ha a imo/exo (accodig o oie) ade vaiable (VARIRE) fo egio oce ad commodiy c i ivolved i a ue coai (uc). 37

38 3 Paamee While e decibe ucual ifomaio of he eegy yem o qualiaive chaaceiic of i eiie (e.g. ocee o commodiie) aamee coai umeical ifomaio. Examle of aamee ae he imo ice of a eegy caie o he iveme co of a echology. Mo aamee ae ime-eie whee a value i ovided (o ieolaed) fo each yea (daayea). The TIMES model geeao diiguihe bewee ue iu aamee ad ieal aamee. The fome ae ovided by he modelle (uually by way of a daa hadlig yem o hell uch a VEDA-FE o ANSWER-TIMES) while he lae ae ieally deived fom he ue iu aamee i combiaio wih ifomaio give by e i ode o calculae fo examle he co coefficie i he objecive fucio. Thi Chae fi cove he ue iu aamee i Secio 3.1 ad he decibe he mo imoa ieal aamee a fa a hey ae eleva fo he baic udeadig of he equaio (Secio 3.2). Secio 3.3 ee he aamee ued fo eoig he eul of a model u. 3.1 Ue iu aamee Thi ecio ovide a oveview of he ue iu aamee ha ae available i TIMES o decibe he eegy yem. Befoe eeig he vaiou aamee i deail i Secio wo eoceig algoihm alied o he ue iu daa ae eeed amely he ie- /exaolaio ad he iheiace/aggegaio ouie. Ue iu aamee ha ae imedeede ca be ovided by he ue fo hoe yea fo which aiical ifomaio o fuue ojecio ae available ad he ie-/exaolaio ouie decibed i Secio ued o adju he iu daa o he yea equied fo he model u. Timelice deede aamee do o have o be ovided o he imelice level of a oce commodiy o commodiy flow. Iead he o-called iheiace/aggegaio ouie decibed i Secio aig he iu daa fom he ue ovided imelice level o he aoiae imelice level a eceay Ie- ad exaolaio of ue iu aamee Time-deede ue iu aamee ae ecified fo ecific yea he o-called daayea (daayea). Thee daayea do o have o coicide wih he modelyea (v o modelyea) eeded fo he cue u. Reao fo diffeece bewee hee wo e ae fo examle ha he eiod defiiio fo he model ha bee aleed afe havig ovided he iiial e of iu daa leadig o diffee mileoeyea ( o mileoey) o ha aiical daa ae oly available fo ceai yea ha do o mach he modelyea. I ode o avoid budeig he ue wih he cumbeome adjume of he iu daa o he modelyeaa ie- /exaolaio ouie i embedded i he TIMES model geeao. The ie-/exaolaio ouie diiguihe bewee a defaul ie-/exaolaio ha i auomaically alied o he iu daa ad a ehaced ue-coolled ie-/exaolaio ha allow he ue o ecify ie-/exaolaio ule fo each ime-eie exlicily. Ideede of he defaul o uecoolled ie-/exaolaio oio TIMES ie-/exaolae (uig he adad algoihm) all co aamee i he objecive fucio o he idividual yea of he model a a of calculaig he aual co deail. 38

39 Defaul ie/exaolaio The defaul ie-/exaolaio ouie ieolae liealy bewee daa oi while i exaolae he fi/la daa oi coaly backwad/fowad. The aamee give i Table 6 ae by defaul NOT ie/exaolaed. All ohe aamee ae by defaul boh ieolaed ad exaolaed. Table 6: Paamee o beig ie/exaolaed by defaul Paamee Juificaio ACTBND CAPBND NCAPBND FLOFR FLOSHAR STGOUTBND STGINBND Boud may be ieded a ecific eiod oly COMBNDNET COMBNDPRD COMCUMNET COMCUMPRD COMCHRBND IREBND IREXBND UCRHST Ue coai may be ieded fo ecific eiod UCRHSRT oly UCRHSRTS NCAPAFM NCAPEFFM NCAPFOMM NCAPFSUBM NCAPFTAXM NCAPAFX NCAPEFFX NCAPFOMX NCAPFSUBX NCAPFTAXX NCAPPASTI NCAPPASTY COMBLVAL PEAKDABL Ieolaio meaigle fo hee aamee (aamee value i a dicee umbe idicaig which MULTI cuve hould be ued). Ieolaio meaigle fo hee aamee (aamee value i a dicee umbe idicaig which SHAPE cuve hould be ued). Paamee decibe a iveme fo a igle viage yea ad i o ieolaed. Paamee decibe umbe of yea ove which o diibue a iveme. Bledig aamee a he mome o ieolaed Ehaced ue-coolled ie/exaolaio The ie-/exaolaio faciliy ovide maximum flexibiliy by allowig he ue o cool he ieolaio of each ime eie eaaely. May boudig coai a well a make ad oduc allocaio coai migh be alicable eihe o oly ecific yea o o he coiuou ime-a of he full ime hoizo o o a ube heeof. The oibiliy of coollig ieolaio o a ime-eie bai imove he ideedece bewee he yea foud i he imay daabae ad he daa acually ued i he idividual u of a TIMES 39

40 model. I hi way he model i made moe flexible wih eec o uig ceaio wih abiay model yea ad eiod legh while uig baically he vey ame iu daabae. The ehaced ieolaio/exaolaio faciliy ovide he ue wih oio o cool he ieolaio ad exaolaio of each idividual ime eie (Table 7). No-defaul ieolaio/exaolaio ca be equeed fo ay aamee by ovidig a addiioal iace of he aamee wih a idicao i he YEAR idex ad a value coeodig o oe of he iege-valued Oio Code (ee Table 7 ad examle below). Thi cool ecificaio acivae he ieolaio/exaolaio ule fo he ime eie ad i diiguihed fom acual ime-eie daa by ovidig a ecial cool label ( 0 ) i he YEAR idex. The aicula ieolaio ule o aly i a fucio of he Oio Code aiged o he cool ecod fo he aamee. Noe ha fo log-liea ieolaio he Oio Code idicae he yea fom which he ieolaio i wiched fom adad o logliea mode. TIMES ue hell() will ovide mechaim fo imbeddig he cool label ad eig he Oio Code hough eaily udeadable elecio fom a ue-fiedly do-dow li makig he ecificaio imle ad aae o he ue. Table 7: Oio code fo he cool of daa ieolaio Oio code 0 (o oe) < YEAR (>= 1000) Acio Ieolaio ad exaolaio of daa i he defaul way a edefied i TIMES. Thi oio doe o equie ay exlici acio fom he ue. No ieolaio o exaolaio of daa (oly valid fo oco aamee). Ieolaio bewee daa oi bu o exaolaio (ueful fo may boud). Ieolaio bewee daa oi eeed ad fillig-i all oi ouide he ieolaio widow wih he EPS value. Thi i ueful fo e.g. he RHS of equaliy-ye ue coai o limiaio o fuue iveme i a aicula iace of a echology which hould ofe have a coiuou value of EPS o be effecive. Foced ieolaio ad boh fowad ad backwad exaolaio houghou he ime hoizo. Ueful fo may aamee ha ae by defaul o ieolaed. Log-liea ieolaio beyod a ecified daa yea ad boh fowad ad backwad exaolaio ouide he ieolaio widow. Log-liea ieolaio i guided by elaive coefficie of aual chage iead of abolue daa value. Examle: Thee omal daa oi i a FLOSHAR daa eie: FLOSHAR(REG1995PRC1COALINPRC1ANNUALUP) = 0.25; FLOSHAR(REG2010PRC1COALINPRC1ANNUALUP) = 0.12; FLOSHAR(REG2020PRC1COALINPRC1ANNUALUP) = 0.05; FLOSHAR i by defaul NOT ieolaed o exaolaed i TIMES. To foce ieolaio/exaolaio of he FLOSHAR aamee he followig cool oio fo hi daa eie hould be added: FLOSHAR(REG0PRC1COALINPRC1ANNUALUP) = 3; 40

41 Log-liea ieolaio mea ha he value i he daa eie ae ieeed a coefficie of aual chage beyod a give YEAR. The YEAR ca be ay yea icludig modelyea. The ue oly ha o ake cae ha he daa value i he daa eie coeod o he ieeaio give o hem whe uig he log-liea oio. Fo imliciy howeve he fi daa oi i alway ieeed a a abolue value becaue log-liea ieolaio equie a lea oe abolue daa oi o a wih. Examle: FLOSHAR(REG0PRC1COALINPRC1ANNUALUP) = 2005; Thi aamee ecifie a log-liea cool oio wih he value fo he hehold YEAR of log-liea ieolaio ake fom The oio ecifie ha all daa oi u o he yea 2005 hould be ieeed omally (a abolue daa value) bu all value beyod ha yea hould be ieeed a coefficie of aual chage. By uig hi ieeaio TIMES will he aly full ieolaio ad exaolaio o he whole of he daa eie. I i he eoibiliy of he ue o eue ha he fi daa oi ad all daa oi u o (ad icludig) he yea 2005 eee abolue value of he aamee ad ha all ubeque daa oi eee coefficie of aual chage. Uig he daa of he examle above he fi daa oi beyod 2005 i foud fo he yea 2010 ad i ha he value of The ieeaio hu equie ha he maximum flow hae of COAL i he commodiy gou INPRC1 i acually mea o iceae by a much a 12% e aum bewee he yea 1995 ad 2010 ad by 5% e aum bewee 2010 ad Alicabiliy All he ehaced ieolaio oio decibed above ae available fo all TIMES aamee excludig iege-valued aamee elaed o he SHAPE ad MULTI able a how i Table 8. Table 8: Paamee which cao be ieolaed Paamee NCAPAFM NCAPEFFM NCAPFOMM NCAPFSUBM NCAPFTAXM NCAPAFX NCAPEFFX NCAPFOMX NCAPFSUBX NCAPFTAXX Comme Paamee value i a dicee umbe idicaig which MULTI cuve hould be ued. Paamee value i a dicee umbe idicaig which SHAPE cuve hould be ued. Howeve aohe oio fo he exaolaio of SHAPE idex aamee i available. The exaolaio ca be doe eihe oly iide he daa oi ovided by he ue o boh iide ad ouide hoe daa oi. Iide he daa oi he SHAPE idex ecified fo ay daayea i exaolaed o all modelyea (v) bewee ha daayea ad he followig daayea fo which he SHAPE idex i ecified. 41

42 Table 9: Oio code fo he exaolaio of SHAPE idexe Oio code Acio <= 0 (o oe) No exaolaio (defaul) 1 Exaolaio bewee daa oi oly >= 2 Exaolaio bewee ad ouide daa oi Examle: The ue ha ecified he followig wo SHAPE idexe ad a cool oio fo exaolaio: NCAPAFX(REG 0 PRC1) = 1; NCAPAFX(REG 1995 PRC1) = 12; NCAPAFX(REG 2010 PRC1) = 13; I hi cae all modelyea (v) bewee 1995 ad 2010 will ge he hae idex 12. No exaolaio i doe fo modelyea (v) beyod 2010 o befoe The exaolaio oio ae cuely available fo he followig SHAPE aamee which ae a idicao fo he SHAPE cuve ha hould be alied o he coeodig aamee: NCAPAFX NCAPFOMX NCAPFSUBX NCAPFTAXX FLOFUNCX Iheiace ad aggegaio of imeliced iu aamee A meioed befoe ocee ad commodiie ca be modelled i TIMES o diffee imelice level. Some of he iu aamee which decibe a oce o a commodiy ae imelice ecific i.e. hey have o be ovided by he ue fo ecific imelice e.g. he availabiliy faco NCAPAF of a owe la oeaig o a DAYNITE imelice level. Duig he oce of develoig a model he imelice eoluio of ome ocee o eve he eie model may be efied. Oe could imagie fo examle he iuaio ha a ue a develoig a model o a ANNUAL imelice level ad efie he model lae by efiig he imelice defiiio of he ocee ad commodiie. I ode o avoid he eed fo all he imelice elaed aamee o be e-eeed agai fo he fie imelice TIMES uo he iheiace ad aggegaio of aamee alog he imelice ee (ee Figue 1). Iheiace i hi coex mea ha iu daa beig ecified o a coae imelice level (highe u he ee) ae iheied o a fie imelice level (lowe dow he ee) wheea aggegaio mea ha imelice ecific daa ae aggegaed fom a fie imelice level (lowe dow he ee) o a coae oe (fuhe u he ee). The iheiace feaue may alo be ueful i ome cae whee he value of a aamee hould be he ame ove all imelice ice i hi cae i i ufficie o ovide he aamee value fo he ANNUAL imelice which i he iheied o he equied fie age imelice The em age imelice level o age imelice i ued i he followig a yoym fo he imelice level o imelice which ae equied by he model geeao deedig o he oce o commodiy imelice eoluio (cl ad coml eecively). 42

43 The e-oceo uo diffee iheiace ad aggegaio ule which deed o he ye of aibue. I Table 12 below he iheiace ad aggegaio ule alied by he eoceo ae lied fo each idividual aamee. The followig iheiace ad aggegaio ule exi i TIMES (Table 10). Table 10: Iheiace ad aggegaio ule Iheiace ule Diec iheiace Weighed iheiace No iheiace Aggegaio ule Sadad aggegaio Weighed aggegaio Deciio A value o a coae imelice i iheied by age imelice below (i he imelice ee) wihou chagig he umeic value. A value o a coae imelice i iheied by age imelice below (i he imelice ee) by weighig he iu value wih he aio of he duaio of he age imelice o he duaio of he coae imelice. Abolue boud aamee ecified o a coae imelice level ha he age imelice level ae o iheied. Iead a coai ummig ove elaed vaiable o he fie imelice i geeaed e.g. a aual ACTBND aamee ecified fo a oce wih a DAYNITE oce imelice level (cl) lead o a coai (EQACTBND) wih he ummaio ove he aciviy vaiable o he DAYNITE level a LHS em ad wih he boud a RHS em. Deciio The value ecified o fie imelice ae aggegaed o he age imelice beig a ae ode i he imelice ee by ummig ove he value o he fie imelice. The value ecified fo fie imelice ae aggegaed o he age imelice beig a ae ode i he imelice ee by ummig ove he weighed value o he fie imelice. The aio of he duaio of he fie imelice o he duaio of he age imelice eve a weighig faco. The diffee aggegaio ule ae illuaed by examle i Figue 9. I hould be oed ha if iu daa ae ecified o wo imelice level diffee fom he age level he he iheiace/aggegaio ouie may lead o icoec eul. Theefoe i i ogly ecommeded o ovide iu daa oly fo imelice o oe imelice level. Oe hould alo oice ha if a mixue of fixed boud wih ue o lowe boud i ecified by he ue o a imelice level diffee fom he age level he he fixed boud ae coveed io ue ad lowe boud. Thee ue ad lowe boud ae he iheied o aggegaed wih he ohe ue-ecified ue o lowe boud o he age imelice level. 43

44 Weighed Iheiace Diec Iheiace Give value = 1.0 ANNUAL (GYRFR=1.0) Give value = 1.0 ANNUAL (GYRFR=1.0) WI (GYRFR=0.6) SU (GYRFR=0.4) WI (GYRFR=0.6) SU (GYRFR=0.4) Tage level Give value = oe Iheied value = 0.6 Give value = oe Iheied value = 0.4 Tage level Give value = oe Iheied value = 1.0 Give value = oe Iheied value = 1.0 WID (GYRFR=0.25) WIN (GYRFR=0.35) SUD (GYRFR=0.15) SUN (GYRFR=0.25) WID (GYRFR=0.25) WIN (GYRFR=0.35) SUD (GYRFR=0.15) SUN (GYRFR=0.25) Weighed Aggegaio ANNUAL (GYRFR=1.0) Sadad Aggegaio ANNUAL (GYRFR=1.0) WI (GYRFR=0.6) SU (GYRFR=0.4) WI (GYRFR=0.6) SU (GYRFR=0.4) Tage level Give value = oe Aggegaed value = 1.58 Give value = oe Aggegaed value = 3.63 Tage level Give value = oe Aggegaed value = 3.0 Give value = oe Aggegaed value = 7.0 WID (GYRFR=0.25) WIN (GYRFR=0.35) SUD (GYRFR=0.15) SUN (GYRFR=0.25) WID (GYRFR=0.25) WIN (GYRFR=0.35) SUD (GYRFR=0.15) SUN (GYRFR=0.25) Give value = 1.0 Give value = 2.0 Give value = 3.0 Give value = 4.0 Give value = 1.0 Give value = 2.0 Give value = 3.0 Give value = 4.0 Figue 9: Iheiace ad aggegaio ule fo imelice ecific aamee i TIMES Oveview of ue iu aamee A li of all ue iu aamee i give i Table 12. I ode o faciliae he ecogiio by he ue of o which a of he model a aamee elae he followig amig coveio aly o he efixe of he aamee (Table 11). Table 11: Namig coveio fo ue iu aamee Pefix ACT CAP COM FLO IRE NCAP STG UC Relaed model comoe Aciviy of a oce Caaciy of a oce Commodiy Poce flow Ie-egioal exchage New caaciy of a oce Soage oce Ue coai 44

45 Table 12: Ue iu aamee i TIMES Iu aamee (Idexe) 21 ACTBND (daayeabd) Relaed e/aamee 22 Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Ui of aciviy [oe]; defaul value: oe Defaul i/e 26 : oe Iace 24 (Requied / Omi / Secial codiio) Sice ie-/exaolaio defaul i oe he boud mu be exlicily ecified fo a mileoeyea ule a ie-/exaolaio oio i e. If he boud i ecified fo a imelice above he oce imelice eoluio (cl) he boud i alied o he um of he aciviy vaiable accodig o he Deciio Boud o he oveall aciviy a oce. Affeced equaio o vaiable 25 Aciviy limi coai (EQ(l)ACTBND) whe i above cl. Diec boud o aciviy vaiable (VARACT) whe a he cl level. May aea i ue coai (EQUC*) if ( ACTBNDLO/F 21 The fi ow coai he aamee ame he ecod ow coai i backe he idex domai ove which he aamee i defied. 22 Thi colum give efeece o elaed iu aamee o e beig ued i he coex of hi aamee a well a ieal aamee/e o eul aamee beig deived fom he iu aamee. 23 Thi colum li he ui of he aamee he oible age of i umeic value [i quae backe] ad he ie- /exaolaio ule ha aly. 24 A idicaio of cicumace fo which he aamee i o be ovided o omied a well a deciio of iheiace/aggegaio ule alied o aamee havig he imelice () idex. 25 Equaio o vaiable ha ae diecly affeced by he aamee. 26 Abbeviaio i/e = ie-/exaolaio 45

46 Iu aamee (Idexe) 21 ACTCOST (daayeacu) B () CAPBND (daayeabd) Relaed e/aamee 22 OBJACOST CSTACTV PAROBJACT TOTACT M D E COEFCPT viy PARCAPLO PARCAPUP Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Moeay ui e ui of aciviy [oe]; defaul value: oe Defaul i/e: adad Caaciy ui [oe]; defaul value: oe Defaul i/e: oe Iace 24 (Requied / Omi / Secial codiio) imelice ee. Sadad aggegaio. Sice ie-/exaolaio i ued-off by defaul he boud mu be ecified fo each mileoeyea deied if o ecific ifomaio egadig ie- /exaolaio oio i give. Deciio Vaiable co aociaed wih he aciviy of a oce. Begiig yea of eiod. Boud o iveme i ew caaciy. Affeced equaio o vaiable 25 X/UP ) ecified i UCNAME. Alied o he aciviy vaiable (VARACT) a a comoe of he objecive fucio (EQOBJVAR). May aea i ue coai (EQUC*) if ecified i UCNAME. Imoe a idiec limi o he caaciy afe equaio (EQCPT) by mea of a diec boud o he caaciy vaiable (VARCAP). May aea i 46

47 Iu aamee (Idexe) 21 CCAP0 (eg) CCAPM (eg) COMBNDNET (daayeacbd) Relaed e/aamee 22 PAT CCOST0 CCOSTM hcombal ccombal Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Caaciy ui [oe]; defaul value: oe Caaciy ui [oe]; defaul value: oe Commodiy ui [oe]; defaul value: oe Defaul i/e: oe Iace 24 (Requied / Omi / Secial codiio) Fo leaig echologie eg whe ETL i ued. Fo leaig echologie eg whe ETL i ued. Sice ie-/exaolaio i ued-off by defaul he boud mu be ecified fo each mileoeyea deied ule a ie- /exaolaio oio i Deciio Iiial cumulaive caaciy of a leaig echology. Maximum cumulaive caaciy. Limi o he e amou of a commodiy wihi a egio fo a aicula imelice. Affeced equaio o vaiable 25 ue coai (EQUC*) if ( CAPBNDLO/F X/UP ) ecified i UCNAME. Cumulaive iveme coai (EQCUINV) ad cumulaive caaciy vaiable (VARCCAP) i edogeou echological leaig fomulaio. Coe ETL equaio. The balace coai i e o a equaliy (EQECOMBAL). Eihe he fie imelice vaiable 47

48 Iu aamee (Idexe) 21 COMBNDPRD (daayeacbd) Relaed e/aamee 22 hcomd ccomd Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Commodiy ui [oe]; defaul value: oe Defaul i/e: oe Iace 24 (Requied / Omi / Secial codiio) give. If he boud i ecified fo a imelice above he commodiy imelice eoluio (coml) he boud i alied o he um of he e commodiy vaiable (VARCOMNET) below i accodig o he imelice ee. Sadad aggegaio. Sice ie-/exaolaio i ued-off by defaul he boud mu be ecified fo each mileoeyea deied ule a ie- /exaolaio oio i give. If he boud i ecified fo a imelice beig above he commodiy imelice eoluio (coml) he boud i alied o he um of he Deciio Limi o he amou of a commodiy oduced wihi a egio fo a aicula imelice. Affeced equaio o vaiable 25 ae ummed (EQ(l)BNDNET) o he boud alied diec o he commodiy e vaiable(varco MNET) whe a he commodiy level (coml). The balace coai i e o a equaliy (EQECOMBAL). Fie imelice vaiable ummed (EQ(l)BNDPRD). o he boud i alied diec o he commodiy oducio vaiable 48

49 Iu aamee (Idexe) 21 COMBPRICE (ccu) COMCSTNET (daayeaccu) Relaed e/aamee 22 COMELAST COMSTEP COMVOC OBJCNCST CSTCOMV PAROBJCOM TOTCOM Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Moeay ui e commodiy ui [oe]; defaul value: oe Defaul i/e: oe Moeay ui e commodiy ui [oe]; defaul value: oe Iace 24 (Requied / Omi / Secial codiio) commodiy oducio vaiable (VARCOMPRD) below i accodig o he himelice ee. Sadad aggegaio. The cool aamee $SET TIMESED YES o acivae elaic demad mu be e. Diec iheiace. Weighed aggegaio. Deciio Bae ice of a demad commodiy fo he elaic demad fomulaio. Co o he e amou of a commodiy wihi a egio fo a Affeced equaio o vaiable 25 (VARCOMPRD) whe a he commodiy level (coml). Cool he icluio of he elaic demad vaiable (VARELAST) i he commodiy balace equaio(eq(l)c OMBAL) Alied o he elaic demad vaiable (VARELAST) i he objecive fucio (EQOBJELS). Foce he e commodiy vaiable (VARCOMNET) 49

50 Iu aamee (Idexe) 21 COMCSTPRD (daayeaccu) Relaed e/aamee 22 hcombal ccombal OBJCPCST CSTCOMV PAROBJCOM TOTCOM hcomd ccomd Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Defaul i/e: adad Moeay ui e commodiy ui [oe]; defaul value: oe Defaul i/e: adad Iace 24 (Requied / Omi / Secial codiio) Diec iheiace. Weighed aggegaio. Deciio aicula imelice. Co o he oducio of a commodiy wihi a egio fo a aicula imelice. Affeced equaio o vaiable 25 o be icluded i he equaliy balace coai (EQECOMBAL). Alied o aid vaiable i he co comoe of he objecive fucio (EQOBJVAR). Foce he commodiy oducio vaiable (VARCOMPRD) o be icluded i he equaliy balace coai (EQECOMBAL). Alied o aid vaiable i he co comoe of he objecive fucio (EQOBJVAR). COMCUMNET bohyea eohyea Commodiy ui The yea y1 ad y2 may Boud o he Foce he e 50

51 Iu aamee (Idexe) 21 (y1y2bd) COMCUMPRD (y1y2bd) Relaed e/aamee 22 hcombal ccombal ccume bohyea eohyea hcomd ccomd ccumd Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 [oe]; defaul value: oe Defaul i/e: o oible Commodiy ui [oe]; defaul value: oe Defaul i/e: o oible Iace 24 (Requied / Omi / Secial codiio) be ay yea of he e allyea; whee y1 may alo be BOH fo fi yea of fi eiod ad y2 may be EOH fo la yea of la eiod. The yea y1 ad y2 may be ay yea of he e allyea; whee y1 may alo be BOH fo fi yea of fi eiod ad y2 may be EOH fo la yea of la eiod. Deciio cumulaive e amou of a commodiy bewee he yea y1 ad y2 wihi a egio fo a aicula imelice. Boud o he cumulaive oducio of a commodiy bewee he yea y1 ad y2 wihi a egio fo a aicula imelice. Affeced equaio o vaiable 25 commodiy vaiable (VARCOMNET) o be icluded i he equaliy balace coai (EQECOMBAL). Geeae he cumulaive commodiy coai (EQ(l)CUMNET ). Foce he e commodiy vaiable (VARCOMPRD) o be icluded i he balace equaio (EQECOMBAL). The cumulaive coai i geeaed 51

52 Iu aamee (Idexe) 21 COMELAST (daayeacbd) COMFR (daayeac) Relaed e/aamee 22 COMBPRICE COMSTEP COMVOC COMPROJ com coml RTCSTSFR Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Dimeiole [oe]; defaul value: oe Defaul i/e: oe Decimal facio [01]; defaul value: imelice duaio (GYRFR) Iace 24 (Requied / Omi / Secial codiio) The cool aamee $SET TIMESED YES o acivae elaic demad mu be e. A elaiciy i equied fo each diecio he demad i emied o move. The idex bd = LO coeod o he diecio of deceaig he demad while bd = UP deoe he diecio fo demad iceae. A diffee value may be ovided fo each diecio hu cuve may be aymmeic. Oly alicable o demad commodiie (comye = DEM ). Affec imelice eoluio a which a Deciio Elaiciy of demad idicaig how much he demad ie/fall i eoe o a ui chage i he magial co of meeig a demad ha i elaic. Facio of he aual demad (COMPROJ) occuig i imelice ; Affeced equaio o vaiable 25 (EQ(l)CUMPRD ). Cool he icluio of he elaic demad vaiable (VARELAST) i he commodiy balace equaio(eq(l)c OMBAL) Alied o he elaic demad vaiable (VARELAST) i he objecive fucio co (EQOBJELS). Alied o he aual demad (COMPROJ) a he RHS of he balace equaio 52

53 Iu aamee (Idexe) 21 COMIE (daayeac) COMPKFLX (daayeac) Relaed e/aamee 22 comeak comk COMPKRSV FLOPKCOI Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Defaul i/e: adad Decimal facio [01]; defaul value: 1 Defaul i/e: adad Scala [oe]; defaul value: oe Defaul i/e: adad Iace 24 (Requied / Omi / Secial codiio) commodiy i acked (RTCSTSFR) ad heeby may affec whe a oce cao oeae (off). Weighed iheiace. Weighed aggegaio. Diec iheiace. Weighed aggegaio. Diec iheiace. Weighed aggegaio. Deciio decibe he hae of he load cuve. Ifaucue o amiio efficiecy of a commodiy. Diffeece bewee he aveage demad ad he eak demad i imelice exeed a Affeced equaio o vaiable 25 (EQ(l)COMBAL ). Ee he eakig equaio (EQPEAK) if a eakig commodiy. Alied whe eig he ue boud of a elaic demad e (VARELAST). Oveall efficiecy alied o he oal oducio of a commodiy i he commodiy balace equaio (EQ(l)COMBAL ). Alied o he oal coumio of a commodiy o aie he caaciy eeded o aify 53

54 Iu aamee (Idexe) 21 COMPKRSV (daayeac) COMPROJ (daayeac) Relaed e/aamee 22 comeak comk COMPKFLX FLOPKCOI COMFR Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Scala [oe]; defaul value: oe Defaul i/e: adad Commodiy ui [oe]; defaul value: oe Defaul i/e: adad Iace 24 (Requied / Omi / Secial codiio) Oly alicable o demad commodiie (comye = DEM ) Deciio facio of he aveage demad. Peak eeve magi a facio of eak demad e.g. if COMPKRSV = 0.2 he oal ialled caaciy mu exceed he eak load by 20 %. Pojeced aual demad fo a commodiy. Affeced equaio o vaiable 25 he eakig coai (EQPEAK). Alied o he oal coumio of a commodiy o aie he caaciy eeded o aify he eakig coai (EQPEAK). Seve a he RHS (afe COMFR alied) of he commodiy balace coai (EQ(l)COMBAL ). Ee he eakig equaio (EQPEAK) if a eakig commodiy. Alied whe eig he ue boud of a elaic 54

55 Iu aamee (Idexe) 21 COMSTEP (cbd) COMTAXNET (daayeaccu) Relaed e/aamee 22 COMBPRICE COMELAST COMVOC cj OBJCNTAX CSTCOMV PAROBJCOM Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Iege umbe [oe]; defaul value: oe Moeay ui e commodiy ui Iace 24 (Requied / Omi / Secial codiio) The cool aamee $SET TIMESED YES o acivae elaic demad mu be e. The umbe of e i equied fo each diecio he demad i emied o move. The idex bd = LO coeod o he diecio of deceaig he demad while bd = UP deoe he diecio fo demad iceae. A diffee value may be ovided fo each diecio hu cuve may be aymmeic. Diec iheiace. Weighed aggegaio. Deciio Numbe of e o ue fo he aoximaio of chage of oduce/coume ulu whe uig he elaic demad fomulaio. Tax o he e amou of a commodiy wihi a Affeced equaio o vaiable 25 demad e (VARELAST). Cool he iace of he elaic demad vaiable (VARELAST) i: he commodiy balace equaio (EQ(l)COMB AL); eig of he e limi fo he elaic demad vaiable (VARELAST ); ee he objecive fucio co (EQOBJELS). Foce he e commodiy vaiable 55

56 Iu aamee (Idexe) 21 COMTAXPRD (daayeaccu) Relaed e/aamee 22 TOTCOM hcombal ccombal OBJCPTAX CSTCOMV PAROBJCOM TOTCOM hcomd ccomd Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 [oe]; defaul value: oe Defaul i/e: adad Moeay ui e commodiy ui [oe]; defaul value: oe Defaul i/e: adad Iace 24 (Requied / Omi / Secial codiio) Diec iheiace. Weighed aggegaio. Deciio egio fo a aicula imelice. Tax o he oducio of a commodiy wihi a egio fo a aicula imelice. Affeced equaio o vaiable 25 (VARCOMNET) o be icluded i he equaliy balace coai (EQECOMBAL). Alied o aid vaiable i he co comoe of he objecive fucio (EQOBJVAR). Foce he commodiy oducio vaiable (VARCOMPRD) o be icluded i he equaliy balace coai (EQECOMBAL). Alied o aid vaiable i he co comoe of he objecive fucio (EQOBJVAR). 56

57 Iu aamee (Idexe) 21 COMSUBNET (daayeaccu) COMSUBPRD (daayeaccu) Relaed e/aamee 22 OBJCNSUB CSTCOMV PAROBJCOM TOTCOM hcombal ccombal OBJCPSUB CSTCOMV PAROBJCOM TOTCOM hcomd ccomd Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Moeay ui e commodiy ui [oe]; defaul value: oe Defaul i/e: adad Moeay ui e commodiy ui [oe]; defaul value: oe Defaul i/e: adad Iace 24 (Requied / Omi / Secial codiio) Diec iheiace. Weighed aggegaio. Diec iheiace. Weighed aggegaio. Deciio Subidy o he e amou of a commodiy wihi a egio fo a aicula imelice. Subidy o he oducio of a commodiy wihi a egio fo a aicula imelice. Affeced equaio o vaiable 25 Foce he e commodiy vaiable (VARCOMNET) o be icluded i he equaliy balace coai (EQECOMBAL). Alied (-) o aid vaiable i he co comoe of he objecive fucio (EQOBJVAR). Foce he commodiy oducio vaiable (VARCOMPRD) o be icluded i he equaliy balace coai (EQECOMBAL). Alied (-) o aid vaiable i he co 57

58 Iu aamee (Idexe) 21 COMVOC (daayeacbd) E () Relaed e/aamee 22 COMBPRICE COMSTEP COMELAST B. D M COEFCPT viy Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Dimeiole [oe]; defaul: oe Defaul i/e: adad Iace 24 (Requied / Omi / Secial codiio) The cool aamee $SET TIMESED YES o acivae elaic demad mu be e. A umbe i equied fo each diecio he demad i emied o move. The idex bd = LO coeod o he diecio of deceaig he demad while bd = UP deoe he diecio fo demad iceae. A diffee value may be ovided fo each diecio hu cuve may be aymmeic. Fo each modelyea eiod Deciio Poible vaiaio of demad i boh diecio whe uig he elaic demad fomulaio. Ed yea of eiod ued i deemiig he legh of each eiod Affeced equaio o vaiable 25 comoe of he objecive fucio (EQOBJVAR). Alied whe eig he boud of a elaic demad e (VARELAST). Alied o he elaiciy vaiable i he objecive fucio co (EQOBJELS). The amou of ew iveme (VARNCAP) caied ove i he caaciy afe 58

59 Iu aamee (Idexe) 21 FLOBND (daayeacgbd) Relaed e/aamee 22 Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Commodiy ui [oe]; defaul: oe Defaul i/e: oe Iace 24 (Requied / Omi / Secial codiio) If he boud i ecified fo a imelice beig above he flow imelice eoluio (cvaf) he boud i alied o he um of he flow vaiable (VARFLO) accodig o he imelice ee ohewie diecly o he flow vaiable. No aggegaio 27. Deciio Boud o he flow of a commodiy o he um of flow wihi a commodiy gou. Affeced equaio o vaiable 25 coai (EQ(l)CPT). Amou of iveme (VARNCAP) emaiig a he modellig hoizo ha eed o be cedied back o he objecive fucio (EQOBJINV). Flow aciviy limi coai (EQ(l)FLOBND) whe i above cvaf Diec boud o aciviy vaiable (VARFLO) whe a he cvaf level. May aea i ue coai 27 Sadad aggegaio o imleme ye. 59

60 Iu aamee (Idexe) 21 FLOCOST (daayeaccu) FLODELIV (daayeaccu) Relaed e/aamee 22 OBJFCOST CSTFLOV PAROBJFLO TOTFLO OBJFDELV CSTFLOV PAROBJFLO TOTFLO Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Moeay ui e commodiy ui [oe]; defaul: oe Defaul i/e: adad Moeay ui e commodiy ui [oe]; defaul: oe Defaul i/e: adad Iace 24 (Requied / Omi / Secial codiio) Diec iheiace Weighed aggegaio Diec iheiace. Weighed aggegaio. Deciio Vaiable co of a oce aociaed wih he oducio/ coumio of a commodiy. Co of a deliveig (coumig) a commodiy o a oce. Affeced equaio o vaiable 25 (EQUC*) if ( FLOBNDLO/F X/UP ) ecified i UCNAME. Alied o he flow vaiable (VARFLO) whe eeig he objecive fucio (EQOBJVAR). May aea i ue coai (EQUC*) if ecified i UCNAME. Alied o he flow vaiable (VARFLO) whe eeig he objecive fucio (EQOBJVAR). May aea i ue coai (EQUC*) if ecified i UCNAME. 60

61 Iu aamee (Idexe) 21 FLOFR (daayeacbd) FLOFUNC (daayeacg1cg2 ) Relaed e/aamee 22 FLOSUM FLOFUNCX COEFPTRAN cffuc cga Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Decimal facio [01]; defaul value: oe Defaul i/e: oe Commodiy ui of cg2/commodiy ui of cg1 [oe]; defaul value: ee ex colum Defaul i/e: adad Iace 24 (Requied / Omi / Secial codiio) FLOFR may be ecified a lowe ue o fixed boud i coa o COMFR. FLOFR ca be ecified fo ay flow vaiable havig a ubaual imelice eoluio. Omied imelice () have he aociaed flow ued off i aid imelice. Weighed iheiace. Weighed aggegaio. If fo he ame idexe he aamee FLOSUM i ecified bu o FLOFUNC he FLOFUNC i e o 1. Imoa faco i deemiig he level a which a oce oeae i ha he deived afomaio aamee (COEFPTRAN) i iheied/aggegaed o Deciio Limi /Load cuve o he flow of commodiy (c) eeig o leavig oce () i a imelice. A key aamee decibig he baic oeaio of o wihi a oce. Se he aio bewee he um of flow i commodiy gou cg2 o he um of flow i commodiy gou cg1 heeby defiig he Affeced equaio o vaiable 25 A hae equaio (EQ(l)FLOFR) limiig he amou of commodiy (c) i geeaed accodig o he boud ye (bd = l idicao). Eablihe he baic afomaio elaiohi (EQPTRANS) bewee oe o moe iu (o ouu) commodiie ad oe o moe ouu (o iu) commodiie. 61

62 Iu aamee (Idexe) 21 FLOFUNCX (daayeacg1cg2 ) Relaed e/aamee 22 FLOFUNC FLOSUM COEFPTRAN Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Defaul exaolaio: oe Iace 24 (Requied / Omi / Secial codiio) he imelice level of he flow vaiable aociaed wih he commodiie i he gou cg1. Povided whe haig baed uo age i deied. Viaged ocee oly Deciio efficiecy of oducig cg2 fom cg1 (ubjec o ay FLOSUM). cg1 ad cg2 may be alo igle commodiie. Age-baed haig cuve (SHAPE) o be alied o he flow aamee (FLOFUNC/ FLOSUM) Affeced equaio o vaiable 25 Eablihe he elaiohi bewee oage level (VARSTGLVL) ad he a elaed commodiy flow (VARFLO) i he oveall oage equaio (EQSTG). Alied o he flow vaiable (VARFLO) i afomaio equaio (EQPTRANS) o accou fo chage i he oeaig chaaceiic of a oce due o he age (umbe of yea ice iallaio) of a oce. 62

63 Iu aamee (Idexe) 21 FLOMARK (daayeacbd) FLOPKCOI (daayeac) Relaed e/aamee 22 COMPKRSV COMPKFLX comeak comk Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Decimal facio [01]; defaul value: oe Defaul i/e: adad Scala [oe]; defaul value: 1 Iace 24 (Requied / Omi / Secial codiio) The ame give facio i alied o all imelice of he commodiy (hi could be geealized o allow ime-liceecific facio if deemed ueful). FLOPKCOI i ecified fo idividual ocee coumig he eak Deciio Poce-wie make hae i oal commodiy oducio. Faco ha emi aibuig le of he aveage demad o he eakig Affeced equaio o vaiable 25 The idividual oce flow vaiable (VARFLO VARIN VARSTGIN/OU T) ae coaied (EQ(l)FLMRK) o a facio of he oal oducio of a commodiy (VARCOMPRD). Foce he commodiy oducio vaiable (VARCOMPRD) o be icluded i he equaliy balace coai (EQECOMBAL). Alied o he flow vaiable (VARFLO) o 63

64 Iu aamee (Idexe) 21 Relaed e/aamee 22 Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Defaul i/e: adad Iace 24 (Requied / Omi / Secial codiio) commodiy c. Diec iheiace. Weighed aggegaio. Deciio equaio (EQPEAK) i iuaio whee he demad i aumed o o eceay occu coicide wih he eak. Affeced equaio o vaiable 25 adju he amou of a commodiy coumed whe coideig he aveage demad coibuig o he eakig coai (EQPEAK). FLOSHAR (daayeaccgb d) Decimal facio [01]; defaul value: oe I/e ove ayea bu o mileoeyea Diec iheiace. Weighed aggegaio. A commo examle fo he ue of FLOSHAR i o ecify he owe o hea aio of CHP la i he backeue oi. Fo examle fo a hea commodiy c= DH of a CHP la = CHP1 ad a commodiy gou cg= CGCHP coaiig he hea ad eleciciy commodiy he FLOSHAR aamee will coai he value 1/(1REH) Shae of flow commodiy c baed uo he um of idividual flow defied by he commodiy gou cg belogig o oce. Whe he commodiy i a iu a EQ(l)INSHR equaio i geeaed. Whe he commodiy i a ouu a EQ(l)OUTSHR equaio i geeaed. 64

65 Iu aamee (Idexe) 21 FLOSUB (daayeaccu) FLOSUM (daayeacg1cc g2) Relaed e/aamee 22 OBJFSUB CSTFLOV PAROBJFLO TOTFLO FLOFUNC FLOFUNCX COEFPTRANS femi cemi Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Moeay ui e commodiy ui [oe]; defaul: oe Defaul i/e: adad Commodiy ui of cg2/commodiy ui of c [oe]; defaul Iace 24 (Requied / Omi / Secial codiio) wih REH beig he owe o hea aio. Fo a backeue owe la FLOSHAR i a fixed boud (bd = FX ) fo a exacio codeig/a-ou CHP la FLOSHAR i ecified a a ue boud (bd = UP ). Diec iheiace. Weighed aggegaio. A commo examle fo he ue of FLOSUM i o decibe he eleciciy lo e hea ui gaied Deciio Subidy o a oce flow. Mulilie alied fo commodiy c of gou cg1 coeodig o he flow ae baed uo Affeced equaio o vaiable 25 Alied wih a miu ig o he flow vaiable (VARFLO) whe eeig he objecive fucio (EQOBJVAR). May aea i ue coai (EQUC*) if ecified i UCNAME. The FLOSUM mulilie i alied alog wih FLOFUNC aamee i he 65

66 Iu aamee (Idexe) 21 FLOTAX (daayeaccu) Relaed e/aamee 22 cffuc cga OBJFTAX CSTFLOV PAROBJFLO Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 value: ee ex colum Defaul i/e: adad Moeay ui e commodiy ui [oe]; defaul: Iace 24 (Requied / Omi / Secial codiio) whe decibig he coa fuel iu lie of exacio codeig/a-ou CHP la. If a FLOSUM i ecified ad o coeodig FLOFUNC he FLOFUNC i e o 1. FLOFUNC i ecified fo a ue commodiy gou cg1 ad o FLOSUM i ecified fo he commodiie i cg1 hee FLOSUM ae e o 1. The deived aamee COEFPTRANS i iheied/aggegaed o he imelice level of he flow vaiable of he commodiy c. Diec iheiace. Weighed aggegaio. Deciio he um of idividual flow defied by he commodiy gou cg2 of oce. Mo ofe ued o defie he emiio ae o o adju he oveall efficiecy of a echology baed uo fuel coumed. Tax o a oce flow. Affeced equaio o vaiable 25 afomaio coefficie (COEFPTRANS) which i alied o he flow vaiable (VARFLO) i he afomaio equaio (EQPTRANS). Alied o he flow vaiable (VARFLO) whe 66

67 Iu aamee (Idexe) 21 GDRATE (allyeacu) Relaed e/aamee 22 TOTFLO OBJDISC OBJDCEOH NCAPDRATE CORSALVI CORSALVD VDADISC Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 oe Defaul i/e: adad Decimal facio [01]; defaul value = oe Defaul i/e: adad Iace 24 (Requied / Omi / Secial codiio) A value mu be ovided fo each egio ad eiod. Deciio Syem-wide dicou ae i egio fo each ime-eiod. Affeced equaio o vaiable 25 eeig he objecive fucio (EQOBJVAR). May aea i ue coai (EQUC*) if ecified i UCNAME. The dicou ae i ake io coideaio whe coucig he objecive fucio dicouig mulilie (OBJDISC) which i alied i each comoe of he objecive fucio (EQOBJVAR EQOBJINV EQOBJFIX EQOBJSALV EQOBJELS). 67

68 Iu aamee (Idexe) 21 GDYEAR Relaed e/aamee 22 OBJDISC TOTOBJ Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Yea [oe]; defaul value = 1990 GILEDNO NCAPILED Decimal facio [01]; defaul value 0.1 Iace 24 (Requied / Omi / Secial codiio) Oly ovided whe he co aociaed wih he lead-ime fo ew caaciy (NCAPILED) ae o o be icluded i he objecive fucio. Deciio Bae yea fo dicouig. If he aio of leadime (NCAPILED) o he eiod duaio (D) i below hi hehold he he lead-ime coideaio will be Affeced equaio o vaiable 25 The yea o which all co ae o be dicoued i ake io coideaio whe coucig he objecive fucio dicouig mulilie (OBJDISC) which i alied i each of he comoe of he objecive fucio (EQOBJVAR EQOBJINV EQOBJFIX EQOBJSALV EQOBJELS). Peve he iveme co aociaed wih iveme leadime fom eegy he iveme comoe of he 68

69 Iu aamee (Idexe) 21 GNOINTERP Relaed e/aamee 22 All aamee ha ae omally ubjeced o ieolaio / exaolaio Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Biay idicao [0 o 1]; defaul value = 0 GTLIFE NCAPTLIFE Scala [oe]; defaul value = 10 GYRFR (all) RTCSTSFR RSSTGPRD Facio [01]; defaul value = oe; oly fo he ANNUAL imelice a value of 1 i edefied Iace 24 (Requied / Omi / Secial codiio) Oly ovide whe ieolaio / exaolaio i o be ued off fo all aamee. Ieolaio of co aamee i alway doe. Mu be ovided fo each egio ad imelice. Deciio igoed i he objecive fucio co. Swich fo geeally uig-o (= 0 ) ad uig-off (= 1 ) ae ie- / exaolaio. Defaul value fo he echical lifeime of a oce if o ovided by he ue. Duaio of imelice a facio of a yea. Ued fo haig he load cuve ad liig u imelice duaio fo ieegioal exchage. Affeced equaio o vaiable 25 objecive fucio (EQOBJINV). Alied o vaiou vaiable (VARNCAPPA STI VARCOMX VARIRE VARFLO VARSIN/OUT) i he commodiy balace equaio 69

70 Iu aamee (Idexe) 21 IREBND (daayeacalli ebd) IREFLO (1daayeac12c 22) Relaed e/aamee 22 oie oie Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Commodiy ui [oe]; defaul value = oe Defaul i/e: oe Commodiy ui c2/commodiy ui c1 [oe]; defaul value = 1 Defaul i/e: adad Iace 24 (Requied / Omi / Secial codiio) Oly alicable fo ieegioal exchage ocee (IRE). If he boud i ecified fo a imelice () beig above he commodiy (c) imelice eoluio he boud i alied o he um of he imo/exo accodig o he imelice ee. Sadad aggegaio. Oly alicable fo ieegioal exchage ocee (IRE) bewee wo ieal egio. Noe ha fo each diecio of ade a eaae IREFLO eed o be ecified. Simila o FLOFUNC fo adad ocee. Diec iheiace. Deciio Boud o he oal imo (exo) of commodiy (c) fom (o) egio all i (ou of) egio. Efficiecy of exchage oce fom commodiy c1 i egio 1 o commodiy c2 i he egio2 i imelice 2; he imelice 2 efe o he 2 egio. Affeced equaio o vaiable 25 (EQ(l)COMBAL ). Cool he iace fo which he ade boud coai (EQ(l)IREBND) i geeaed ad he RHS. Alied o he exchage flow vaiable (VARIRE) i he ie-egioal ade equaio (EQIRE). Alied o he exchage flow vaiable (VARIRE) whe 70

71 Iu aamee (Idexe) 21 Relaed e/aamee 22 Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Iace 24 (Requied / Omi / Secial codiio) Weighed aggegaio. Deciio Affeced equaio o vaiable 25 a boud o ieegioal ade i o be alied (EQ(l)IREBND). IREFLOSUM (daayeac1ie c2io) oie Commodiy ui c2/commodiy ui c1 [oe]; defaul value = 1 Defaul i/e: adad Oly alicable fo ieegioal exchage ocee (IRE). Sice he efficiecy IREFLO ca oly be ued fo exchage bewee ieal egio IREFLOSUM may be ued o defie a efficiecy fo a imo/exo wih a exeal egio by ecifyig he ame Auxiliay coumio (io = IN owig o he commodiy eeig he oce) o oducio/ emiio (io = OUT owig o he commodiy leavig he oce) of commodiy c2 due o he IMPo / EXPo (idex ie) of he commodiy c1 i egio 28 The mulilie i alied o he flow vaiable (VARIRE) aociaed wih a ie-egial exchage i he commodiy balace coai (EQ(l)COMBAL ). If a flow hae (FLOSHAR) i 28 The idexig of auxiliay coumio flow o emiio of ie-egioal exchage ocee i illuaed i he figue below. 71

72 Iu aamee (Idexe) 21 Relaed e/aamee 22 Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Iace 24 (Requied / Omi / Secial codiio) commodiy fo c1 ad c2 ad he value 1- efficiecy a auxiliay coumio. Diec iheiace. Weighed aggegaio. Deciio Affeced equaio o vaiable 25 ovided fo a ie-egioal exchage oce he he mulilie i alied o he flow vaiable (VARIRE) i he hae coai (EQ(l)IN/OUTS HR). If a co i ovide fo he flow (FLOCOST o FLODELIV) he he faco i alied o he flow vaiable (VARIRE) i he 72

73 Iu aamee (Idexe) 21 IREPRICE (daayeacall iecu) Relaed e/aamee 22 OBJIPRIC CSTCOMV PAROBJCOM TOTCOM oie Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Moeay ui / commodiy ui [oe]; defaul value: oe Defaul i/e: adad Iace 24 (Requied / Omi / Secial codiio) Oly alicable fo ieegioal exchage ocee (IRE). Igoed if all i a ieal egio. Diec iheiace. Weighed aggegaio. Deciio IMPo/EXPo ice (idex ie) fo o/fom a ieal egio of a commodiy (c) oigiaig fom/headig o a exeal egio all. Affeced equaio o vaiable 25 vaiable comoe of he objecive fucio (EQOBJVAR). The ice of he exchage commodiy i alied o he ade flow vaiable (VARIRE) i he vaiable co comoe of he objecive fucio (EQOBJVAR). IREXBND (alldaayeac iebd) oie Commodiy ui [oe]; defaul value: oe Defaul i/e: oe Oly alicable fo ieegioal exchage ocee (IRE). Povide wheeve a ade flow i o be coaied. Noe ha he limi i eihe imoed by ummig lowe o liig highe flow vaiable (VARIRE) whe ecified a ohe Boud o he oal IMPo (EXPo) (idex ie) of commodiy c i egio all wih all ouce (deiaio). The ade limi equaio EQ(l)XBND geeaed eihe um lowe flow vaiable (VARIRE) o li (accodig o he imelice ee) coae vaiable. 73

74 Iu aamee (Idexe) 21 IRECCVT (1c12c2)) Relaed e/aamee 22 IRETSCVT oie Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Scala Defaul value = 1 if commodiy ame ae he ame i boh egio I/e: oe Iace 24 (Requied / Omi / Secial codiio) ha he acual flow level (a deemied by he commodiy ad oce level (COMTSL/ PRCTSL ). Requied fo maig commodiie ivolved i ie-egioal exchage bewee wo egio wheeve commodiie aded ae i diffee ui i he egio. Deciio Coveio faco bewee commodiy ui i egio 1 ad egio 2. Exee he amou of commodiy c2 i egio 2 equivale o 1 ui of commodiy c1 i egio 1. Affeced equaio o vaiable 25 The coveio faco i alied o he flow vaiable (VARIRE) i he ie-egioal balace coai (EQIRE). Similaly alied o he he flow vaiable (VARIRE) whe a ie-egioal exchage i bouded i he limi coai (EQ(l)IREBND). Similaly alied o he he flow vaiable (VARIRE) whe a exchage wih 74

75 Iu aamee (Idexe) 21 IRETSCVT (1122) Relaed e/aamee 22 IRECCVT oie Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Scala [oe]; defaul value = 1 if imelice ee ad ame ae he ame i boh egio I/e: oe Iace 24 (Requied / Omi / Secial codiio) Ued fo maig imelice i diffee egio. Requied if imelice defiiio ae diffee i he egio. Deciio Maix fo maig imelice; he value fo (1122) give he facio of imelice 2 i egio 2 ha fall i imelice 1 i egio 1. Affeced equaio o vaiable 25 a exeal egio i bouded (EQ(l)XBND). The coveio faco i alied o he flow vaiable (VARIRE) i he ie-egioal balace coai (EQIRE). Similaly alied o he he flow vaiable (VARIRE) whe a ie-egioal exchage i bouded i he limi coai (EQ(l)IREBND). Similaly alied o he he flow vaiable (VARIRE) whe a exchage wih a exeal egio i bouded 75

76 Iu aamee (Idexe) 21 MULTI (jallyea) NCAPAF (daayeabd) Relaed e/aamee 22 NCAPAFM NCAPFOMM NCAPFSUBM NCAPFTAXM NCAPAFA NCAPAFS NCAPAFM NCAPAFX COEFAF Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Scala [oe]; defaul value = oe Decimal facio [01]; defaul value = 1 Defaul i/e: adad Iace 24 (Requied / Omi / Secial codiio) Oly ovided whe he elaed haig aamee ae o be ued. NCAPAF NCAPAFA ad NCAPAFS ca be alied imulaeouly. Diec iheiace. Weighed aggegaio. Deciio Mulilie able ued fo ay haig aamee (**M) o adju he coeodig echical daa a fucio of he yea; he able coai diffee mulilie cuve ideified by he idex j. Availabiliy faco elaig a ui of oducio (oce aciviy) i imelice o he cue ialled caaciy. Affeced equaio o vaiable 25 (EQ(l)XBND). {See Relaed Paamee} The coeodig caaciy-aciviy coai (EQ(l)CAPACT ) will be geeaed fo ay imelice. If he oce imelice level (PRCTSL) i below aid level he aciviy vaiable will be ummed. 76

77 Iu aamee (Idexe) 21 NCAPAFA (daayeabd) NCAPAFS (daayeabd) Relaed e/aamee 22 NCAPAFA NCAPAFS NCAPAFM NCAPAFX COEFAF Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Decimal facio [01]; defaul value = 1 Defaul i/e: adad Decimal facio [01]; defaul value = 1 Defaul i/e: adad Iace 24 (Requied / Omi / Secial codiio) Povided whe ANNUAL level oce oeaio i o be coolled. NCAPAF NCAPAFA ad NCAPAFS ca be alied imulaeouly. NCAPAFA i alway aumed o be oviage deede eve if he oce i defied a a viaged oe; fo viage-deede aual availabiliy NCAPAFS wih = ANNUAL ca be ued. NCAPAF NCAPAFA ad NCAPAFS ca be alied imulaeouly. NCAPAFS beig ecified fo imelice beig below he oce imelice level ae igoed. No iheiace. No aggegaio. Deciio Aual availabiliy faco elaig he aual aciviy of a oce o he ialled caaciy. Availabiliy faco elaig he aciviy of a oce i a imelice beig a o above he oce imelice level (cl) o he ialled caaciy. If fo examle he oce imelice Affeced equaio o vaiable 25 The coeodig caaciy-aciviy coai (EQ(l)CAPACT ) will be geeaed fo he ANNUAL imelice. If he oce imelice level (PRCTSL) i below aid level he aciviy vaiable will be ummed. The coeodig caaciy-aciviy coai (EQ(l)CAPACT ) will be geeaed fo a imelice beig a o above he oce imelice 77

78 Iu aamee (Idexe) 21 NCAPAFM (daayea) NCAPAFX (daayea) Relaed e/aamee 22 NCAPAF NCAPAFA NCAPAFS MULTI COEFAF NCAPAF NCAPAFA NCAPAFS SHAPE COEFAF Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Iege umbe Defaul value: 0 (o mulilie alied) I/e o oible Iege umbe Defaul value: 0 (o hae cuve alied) Defaul exaolaio oe Iace 24 (Requied / Omi / Secial codiio) If moe ha oe mulilie cuve ae ecified by he ue oly oe i ued (he oe havig he highe umbe). Povided whe haig baed uo age i deied. NCAPAFX i alied o NCAPAF ad NCAPAFS bu o he aual availabiliy Deciio level i DAYNITE ad NCAPAFS i ecified fo imelice o he SEASONAL level he um of he DAYNITE aciviie wihi a eao ae eiced bu o he DAYNITE aciviie diecly. Peiod eiive mulilie cuve (MULTI) o be alied o he availabiliy faco aamee (NCAPAF/AFA/A FS) of a oce. Age-baed haig cuve (SHAPE) o be alied o he availabiliy faco aamee (NCAPAF/AFA/A FS) of a oce. Affeced equaio o vaiable 25 level (cl). If he oce imelice level i below aid level he aciviy vaiable will be ummed. {See Relaed Paamee} {See Relaed Paamee} 78

79 Iu aamee (Idexe) 21 NCAPBND (daayeabd) Relaed e/aamee 22 Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Caaciy ui [oe]; defaul value: oe Defaul i/e: oe Iace 24 (Requied / Omi / Secial codiio) NCAPAFA. If he oce i oviaged he SHAPE aamee i alied o NCAPAF(S) of he viage eiod i.e. fo he availabiliy faco i i aumed ha he oce behave a a viaged oe. Povided fo each oce o have i oveall ialled caaciy (VARNCAP) limied i a eiod. A defaul ie- /exaolaio i uedoff o he boud mu be exlicily ecified fo mileoeyea ule a ie-/exaolaio oio i give e.g. NCAPBND(R 0 P) =2 which u o ieolaio fo NCAPBND fo all Deciio Boud o he emied level o iveme i ew caaciy Affeced equaio o vaiable 25 Imoe a idiec limi o he caaciy afe equaio (EQCPT) by mea of a diec boud o he ew iveme caaciy vaiable (VARNCAP). May aea i ue coai (EQUC*) if ( NCAPBNDLO/ FX/ UP ) ecified i 79

80 Iu aamee (Idexe) 21 NCAPCLED (daayeac) NCAPCOM (daayeacio) NCAPCOST (daayea) Relaed e/aamee 22 NCAPICOM COEFICOM ccaflo ccoly OBJICOST OBJSCC CSTINVV Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Yea [oe]; defaul value: = NCAPILED Defaul i/e: adad Commodiy ui e caaciy ui [oe]; defaul value: oe Defaul i/e: adad Moeay ui e caaciy ui [oe]; defaul Iace 24 (Requied / Omi / Secial codiio) ocee (ee Table 7). Povided whe a commodiy mu be available io o availabiliy of a oce. So if he oce i available i he yea B(v) NCAPILED-1 he commodiy i oduced duig he ime a [B(v)ILED-CLED B(v) NCAPILED-1]. Uually ued whe modellig he eed fo fabicaio of eaco fuel he eiod befoe a eaco goe olie. Povided whe he coumio o oducio of a commodiy i ied o he level of he ialled caaciy. Povided wheeve hee i a co aociaed wih uig ew caaciy i Deciio Lead ime equieme fo a commodiy duig coucio (NCAPICOM) io o he iiial availabiliy of he caaciy. Emiio (o ladue) of commodiy c aociaed wih he caaciy of a oce fo each yea aid caaciy exi. Iveme co of ew ialled caaciy accodig Affeced equaio o vaiable 25 UCNAME. Alied o he iveme vaiable (VARNCAP) i he commodiy balace (EQ(l)COMBAL ) of he iveme eiod o eviou eiod. Alied o he caaciy vaiable (VARCAP) i he commodiy balace (EQCOMBAL). Alied o he iveme vaiable 80

81 Iu aamee (Idexe) 21 NCAPDCOST (daayeacu) NCAPDELIF (daayea) Relaed e/aamee 22 PAROBJINV TOTINV NCAPDLAG CORSALVD OBJDCOST CSTDECV PAROBJDEC TOTDEC NCAPDLIFE CORSALVD DURMAX OBJCRFD SALVDEC Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 value: oe Defaul i/e: adad Moeay ui e caaciy ui [oe]; defaul value: oe Defaul i/e: adad Yea [oe]; defaul value: NCAPDLIFE Defaul i/e: adad Iace 24 (Requied / Omi / Secial codiio) lace. Povided whe hee ae decommiioig co aociaed wih a oce. Decommiioig of a oce ad he ayme of decommiioig co may be delayed by a lag ime (NCAPDLAG). Povided whe he imefame fo ayig fo decommiio i diffee fom ha of he acual decommiioig. Deciio o he iallaio yea. Co of dimalig a faciliy afe he ed of i lifeime. Ecoomic lifeime of he decommiioig aciviy. Affeced equaio o vaiable 25 (VARNCAP) whe eeig he objecive fucio (EQOBJNV). May aea i ue coai (EQUC*) if ecified i UCNAME. Alied o he cue caaciy ubjec o decommiioig (VARNCAPNC APPASTI) whe eeig he objecive fucio (EQOBJNV). Alied o he iveme vaiable (VARNCAP) whe eeig he alvage oio of he objecive fucio 81

82 Iu aamee (Idexe) 21 NCAPDISC (daayeaui) NCAPDLAG (daayea) Relaed e/aamee 22 dcca COEFOCOM DURMAX OBJDLAGC Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Caaciy ui [oe]; defaul value: oe No i/e Yea [oe]; defaul value: NCAPDLIFE Defaul i/e: adad Iace 24 (Requied / Omi / Secial codiio) Ued fo lumy iveme. Requie MIP. Povided whe hee i a lag i he decommiioig of a oce (e.g. o allow he uclea coe o educe i adiaio). Deciio Size of caaciy ui ha ca be added. Numbe of yea delay befoe decommiioig ca begi afe he lifeime of a echology ha eded. Affeced equaio o vaiable 25 (EQOBJSALV). Alied o he lumy iveme iege vaiable (VARDNCAP) i he dicee iveme equaio (EQDSCNCAP) o e he coeodig adad iveme vaiable level (VARNCAP). Delay alied o a decommiioig flow (VARFLO) i he balace equaio (EQ(l)COMBAL ) a oducio. Delay alied o he cue caaciy ubjec o decommiioig 82

83 Iu aamee (Idexe) 21 NCAPDLAGC (daayeacu) NCAPDLIFE (daayea) Relaed e/aamee 22 NCAPDLAG OBJDLAGC CSTFIXV PAROBJFIX TOTFIX DURMAX Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Moeay ui e caaciy ui [oe]; defaul value: oe Defaul i/e: adad Yea [oe]; defaul value: oe Defaul i/e: adad Iace 24 (Requied / Omi / Secial codiio) Povided whe hee i a co duig ay lag i he decommiioig (e.g. ecuiy). Povided whe a oce ha a decommiioig hae. Deciio Co occuig duig he lag ime afe he echical lifeime of a oce ha eded ad befoe i decommiioig a. Techical ime fo dimalig a faciliy afe he ed i echical lifeime lu ay lag ime (NCAPDLAG). Affeced equaio o vaiable 25 (VARNCAPNC APPASTI) whe eeig he objecive fucio comoe (EQOBJINV EQOBJFIX EQOBJSALV). Co duig delay alied o he cue caaciy ubjec o decommiioig (VARNCAPNC APPASTI) whe eeig he objecive fucio comoe (EQOBJFIX EQOBJSALV). Decommiioig ime imacig (VARNCAPNC APPASTI) whe eeig he objecive fucio comoe 83

84 Iu aamee (Idexe) 21 NCAPDRATE (daayea) NCAPELIFE (daayea) NCAPFOM (daayeacu) Relaed e/aamee 22 GDRATE CORSALVI CORSALVD NCAPTLIFE CORSALVI OBJCRF OBJFOM CSTFIXV PAROBJFIX Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Pece [oe]; defaul value: GDRATE Defaul i/e: adad yea [oe]; defaul value: NCAPTLIFE Defaul i/e: adad Moeay ui e caaciy ui [oe]; defaul Iace 24 (Requied / Omi / Secial codiio) Povided if he co of boowig fo a oce i diffee fom he adad dicou ae. Povided oly whe he ecoomic lifeime diffe fom he echical lifeime (NCAPTLIFE). Povided whe hee i a fixed co aociaed wih he ialled caaciy. Deciio Techology ecific dicou ae. Ecoomic lifeime of a oce. Fixed oeaig ad maieace co e ui of caaciy Affeced equaio o vaiable 25 (EQOBJINV EQOBJSALV). Dicou ae alied o iveme (VARNCAPNC APPASTI) whe eeig he objecive fucio comoe (EQOBJINV EQOBJSALV). Ecoomic lifeime of a oce whe coig iveme (VARNCAPNC APPASTI) o caaciy i he objecive fucio comoe (EQOBJINV EQOBJSALV EQOBJFIX). Fixed oeaig ad maieace co aociaed 84

85 Iu aamee (Idexe) 21 NCAPFOMM (daayea) NCAPFOMX (daayea) NCAPFSUB (daayeacu) Relaed e/aamee 22 TOTFIX NCAPFOM MULTI NCAPFOM SHAPE OBJFSB CSTFIXV PAROBJFIX TOTFIX Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 value: oe Defaul i/e: adad Iege umbe Defaul value: 0 (o mulilie cuve alied) I/e: o oible Iege umbe Defaul value: 0 (o hae cuve alied) Defaul i/e: oe Moeay ui e caaciy ui [oe]; defaul value: oe Iace 24 (Requied / Omi / Secial codiio) Povided whe haig baed uo he eiod i deied. If moe ha oe mulilie cuve ae ecified by he ue oly oe i ued (he oe havig he highe umbe). Povided whe haig baed uo age i deied. Povided whe hee i a ubidy fo aociaed wih he level of ialled caaciy. Deciio accodig o he iallaio yea. Peiod eiive mulilie cuve (MULTI) alied o he fixed oeaig ad maieace co (NCAPFOM). Age-baed haig cuve (SHAPE) o be alied o he fixed oeaig ad maieace co. Subidy e ui of ialled caaciy. Affeced equaio o vaiable 25 wih oal ialled caaciy (VARNCAPNC APPASTI) whe eeig he objecive fucio comoe (EQOBJFIX). {See Relaed Paamee} {See Relaed Paamee} Fixed ubidy aociaed wih oal ialled caaciy 85

86 Iu aamee (Idexe) 21 NCAPFSUBM (daayea) NCAPFSUBX (daayea) NCAPFTAX (daayeacu) Relaed e/aamee 22 NCAPFSUB MULTI NCAPFSUB SHAPE OBJFTAX CSTFIXV PAROBJFIX TOTFIX Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Defaul i/e: adad Iege umbe Defaul value: 0 (o mulilie cuve alied) I/e: o oible Iege umbe Defaul value: 0 (o hae cuve alied) Defaul i/e: oe moeay ui e caaciy ui [oe]; defaul value: oe Defaul i/e: Iace 24 (Requied / Omi / Secial codiio) Povided whe haig baed uo he eiod i deied. If moe ha oe mulilie cuve ae ecified by he ue oly oe i ued (he oe havig he highe umbe). Povided whe haig baed uo age i deied. Povided whe hee i a fixed ax baed uo he level of he ialled caaciy. Deciio Peiod eiive mulilie cuve (MULTI) alied o he ubidy (NCAPFSUB). Age-baed haig cuve (SHAPE) o be alied o he fixed ubidy (NCAPFSUB). Tax e ui of ialled caaciy. Affeced equaio o vaiable 25 (VARNCAPNC APPASTI) whe eeig he objecive fucio comoe (EQOBJFIX) wih a miu ig. {See Relaed Paamee} {See Relaed Paamee} Fixed ubidy aociaed wih oal ialled caaciy (VARNCAPNC 86

87 Iu aamee (Idexe) 21 NCAPFTAXM (daayea) NCAPFTAXX (daayea) NCAPICOM (daayeac) Relaed e/aamee 22 NCAPFTAX MULTI NCAPFTAX SHAPE NCAPCLED ccaflo ccoly Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 adad Iege umbe Defaul value: 0 (o mulilie cuve alied) I/e o oible Iege umbe Defaul value: 0 (o hae cuve alied) Defaul i/e: oe Commodiy ui e caaciy ui [oe]; defaul value: oe Defaul i/e: adad Iace 24 (Requied / Omi / Secial codiio) Povided whe haig baed uo he eiod i deied. If moe ha oe mulilie cuve ae ecified by he ue oly oe i ued (he oe havig he highe umbe). Povided whe haig baed uo age i deied. Povided whe a commodiy i eeded i he eiod i which he ew caaciy i o be available o befoe NCAPCLED If NCAPCLED i Deciio Peiod eiive mulilie cuve (MULTI) alied o he ax (NCAPFTAX). Age-baed haig cuve (SHAPE) o be alied o he fixed ubidy (NCAPFSUB). Amou of commodiy (c) equied fo he coucio of ew caaciy. Affeced equaio o vaiable 25 APPASTI) whe eeig he objecive fucio comoe (EQOBJFIX). {See Relaed Paamee} {See Relaed Paamee} Alied o he iveme vaiable (VARNCAP) i he aoiae commodiy coai 87

88 Iu aamee (Idexe) 21 NCAPILED () Relaed e/aamee 22 COEFCPT COEFICOM DURMAX Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Yea [oe]; defaul Iace 24 (Requied / Omi / Secial codiio) ovided he commodiy i equied duig he yea [B(v)NCAPCLEDB(v )NCAPILED- NCAPCLED]. If hi ime a moe ha oe eiod he commodiy flow i li u ooioally bewee he eiod. Fo he commodiy balace he commodiy equieme i a eiod i coveed i a aveage aual commodiy flow fo he eie eiod alhough he coucio may ake lace oly fo a few yea of he eiod Negaive value decibe oducio (e.g. emiio) a he ime of a ew iveme Povided whe hee i a delay bewee whe he Deciio Lead ime bewee iveme deciio ad acual Affeced equaio o vaiable 25 (EQ(l)COMBAL ) a a of coumio. Alied o he iveme 88

89 Iu aamee (Idexe) 21 Relaed e/aamee 22 Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 value: oe Defaul i/e: adad Iace 24 (Requied / Omi / Secial codiio) iveme deciio occu (NCAPILED-1) ad whe he caaciy (ew caaciy o a iveme) i iiially available. Fo a iveme he iveme co ae ake fom he PASTYEAR. Imac he imig of he haig aamee. Deciio availabiliy of ew caaciy (= coucio ime) Affeced equaio o vaiable 25 vaiable (VARNCAP) balace coai (EQ(l)COMBAL ) a a of coumio if hee i a aociaed flow. I combiaio wih he eiod duaio D ued a idicao o diiguih mall ad lage iveme (VARNCAP) ad hu ifluece he way he iveme ad fixed co ae eaed i he objecive fucio (EQOBJINV EQOBJFIX EQOBJSALV). NCAPISUB OBJISUB moeay ui e Povided whe hee i a Subidy e ui of Alied o he 89

90 Iu aamee (Idexe) 21 (daayeacu) NCAPITAX (daayeacu) NCAPOCOM (daayeac) Relaed e/aamee 22 OBJSCC CSTINVV CSTSALV PAROBJINV PAROBJSAL TOTINV TOTSAL OBJITAX OBJSCC CSTINVV CSTSALV PAROBJINV PAROBJSAL TOTINV TOTSAL NCAPVALU OBJLATV Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 caaciy ui [oe]; defaul value: oe Defaul i/e: adad moeay ui e caaciy ui [oe]; defaul value: oe Defaul i/e: adad Commodiy ui e caaciy ui Iace 24 (Requied / Omi / Secial codiio) ubidy fo ew iveme i a eiod. Povided whe hee i a ax aociaed wih ew iveme i a eiod. Povided whe hee i a commodiy eleae Deciio ew ialled caaciy. Tax e ui of ew ialled caaciy Amou of commodiy c e Affeced equaio o vaiable 25 iveme vaiable (VARNCAP) whe eeig he objecive fucio (EQOBJNV) wih a miu ig. May aea i ue coai (EQUC*) if ecified i UCNAME. Alied o he iveme vaiable (VARNCAP) whe eeig he objecive fucio (EQOBJNV). May aea i ue coai (EQUC*) if ecified i UCNAME. Alied o he iveme 90

91 Iu aamee (Idexe) 21 NCAPPASTI (v) Relaed e/aamee 22 PAROBJLAT TOTLAT ccaflo ccoly NCAPPASTY OBJPASTI PARPASTI Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 [oe]; defaul value: oe Defaul i/e: adad caaciy ui [oe]; defaul value: oe No i/e Iace 24 (Requied / Omi / Secial codiio) aociaed wih he decommiioig. The yea idex of he aamee coeod o he viage yea. If he decommiioig ime (NCAPDLIFE) fall i moe ha oe eiod i li u ooioally amog he eiod. Fo he commodiy balace he commodiy eleae i a eiod i coveed i a aveage aual commodiy flow fo he eie eiod alhough he dimalig may ake lace oly fo a few yea of he eiod. Pa iveme ca alo be ecified fo mileoeyea e.g. if he mileoeyea i a hioic yea o ha caaciy addiio ae Deciio ui of caaciy eleaed duig he dimalig of a oce. Iveme i ew caaciy made befoe he begiig of he model hoizo (i he yea ecified by ayea). Affeced equaio o vaiable 25 vaiable (VARNCAP) i he aoiae commodiy coai (EQ(l)COMBAL ) a a of oducio i he aoiae eiod. EQ(l)COMBAL EQCPT EQOBJINV EQOBJSALV EQOBJFIX 91

92 Iu aamee (Idexe) 21 NCAPPASTY (ayea) NCAPPKCNT (daayea) Relaed e/aamee 22 NCAPPASTI comeak comk ckaf cko Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Yea [oe]; defaul value: oe No i/e Decimal facio [01]; defaul value: 1 Defaul i/e: adad Iace 24 (Requied / Omi / Secial codiio) kow o if laed fuue iveme ae aleady kow. Povided o ead a igle a iveme (NCAPPASTI) back ove eveal yea (e.g. ca i he eiod befoe he 1 mileoey wee bough ove he eviou 15 yea). If ovela wih ohe a iveme he caaciy value ae added. If he idicao PRCPKAF i ecified he NCAPPKCNT i e equal o he availabiliie NCAPAF. Diec iheiace. Weighed aggegaio. Deciio Numbe of yea o go back o calculae a liea build-u of a iveme Facio of caaciy ha ca coibue o eakig equaio. Affeced equaio o vaiable 25 {See NCAPPASTI} Alied o iveme i caaciy (VARNCAP NCAPPASTI) i he eakig coai (EQPEAK). NCAPTLIFE (daayea) NCAPELIFE COEFCPT Yea [oe]; defaul Execed fo all echologie. Techical lifeime of a oce. Imac all calculaio ha 92

93 Iu aamee (Idexe) 21 NCAPVALU (daayeaccu) PRAT (eg) Relaed e/aamee 22 COEFRPTI DURMAX NCAPOCOM OBJLATV PAROBJLAT TOTLAT PBT PAT CCOST0 Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 value: GTLIFE Defaul i/e: adad Moeay ui / commodiy ui [oe]; defaul value: oe Defaul i/e: adad Scala [01]; defaul Iace 24 (Requied / Omi / Secial codiio) Povided whe a eleaed commodiy ha a value. Povided fo leaig echologie (eg) whe ETL i ued. Deciio Value of a commodiy eleaed a decommiioig (NCAPOCOM). Poge aio idicaig he do i he iveme Affeced equaio o vaiable 25 ae deede uo he availabiliy of iveme (VARNCAP) icludig caaciy afe (EQCPT) commodiy flow (EQ(l)COMBAL ) co (EQOBJINV EQOBJFIX EQOBJVAR EQOBJSALV). Alied o he iveme elaed (VARNCAP NCAPPASTI) eleae flow a decommiioig i he objecive fucio (EQOBJSALV). Fudameal faco o decibe he leaig cuve 93

94 Iu aamee (Idexe) 21 PRCACTFLO (daayeacg) Relaed e/aamee 22 CCAPK BETA ALPH PRCCAPACT cacu cg caie Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 value oe Commodiy ui / aciviy ui [oe]; defaul value: 1 Defaul i/e: adad Iace 24 (Requied / Omi / Secial codiio) Oly (aely) ovided whe he aciviy ad flow vaiable of a oce ae i diffee ui. Deciio co each ime hee i a doublig of he ialled caaciy. Coveio faco fom ui of aciviy o ui of hoe flow vaiable ha defie he aciviy (imay commodiy gou). Affeced equaio o vaiable 25 ad hu effec ealy all equaio ad vaiable elaed o edogeou echology leaig (ETL). Alied o he imay commodiy (ccg) flow vaiable (VARFLO VARIRE) o elae oveall aciviy (VARACT i EQACTFLO). Whe he Reducio algoihm acivaed i i alied o he aciviy vaiable (VARACT) i hoe cae whee he flow vaiable 94

95 Iu aamee (Idexe) 21 PRCCAPACT () Relaed e/aamee 22 PRCACTFLO cacu Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Aciviy ui / caaciy ui [oe]; defaul value: 1 Defaul i/e: adad Iace 24 (Requied / Omi / Secial codiio) Deciio Coveio faco fom caaciy ui o aciviy ui aumig ha he caaciy i ued fo oe yea. Affeced equaio o vaiable 25 (VARFLO) ca be elaced by he aciviy vaiable (e.g. he aciviy i defied by oe commodiy flow). Alied alog wih he availabiliy faco (NCAPAF) o he iveme (VARNCAP NCAPPASTI) i he uilizaio equaio (EQ(l)CAPACT). Alied o he iveme (VARNCAP NCAPPASTI) i he eak coai (EQPEAK). Alied o he iveme (VARNCAP 95

96 Iu aamee (Idexe) 21 Relaed e/aamee 22 Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Iace 24 (Requied / Omi / Secial codiio) Deciio Affeced equaio o vaiable 25 NCAPPASTI) i he commodiy ecific caaciy uilizaio coai (EQLCAFLAC) i he VTT exeio (ee Table 16). Alied o he iveme o (VARNCAP NCAPPASTI) i he caaciy uilizaio coai fo exacio codeig CHP la fo codeig mode (ECTAFCON) ad backeue mode (ECTAFCHP) i he IER exeio (ee Table 16). Alied o he 96

97 Iu aamee (Idexe) 21 SC0 (eg) Relaed e/aamee 22 Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Moeay ui / caaciy ui [oe]; defaul value oe Iace 24 (Requied / Omi / Secial codiio) Fo leaig echologie eg whe ETL i ued. Deciio Iiial ecific iveme co. Affeced equaio o vaiable 25 iveme (VARNCAP NCAPPASTI) of exacio codeio CHP la i he eak coai (EQPEAK) wih a coveio faco coveig he iu-oieed caaciy defiiio io eleciciy em i he IER exeio (ee Table 16). Defie ogehe wih CCAP0 iiial oi of leaig cuve ad affec hu he coe equaio ad vaiable of edogeou echological leaig (ETL). SEG Iege Fo leaig echologie Numbe of Ifluece he 97

98 Iu aamee (Idexe) 21 Relaed e/aamee 22 Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Iace 24 (Requied / Omi / Secial codiio) (eg) [oe]; eg whe ETL i ued. Cuely limied o ix egme by e k. SHAPE (jage) STGEFF (daayea) FLOFUNC FLOSUM NCAPAFX NCAPFOMX NCAPFSUBX NCAPFTAXX c cgi cg Scala [oe]; defaul value = oe Decimal facio [oe]; defaul value: 1 Defaul i/e: adad Povided fo each age deede haig cuve ha i o be alied. Oly alicable o oage ocee (STG): imelice oage ieeiod oage o igh oage device. Deciio egme. Mulilie able ued fo ay haig aamee (**X) o adju he coeodig echical daa a fucio of he age; he able ca coai diffee mulilie cuve ha ae ideified by he idex j. Efficiecy of oage oce. Affeced equaio o vaiable 25 iecewie liea aoximaio of he cumulaive co cuve (EQCOS EQLA1 EQLA2). {See Relaed Paamee} Alied o he oage ouu flow (VARSOUT) i he commodiy balace (EQ(l)COMBAL ) fo he oed 98

99 Iu aamee (Idexe) 21 STGCHRG (daayea) STGLOSS (daayea) Relaed e/aamee 22 c cgi cg c cgi cg Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Scala [oe]; defaul value: oe Defaul i/e: adad Scala [oe]; defaul value: oe Defaul i/e: adad Iace 24 (Requied / Omi / Secial codiio) Oly alicable o oage ocee (STG): imelice oage ieeiod oage o igh oage device. Oly alicable o oage ocee (STG): imelice oage ieeiod oage o igh oage device. Deciio Aual exogeou chagig of a oage echology i a aicula imelice. Aual eegy lo of a oage oce e ui of aveage eegy oed. Affeced equaio o vaiable 25 commodiy. Exogeou chagig of oage ee oage equaio (EQSTGTSS EQSTGIPS) a igh-had ide coa. Soage oce bewee imelice (EQSTGTSS): alied o he aveage oage level (VARACT) bewee wo coecuive imelice. Soage oce bewee eiod (EQSTGIPS): alied o he aveage oage level fom he 99

100 Iu aamee (Idexe) 21 STGINBND (daayeacbd) STGOUTBND (daayeacbd) Relaed e/aamee 22 c cgi cg c cgi cg Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Commodiy ui [oe]; defaul value: oe Defaul i/e: oe Commodiy ui [oe]; defaul value: oe Defaul i/e: oe Iace 24 (Requied / Omi / Secial codiio) Oly alicable o oage ocee (STG): imelice oage ieeiod oage o igh oage device. Oly alicable o oage ocee (STG): imelice oage ieeiod oage o igh oage device. Deciio Boud o he iu flow of a oage oce i a imelice. Boud o he ouu flow of a oage oce i a imelice. Affeced equaio o vaiable 25 eeiod (VARACT) ad he e iflow (VARSIN- VARSOUT) of he cue eiod. Soage iu boud coai (EQ(l)STGIN) whe i above cl of he oage oce. Diec boud o oage iu flow (VARSTGIN) whe a he cl level. Soage ouu boud coai (EQ(l)STGIN) whe i above cl of he oage oce. Diec boud o oage ouu flow vaiable 100

101 Iu aamee (Idexe) 21 UCACT (ucidedaayea ) UCFLO (ucidedaayea c) UCIRE (ucidedaayea c) UCCOMCON (ucidedaayea c) UCCOMPRD (ucidedaayea Relaed e/aamee 22 uc ucgma uc uc uc ucgmac uc ucgmac Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Noe [oe]; defaul value: oe Defaul: i/e: adad Noe [oe]; defaul value: oe Defaul: i/e: adad Noe [oe]; defaul value: oe Defaul: i/e: adad Noe [oe]; defaul value: oe Defaul: i/e: adad Noe [oe]; defaul Iace 24 (Requied / Omi / Secial codiio) Ued i ue coai. Diec iheiace. Weighed aggegaio. Ued i ue coai. Diec iheiace. Weighed aggegaio. Ued i ue coai. Diec iheiace. Weighed aggegaio. Ued i ue coai. No iheiace/aggegaio (migh be chaged i he fuue). Ued i ue coai. No Deciio Coefficie of he aciviy vaiable VARACT i a ue coai. Coefficie of he flow VARFLO vaiable i a ue coai. Coefficie of he ade vaiable VARIRE i a ue coai. Coefficie of he commodiy coumio vaiable VARCOMCON i a ue coai. Coefficie of he e commodiy Affeced equaio o vaiable 25 (VARSTGOUT) whe a he cl level. EQ(l)UCXXX EQ(l)UCXXX EQ(l)UCXXX EQ(l)UCXXX EQ(l)UCXXX 101

102 Iu aamee (Idexe) 21 c) UCCAP (ucidedaayea ) UCNCAP (ucidedaayea ) UCRHS (ucbd) UCRHSR (ucbd) Relaed e/aamee 22 uc ucgma uc ucgma uc ucum ucum ucum uc uceach ucum Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 value: oe Defaul: i/e: adad Noe [oe]; defaul value: oe Defaul: i/e: adad Noe [oe]; defaul value: oe Defaul: i/e: adad Noe [oe]; defaul value: oe Defaul i/e: oe Noe [oe]; defaul Iace 24 (Requied / Omi / Secial codiio) iheiace/aggegaio (migh be chaged i he fuue). Ued i ue coai. Ued i ue coai. Ued i ue coai. Ued i ue coai. Deciio oducio vaiable VARCOMPRD i a ue coai. Coefficie of he aciviy vaiable VARCAP i a ue coai. Coefficie of he aciviy vaiable VARNCAP i a ue coai. RHS coa wih boud ye of bd of a ue coai. RHS coa wih boud ye of bd of Affeced equaio o vaiable 25 EQ(l)UCXXX EQ(l)UCXXX RHS (igh-had ide) coa of a ue coai which i ummig ove egio (ucum) eiod (ucum) ad imelice (ucum) (EQ(l)UC). RHS coa of ue coai 102

103 Iu aamee (Idexe) 21 UCRHST (ucdaayeabd) Relaed e/aamee 22 ucum uc ucum uceach ucucc ucum Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 value: oe Defaul i/e: oe Noe [oe]; defaul value: oe Defaul i/e: oe Iace 24 (Requied / Omi / Secial codiio) Ued i ue coai. Deciio a ue coai. RHS coa wih boud ye of bd of a ue coai. Affeced equaio o vaiable 25 which ae geeaed fo each ecified egio (uceach) ad ae ummig ove eiod (ucum) ad imelice (ucum) (EQ(l)UCR). RHS coa of ue coai which ae geeaed fo each ecified eiod (uceach) ad ae ummig ove egio (ucum) ad imelice (ucum) (EQ(l)UCT). If ucucc iead of uceach i ecified he coai will be 103

104 Iu aamee (Idexe) 21 UCRHSRT (ucdaayeabd) Relaed e/aamee 22 uc uceach uceach ucucc ucum Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Noe [oe]; defaul value: oe Defaul i/e: oe Iace 24 (Requied / Omi / Secial codiio) Ued i ue coai. Deciio RHS coa wih boud ye of bd of a ue coai. Affeced equaio o vaiable 25 geeaed a dyamic coai bewee he wo ucceive eiod (EQ(l)UCSU). RHS coa of ue coai which ae geeaed fo each ecified egio (uceach) ad eiod (uceach) ad ae ummig ove imelice (ucum) (EQ(l)UCRT). If ucucc iead of uceach i ecified he coai will be geeaed a dyamic coai bewee he wo ucceive 104

105 Iu aamee (Idexe) 21 UCRHSTS (ucdaayeabd) UCRHSRTS (ucdaayeabd Relaed e/aamee 22 uc ucum uceach ucucc uceach uc uceach uceach Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 Noe [oe]; defaul value: oe Defaul i/e: oe Iace 24 (Requied / Omi / Secial codiio) Ued i ue coai. No iheiace/aggegaio. Deciio RHS coa wih boud ye of bd of a ue coai. Noe Ued i ue coai. RHS coa wih boud ye of bd of Affeced equaio o vaiable 25 eiod (EQ(l)UCRSU). RHS coa of ue coai which ae geeaed fo each ecified eiod (uceach) ad imelice (uceach) ad ae ummig ove egio (ucum) (EQ(l)UCTS). If ucucc iead of uceach i ecified he coai will be geeaed a dyamic coai bewee he wo ucceive eiod (EQ(l)UCSUS). RHS coa of 105

106 Iu aamee (Idexe) 21 Relaed e/aamee 22 ) ucucc uceach Ui / Rage & Defaul value & Defaul ie- /exaolaio 23 [oe]; defaul value: oe Defaul i/e: oe Iace 24 (Requied / Omi / Secial codiio) No iheiace/aggegaio. Deciio a ue coai. Affeced equaio o vaiable 25 ue coai which ae geeaed fo each ecified egio (uceach) eiod (uceach) ad imelice (uceach) (EQ(l)UCRTS). If ucucc iead of uceach i ecified he coai will be geeaed a dyamic coai bewee he wo ucceive eiod (EQ(l)UCRSUS). 106

107 3.2 Ieal aamee Table 13 give a oveview of ieal aamee geeaed by he TIMES eoceo. Simila o he deciio of he ieal e o all ieal aamee ued wihi TIMES ae dicued. The li give i Table 13 focue maily o he aamee ued i he eaaio ad ceaio of he equaio i Chae 5. I addiio o he ieal aamee lied hee he TIMES eoceo comue addiioal ieal aamee which ae eihe ued oly a auxiliay aamee beig valid oly i a ho ecio of he code o which ae ioduced o imove he efomace of he code egadig comuaioal ime. Table 13: Ieal aamee i TIMES Ieal aamee 29 (Idexe) ALPH (keg) BETA (keg) CCAPK (keg) CCOST0(eg) CCOSTK (keg) CCOSTM (eg) Iace (Requied / Omi / Secial codiio) Fo leaig echologie eg whe ETL i ued. Fo leaig echologie eg whe ETL i ued. Fo leaig echologie eg whe ETL i ued. Fo leaig echologie eg whe ETL i ued. Fo leaig echologie eg whe ETL i ued. Fo leaig echologie eg whe ETL i ued. Deciio Axi iece o cumulaive co axi fo deciio of liea equaio valid fo egme k. Sloe of cumulaive co cuve i egme k ( = ecific iveme co). Cumulaive caaciy a kikoi k. Iiial cumulaive co of leaig echology eg. Cumulaive iveme co a kikoi k. Maximum cumulaive co baed o CCAPM. 29 The fi ow coai he aamee ame he ecod ow coai i backe he idex domai fo which he aamee i defied. 107

108 Ieal aamee 29 (Idexe) COEFAF (vbd) COEFCPT (v) COEFICOM (vc) Iace (Requied / Omi / Secial codiio) Fo each echology a he level of oce oeaio (PRCTSL). Fo each echology he amou of a iveme (VARNCAP) available i he eiod. Wheeve hee i a commodiy equied duig coucio he coumig beig ake fom he balace coai (EQ(l)COMBAL). Alied o he iveme vaiable (VARNCAP) of eiod v i he commodiy balace (EQ(l)COMBAL) of eiod. The duaio duig which he commodiy i oduced a i he yea B(v)NCAPILED(v)- NCAPCLED(v) ad ed i he yea B(v)NCAPILED(v)-1. Deciio Availabiliy coefficie of he caaciy (ew iveme vaiable VARNCAP lu ill exiig a iveme NCAPPASTI) i EQ(l)CAPACT; COEFAF i deived fom he availabiliy iu aamee NCAPAF NCAPAFA ad NCAPAFS akig io accou ay ecified MULTI o SHAPE mulilie. Facio of caaciy buil i eiod v ha i available i eiod ; migh be malle ha 1 due o NCAPILED i viage eiod o he fac ha he lifeime ed wihi a eiod. Coefficie fo commodiy equieme duig coucio i eiod due o iveme deciio i eiod v (ee alo NCAPICOM). 108

109 Ieal aamee 29 (Idexe) COEFOCOM (vc) COEFPTRAN (vcgccomg) COEFRPTI (v) CORSALVD (vcu) CORSALVI (vcu) D () Iace (Requied / Omi / Secial codiio) Wheeve hee i a commodiy eleaed duig decomiioig he oducio beig added o he balace coai (EQ(l)COMBAL). Alied o he iveme vaiable (VARNCAP) of eiod v i he commodiy balace (EQ(l)COMBAL) of eiod. The eleae occu duig he decommiioig lifeime NCAPDLIFE. Fo each flow hough a oce. Fo each echology whoe echical life (NCAPTLIFE) i hoe ha he eiod. Fo each echology exiig a he ed of he modellig hoizo wih decommiioig co adjume i he objecive fucio. Fo each oce exedig a he ed of he modellig hoizo adjume i he objecive fucio. Fo each eiod D() = E() B()1. Duaio of eiod. Deciio Coefficie fo commodiy eleae duig decommiioig ime i eiod due o iveme made i eiod v. Coefficie of flow vaiable of commodiy c belogig o commodiy gou cg i EQPTRANS equaio bewee he commodiy gou cg ad comg. Numbe of eeaed iveme of oce i eiod v whe he echical lifeime miu he coucio ime i hoe ha he eiod duaio; Rouded o he ex lage iege umbe. Coecio faco fo decommiioig co akig io accou echical dicou ae ad ecoomic decommiioig ime. Coecio faco fo iveme co akig io accou echical dicou ae ecoomic lifeime ad a ue-defied dicou hif (iggeed by he cool wich MIDYEAR (ee Table 15). 109

110 Ieal aamee 29 (Idexe) Iace (Requied / Omi / Secial codiio) Deciio DURMAX Fo he model. Maximum of NCAPILED NCAPTLIFE NCAPDLAG NCAPDLIFE NCAPDELIF ove all egio eiod ad ocee. M (v) Fo each eiod if he duaio of he eiod i eve he middle yea of he eiod i B() D()/2 1 if he eiod i ueve he middle yea i B() D()/ Middle yea of eiod. MINYR Fo he model Miimum yea ove = M() D() 1; ued i objecive fucio. MIYRV1 Fo he model Fi yea of model hoizo. MIYRVL Fo he model La yea of model hoizo. NTCHTEG (eg) OBJACOST (ycu) OBJCNCST (yccu) OBJCNSUB (yccu) Fo leaig echologie eg whe ETL wih echology clue i ued. Fo each oce wih aciviy co. Ee he objecive fucio (EQOBJVAR). Fo each commodiy wih co o he e oducio. Ee he objecive fucio (EQOBJVAR). Fo each commodiy wih ubidie o he e oducio. Ee he objecive fucio (EQOBJVAR). Numbe of ocee uig he ame key echology eg. Ie-/Exaolaed vaiable co (ACTCOST) fo aciviy vaiable (VARACT) fo each yea. Ie-/Exaolaed co o e oducio (COMCSTNET) of commodiy (c) fo each yea aociaed wih he vaiable VARCOMNET. Ie-/Exaolaed ubidy o e oducio (COMSUBNET) of commodiy (c) fo each yea aociaed wih he vaiable VARCOMNET. 110

111 Ieal aamee 29 (Idexe) OBJCNTAX (yccu) OBJCPCST (yccu) OBJCPSUB (yccu) OBJCPTAX (yccu) OBJCRF (ycu) OBJCRFD (ycu) OBJDCEOH (cu) Iace (Requied / Omi / Secial codiio) Fo each commodiy wih axe o he e oducio. Ee he objecive fucio (EQOBJVAR). Fo each commodiy wih co o he cumulaive oducio. Ee he objecive fucio (EQOBJVAR). Fo each commodiy wih ubidie o he cumulaive oducio. Ee he objecive fucio (EQOBJVAR). Fo each commodiy wih axe o he cumulaive oducio. Ee he objecive fucio (EQOBJVAR). Fo each echology wih iveme co. Ee objecive fucio (EQOBJINV). Fo each echology wih decommiioig co. Ee objecive fucio (EQOBJINV). Ee objecive fucio (EQOBJSALV). Deciio Ie-/Exaolaed ax o e oducio (COMTAXNET) of commodiy (c) fo each yea aociaed wih he vaiable VARCOMNET. Ie-/Exaolaed co o oducio (COMCSTPRD) of commodiy (c) fo each yea aociaed wih he vaiable VARCOMPRD. Ie-/Exaolaed ubidy o oducio (COMSUBPRD) of commodiy (c) fo each yea aociaed wih he vaiable VARCOMPRD. Ie-/Exaolaed ax o oducio (COMTAXPRD) of commodiy (c) fo each yea aociaed wih he vaiable VARCOMPRD. Caial ecovey faco of iveme i echology i objecive fucio akig io accou he ecoomic lifeime (NCAPELIFE) ad he echology ecific dicou ae (NCAPDRATE) o if he lae i o ecified he geeal dicou ae (GDRATE). Caial ecovey faco of decommiioig co i echology akig io accou he ecoomic lifeime (NCAPDELIF) ad he echology ecific dicou ae (NCAPDRATE) o if he lae i o ecified he geeal dicou ae (GDRATE). Dicou faco fo he yea EOH 1 baed o he geeal dicou ae (GDRATE). 111

112 Ieal aamee 29 (Idexe) OBJDCOST (ycu) OBJDISC (ycu) OBJDIVI (v) OBJDIVIII (v) OBJDIVIV (v) OBJDLAGC (ycu) OBJFCOST (yccu) Iace (Requied / Omi / Secial codiio) Fo each echology wih decommiioig co. Ee objecive fucio (EQOBJINV). Ee objecive fucio (EQOBJINV EQOBJVAR EQOBJFIX EQOBJSALV EQOBJELS). Ee objecive fucio (EQOBJINV). Ee objecive fucio (EQOBJINV). Ee objecive fucio (EQOBJFIX). Ee objecive fucio (EQOBJFIX). Fo each flow vaiable wih flow elaed co. Ee objecive fucio (EQOBJVAR). Deciio Ie-/Exaolaed decommiioig co (NCAPDCOST) fo each yea elaed o he iveme (VARNCAP) of oce. Aual dicou faco baed o he geeal dicou ae (GDRATE) o dicou co i he yea y o he bae yea (GDYEAR). Divio fo iveme co (eiod duaio echical lifeime o iveme lead ime deedig o he iveme cae 1a 1b 2a 2b). Divio fo decommiioig co ad alvagig of decommiioig co (eiod duaio echical lifeime o decommiioig ime deedig o he iveme cae 1a 1b 2a 2b). Divio fo fixed oeaig ad maieace co ad alvagig of iveme co. Ie-/Exaolaed fixed caaciy (VARNCAPNCAPPASTI) co bewee he ed of he echical lifeime ad he begiig of he decommiioig fo each yea. Ie-/Exaolaed flow co (FLOCOST) fo each yea fo he flow o ade vaiable (VARFLO VARIRE) a well a caaciy elaed flow (ecified by NCAPCOM NCPICOM NCAPOCOM). 112

113 Ieal aamee 29 (Idexe) OBJFDELV (yccu) OBJFOM (ycu) OBJFSB (ycu) OBJFSUB (yccu) OBJFTAX (yccu) OBJFTX (ycu) OBJICOST (ycu) Iace (Requied / Omi / Secial codiio) Fo each flow wih delivey co. Ee objecive fucio (EQOBJVAR). Fo each oce wih fixed oeaig ad maieace co. Ee he objecive fucio (EQOBJFIX). Fo each oce wih ubidy o exiig caaciy. Ee objecive fucio (EQOBJFIX). Fo each flow vaiable wih ubidie. Ee objecive fucio (EQOBJVAR). Fo each flow vaiable wih axe. Ee objecive fucio (EQOBJVAR). Fo each oce wih axe o exiig caaciy. Ee objecive fucio (EQOBJFIX). Fo each oce wih iveme co. Ee objecive fucio (EQOBJINV). Deciio Ie-/Exaolaed delivey co (FLODELIV) fo each yea fo he flow o ade vaiable (VARFLO VARIRE) a well a caaciy elaed flow (ecified by NCAPCOM NCPICOM NCAPOCOM). Ie-/Exaolaed fixed oeaig ad maieace co (NCAPFOM) fo he ialled caaciy (VARNCAPNCAPPASTI) fo each yea. Ie-/Exaolaed ubidy (NCAPFSUB) o ialled caaciy (VARNCAPNCAPPASTI) fo each yea. Ie-/Exaolaed ubidy (FLOSUB) fo he flow o ade vaiable (VARFLO VARIRE) fo each yea a well a caaciy elaed flow (ecified by NCAPCOM NCPICOM NCAPOCOM). Ie-/Exaolaed ax (FLOTAX) fo flow o ade vaiable (VARFLO VARIRE) fo each yea a well a caaciy elaed flow (ecified by NCAPCOM NCPICOM NCAPOCOM). Ie-/Exaolaed ax (NCAPFTAX) o ialled caaciy (VARNCAPNCAPPASTI) fo each yea. Ie-/Exaolaed iveme co (NCAPCOST) fo iveme vaiable (VARNCAP) fo each yea. 113

114 Ieal aamee 29 (Idexe) OBJIPRIC (ycalliecu) OBJISUB (ycu) OBJITAX (ycu) OBJPASTI (vcu) OBJSIC (veg) OBJSSC (vcu) Iace (Requied / Omi / Secial codiio) Fo each imo/exo flow wih ice aiged o i. Ee objecive fucio (EQOBJVAR). Fo each oce wih ubidy o ew iveme. Ee objecive fucio (EQOBJINV). Fo each oce wih axe o ew iveme. Ee objecive fucio (EQOBJINV). Ee objecive fucio (EQOBJINV). Fo leaig echologie. Ee objecive fucio (EQOBJINV). Fo ocee wih iveme co. Ee objecive fucio (EQOBJSALV). Fo leaig echologie eg whe ETL i ued. Fo leaig echologie eg whe ETL i ued. Deciio Ie-/Exaolaed imo/exo ice (IREPRICE) fo imo/exo vaiable (VARIRE) fo each yea. Ie-/Exaolaed ubidy (NCAPISUB) o ew caaciy (VARNCAP) fo each yea. Ie-/Exaolaed ax (NCAPITAX) o ew caaciy (VARNCAP) fo each yea. Coecio faco fo a iveme. Iveme co elaed alvage value of leaig echology eg wih viage eiod v a yea EOH1. Iveme co elaed alvage value of oce wih viage eiod v a yea EOH1. PAT (eg) Leaig cuve coefficie i he elaiohi: SC = PAT * VARCCAP^(-PBT). PBT Leaig cuve exoe PBT(eg) = LOG(PRAT(eg))/LOG(2). (eg) PYRV1 Fo he model Miimum of ayea ad MINYR. 114

115 Ieal aamee 29 (Idexe) RSSTGPRD () RTPFFCX (vcgccg) Iace (Requied / Omi / Secial codiio) Oly alicable o oage ocee (STG): imelice oage ieeiod oage o igh oage device. The efficiecy aamee COEFPTRAN i mulilied by he faco (1RTPFFCX). Ee EQPTRANS equaio. Deciio Numbe of oage eiod i a yea fo each imelice. Aveage SHAPE mulilie of he aamee FLOFUNC ad FLOSUM efficiecie i he EQPTRANS equaio i he eiod () fo caaciy wih viage eiod (v). The SHAPE cuve which hould be ued i ecified by he ue aamee FLOFUNCX. The SHAPE feaue allow o ale echical aamee give fo he viage eiod a a fucio of he age of he iallaio. 115

116 Ieal aamee 29 (Idexe) RTCSTSFR (c) Iace (Requied / Omi / Secial codiio) You modified he deciio of COMFR by ayig ha i "Affec imelice eoluio a which a commodiy i acked (RTCSTSFR) ad heeby may affec whe a oce ca oeae (RTPSOFF)". Acually COMFR affec he imelice facio (RTCSTSFR) of ay commodiy fo which COMFR ha bee ovided. Fo examle if a oce oeae a he SEASON level bu oduce a DAYNITE level commodiy COMFR will deemie he DAYNITE facio oduced wihi each SEASON! A I have ied o ay hi alie o all commodiie (hi i o my deig a all bu migh be ueful). Thu I hik ha he eviou deciio wa moe coec ("affec all commodiie hough RTCSTSFR"). Deciio The effecive hadlig of imelice aggegaio/diaggegaio. If i below i he imelice ee he value i 1 if i below he value i COMFR() / COMFR() fo demad commodiie wih COMFR give ad GYRFR() / GYRFR() fo all ohe commodiie. The aamee i ued o mach he imelice eoluio of flow vaiable (VARFLO/VARIRE) ad commodiie. RTCSTSFR i he coefficie of he flow vaiable which i oducig o coumig commodiy c i he commodiy balace of c. If imelice coeod o he commodiy imelice eoluio of c ad imelice o he imelice eoluio of he flow vaiable wo cae may occu: The flow vaiable ae o a fie imelice level ha he commodiy balace: i hi cae he flow vaiable wih imelice beig below i he imelice ee ae ummed o give he aggegaed flow wihi imelice. RTCSTSFR ha he value 1. 1) The flow vaiable ae o coae imelice level ha he commodiy balace: i hi cae he flow vaiable i li-u o he fie imelice level of he commodiy balace accodig o he aio of he imelice duaio of o : RTCSTSFR ha he value = COMFR() / COMFR(1) fo demad commodiie ad GYRFR() / GYRFR(1) ohewie. Whe COMFR i ued he demad load cuve i moved o he demad oce. Thu i i oible o model demad ocee o a ANNUAL level ad eue a he ame ime ha he oce follow he give load cuve COMFR. 116

117 Ieal aamee 29 (Idexe) SALVDEC (vkll) SALVINV (vk) YEARVAL (y) Iace (Requied / Omi / Secial codiio) Fo hoe echology wih alvage co icued afe he model hoizo he coibuio o he objecive fucio. Fo hoe echology wih alvage co icued afe he model hoizo he coibuio o he objecive fucio. A value fo each yea. Deciio Salvage ooio of decommiioig co made a eiod v wih commiioig yea k. Salvage ooio of iveme made a eiod v wih commiioig yea k. Numeical value of yea idex (e.g. YEARVAL( 1984 ) equal 1984). 117

118 3.3 Reo aamee The aamee geeaed ieally by TIMES o docume he eul of a model u ae lied i Table 14. Thee aamee ca be imoed io he VEDA-BE ool fo fuhe eul aalyi. The li of eo aamee ha ae coveed ou of he GDX 30 file via he gdx2veda GAMS uiliy io a VEDA-BE comaible foma accodig o he file ime2veda.vdd 31. Noe ha ome of he eul ae o afeed io aamee bu ae diecly acceed hough he ime2veda.vdd file (amely: hadow ice of commodiy balace of eakig equaio oal dicoued value of objecive fucio). The followig amig coveio aly o he efixe of he eo aamee: CST: deailed aual udicoued co aamee; oe ha alo he co of a iveme which ae coa i he objecive fucio ae beig eoed; DPAR: hadow ice; PAR: imal oluio; TOT: Aual udicoued co by ye. Table 14: Reo aamee i TIMES Reo aamee 32 (Idexe) CSTACTV (v) Deciio Aual udicoued vaiable co (caued by ACTCOST) i eiod () aociaed wih he oeaio (aciviy) of a oce () wih viage eiod (v). 30 GDX ad fo GAMS Daa Exchage. A GDX file i a biay file ha oe he value of oe o moe GAMS ymbol uch a e aamee vaiable ad equaio. GDX file ca be ued o eae daa fo a GAMS model ee eul of a GAMS model oe eul of he ame model uig diffee aamee ec. A GDX file doe o oe a model fomulaio o execuable aeme. 31 The ue of he gdx2veda ool ogehe wih he ime2veda.vdd cool file a well a he VEDA-BE ofwae ae decibed i a eaae docume. 32 The fi ow coai he aamee ame he ecod ow coai i backe he idex domai fo which he aamee i defied. 118

119 Reo aamee 32 (Idexe) CSTCOMV (c) CSTDECV (v) CSTFIXV (v) CSTFLOV (vc) CSTINVV (v) CSTLATV () CSTSALV (v) FIN (vc) FOUT (vc) PARACTL (v) Deciio Aual udicoued commodiy (c) elaed co (caued by IREPRICE COMCSTNET COMTAXNET COMSUBNET COMCSTPRD COMTAXPRD COMSUBPRD) i eiod (). Aual udicoued decommiioig co (caued by NCAPDCOST) i eiod () aociaed wih he dimalig of oce () wih viage eiod (v). Aual udicoued fixed oeaig ad maieace co (caued by NCAPFOM NCAPFTAX NCAPFSUB NCAPDLAGC) i eiod () aociaed wih he ialled caaciy of oce (). Aual udicoued flow elaed co (caued by FLOCOST FLODELV FLOTAX FLOSUB) i eiod () aociaed wih a commodiy (c) flow i/ou of a oce () wih viage eiod (v) a well a caaciy elaed commodiy flow (ecified by NCAPCOM NCAPICOM NCAPOCOM). Aual udicoued iveme co (caued by NCAPCOST) i eiod () ead ove he ecoomic lifeime (NCAPELIFE) of a oce () wih viage eiod (v). Aual udicoued lae eveue which ae caued by uk maeial (NCAPOCOM) i eiod () havig a alvage value (NCAPVALU) aociaed wih oce () wih viage eiod (v). Udicoued alvage value of co (NCAPCOST NCAPDLAGC NCAPDCOST) aociaed wih iveme (VARNCAP NCAPPASTI) of which he echical lifeime exceed he ed of he model hoizo; he oal alvage value aociaed wih he iveme of oce () i eoed fo he viage yea (v). Iu flow (coumio) of commodiy (c) i eiod () ad imelice () io oce () wih viage eiod (v) icludig exchage ocee. Ouu flow (oducio) of commodiy (c) i eiod () ad imelice () io oce () wih viage eiod (v) icludig exchage ocee. Level value of aciviy vaiable (VARACT) i eiod () ad imelice () of oce () wih viage eiod (v). 119

120 Reo aamee 32 (Idexe) PARACTM (v) PARCAPL () PARCAPLO () PARCAPM () PARCAPUP () PARCOMBALEM (c) Deciio Udicoued aual educed co of aciviy vaiable (VARACT) i eiod () ad imelice () of oce () wih viage eiod (v); he educed co decibe i he cae ha he aciviy vaiable i a i lowe (ue) boud he co iceae (deceae) of he objecive fucio caued by a iceae of he lowe (ue) boud by oe ui; he educed co ca alo be ieeaed a he eceay deceae=ubidy (iceae=ax) of he co coefficie of he aciviy vaiable i he objecive fucio o ha he aciviy vaiable will leave i lowe (ue) boud. Exiig caaciy of oce () i eiod () (deived fom VARNCAP i eviou eiod ad ill exiig a iveme NCAPPASTI). Lowe boud o caaciy vaiable (CAPBND( LO )) oly eoed if he lowe boud i geae ha zeo. Udicoued educed co of caaciy vaiable (VARCAP); oly eoed i hoe cae i which he caaciy vaiabel i geeaed (boud CAPBND ecified o edogeou echology leaig i ued); he educed co decibe i he cae ha he caaciy vaiable i a i lowe (ue) boud he co iceae (deceae) of he objecive fucio caued by a iceae of he lowe (ue) boud by oe ui; he educed co ca alo be ieeaed a he eceay deceae=ubidy (iceae=ax) of he co coefficie of he caaciy vaiable i he objecive fucio o ha he caaciy vaiable will leave i lowe (ue) boud. Ue boud o caaciy vaiable (CAPBND( UP )) oly eoed; if he ue boud i malle ha ifiiy. Udicoued aual hadow ice of commodiy balace (EQECOMBAL) beig a ic equaliy. The magial value decibe he co iceae i he objecive fucio if he diffeece bewee oducio ad coumio i iceaed by oe ui. The magial value ca be deemied by he oducio ide (iceaig oducio) bu ca alo be e by he demad ide (e.g. deceae of coumio by eegy avig o ubiuio meaue). 120

121 Reo aamee 32 (Idexe) PARCOMBALGM (c) PARCOMNETL (c) PARCOMNETM (c) PARCOMPRDL (c) PARCOMPRDM (c) PARFLO (vc) PARFLOM (vc) PARIRE (vcie) Deciio Udicoued aual hadow ice of commodiy balace (EQGCOMBAL) beig a iequaliy (oducio beig geae o equal coumio); oiive umbe if oducio equal coumio; he magial value decibe he co iceae i he objecive fucio if he diffeece bewee oducio ad coumio i iceaed by oe ui. The magial value ca be deemied by he oducio ide (iceaig oducio) bu ca alo be e by he demad ide (e.g. deceae of coumio by eegy avig o ubiuio meaue). Level value of he vaiable coeodig he e level of a commodiy (c) (VARCOMNET). The e level of a commodiy i equivale o he oal oducio miu oal coumio of aid commodiy. I i oly eoed if a boud co i ecified fo i o i i ued i a ue coai. Udicoued aual educed co of he VARCOMNET vaiable of commodiy (c). I i oly eoed if a boud co i ecified fo i o i i ued i a ue coai. Level value of he commodiy oducio vaiable (VARCOMPRD). The vaiable decibe he oal oducio of a commodiy. I i oly eoed if a boud co i ecified fo i o i i ued i a ue coai. Udicoued aual educed co of he commodiy oducio vaiable (VARCOMPRD). I i oly eoed if a boud co i ecified fo i o i i ued i a ue coai. Flow of commodiy (c) eeig o leavig oce () wih viage eiod (v) i eiod (). Dicoued educed co of flow vaiable of commodiy (c) i eiod () of oce () wih viage eiod eiod (v); he educed co decibe i he cae ha he flow vaiable i a i lowe (ue) boud he co iceae (deceae) of he objecive fucio caued by a iceae of he lowe (ue) boud by oe ui; he educed co ca alo be ieeaed a he eceay deceae=ubidy (iceae=ax) of he co coefficie of he flow vaiable i he objecive fucio o ha he flow will leave i lowe (ue) boud. Ie-egioal exchage flow of commodiy (c) i eiod () via exchage oce () eeig egio () a imo (ie= IMP ) o leavig egio () a exo (ie= EXP ). 121

122 Reo aamee 32 (Idexe) PARIREM (vcie) PARNCAPL (v) PARNCAPM (v) PAROBJACT (vycu) PAROBJCOM (yccu) PAROBJDEC (vycu) PAROBJELS (yccu) Deciio Dicoued educed co of ie-egioal exchage flow vaiable of commodiy (c) i eiod () of exchage oce wih viage eiod (v); he educed co decibe i he cae ha he flow vaiable i a i lowe (ue) boud he co iceae (o deceae) of he objecive fucio caued by a iceae of he lowe (ue boud) by oe ui; he educed co ca alo be ieeaed a he eceay deceae=ubidy (iceae=ax) of he co coefficie of he flow vaiable i he objecive fucio o ha he flow will leave i lowe (ue) boud. Level value of iveme vaiable (VARNCAP) of oce () i eiod (v). Udicoued educed co of iveme vaiable (VARNCAP) of oce (); oly eoed whe he caaciy vaiable i a i lowe o ue boud; he educed co decibe i he cae ha he iveme vaiable i a i lowe (ue) boud he co iceae (deceae) of he objecive fucio caued by a iceae of he lowe (ue) boud by oe ui; he educed co ca alo be ieeaed a he eceay deceae=ubidy (iceae=ax) of he co coefficie of he iveme vaiable i he objecive fucio o ha he iveme vaiable will leave i lowe (ue) boud. Aual dicoued vaiable co (caued by ACTCOST) i yea (y) aociaed wih he oeaio (aciviy) of a oce () wih viage eiod (v). Aual dicoued commodiy (c) elaed co (caued by IREPRICE COMCSTNET COMTAXNET COMSUBNET COMCSTPRD COMTAXPRD COMSUBPRD) i yea (y). Aual dicoued decommiioig co (caued by NCAPDCOST) i yea (y) aociaed wih he dimalig of oce () wih viage eiod (v). Aual dicoued chage i he objecive fucio due o elaic demad chage of commodiy (c). Whe elaic demad ae ued he objecive fucio decibe he uiliy ( = coume ulu lu oduce ulu) which eache i maximum i he equilibium of demad ad uly. 122

123 Reo aamee 32 (Idexe) PAROBJFIX (vycu) PAROBJFLO (vyccu) PAROBJINV (vycu) PAROBJLAT (ycu) PAROBJSAL (vcu) PARPASTI () PARPEAKM (c) REGOBJ () Deciio Aual dicoued fixed oeaig ad maieace co (caued by NCAPFOM NCAPFTAX NCAPFSUB NCAPDLAGC) i yea (y) aociaed wih he ialled caaciy of oce (). Aual dicoued flow elaed co (caued by FLOCOST FLODELV FLOTAX FLOSUB) i yea (y) aociaed wih a commodiy (c) flow i/ou of a oce () wih viage eiod (v) a well a caaciy elaed commodiy flow (ecified by NCAPCOM NCAPICOM NCAPOCOM). Aual dicoued iveme co (caued by NCAPCOST) i yea (y) ead ove he ecoomic lifeime (NCAPELIFE) of a oce () wih viage eiod (v). Aual dicoued lae eveue (ee ecio 5.2 o objecive fucio) which ae caued by uk maeial (NCAPOCOM) eleaed i yea (y) havig a alvage value (NCAPVALU) aociaed wih oce () wih viage eiod (v). Dicoued alvage value of co (NCAPCOST NCAPDLAGC NCAPDCOST) aociaed wih iveme (VARNCAP NCAPPASTI) of which he echical lifeime exceed he ed of he model hoizo; he oal alvage value aociaed wih he iveme of oce () i eoed fo he viage yea (v). Reidual caaciy of a iveme (NCAPPASTI) of oce () ill exiig i eiod (). Udicoued aual hadow ice of eakig equaio (EQPEAK) aociaed wih commodiy (c); ice he eakig equaio i a mo oly bidig fo oe imelice () a hadow ice oly exi fo oe imelice. The hadow ice ca be ieeaed a a addiioal emium o he hadow ice of he commodiy balace which coume of commodiy (c) have o ay fo coumio duig eak ime he emium i ued (beided ohe ouce) o cove he caaciy elaed co (e.g. iveme co) of caaciy coibuig eeve caaciy duig eak ime. Dicoued objecive value (EQOBJ) fo each egio (). 123

124 Reo aamee 32 (Idexe) TOTACT (ycu) TOTCOM (ycu) TOTDEC (ycu) TOTFIX (ycu) TOTFLO (ycu) TOTINV (ycu) TOTLAT (ycu) TOTOBJ (ycu) TOTSAL (ycu) VDADISC () Deciio Toal aual dicoued vaiable co of all ocee i a egio (). Toal aual dicoued commodiy co (icl. imo/exo ice) i egio () ove all commodiie. Toal aual dicoued decommiioig co of all ocee i egio (). Toal aual dicoued fixed ad oeaig maieace co of all ocee i egio (). Toal aual dicoued flow elaed co of all commodiy flow i egio (). Toal aual dicoued iveme co of all ocee i egio (). Toal aual dicoued lae eveue of all ocee i egio (). Toal aual dicoued objecive fucio fo each egio (). Toal aual dicoued alvage co of all ocee i egio (). Sum of aual ee value faco OBJDISC ove yea wihi eiod. The effec of oe ui of vaiable co o he objecive coefficie of a vaiable i eiod i he um of aual ee value faco i ha eiod. Thu he um of he aual ee value faco i ued fo eiod co/hadow ice. 124

125 4 Vaiable Thi chae decibe each vaiable ame defiiio ad ole i he TIMES Liea Pogam. To faciliae ideificaio of he vaiable whe examiig he model ouce code all vaiable ame a wih he efix VAR. The value aiged o each vaiable idexed by ome ime eiod eee he aveage value i ha ime eiod bu he cae of VARNCAP(v) i a exceio ice ha vaiable eee a oi-wie iveme decided a ime eiod v. VARNCAP i dicued i deail below. Table 4.1 i a li of TIMES vaiable by caegoy wih bief deciio of each vaiable. Remak o Table 4.1 May vaiable ha ae elaed o a oce have wo eiod idexe: eee he cue eiod ad v eee he viage of a oce i.e. he eiod whe he iveme i ha oce wa decided. Fo he VARNCAP vaiable i by defiiio equal o v. Fo ohe vaiable v if he oce i viaged (cvi) i.e. he chaaceiic of he oce deed o he viage yea. If he oce i o-viaged he chaaceiic of he caaciy of a oce ae o diffeeiaed by i viage ucue o ha he viage idex i acually o eeded fo he vaiable of a o-viaged oce. I hee cae he viage idex v i by coveio e equal o he eiod idex. I Table 4.1 he vaiable ae lied accodig o five caegoie deedig o wha TIMES eiy hey eee. I he e of he chae he vaiable ae lied ad fully decibed i alhabeical ode. Table 4.1 doe o li he vaiable ued i he wo exeio of TIMES ETL ad Climae Module which ae fully documeed i chae 6 ad 7 eecively. I he Objecive fucio caegoy able 4.1 alo li eveal aamee ha ad fo ceai oio of he objecive fucio. Thee ae o boa fide GAMS vaiable bu moly eve a coveie laceholde fo hi documeaio ad alo a ueful aamee ha may be eoed i he oluio. 125

126 Table 4.1. Li of TIMES vaiable by caegoy Caegoy Vaiable ame Bief deciio Poce elaed VARACT Aual aciviy of a oce VARCAP Cue caaciy of a oce all viage ogehe VARNCAP Iveme (ew caaciy) i a oce VARDNCAP Biay vaiable ued wih he dicee iveme oio (ee ecio ) Commodiy elaed VARBLND Bledig vaiable (fo oil efiig) VARCOMNET Ne amou of a commodiy VARCOMPRD Go oducio of a commodiy VARELAST Vaiable ued o diceize demad cuve Flow (Poce ad Commodiy) elaed VARFLO Flow of a commodiy i o ou of a oce VARIRE Flow of a commodiy i o ou of a exchage VARSIN/OUT Objecive fucio elaed VAROBJ oce (ade vaiable) Flow of a commodiy i o ou of a oage oce Vaiable eeeig he oveall objecive fucio (all egio ogehe) The followig 10 aamee ae o ue vaiable of he LP maix OBJR Paamee eeeig a egioal comoe of he objecive fucio. INVCOST Paamee eeeig he iveme oio of a egioal comoe of he objecive fucio INVTAXSUB Paamee eeeig he axe ad ubidie aached o he iveme oio of a egioal comoe of he objecive fucio INVDECOM Paamee eeeig he caial co aached o he dimalig (decommiioig) oio of a egioal comoe of he objecive fucio FIXCOST Paamee eeeig he fixed aual co oio of a egioal comoe of he objecive fucio FIXTAXSUB Paamee eeeig he axe ad ubidie aached o fixed aual co of a egioal comoe of he objecive fucio VARCOST Paamee eeeig he vaiable aual co oio of a egioal comoe of he objecive fucio 126

127 Caegoy Vaiable ame Bief deciio ELASTCOST Vaiable eeeig he demad lo oio of a egioal comoe of he objecive fucio LATEREVENUES Paamee eeeig he lae eveue oio of a egioal comoe of he objecive fucio. SALVAGE Paamee eeeig he alvage value oio of a egioal comoe of he objecive fucio Ue Coai elaed 33 VARUC VARUCR VARUCT VARUCRT VARUCTS VARUCRTS VARUCSU Vaiable eeeig he LHS exeio of a ue coai ummig ove egio (ucum) eiod (ucum) ad imelice (ucum). Vaiable eeeig he LHS exeio of a ue coai ummig ove eiod (ucum) ad imelice (ucum) ad beig geeaed fo he egio ecified i uceach. Vaiable eeeig he LHS exeio of a ue coai ummig ove egio (ucum) ad imelice (ucum) ad beig geeaed fo he eiod ecified i uceach. Vaiable eeeig he LHS exeio of a ue coai ummig ove imelice (ucum) ad beig geeaed fo he egio ecified i uceach ad eiod i uceach. Vaiable eeeig he LHS exeio of a ue coai ummig ove egio (ucum) ad beig geeaed fo he eiod ecified i uceach ad imelice i uceach. Vaiable eeeig he LHS exeio of a ue coai ummig ove eiod beig geeaed fo he egio ecified i uceach he eiod i uceach ad imelice i uceach. Vaiable eeeig he LHS exeio of a 33 I cae he dolla cool aamee VARUC i e o YES he ue coai ae alway ic equaliie (l=e) wih he RHS coa elaced by he ue coai vaiable give i he able. The RHS boud aamee (UCRHS(R)(T)(S)) ae he alied o hee ue coai elaed vaiable. 127

128 Caegoy Vaiable ame Bief deciio dyamic ue coai ummig ove egio (ucum) ad imelice (ucum) ad beig geeaed fo he eiod ecified i VARUCSUS VARUCRSUS VARUCRSU ucucc. Vaiable eeeig he LHS exeio of a dyamic ue coai ummig ove egio (ucum) ad beig geeaed fo he eiod ecified i ucucc ad imelice i uceach. Vaiable eeeig he LHS exeio of a dyamic ue coai ummig ove eiod beig geeaed fo he egio ecified i uceach he eiod i ucucc ad imelice i uceach. Vaiable eeeig he LHS exeio of a dyamic ue coai ummig ove imelice (ucum) ad beig geeaed fo he egio ecified i uceach ad eiod i ucucc. Noaio fo idexe: The followig idexe ae ued i he emaie of hi chae: = egio; v = viage; = ime eiod; y = yea; = oce; c c = commodiy; = imelice; ie = imo o exo; l = ee of a coai ( = o ). I addiio ome idexe (u; ble; o; j; uc) ae ued fo ecific vaiable oly ad ae defied i hei coex. 4.1 VARACT(v) Defiiio: he oveall aciviy of a oce. VARACT i defied by he EQACTFLO equaio eihe a he um of ouflow o a he um of iflow of a aicula (ue eleced) gou of commodiie adequaely omalized. If he oce i o viaged he viage idex v i by coveio e equal o he eiod idex. Role: eo he aciviy of a oce ad imlicily defie how he caaciy i meaued ice he aciviy i bouded by he available caaciy i he coai EQ(l)CAPACT e.g. if he aciviy of a coal owe la i defied ove i eleciciy ouu he caaciy i meaued i em of he ouu commodiy e.g. MW elecic. Similaly if he aciviy vaiable eee he iu flow of coal he caaciy of he coal la i meaued i em of he iu commodiy e.g. MW coal. 128

129 4.2 VARBLND(bleo) Defiiio: amou of he bledig ock o i eegy volume o weigh ui eeded fo he oducio of he bledig oduc ble i oil efiey modelig. Role: ued fo ecifyig coai o qualiy of he vaiou efied eoleum oduc. 4.3 VARCAP() Defiiio: he ialled caaciy i lace i ay give yea of all viage of a oce deemied by he equaio EQ(l)CPT. The vaiable i equal o he um of all eviouly made iveme i ew caaciy lu ay emaiig eidual caaciy ialled befoe he modelig hoizo ha ha o ye eached he ed of hei echical lifeime. Role: I mai uoe i o allow he oal caaciy of a oce o be bouded. The vaiable i oly ceaed whe o a caaciy (CAPBND) of oal caaciy i lace i ecified. I cae ha oly oe lowe o oe ue caaciy boud i ecified he caaciy vaiable i o geeaed bu he boud i diecly ued i he EQ(l)CPT coai. o he caaciy vaiable i eeded i a ue coai o o he oce i a leaig echology (eg) i cae ha edogeou echological leaig i ued. 4.4 VARCOMNET(c) Defiiio: he e amou of a commodiy a eiod imelice. I i equal o he diffeece bewee amou ocued (oduced lu imoed) miu amou dioed (coumed lu exoed). Role: The vaiable i oly ceaed if a boud i imoed o a co i exlicily aociaed wih he e level of a commodiy. 4.5 VARCOMPRD(c) Defiiio: he amou of commodiy c ocued a ime eiod imelice. Role: hi vaiable i oly ceaed if a boud i imoed o oal oducio of a commodiy o a co i exlicily aociaed wih oducio level of a commodiy. The vaiable i defied hough he equaio EQECOMPRD. 4.6 VARDNCAP(u) 129

130 Defiiio: hi vaiable i ued oly fo ocee eleced by he ue a beig dicee i.e. fo which iveme a eiod may oly be equal o oe of a e of dicee ize ecified by he ue. Fo uch ocee VARDNCAP i a biay deciio vaiable equal o 1 if he iveme i equal o ize u ad 0 ohewie. Thak o a addiioal coai oly oe of he vaiou oeial ize allowed fo he iveme a eiod i ideed allowed. Role: ueful o mahemaically exe he fac ha iveme i oce a eiod may oly be doe i dicee ize. See equaio EQDSCNCAP i chae VARELAST(cjl) Defiiio: hee vaiable ae defied wheeve a demad i declaed o be ice elaic. Thee vaiable ae idexed by j whee j u ove he umbe of e ued fo diceizig he demad cuve of commodiy c (c = eegy evice oly). The j h vaiable ad fo he oio of he demad ha lie wihi diceizaio ieval j o ide l (l idicae eihe iceae o deceae of demad w... he efeece cae demad). Each ELAST vaiable i bouded uwad via equaio EQBNDELAS. Role: Each elaic demad i exeed a he um of hee vaiable. I he objecive fucio hee vaiable ae ued o bea he co of demad loe a exlaied i PART I chae VARFLO(vc) Defiiio: hee vaiable ad fo he idividual commodiy flow i ad ou of a oce. If he oce i o viaged he viage idex v i by coveio e equal o he eiod idex. Role: The flow vaiable ae he fudameal quaiie defiig he deailed oeaio of a oce. They ae ued o defie he aciviy of a oce (VARACT) i a ue choe mae. They ae alo eeial fo exeig vaiou coai ha balace he flow of a commodiy o ha cool he flexibiliy of ocee. 4.9 VARIRE(vcie) Defiiio: he ie-egioal exchage vaiable (i=impo e=expo) ha ack imo (ie=i)o exo (ie=e) of a commodiy bewee egio ad ohe egio. The egio() adig wih i (ae) o ecified via hi vaiable bu ahe via he oce(e) hough which he imo/exo i accomlihed. The oology e oie(c c ) of a exchage oce idicae he (igle) egio wih which egio i adig commodiy c (which may have he diffee ame c i egio ). Each ade oce may ade moe ha oe commodiy. Ohewie VARIRE oeae i a mae 130

131 imila o VARFLO fo coveioal ocee. A oio exi fo adig wih a exeal egio ha i o modeled exlicily (exogeou adig). If he oce i o viaged he viage idex v i by coveio e equal o he eiod idex. Role: he ole of a IRE vaiable i o embody he amou of a commodiy i o ou of a adig oce VARNCAP(v) Defiiio: he amou of ew caaciy (o wha ha adiioally bee called iveme i ew caaciy o caaciy build-u) a eiod v. A aleady meioed VARNCAP eee he oal iveme i echology a eiod v oly whe ILEDTLIFE D(v). Whe ILEDTLIFE < D(v) he model aume ha he iveme i eeaed a may ime a eceay wihi he eiod o ha he life of he la eeiio i beyod he ed of eiod v. I hi cae VARNCAP eee he caaciy level of he igle iveme. Figue 1 illuae a cae whee he iveme i made wice i eiod v (ad ome caaciy ill emai afe eiod v). The aveage caaciy i eiod v eulig fom he iveme VARNCAP(v) i le ha VARNCAP(v) due o he delay ILED (i i equal o VARNCAP(v)* D(v)/TLIFE). The aveage caaciy i eiod v1 due o VARNCAP(v) i alo le ha VARNCAP(v) becaue he ed of life of he ecod oud of iveme occu befoe he ed of eiod v1. Thee adjume ae made i evey equaio ivolvig VARNCAP by he ieal aamee COEFCPT. VARNCAP Reulig aveage caaciy i eiod v Reulig aveage caaciy i eiod v1 ILED TLIFE TLIFE D(v) D(v1) Figue 1: Examle of a eeaed iveme i ame eiod 131

132 Role: The ew caaciy (i.e. iveme) vaiable ae fudameal i defiig he iveme deciio ad may ohe quaiie deived fom i (fo iace oce caaciie). They lay a key ole i he model ucue ad ievee i he majoiy of coai. They ae oably ued i equaio ha defie he coevaio of caaciy ad hoe ha ie he aciviy of a oce o i caaciy. The omieece of VARNACP i i a due o he fac ha he VARCAP vaiable i o alway defied i TIMES by deig. Noe ha eidual caaciy o caaciy i lace io o he iiial model yea i hadled a a coa i lace of VARNCAP give by he iu aamee NCAPPASTI(y) which decibe he iveme made io o he fi eiod i he ayea y VAROBJ(y 0 ) ad elaed vaiable Defiiio: equal o he objecive fucio of he TIMES LP i.e. he oal co of all egio dicoued o yea y 0. Role: hi i he quaiy ha i miimized by he TIMES oimize. Remak: The ex 10 vaiable do o diecly coeod o GAMS vaiable. They ae ued i he documeaio (eecially ecio 5.2) a coveie iemediae laceholde ha caue ceai oio of he co objecive fucio. The eade i ivied o look a ecio 5.2 which exlai how hee vaiou co ee he comoiio of he objecive fucio. Mo of hee vaiable ae defied a eoig aamee ha ae made available o he VEDA-BE eul aalye a how i ecio VAROBJR( y 0 ) Defiiio: equal o he um of he vaiou iece of he oal co of egio dicoued o yea y 0. Role: hi i o a ue vaiable i he GAMS code. I i ued oly a a coveie lace holde fo wiig he coeodig oio of he objecive fucio i hi documeaio. I may alo be eoed i VEDA-BE INVCOST(y) Defiiio: equal o he oio of he co objecive fo yea y egio ha coeod o iveme. Role: i i ued maily a a coveie lace holde fo wiig he coeodig oio of he objecive fucio. I may alo be eoed i VEDA-BE INVTAXSUB(y) Defiiio: equal o he oio of he co objecive fo yea y egio ha coeod o iveme axe ad ubidie. Role: i i ued maily a a coveie lace holde fo wiig he coeodig oio of he objecive fucio. I may alo be eoed i VEDA-BE. 132

133 INVDECOM(y) Defiiio: equal o he oio of he co objecive fo yea y egio ha coeod o caial co liked o decommiioig of a oce. Role: i i ued maily a a coveie lace holde fo wiig he coeodig oio of he objecive fucio. I may alo be eoed i VEDA-BE FIXCOST(y) Defiiio: equal o he oio of he co objecive fo yea y egio ha coeod o fixed aual co. Role: i i ued maily a a coveie lace holde fo wiig he coeodig oio of he objecive fucio. I may alo be eoed i VEDA-BE FIXTAXSUB(y) Defiiio: equal o he oio of he co objecive fo yea y egio ha coeod o axe ad ubidie aached o fixed aual co. Role: i i ued maily a a coveie lace holde fo wiig he coeodig oio of he objecive fucio. I may alo be eoed i VEDA-BE VARCOST(y) Defiiio: equal o he oio of he co objecive fo yea y egio ha coeod o vaiable aual co. Role: i i ued maily a a coveie lace holde fo wiig he coeodig oio of he objecive fucio. I may alo be eoed i VEDA-BE ELASTCOST(y) Defiiio: equal o he oio of he co objecive fo yea y egio ha coeod o he co icued whe demad ae educed due o hei ice elaiciy. Role: i i ued maily a a coveie lace holde fo wiig he coeodig oio of he objecive fucio. I may alo be eoed i VEDA-BE LATEREVENUES(y) Defiiio: equal o he oio of he co objecive fo yea y egio ha coeod o ceai lae eveue fom he ecyclig of maeial fom dimaled ocee ha occu afe he ed-of-hoizo. Role: hi i o a ue vaiable i he GAMS code. I i ued oly a a coveie lace holde fo wiig he coeodig oio of he objecive fucio i hi documeaio. I may alo be eoed i VEDA-BE.coveie a a elaceme fo he um of he comoe of he oal co SALVAGE(y 0 ) Defiiio: equal o he oio of he co objecive fo egio ha coeod o he alvage value of iveme ad ohe oe-ime co. I i dicoued o ome bae yea y 0 Role: i i ued maily a a coveie lace holde fo wiig he coeodig oio of he objecive fucio. I may alo be eoed i VEDA-BE. 133

134 4.12 VARSIN/SOUT(vc) Defiiio: flow eeig/leavig a eiod a oage oce oig commodiy c. The oce may be viaged. If he oce i o viaged he viage idex v i by coveio e equal o he eiod idex. Fo oage bewee imelice (cg) ad igh-oage device (c) he imelice idex of he oage flow i deemied by he imelice eoluio of he oage (e.g. DAYNITE fo a day oage). Fo a oage oeaig bewee eiod (cgi) he oage flow ae alway o a aual level ad hece he imelice i he alway e o ANNUAL. Role: o oe ome commodiy o ha i may be ued i a ime lice o eiod diffee fom he oe i which i wa ocued; ee he exeio fo he oage coai. The emaiig TIMES vaiable ae all aached o ue coai. Ue coai ae quie flexible ad may ivolve ay of he uual TIMES vaiable. Two vaia of fomulaig a ue coai exi. I he fi cae a LHS exeio coaiig exeio ivolvig he diffee TIMES vaiable ae bouded by a RHS coa (give by he iu aamee UCRHS(R)(T)(S)). I he ecod cae he coa o he RHS i elaced by a vaiable. The boud UCRHS(R)(T)(S) i he alied o hi vaiable. I he lae cae he ue coai ae alway geeaed a ic equaliie while i he fi cae he equaio ig of he ue coai i deemied by he boud ye. The ue coai elaed vaiable ae i fac eduda bu quie ueful i ovidig eamlied exeio fo he ue coai (ee chae 5). By eig he dolla cool aamee VARUC o YES i he u-file he vaiable baed fomulaio i acivaed (ecod cae). A a defaul he fomulaio wihou ue coai vaiable will be geeaed. Each of he lied vaiable i elaed o a ecific cla of ue coai deedig o whehe he ue coai i ceaed fo each eiod egio o ime lice o oly a ube of hee idice. I addiio ome ue coai ae defied fo ai of ucceive ime eiod (dyamic ue coai o gowh coai). Each vaiable ha a lea oe idex (eeeig he ue coai uc fo which hi vaiable i defied) ad may have u o hee addiioal idexe amog ad Vaiable ued i Ue Coai VARUC(uc) Vaiable eeeig he LHS exeio of he ue coai EQEUC(uc) ummig ove egio (ucum) eiod (ucum) ad imelice (ucum). 134

135 VARUCR(uc) Vaiable eeeig he LHS exeio of he ue coai EQEUCR(uc) ummig ove eiod (ucum) ad imelice (ucum) ad beig geeaed fo he egio ecified i uceach VARUCT(uc) Vaiable eeeig he LHS exeio of he ue coai EQEUCT(uc) ummig ove egio (ucum) ad imelice (ucum) ad beig geeaed fo he eiod ecified i uceach VARUCRT(uc) Vaiable eeeig he LHS exeio of he ue coai EQEUCRT(uc) ummig ove imelice (ucum) ad beig geeaed fo he egio ecified i uceach ad eiod i uceach VARUCTS(uc) Vaiable eeeig he LHS exeio of he ue coai EQEUCTS(uc) ummig ove egio (ucum) ad beig geeaed fo he eiod ecified i uceach ad imelice i uceach VARUCRTS(uc) Vaiable eeeig he LHS exeio of he ue coai EQEUCRTS(uc) ummig ove eiod beig geeaed fo he egio ecified i uceach he eiod i uceach ad imelice i uceach VARUCSU(uc) Vaiable eeeig he LHS exeio of a dyamic ue coai o a gowh coai EQEUCSU(uc) ummig ove egio (ucum) ad imelice (ucum) ad beig geeaed fo he eiod ecified i ucucc VARUCSUS(uc) Vaiable eeeig he LHS exeio of a dyamic ue coai o a gowh coai EQEUCSUS(uc) ummig ove egio (ucum) ad beig geeaed fo he eiod ecified i ucucc ad imelice i uceach VARUCRSUS(uc) Vaiable eeeig he LHS exeio of a dyamic ue coai o a gowh coai EQEUCRSUS(uc) ummig ove eiod beig geeaed fo he egio ecified i uceach he eiod i ucucc ad imelice i uceach VARUCRSU(uc) Vaiable eeeig he LHS exeio of a dyamic ue coai o a gowh coai EQEUCRSU(uc) ummig ove imelice (ucum) ad beig geeaed fo he egio ecified i uceach ad eiod i ucucc. 135

136 5 Equaio Thi chae i divided io fou ecio: he fi ecio decibe he mai oaioal coveio adoed i wiig he mahemaical exeio of he eie chae. The ex wo ecio ea eecively he TIMES objecive fucio ad he liea coai of he model. The hid ecio i devoed o he addiioal coai ad objecive fucio addiio ha ae equied fo he wo MIP oio of he model Dicee (lumy) Iveme ad Edogeou Techology Leaig. Each equaio ha a uique ame ad i decibed i a eaae ubecio. The equaio ae lied i alhabeical ode i each ecio. Each ubecio coai ucceively he ame li of idice ad ye of he equaio he elaed vaiable ad ohe equaio he uoe of he equaio ay aicula emak alyig o i ad fially he mahemaical exeio of he coai o objecive fucio. The mahemaical fomulaio of a equaio a wih he ame of he equaio i he foma: EQXXX ijkl whee XXX i a uique equaio ideifie ad ijk.. ae he equaio idexe amog hoe decibed i chae 2. Some equaio ame alo iclude a idex l coollig he ee of he equaio. Nex o he equaio ame i a logical codiio ha he equaio idexe mu aify. Tha codiio coiue he domai of defiiio of he equaio. I i ueful o emembe ha he equaio i ceaed i mulile iace oe fo each combiaio of he equaio idexe ha aifie he logical codiio ad ha each idex i he equaio idex li emai fixed i he exeio coiuig each iace of he equaio. 5.1 Noaioal coveio We ue he followig mahemaical ymbol fo he mahemaical exeio ad elaio coiuig he equaio: The codiio ha aly o each equaio ae mahemaically exeed uig he ymbol (meaig uch ha o oly whe ) followed by a logical exeio ivolvig he uual logic oeao: (AND) (OR) ad NOT. Wihi he mahemaical exeio of he coai we ue he uual ymbol fo he aihmeic oeao ( / Σ ec). Howeve i ode o imove he wiig ad legibiliy of all exeio we ue ome imlificaio of he uual mahemaical oaio coceig he ue of mulile idexe which we decibe i he ex wo ubecio Noaio fo ummaio Whe a exeio A(ijk ) i ummed he ummaio mu ecify he age ove which he idexe ae allowed o u. Ou oaioal coveio ae a follow: Whe a igle idex j u ove a oe-dimeioal e A he uual oaio i ued a i: Exeio j whee A i a igle dimeioal e. j A 136

137 Whe a ummaio mu be doe ove a ube of a muli-dimeioal e we ue a imlified oaio whee ome of he uig idexe ae omied if hey ae o acive fo hi ummaio. Examle: coide he 3-dimeioal e o coiig of all quadule {cio} uch ha oce i egio ha a flow of commodiy c wih oieaio io (ee able 3 of chae 2). If i i deied o um a exeio A cio ove all commodiie c keeig he egio () oce () ad oieaio (io) fixed eecively a 1 1 ad IN we will wie by a ligh abue of oaio: A ( c IN) o eve moe imly: c o 1 c o( IN ) 1 1 A ( 1 1 c IN ) if he coex i uambiguou. Eihe of hee oaio clealy idicae ha ad io ae fixed ad ha he oly acive uig idex i c. (The adiioal mahemaical oaio would have bee: A( c IN ) 1 1 { c IN } o bu hi may have hidde he fac ha c i he oly uig idex acive i he um) Noaio fo logical codiio We ue imila imlifyig oaio i wiig he logical codiio of each equaio. A logical codiio uually exee ha ome aamee exi (i.e. ha bee give a value by he ue) ad/o ha ome idexe ae eiced o ceai ube. A yical examle of he fome would be wie a: ACTBND bd which ead: he ue ha defied a aciviy boud fo oce i egio ime-eiod imelice ad ee bd. The idexe may omeime be omied whe hey ae he ame a hoe aached o he equaio ame. A yical examle of he lae i he fi codiio fo equaio EQACTFLO v (ee ecio 5.3.1) which we wie imly a: viy which i ho fo: { v } viy wih he meaig ha ome caaciy of oce i egio ceaed a eiod v exi a eiod. Agai hee he idice have bee omied fom he oaio ice hey ae aleady lied a idice of he equaio ame Uig Idicao fucio i aihmeic exeio Thee ae iuaio whee a exeio A i eihe equal o B o o C deedig o whehe a ceai codiio hold o o i.e.: A = Bif Cod A = C if NOT Cod Thi may alo be wie a: A = B ( Cod) C ( NOT Cod) whee i i udeood ha he oaio (Cod) i he idicao fucio of he logical codiio i.e. (Cod)=1 if Cod hold ad 0 if o. Thi oaio ofe make equaio moe legible ad comac. A good examle aea i EQCAPACT

138 5.2 Objecive fucio EQOBJ Equaio EQOBJ Tye = No Bidig (MIN) Idice: egio (); ae of he wold (w); oce (); ime-lice (); ad eha ohe... Relaed Vaiable: All Puoe: he objecive fucio i he cieio ha i miimized by he TIMES model. I eee he oal dicoued co of he eie oibly muli-egioal yem ove he eleced laig hoizo. I i alo equal o he egaive of he dicoued oal ulu (lu a coa) a dicued i PART I chae 3 ad Ioducio ad oaio The TIMES objecive fucio iclude a umbe of iovaio comaed o hoe of moe adiioal eegy model uch a MARKAL EFOM MESSAGE ec. The mai deig choice ae a follow: - The objecive fucio may be hough of a he dicoued um of e aual co (i.e. co miu eveue) a ooed o e eiod co 34. Noe ha ome co ad eveue ae icued afe he ed of hoizo (EOH). Thi i he cae fo iace fo ome iveme ayme ad moe fequely fo ayme ad eveue aached o decommiioig aciviie. The a iveme (made befoe he fi yea of he hoizo) may alo have ayme wihi hoizo yea (ad eve afe EOH!). Thee ae alo efleced i he objecive fucio. Howeve i hould be clea ha uch ayme ae how i OBJ oly fo eoig uoe ice uch ayme ae eiely uk i.e. hey ae o affeced by he model deciio. - The model ue a geeal dicou ae d(y) (yea deede) a well a echology ecific dicou ae d () (eiod deede). The fome i ued o: a) dicou fixed ad vaiable oeaig co ad b) dicou iveme co ayme fom he oi of ime whe he iveme acually occu o he bae yea choe fo he comuaio of he ee value of he oal yem co. The lae ae ued oly o calculae he aual ayme eulig fom a lum-um iveme i ome yea. Thu he oly lace whee d () ievee i o comue he Caial Recovey Faco (CRF) dicued fuhe dow. 34 The acual imlemeaio of OBJ i he GAMS ogam i diffee fom he oe decibed i he documeaio ice he aualizig of he vaiou co comoe i o efomed i he GAMS code of he OBJ equaio bu ahe i he eoig ecio of he ogam fo imoved code efomace. Howeve deie he imlificaio he GAMS code eul i a objecive fucio ha i fully equivale o he oe i hi documeaio. 138

139 Fo coveiece we eea below ha oaio which i moe eecially ued i he objecive fucio (ee chae 3 fo he comlee TIMES oaio) Noaio elaive o ime MILESTONEYEARS: he e of all mileoe yea (by coveio: middle yea ee below M() ) PASTYEARS: Se of yea io o a of hoizo fo which hee i a a iveme (afe ieolaio of ue daa). MODELYEARS: ay yea wihi he model hoizo FUTUREYEARS: e of yea oeio o EOH YEARS e of yea befoe duig ad afe laig hoizo ay membe of MILESTONEYEARS o PASTYEARS. By coveio a eiod i eeeed by i middle yea (ee below M()). Thi coveio ca be chaged wihou aleig he exeio i hi docume. B() : he fi yea of he eiod eeeed by E() : he la yea of he eiod eeeed by D() : he umbe of yea i eiod. By defaul D()=1 fo all a yea. Thu D()=E()-B()1 M(): he middle yea o mileoe yea of eiod. Sice eiod may have a eve o a odd umbe of yea M() i o alway exacly ceeed a he middle of he eiod. I i defied a follow: M() = [B()(D()-1)/2] whee [x] idicae he lage iege le ha o equal o x. Fo examle eiod fom 2011 o 2020 iclude 10 yea ad i middle yea i [ ] o 2015 (lighly lef of he middle) wheea he eiod fom 2001 o 2015 ha 15 yea ad i middle yea i : [20017] o 2008 (i.e. he ue middle i hi examle) y : uig yea agig ove MODELYEARS fom B 0 o EOH. k : dummy uig idex of ay yea eve ouide hoizo v: uig idex fo a yea ued whe i eee a viage yea fo ome iveme. v() viage of oce (defied oly if i viaged) B 0 : iiial yea (he igle yea of fi eiod of he model u) EOH : La yea i hoizo fo a give model u. Similaly by a ligh abue of oaio he above eiie ae exeded a follow whe he agume i a aicula yea ahe ha a model yea (I hik ha oaio i o eeded): B(y) : fi yea of he eiod coaiig yea y (iead of B(T(y)) ) T(y) he mileoe yea of he eiod coaiig yea y (ame a M(y) i ou ee coveio) M(y) : middle yea of he eiod coaiig yea y (iead of M(T(y)) ) D(y) : umbe of yea of he eiod coaiig yea y (iead of D(T(y)) 139

140 Ohe oaio d(y) : geeal (ocial) dicou ae (ime deede alhough o how i oaio) (y) : geeal dicou faco: (y)=1/(1d(y)) (ime deede alhough o how i oaio) d () : echology ecific dicou ae (model yea deede) () : echology ecific dicou faco: ()=1/(1d ()) DISC(yz): Value dicoued o he begiig of yea z of a $1 ayme made a begiig of yea y uig geeal dicou faco. DISC(yz) = Π u=z o y-1 (u) CRF (): Caial ecovey faco uig a (echology ecific) dicou ae ad a ecoomic life aoiae o he ayme beig coideed. Thi quaiy i ued o elace a iveme co by a eie of aual ayme ead ove ome a of ime CRF ={1- ()}/{1- () ELIFE }. Noe ha a CRF uig he gebeal dicou ae i alo defied ad uded i he SALVAGE oio of he objecive fucio. OBJ(z): Toal yem co dicoued o he begiig of yea z INDIC(x): 1 if logical exeio x i ue 0 if o E i he malle iege lage ha of equal o E Remide of ome echology aibue ame (each i idexed by ) TLIFE Techical life of a echology ELIFE Ecoomic life of a echology i.e. eiod ove which iveme ayme ae ead (defaul = TLIFE) DLAG Lag afe ed of echical life afe which decommiioig may a DLIFE duaio of decommiioig fo ocee wih ILED>0 (ohewie =1) DELIF Ecoomic life fo decommiioig uoe (defaul DLIFE). ILED Lead-ime fo he coucio of a oce. TLIFE a afe he ed of ILED ILED Mi =Mi {1/10 * D() 1/10 * TLIFE. } Thi hehold eve o diiguih mall fom lage ojec; i igge a diffee eame of iveme imig Dicouig oio Thee ae wo aleae dicouig mehod i TIMES. The defaul mehod i o aume ha all ayme occu a he begiig of ome yea. The aleae mehod (acivaed by a wich ee PART III) aume ha iveme ae icued a he begiig of ome yea bu ha all aual (o aualized) ayme occu a he middle of ome yea. Secio exlai he wo mehod Comoe of he Objecive fucio The objecive fucio i he um of all egioal objecive all of hem dicoued o he ame ue-eleced bae yea a how i equaio (A) below 140

141 EQOBJ(z) z MODELYEARS VAR OBJ ( z) = REG REG OBJ ( z ) ( A) Each egioal objecive OBJ(z) i decomoed io he um of ie comoe o faciliae exoiio a e exeio (B) below. EQOBJ(z) z MODELYEARS REG REG OBJ( z ) = y ( ) INVCOST( y) INVTAXSUB( y) INVDECOM ( y) FIXCOST( y) DISC( y z) FIXTAXSUB( y) VARCOST( y) ELASTCOST ( y) LATEREVENUES( y) SALVAGE( z) ( B) The egioal idex i omied fom he ie comoe fo imliciy of oaio. The fi ad ecod em ae liked o iveme co. The hid em i liked o decommiioig caial co he fouh ad fifh em o fixed aual co he ixh em o all vaiable co (co ooioal o ome aciviy) he eveh o demad lo co. The eigh co (acually a eveue) accou fo commodiy ecyclig occuig afe EOH ad he ih em i he alvage value of all caial co of echologie whoe life exed beyod EOH. The 9 comoe ae eeed i he ie ubecio o Iveme co: INVCOST(y) Thi ubecio ee he comoe of he objecive fucio elaed o iveme co which occu i he yea a iveme i decided ad/o duig he coucio lead-ime of a faciliy. Remak a) The iveme co hould be he oveigh iveme co (excludig ay iee aid duig coucio) wheeve he coucio lead ime i exlicily modeled (i.e. cae 2 ae ued ee below). I uch a cae he iee duig coucio ae edogeouly calculaed by he model ief a will be aae i he equel. If o lead-ime i ecified (ad hu cae 1 ae ued) he full co of iveme hould be ued (icludig iee duig coucio if ay) 35. b) Each idividual iveme hyically occuig i yea k eul i a eam of aual ayme ead ove eveal yea i he fuue. The eam a i yea k ad cove yea k k1 kelife-1 whee ELIFE i he ecoomic life of 35 Ideally i would be deiable ha cae 1 be ued oly fo hoe iveme ha have o lead ime (ad hu o iee duig coucio). Howeve if a ue emloy cae 1 fo ojec eve hough hee ae igifica IDC he lae hould be icluded i he iveme co. 141

142 he echology. Each yealy ayme i equal o a facio CRF of he iveme co (CRF = Caial Recovey Faco). Noe ha if he echology dicou ae i equal o he geeal dicou ae he he eam of ELIFE yealy ayme i equivale o a igle ayme of he whole iveme co locaed a yea k iamuch a boh have he ame dicoued ee value. If howeve he echology dicou ae i choe diffee fom he geeal oe he he eam of ayme ha a diffee ee value ha he lum um a yea k. I i he ue eoibiliy o chooe echology deede dicou ae ad heefoe o decide o ale he effecive value of iveme co. c) I addiio o eadig he ayme eulig fom iveme co a majo TIMES efieme i ha he hyical iveme ielf doe o occu i a igle yea bu ahe a a eie of aual iceme. Fo iace if he model ive 3 GW of elecic caaciy i a eiod exedig fom 2011 o 2020 he hyical caaciy iceae may be delayed ad/o may be ead ove eveal yea. The exac way he delayig ad eadig ae effeced deed o eveal codiio which ae ecified fuhe dow a fou eaae cae ad which ae fucio boh of he aue of he echology ad of he legh of he eiod i which he iveme ake lace elaive o he echology echical life. The eadig of iveme ad he eadig of ayme decibed i he eviou aagah hel guaaee a mooh ajecoy fo mo iveme ayme a moe ealiic eeeaio ha wha hae i ohe model. Examle I.1.a of figue 5.1 how a cae whee he hyical iveme i ead ove fou yea ad each iceme caial ayme ae fuhe ead ove 3 yea. d) The above wo emak eail ha ayme of iveme co may well exed beyod he hoizo. We hall alo ee ha ome iveme ayme occu i yea io o he begiig of he laig hoizo (cae 1 oly). e) Taxe ad ubidie o iveme ae eaed exacly a iveme co i he objecive fucio. f) Sice he model ha he caabiliy o eee uk maeial ad eegy caie (i.e. hoe embedded i a echology a coucio ime uch a he uaium coe of a uclea eaco o he eel imbedded i a ca) hee uk commodiie have a imac o co. Two oibiliie exi: if he maeial i oe whoe oducio i exlicily modeled i he RES he hee i o eed o idicae he co coeodig o he uk maeial which will be imlicily accoued fo by he model ju like ay ohe flow. If o he ohe had he maeial i o ecifically modeled i he RES he he co of he uk maeial hould be icluded i he echology iveme co ad will he be hadled exacly a iveme co. The fou iveme cae A meioed above he imig of he vaiou ye of ayme ad eveue i made a ealiic ad a mooh a oible. All iveme deciio eul i iceme ad/o deceme i he caaciy of a oce a vaiou ime. Thee iceme o deceme may occu i ome cae i oe lage lum fo iace i he cae of a lage ojec (hydoelecic la alumium la ec.) ad i ohe cae i mall 142

143 addiio o ubacio o caaciy (e.g. buyig o eiig ca o heaig device). Deedig o which cae i coideed he aumio egadig he coeodig eam of ayme (o eveue) diffe makedly. Theefoe he diicio bewee mall ad lage ojec (called cae 1 ad 2 below) will be cucial fo wiig he caial co comoe of he objecive fucio. A ecod diicio come fom he elaive legh of a ojec echical life v. ha of he eiod whe he iveme occu. Namely if he life of a iveme i le ha he legh of he eiod he i i clea ha he iveme mu be eeaed all alog he eiod. Thi i o o whe he echical life exed beyod he eiod ed. Alogehe hee wo diicio eul i fou muually excluive cae each of which i eaed eaaely. I wha follow we ee he mahemaical exeio fo he INVCOST comoe ad oe gahical examle fo each cae. Cae 1.a If ILED ILEDMi ad TLIFE ILED D( ) (Small diviible ojec o-eeiive ogeive iveme i eiod) Hee we make wha aea o be he mo aual aumio i.e. ha he iveme occu i mall yealy iceme ead liealy ove D() yea. Peciely he caaciy addiio a a yea M()-D()1 ad ed a yea M() which mea ha ayme a ealie ha he begiig of he eiod ad ed a he middle of he eiod ee examle. Thi eem a moe ealiic comomie ha aig he ayme a he begiig of he eiod ad oig hem a he ed ice ha would mea ha duig he whole eiod he aid fo caaciy would acually o be ufficie o cove he caaciy eleced by he model fo ha eiod. Cae 1.a Examle: D()=4 TLIFE=5ELIFE=3 M()=B()1 D() TLIFE ELIFE Iveme ad ayme: Payme: oly B() M() 143

144 EQINVCOST(y) deal wih liea iveme buildu ove a a equal o eiod legh edig a middle of eiod Mi{ M ( ) y} INVCOST( y) = INDIC(1. a) MILESTONE PASTYRS v= Max{ M ( ) D( ) 1 y ELIFE 1} VAR NCAP D( ) NCAP PASTI CRF NCAP COST v eue ha ayme o afe ELIFE Ueful Rage fo y : { M ( ) D( ) 1 M ( ) ELIFE 1} (I.1.a) Comme: The ummad eee he ayme effeced i yea y due o he iveme iceme ha occued i yea v (ecall ha iveme ayme ae ead ove ELIFE). The ummad coi of hee faco: he fi i he amou of iveme i yea v he ecod i he caial ecovey faco ad he hid i he ui iveme co. The oue ummaio i ove all eiod (oe ha eiod lae ha T(y) ae eleva becaue whe y fall ea he ed of a eiod he ex eiod iveme may have aleady aed). The ie ummaio i ove a a of D() ceeed a B() bu ucaed a yea y. Alo he lowe ummaio boud eue ha a iveme iceme which occued i yea v ha a ayme i yea y oly if y ad v ae le ha ELIFE yea aa. Cae 1.b if ILED ILEDMi ad TLIFE ILED < D( ) Small ojec eeaed iveme i eiod Noe ha i hi cae he iveme i eeaed a may ime a eceay o cove he eiod legh (ee figue). I hi cae he aumio ha he iveme i ead ove D() yea i o ealiic. I i much moe aual o ead he iveme ove he echical life of he oce beig iveed i becaue hi eue a mooh coa eam of mall iveme duig he whole eiod (ay ohe choice of he ime a ove which iveme i ead would lead o a ueve eam of icemeal iveme). The umbe of e-iveme i he eiod i called C ad i eaily comued o a o cove he eie eiod. A a eul of hi dicuio he fi iveme cycle a a yea B( ) TLIFE / 2 (meaig he malle iege o le ha he oead) ad ed TLIFE yea lae whe he ecod cycle a ec a may ime a eceay o cove he eie eiod. The la cycle exed ove he ex eiod() ad ha i ake io accou i he caaciy afe equaio of he model. A befoe each caaciy iceme eul i a eam of ELIFE ayme a yea v v1 ec. 144

145 Cae 1.b Examle D=5 TLIFE=4 ELIFE=3 D() TLIFE ELIFE Iveme ad ayme: Payme oly: B() MILESTONE Mi{ y B( ) TLIFE / 2 C TLIFE 1} INVCOST ( y) = INDIC(1. b) v= Max{ B( ) TLIFE / 2 y ELIFE 1 VAR NCAP TLIFE CRF NCAP COST v Releva age fo y: { B( ) TLIFE / 2 B( ) TLIFE / 2 C TLIFE ELIFE 2} (I.1.b) Comme: he exeio i imila o ha i cae 1.a. exce ha i) he iveme i ead ove he echical life ahe ha he eiod legh ad ii) he iveme cycle i eeaed moe ha oce. Cae 2.a: ILED > ILEDMi ad ILED TLIFE D( ) (Lage idiviible ojec ueeaed iveme i eiod) Hee i i aumed ha coucio i ead ove he lead-ime (a vey ealiic aumio fo lage ojec) ad caaciy become available a he ed of he lead ime i a lum quaiy (ee figue). 145

146 Iveme: ad ayme D() Cae 2a Examle: D()=8 ILED=4 TLIFE=6ELIFE=3 ILED ELIFE TLIFE Payme oly: B() deal wih liea iveme buildu ove a a of ILED aig a begiig of eiod INVCOST( y) = PASTYEARS MILESTONEYEARS T ( y) INDIC(2. a) INDIC(2. a) Mi( 1 y) k = Max{ ILED y ELIFE 1} Mi( B( ) ILED 1 y) k = Max{ B( ) y ELIFE 1} NCAP PASTI ILED VAR NCAP CRF NCAP COST ILED CRF NCAP COST B( ) ILED Ueful Rage { B( ) B( ) fo y : ILED ELIFE 2} (I.2.a) Comme: he mai diffeece wih cae I.1.a) i ha he iveme coucio a a yea B() ad ed a yea B()ILED -1 (ee examle). A befoe ayme fo each yea coucio ead ove ELIFE yea. 146

147 Cae 2.b: ILED > ILED ad TLIFE ILED D( ) Mi < (Lage idiviible Pojec eeaed iveme i eiod) 2b Examle : D()=13 ILED=4 TLIFE=5ELIFE=3 C=2 Iveme ad ayme: Iveme Payme oly ILED D() TLIFE TLIFE B() Thi cae i imila o cae I.2.a bu he iveme i eeaed moe ha oce ove he eiod each cycle beig TLIFE yea log. A i cae I.2.a each coucio i ead ove oe lead ime ILED. I hi cae he exac ae of yealy iveme i comlex o ha we have o ue a algoihm iead of a cloed fom ummaio. ALGORITHM (Ouu: he veco of ayme P (y) a each yea y due o VARNCAP ) Se 0: Iiializaio (NI(u) eee he amou of ew iveme made i yea u) NI ( u) : 0 B( ) u B( ) ILED ( C 1) TLIFE 1 = Se 1: Comue umbe of eeiio of iveme C = D( ) ILED TLIFE Se 2: fo each yea u i age: 147

148 B( ) u B( ) ILED ( C 1) TLIFE 1 Comue: Fo I = 1 o C Fo u = B( ) ( I 1) TLIFE Nex u Nex I o NCAP COSTB ( ) ( NI( u) : = NI( u) ILED B( ) ( I 1) TLIFE ILED 1 I 1) TLIFE ILED Se 3: Comue ayme icued i yea y ad eulig fom vaiable VARNCAP Fo each y i age: B( ) y B( ) ( C 1) TLIFE ILED ELIFE 2 Comue: (I.2.b) P ( y) = u= Max y NI ( u) VAR NCAP CRF { B( ) y ELIFE 1} END ALGORITHM INVCOST ( y) = MILESTONES T ( y) INDIC(2. b) P ( y) Taxe ad ubidie o iveme EQ INVTAXSUB( y) y MODELYEARS We aume ha axe/ubidie o iveme occu a eciely he ame ime a he iveme. Theefoe exeio fo axe/ubidie ae ideical o hoe fo iveme co wih NCAPCOST elaced by: (NCAPITAX - NCAPISUB) Decommiioig (dimalig) caial co: COSTDECOM(y) Remak a) Decommiioig hyically occu afe he ed-of-life of he iveme ad may be delayed by a oioal lag eiod (e.g. a coolig off of he oce befoe dimalig may ake lace). The decommiioig co follow he ame ae ad ule a hoe fo iveme co. I aicula he ame fou cae ha wee defied fo iveme co ae ill alicable. b) The ame icile eide ove he imig of ayme of decommiioig co a wee defied fo iveme co amely he decomoiio of ayme io a eam of ayme exedig ove he ecoomic life of decommiioig DELIF. 148

149 c) A decommiioig ime he ecueaio of embedded maeial i allowed by he model. Thi i eaed a exlaied fo iveme co i.e. eihe a a exlici commodiy flow o a a cedi (eveue) ubaced by he ue fom he decommiioig co. g) Decommiioig aciviie may alo eceive axe o ubidie which ae ooioal o he coeodig decommiioig co. EQ COSTDECOM ( y) y MODELYEARS Cae 1.a) If ILED ILEDMi ad TLIFE ILED D( ) (Small diviible ojec o-eeiive ogeive iveme i eiod) I hi cae decommiioig occu exacly TLIFEDLAG yea afe iveme. Fo mall ojec (cae 1.a ad 1.b) i i aumed ha decommiioig ake exacly oe yea ad alo ha i co i aid ha ame yea (hi i he ame a ayig ha DLIFE=DELIF=1). Thi i a omal aumio fo mall ojec. A how i he examle below alo ayme made a yea y come fom iveme made a eiod T(y) o ealie. Hece he ummaio o a T(y). DECOMCOST ( y) = MILESTONES PASTYEARS T ( y) VAR NCAP INDIC(1. a) D( ) NCAP PASTI NCAP DCOST y TLIFE 1 if M ( ) D( ) 1 TLIFE y M ( ) TLIFE 0 ohewie (III.1.a) Comme: Noe ha he co aibue i idexed a he yea whe he iveme aed o oeae. We have adoed hi coveio houghou he objecive fucio. 149

150 Examle III.1.a: D()=4 TLIFE=5 M()=B()1 DLIFE=DELIF=1 D() TLIFE Iveme: Decommiioig ad ayme B() M() Cae 1.b) if ILED ILED ad TLIFE ILED D( ) Mi < Small ojec eeaed iveme i eiod Thi co exeio i imila o I.1.b bu wih ayme hifed o he igh by TLIFE (ee examle). The ie ummaio diaea becaue of he aumio ha DELIF=1. Noe alo ha a iveme have o effec i hi cae becaue hi cae doe o aie whe D()=1 which i alway he cae fo a eiod. DECOMCOST( y) = MILESTONES T ( y) VAR NCAP INDIC(1. b) TLIFE NCAP DCOST y TLIFE TLIFE 1 if B( ) 2 0 ohewie TLIFE y B( ) 2 C TLIFE 1 whee C = D( ) TLIFE (III.1.b) 150

151 Examle III.1.b D=5 TLIFE=4 DLIFE=DELIF=1 C=2 D() TLIFE Iveme: Decommi Boh B() Cae 2.a: ILED > ILEDMi ad ILED TLIFE D( ) (Lage idiviible ojec ueeaed iveme i eiod) I hi iuaio i i aumed ha decommiioig of he la occu ove a eiod of ime called DLIFE aig afe he ed of he echical oce life lu a ime DLAG (ee examle). DLAG i eeded e.g. fo a eaco o cool dow o fo ay ohe eao. Fuhemoe he ayme ae ow ead ove DELIF which may be laege ha oe yea.. DECOMCOST ( y) = MILESTONES T ( y) INDIC(2. a) Mi{ y B( ) ILED TLIFE DLAG DLIFE 1} k = Max{ B( ) ILED TLIFE DLAG y DELIF 1} VAR NCAP CRF NCAP DCOST DLIFE B( ) ILED PASTYEARS INDIC(2. a) Mi{ y TLIFE DLAG DLIFE 1} k = Max{ TLIFE DLAG y DELIF 1} NCAP PASTI DLIFE CRF NCAP DCOST (III.2.a) Ueful Rage fo y : { B( ) ILED TLIFE DLAG 1 ame DELIF 1} 151

152 Examle II.2.a: D()=8 ILED=4 TLIFE=6 DLAG=2 DLIFE=3 DELIF=2 Iveme: Decommiioig ad ayme Decommiioig Payme oly: D() ILED TLIFE DLAG DLIFE B() Cae 2.b: ILED > ILEDMi ad TLIFE ILED < D( ) (Big ojec eeaed iveme i eiod) Hee oo he decommiioig ake lace ove DLIFE bu ow coay o cae 2.a he oce i eeaed moe ha oce i he eiod. The la iveme ha life exedig ove followig eiod a i all imila cae. The eulig eam of yealy ayme i comlex ad heefoe we ae foced o ue a algoihm ahe ha a cloed fom ummaio. See alo examle below. ALGORITHM (aly o each uch ha T(y) ) Se 0: Iiializaio P ( y) : 0 B( ) ILED TLIFE DLAG y ame ( C 1) TLIFE DLIFE DELIF 2 = Whee: C = D( ) ILED TLIFE Se 1: Comue ayme veco 152

153 Fo I = 1 o C Fo J= 1 o Fo P ame Nex L Nex J Nex I END ALGORITHM DLIFE L = 1 o DELIF ( B( ) ILED I TLIFE DLAG J L 2) NCAP DCOST B( ) ILED ( I 1) TLIFE DLIFE : = DECOMCOST ( y) = INDIC( III.2. b) P ( y) VAR NCAP MILESTONES T ( y) CRF III.2.b Examle III.2.b: D()=13 ILED=4 TLIFE=5DLAG=2 DLIFE=3 DELIF=2 C=2 Coucio Decommiioig ad Payme D() Decommiioig Payme oly ILED TLIFE TLIFE B() DLAG DLIFE DLAG DLIFE Fixed aual co: FIXCOST(y) SURVCOST(y) The fixed aual co ae aumed o be aid i he ame yea a he acual oeaio of he faciliy. Howeve he eadig of he iveme decibed i ubecio

154 eul i a aeig i ad a aeig ou of hee co. Taxe ad ubidie o fixed aual co ae alo acceed by he model. Thee ae wo ye of fixed aual co FIXCOST(y) which i icued each yea fo each ui of caaciy ill oeaig ad SURVCOST(y) which i icued each yea fo each ui of caaciy i i DLAG ae (hi i a co icued fo uveillace of he faciliy duig he lag ime defoe i demoliio). Agai hee he ame claificaio of cae i adoed a i eviou ubecio o caial co. Noe ha by aumio SURVCOST(y) occu oly i cae 2. DLAG i allowed o be oiive eve i cae 1a bu ha i hi cae he uveillace co ae aumed o be egligible. Fially oe ha FIXCOST(y) eed be comued oly fo yea y wihi he laig hoizo wheea SURVCOST(y) may exi fo yea beyod he hoizo 154

155 Cae 1.a) If ILED ILED ad TLIFE ILED D( ) Mi (Small ojec igle iveme i eiod) EQ FIXCOST( y) y EOH The figue of he examle how ha ayme made i yea y may come fom iveme made a eiod befoe T(y) a T(y) ielf o a eiod afe T(y). Noe ha he co aibue i muilied by wo faco: he SHAPE which ake io accou he viage ad age of he echology ad he MULTI aamee which ake io accou he ue ime a which he co i aid (he oaio below fo SHAPE ad MULTI i imlified: i hould alo ecify ha hee wo aamee ae hoe eaiig o he FOM aibue). FIXCOST ( y) = INDIC( IV.1. a) NCAP FOM MILESTONES PASTYEARS v SHAPE( v y v) MULTI ( y) Mi( M ( ) y) v= Max{ M ( ) D( ) 1 y TLIFE 1} VAR NCAP D( ) NCAP PASTI ( IV.1. a) The ueful age fo y i : { M ( ) D( ) 1 M ( ) TLIFE ad y EOH 1} Examle: Examle IV.1.a: D()=4 TLIFE=5 M()=B()1 D() TLIFE Iveme ad fixed co ayme: Fixed Co Payme oly B() M() 155

156 Cae 1.b if ILED ILED ad TLIFE ILED D( ) Mi < (Small ojec eeaed iveme i eiod) The figue how ha ayme made a yea y may come fom iveme made a befoe o afe eiod T(y). Noe ha ou exeio ake io accou he viage d age of he FOM beig aid via he SHAPE aamee ad alo he ue ime via MULTI boh eaiig o he FOM aibue. Mi( y B( ) TLIFE / 2 C TLIFE 1} VAR NCAP FIXCOST( y) = INDIC( IV.1. b) MILESTONES v= Max{ B( ) TLIFE / 2 y TLIFE 1} TLIFE NCAP FOM v SHAPE( y v) MULTI( y) whee (IV.1.b) C = D( ) TLIFE Ueful Rage fo y : TLIFE B( ) 2 ad y EOH B( ) TLIFE 2 ( C 1) TLIFE Examle: Examle IV.1.b D=5 TLIFE=4 C=2 D() TLIFE Iveme ad Fixed co ayme Fixed co Payme oly B() 156

157 Cae 2.a: ILED > ILED ad ILED TLIFE D( ) Mi (Lage idiviible ojec ueeaed iveme i eiod) i) FIXCOST(y) The figue of he examle how ha ayme made i yea y may come fom iveme made a eiod T(y) o ealie bu o lae. Agai hee he SHAPE ha he coec viage yea ad age a i wo aamee wheea MULTI ha he cue yea a i aamee. Boh eai o FOM. B( ) ILED y B( ) ILED ( VAR NCAP ) FIXCOST ( y) INDIC(2. a) NCAP FOM B( ) 1 if 0 = ILED MILESTONES T ( y) INDIC(2. a) PASTYEARS ( NCAP PASTI ) TLIFE 1 SHAPE( y B( ) ILED ) MULTI ( y) ohewie NCAP FOM 1 0 if y TLIFE 1 ohewie SHAPE( y ) MULTI( y) (IV.2.a) Ueful Rage fo y: { B( ) ILED B( ) ILED TLIFE 1} ad y EOH ii) SURVCOST (Suveillace co fo ame cae 2.a. See ame examle) MILESTONES T ( y) 1 if B( ) ILED TLIFE 0 ( VAR NCAP ) INDIC( IV.2. a) NCAP DLAGCB( ) y B( ) ILED TLIFE ILED DLAG 1 ohewie 157

158 INDIC( IV.2. a) PASTYEARS 1 if TLIFE 0 ( NCAP PASTI ) y TLIFE DLAG NCAP DLAGC 1 ohewie (IV.2.a ) Ueful Rage { B( ) ILED TLIFE ame DLAG 1} fo y : oe ha y may be l ag e ha EOH Examle IV.2.a ad IV.2.a : D()=8 ILED=4 TLIFE=6 DLAG=2 Coucio Fixed co Payme oly D() Suveillace Co ayme oly ILED TLIFE DLAG B() Remak: agai hee he co aibue i idexed by he yea whe iveme aed i life. Alo oe ha by choice we have o defied he SHAPE o MULTI aamee fo uveillace co. 158

159 Cae 2.b: ILED > ILED ad TLIFE ILED D( ) Mi < (Big ojec eeaed iveme i eiod) i. Fixed O&M co The co exeio ake io accou he viage ad he age of he FIXOM beig aid a ay give yea y. See oe i fomula ad figue fo a exlaaio. SHAPE( y B( ) ILED ( VAR NCAP ) ( ) MILESTONES T ( y) INDIC 2. b) NCAP FOM B( ILED I 1 I TLIFE ) 0 if 0 I C 1 ohewie TLIFE whee : y B( ) ILED I = TLIFE ad C = D( ) ILED TLIFE I i he idex of he iveme cycle whee y lie. I vaie fom 0 o C-1 Rage fo y: { B( ) ILED B( ) ILED C TLIFE 1} ad y EOH (IV.2.b) Remak: ame a above coceig he idexig of he co aibue ii. SURVCOST(y) (uveillace co fo ame cae; he ame examle alie) SURVCOST 1 if 0 B( ) ILED ( I 1) TLIFE ( VAR NCAP ) ( ) MILESTONES T ( y) y) = INDIC(2. b) NCAP DLAGCB( ILED I y ame DLAG 1 ad 0 I C 1 ohewie TLIFE 159

160 whee : y B( ) ILED TLIFE I = TLIFE ad C = D( ) ILED TLIFE Noe ha y may exceed EOH (IV.2.b ) Examle fo IV.2.b ad IV.2.b : D()=13 ILED=4 TLIFE=5 DLAG=2 C=2 Coucio Fixed co Payme oly Coucio ad fixed co Suveillace Co ayme oly ILED D() TLIFE DLAG TLIFE DLAG Suveillace ad fixed co ayme B() Remak: ame a ecedely egadig he idexig of he co aibue NCAPDLAGC Aual axe/ubidie o caaciy: FIXTAXSUB(Y) I i aumed ha hee axe (ubidie) ae aid (accued) a exacly he ame ime a he fixed aual co. Theefoe he exeio IV of ubecio ae valid elacig he co aibue by NCAPFTAX - NCAPFSUB Vaiable aual co VARCOST(y) y EOH Vaiable oeaio co ae eaed i a aighfowad mae (he ame a i MARKAL) aumig ha each aciviy ha a coa aciviy ove a give eiod. 160

161 I hi ubecio he ymbol VARXXX i ay vaiable of he model ha eee a aciviy a eiod. Theefoe XXX may be ACT FLO COMX COMT ec. Noe ha if ad whe he echology i viaged he vaiable ha a idex v idicaig he viage yea wheea T(y) idicae he eiod whe he aciviy ake lace. Similaly he ymbol XXXCOST k eee he value i yea k of ay co aibue ha alie o vaiable VARXXX. Fially he exeio ae wie oly fo he yea wihi hoizo ice a yea do o have a diec imac o vaiable co ad ice o vaiable co ayme occu afe EOH. Noe alo ha he SHAPE ad MULTI aamee ae o alicable o vaiable co. A aed i he ioducio he ayme of vaiable co i coa ove each eiod. Theefoe he exeio below i aiculaly imle. VARCOST y EOH ( v T ( y) y) = VAR XXX XXX COST y (VI) Co of demad educio ELASTCOST(y) Whe elaic demad ae ued he objecive fucio alo iclude a co eulig fom he lo of welfae due o he educio (o iceae) of demad i a give u comaed o he bae u. See PART I chae 6 fo a heoeical juificaio. COM STEPlo ELASTCOST ( y) = j= 1 COM BPRICE 1 ( 1/ 2) COM ELAST j COM VOC ( ) lo T ( y) lo T y T ( y) 1 VAR COM STEPlo ELAST lo j T ( y) COM STEPu j= 1 y EOH COM BPRICE ( j 1/ 2) COM VOC 1 COM STEPu VAR 1 COM ELAST u T y u T ( y ) ( ) T ( y) (VII) ELAST u j T ( y) Salvage value: SALVAGE (EOH1) Iveme whoe echical live exceed he model hoizo eceive a SALVAGE value fo he uued oio of hei echical live. Salvage alie o eveal ye of co: iveme co uk maeial co a well a decommiioig co ad uveillace 161

162 co. SALVAGE i eoed a a igle lum um eveue accuig eciely a he ed of he hoizo (ad he dicoued o he bae yea like all ohe co). The alvagig of a echology co i a exemely imoa feaue of ay dyamic laig model wih fiie hoizo. Wihou i iveme deciio made owad he ed of he hoizo would be eiouly dioed ice hei full value would be aid bu oly a facio of hei echical life would lie wihi he hoizo ad oduce ueful ouu. Wha ae he co ha hould igge a alvage value? The awe i: ay co ha ae diecly o idiecly aached o a iveme. Thee iclude iveme co ad decommiioig co. Fixed aual co ad vaiable co do o equie alvage value ice hey ae aid each yea i which hey occu ad hei comuaio ivolve oly yea wihi he hoizo. Howeve uveillace co hould be alvaged becaue whe we comued hem i ecio we allowed y o lie beyod EOH (fo coveiece). Thu SALVAGE i he um of hee alvage value SALVAGE( EOH 1) = SALVINV ( EOH 1) SALVDECOM ( EOH 1) SALVSURV ( EOH 1) We ea each comoe eaaely aig wih SALVINV. A). Salvagig iveme co (fom ubecio ad 5.1.2) The icile of alvagig i imle ad i ued i ohe echology model uch a MARKAL ec: a echology wih echical like TLIFE bu which ha oly e x yea wihi he laig hoizo hould igge a eayme o comeae fo he uued oio TLIFE-x of i acive life. The comuaio of he alvage value obey a imle ule decibed by he followig eul: 162

163 Reul 1 The alvage value (calculaed a yea k) of a ui iveme made i yea k ad whoe echical life i TL i: S( k TL) = 0 if k TL EOH S( k TL) = 1 if k > EOH TL (1 d) S( k TL) = (1 d) EOH TL 1 k 1 1 ohewie whee d i he geeal dicou ae Noe ha he ecod cae may ideed aie becaue ome iveme will occu eve afe EOH. Sice we wa o calculae all alvage a he igle yea (EOH1) he above exeio fo S(kTL) mu be dicoued (mulilied) by: EOH 1 1 d ( ) k Fially aohe coecio mu be made o hee exeio wheeve he ue chooe o uilize a echology ecific dicou ae. The coecio faco which mu mulily evey iveme (ad of coue evey alvage value) i: CRF CRF = i ( 1 i ) i 1 ( 1 i ) ELIFE ELIFE whee i ihe geeal dicou ae i i he echo log y ecific dicou ae ad ELIFE i he ecoomic life of he iveme Noe: he ime idexe have bee omied fo claiy of he exeio. The fial eul of hee exeio i Reul 2 exeig he alvage value dicoued o yea EOH1 of a ui iveme wih echical life TL made i yea k a follow. Reul 2 will be ued i alvage exeio fo iveme ad axe/ubidie o iveme. 163

164 SAL( k TL) = 0 Reul 2 if k TL EOH CRF SAL( k TL) = CRF if k EOH 1 EOH 1 (1 d) SAL( k TL) = 1 (1 d) 1 k TL TL CRF CRF ohewie whee d i he geeal dicou ae ad d i he echology ecific dicou ae Thee exeio may ow be adaed o each cae of iveme (ad axe/ubidie o iveme). We eumeae hee cae below. Noe ha o imlify he equaio we have omied he ecod agume i SAL (i i alway TLIFE i he exeio). Cae 1.a ILED ILEDMi ad TLIFE ILED D( ) (Small diviible ojec o-eeiive ogeive iveme i eiod) M ( ) SALVINV ( EOH 1) = INDIC( I.1. a) v= M ( ) D( ) 1 VAR NCAP D( ) NCAP PASTI NCAP COST SAL( v) v whee SAL(v) i equal o SAL(vTLIFE ) defied i Reul 2. Noe ha SAL(v) = 0 wheeve v TLIFE EOH 1 (ee Reul 2) (VIII.1.a) Cae 1.b ILED ILED ad TLIFE ILED D( ) Mi < Small Pojec eeaed iveme i eiod B( ) TL / 2 C TLIFE 1 SALVINV ( EOH 1) = INDIC( I.1. b) v= B( ) TL / 2 ( C 1) TLIFE VAR NCAP TLIFE NCAP COST v SAL( v) Noe agai hee ha SAL( v) equal 0 if v TLIFE EOH 1 (VIII.1.b) 164

165 Cae 2.a: ILED > ILED ad ILED TLIFE D( ) Mi (Lage idiviible ojec ueeaed iveme i eiod) SALVINV ( EOH 1) = VAR NCAP NCAP COSTB( ) MILESTONESYEARS ILED SAL( B( ) ILED ) Noe ha SAL ( B( ) ILED ) = 0 wheeve B( ) ILED TLIFE EOH 1 (VIII.2.a) Cae 2.b: ILED > ILED ad TLIFE ILED D( ) Mi < (Lage idiviible Pojec eeaed iveme i eiod) SALVINV EOH 1) = VAR NCAP NCAP COST ( ) ( 1 ( B C ) TLIFE ILED SAL ( B( ) ( C 1) TLIFE ILED ) Noe agai ha SAL ( B( ) ( C 1) TLIFE ILED ) = 0 wheeve B( ) ( C 1) TLIFE ILED TLIFE EOH 1 (VIII.2.b) NOTE: alvage co of axe/ubidie o iveme co ae ideical o he above elacig NCAPCOST by {NCAPITAX NCAPISUB}. B). Savage value of decommiioig co (fom ubecio 5.1.3) Fo decommiioig co i hould be clea ha he iggeig of alvage i ill he fac ha ome eidual life of he iveme ielf exi a EOH1. Wha mae i o ha he decommiioig occu afe EOH bu ha ome of he iveme life exed beyod EOH. Theefoe Reul 1 deived above fo iveme co ill alie o decommiioig. Fuhemoe he coecio faco due o he ue of echology ecific dicou ae i alo ill alicable (wih ELIFE elaced by DELIF). Howeve he fuhe dicouig of he alvage o big i o EOH1 i ow diffee fom he oe ued fo iveme. The dicouig deed o he yea l whe he decommiioig occued ad i hu equal o: (1 d) EOH 1 l whee l i he yea whe decommiioig occu. l deed o each cae ad I cae 1.a ad 1.b willbe comued below l=tlife k 165

166 I cae 2.a I cae 2.b fom k i fixed a B()ILEDTLIFE bu l vaie fom (B()ILED TLIFEDLAG) o (ame DLIFE-1) k i fixed a B()ILED(C-1)TLIFE bu l vaie (B()ILEDC x TLIFEDLAG) o (ame DLIFE-1) I i helful o look a he examle fo each cae i ode o udead hee exeio. Fially he equivale of Reul 2 i give a Reul 3 fo decommiioig. Reul 3 The Salvage Value of a decommiioig co occuig a iveme akig lace a yea k i : a yea l fo SAL( k l) = 0 if k TL EOH CRF SAL( k l) = CRF (1 i) EOH 1 l if k EOH 1 TLIFE k l (1 d ) (1 d ) SAL( k l) = TLIFE (1 d ) 1 EOH 1 l CRF CRF ohewie ad d whee d i he geeal dicou ae i he echology ecific dicou ae We ae ow eady o wie he alvage value of decommiioig co i each cae. 166

167 Cae 1.a ILED ILED ad TLIFE ILED D( ) Mi (Small diviible ojec o-eeiive ogeive iveme i eiod) SALVDECOM ( EOH 1) = INDIC(1. a) M ( ) v= M ( ) D( ) 1 VAR NCAP D( ) NCAP PASTI NCAP DCOST SAL( v v TLIFE v ) whee SAL( k l) i defied i Re ul 3. Noe ha SAL( v x) i alway 0 wheeve v TLIFE EOH 1 ( IX.1.a) Cae 1.b ILED ILED ad TLIFE ILED D( ) Mi < Small Pojec eeaed iveme i eiod SALVDECOM ( EOH 1) = INDIC(1. b) B( ) TL / 2 C TLIFE 1 v= B( ) TL / 2 ( C 1) TLIFE VAR NCAP TLIFE NCAP DCOST v SAL( v v TLIFE ) Noe agai hee ha SAL( k l) equal 0 if k TLIFE EOH 1 (IX.1.b) Cae 2.a: ILED > ILED ad ILED TLIFE D( ) Mi (Lage idiviible ojec ueeaed iveme i eiod) SALVDECOM ( EOH 1) = MILESTONESYEARS INDIC(2. a) VAR NCAP NCAP COST B( ) ILED ame DLIFE 1 l= B( ) TLIFE DLAG SAL( B( ) ILED l) Noe ha SAL i 0 wheeve B( ) ILED TLIFE EOH 1 (IX.2.a) 167

168 Cae 2.b: ILED > ILED ad TLIFE ILED D( ) Mi < (Lage idiviible Pojec eeaed iveme i eiod) SALVDECOM ( EOH 1) = ame DLIFE 1 l= B( ) ILED C TLIFE DLAG SAL MILESTONYEARS INDIC(2. b) VAR NCAP NCAP DCOST [ B( ) ILED ( C 1) TLIFE l] B( ) ( C 1) TLIFE ILED whee C = D( ) ILED TLIFE Noe agai ha SAL i 0 wheeve B( ) C TLIFE ILED EOH 1 (IX.2.b) C) Salvage Value of Suveillace Co Similaly o he alvagig of decommiioig co he baic alvage value facio S(km) defied i Reul 1 a he begiig of Secio ae ued a he bai fo he alvage value of uveillace co. Howeve ulike wih decommiioig co hee i o eed o make coecio fo echology-ecific dicou ae a he co do o eee caial co. I addiio he dicouig o EOH1 mu be made eaaely fo each uveillace yea. Noe ha oly Cae 2 have uveillace co. Cae 2.a: ILED > ILED ad ILED TLIFE D( ) Mi (Lage idiviible ojec ueeaed iveme i eiod) SALVSURV ( EOH 1) = MILESTONESYEARS INDIC(2. a) S( B( ) ILED TLIFE ) VAR NCAP NCAP DLAGC B( ) ILED ame DLAG 1 l= B( ) ILED TLIFE DISC( l EOH 1) Noe ha S( k m) = 0 wheeve k m EOH 1. (X.2.a) 168

169 Cae 2.b: ILED > ILED ad TLIFE ILED D( ) Mi < (Lage idiviible ojec eeaed iveme i eiod) SALVSURV ( EOH 1) = INDIC(2. b) S[ B( ) ILED ( C 1) TLIFE TLIFE ] VAR NCAP NCAP DLAGC B( ) ILED ( C 1) TLIFE ame DLAG 1 l= B( ) ILED C TLIFE DISC( l EOH 1) whee : C = D( ) ILED TLIFE Noe agai ha S( k m) = 0 wheeve k m EOH 1. (X.2.b) Lae eveue fom edogeou commodiy ecyclig afe EOH LATEREVENUE(y) Lae eveue coi of eveue fom ay maeial ad eegy which had bee embedded i ome ocee ad which ae eleaed afe EOH. Such eveue exi oly if a exogeou alvage value wa declaed by he ue fo he uk maeial. Noe: Fo maeial eleaed wihi he hoizo he eveue i eihe exlici (ad he i i he ue eoibiliy o idicae a egaive co cedi-- a dimalig ime) o he eveue i imlici ad he he ue mu ecify a hyical eleae of he maeial a dimalig ime ad he model will coecly ice hi maeial wihi he RES. LATEREVENUES(y) y EOH1 The lae eveue come oly fom he eale a dimalig ime of maeial ad/o eegy ha wee uk a coucio ime. Theefoe he LATEREVENUES exeio ae ideical o he decommiioig co exeio wih he NCAPDCOST aibue elaced by NCAP VAL( c) NCAP OCOM( c) c whee he ummaio exed ove all commodiie c fo which a NCAPOCOM aibue i defied (defaul o zeo if udefied) LATEREVENUES(y) i eoed a a lum um dicoued o he ue eleced bae yea. 169

170 The wo dicouig mehod fo aual ayme I he objecive fucio of TIMES all co ad ayme ae aumed o occu a he begiig of each yea. I he cae of iveme co hi mea ha he aualized ayme made i he begiig of each yea wihi he ecoomic lifeime ae equivale o a lum-um iveme co aid a he begiig of he fi oeaio yea if he aual ayme ae dicoued back o ha oi by he echology-ecific dicou ae (fo iace i cae 1a each lum um i equal o NCAPCOST/D()). Similaly i he cae of oeaio co (e.g. NCAPFOM) he oal aual co ae aumed o occu a he begiig of each oeaig yea. Becaue he oeaig co ca evehele be aumed o be ead coiuouly houghou he yea hi kid of begiig-of-yea dicouig mehod ioduce a mall bia i he dicouig of diffee co comoe. Fo examle he oeaig co i he fi yea of oeaio hould be aumed o occu abou half a yea lae i ime comaed o he iveme ad o a he ame ime a aumed i TIMES. Thi ime-diffeece hould be efleced i he dicouig alied bu i i igoed i TIMES. I TIMES hee i a oio o coec hi mall bia by uig o-called mid-yea dicouig. The oio i acivaed by he wich MIDYEAR (ee Pa II Cool vaiable). The coecio ha ae eeded i ode o ue mid-yea dicouig i TIMES ca be made i he followig wo e: 1. Fi imly aume ha iead of he begiig of each yea all ayme ae made i he mid-oi of each yea i TIMES. A uch hi aumio doe chage he objecive fucio i ay way; i i oly a chage i hikig. Howeve i alo mea ha iead of he begiig of he bae yea all co ae aumed o be dicoued o he mid-oi of he bae yea. 2. Secod make he eceay coecio o he dicouig of all hoe co comoe ha cao be aumed o be acually aid a he mid-oi of he yea. By goig hough he vaiou co comoe he followig cocluio hold fo e 2: All vaiable co ad fixed oeaio ad uveillace co ca be aumed o be aid i he mid-oi of each yea. Theefoe o chage i eeded i he dicouig of hee ayme. The lum-um iveme co i Cae 1 (NCAPCOST/D(T)) hould be aumed o occu a he begiig of he iveme yea iead of he mid-oi of ha yea. All he lum-um iveme co i Cae 2 (NCAPCOST/ILED) ca be aumed o occu i he mid-oi of each coucio yea. Theefoe o chage i eeded i he dicouig of he aualized iveme ayme. The decommiioig co i Cae 1 ca be aumed o be aid i he mid-oi of he yea becaue i hee cae i i aumed ha decommiioig ake exacly oe yea ad i i heefoe oly aual o aume ha o he aveage he co occu a he mid-oi. 170

171 The lum-um decommiioig co i Cae 2 (NCAPDCOST/DLIFE) ca be aumed o occu a he mid-oi of each yea wihi he decommiioig lifeime. Theefoe o chage i eeded i he dicouig of he aualized ayme. Coequely he oveall cocluio i ha he oly coecio eeded i he dicouig of vaiou co comoe i elaed o he iveme co i Cae 1. If we aume ha he Caial Recovey Faco ued i he begiig-of-yea dicouig (CRF beg ) i ill valid fo mid-yea dicouig we hould imly hif he oiio of boh he lum-um iveme ad he aualized ayme half a yea backwad. I em of dicouig hi mea ha i Cae 1 he aualized iveme ayme hould be mulilied by he faco (1d(y)) 0.5 whee d(y) i he geeal dicou ae. Peha he imle way o aly hi coecio i he objecive fucio i o make he adjume o he Caial Recovey Faco. Thu fo Cae 1 we could defie a CRF coeced fo mid-yea dicouig (CRF 1mid ) a follow: CRF 1mid = CRF beg (1d(T(y))) 0.5 Howeve oe could addiioally ague ha he Caial Recovey Faco CRF beg i o loge valid fo mid-yea dicouig. The aualized iveme ayme ca alo be aumed o eee a coiuou eam of co which hould hu be aumed o be aid a he mid-oi of each yea. The hocomig of he oigial CRF beg ca be ee by calculaig i value fo a iveme wih a ecoomic lifeime of ju oe yea. The value of CRF beg i i hi cae exacly 1 alhough i eem obviou ha ome iee hould be ivolved a well. Aumig ha he igle ayme eee a coiuou eam of co he ayme ca be aumed o occu a he mid-oi of he yea ad would hu iclude iee fo half-yea ime. Accodigly we hould coec he defiiio of he CRF oe by aumig ha he aualized ayme occu half a yea fowad i ime wih eec o he lum-um iveme which mea ha we mu iceae he omial ize of he ayme by he coeodig iee fo he half-yea ime. Combiig hee coecio ogehe he geeal dicou ae d(y) hould be imly elaced by he echology-ecific dicou ae d S (T(y)) i he exeio above becaue i addiio o he omial chage i he CRF he ime of he aualized ayme ha bee eoed back o oigial. Howeve o maiai coiecy bewee Cae 1 ad 2 he ame baic coecio o he CRF oe hould be alied o all cae. Theefoe he oal adjume eeded whe akig io accou he coecio o he CRF oe ae he followig: CRF 1mid = CRF 2mid = oe CRF mid = CRF beg (1d S (T(y))) 0.5 (X I.1) oe CRF mid (1d(T(y))) 0.5 (1d(T(y))) 0.5 = CRF beg (X (1d S (T(y))) 0.5 I.2) oe CRF mid (1d(T(y))) 0.5 = CRF beg (1d(T(y))) 0.5 (X (1d S (T(y))) 0.5 I.3) 171

172 Coequely i boh cae he aualized iveme ayme ae he aumed o occu a he mid-oi of each fical yea aig a he ime of he lum-um iveme ad he aual ayme ae equivale o he lum-um iveme whe dicoued back o ha oi by he echology-ecific dicou ae. The imlemeaio of he oioal coecio fo mid-yea dicouig coeod o equaio (XI.1 o XI.3). To be coie he exeio (XI.3) fo CRF 2mid hould alo be ued fo decommiioig co. 5.3 Coai The coai available i TIMES ae how i able 5.1 below ad lae fully decibed i he followig ubecio. The coai ekaed o he imlemeaio of Edogeou Techology Leaig (ETL) ad hoe elaed o he Climae Module ae how ad decibed i wo eaae chae (chae 6 ad 7 eecively) Table 5.1. Li of TIMES equaio Equaio Name Sho deciio EQACTFLO Equaliy elaiohi ha defie he aciviy of a oce i em of i flow vaiable EQ(l)ACTBND Boud o he aciviy of a oce EQ(l)BLND Secial bledig coai ued o ecify he comoiio of efied oil oduc BNDELAST Ue boud o each of he e vaiable ued o diceize he demad whe elaic demad feaue i ued EQ(l)BNDNET Boud o he e amou (oducio miu coumio) of a commodiy EQBNDPRD Boud o he oal oducio of a commodiy EQ(l)CAPACT Relae he aciviy of a oce o i available caaciy. May be igid (=) o flexible (<=) EQ(l)CPT Calculae he cue caaciy of a oce i em of all a ad cue iveme i ha oce. EQ(l)COMBAL Balace equaio of a commodiy EQECOMPRD Defiiio of he oal oducio of a commodiy EQ(l)CUMNET Boud o he cumulaive oducio of a commodiy ove a ime ieval EQ(l)CUMPRD Boud o he cumulaive e quaiy of a commodiy ove aime ieval EQDSCNCAP ad EQDSCONE Thee wo coai eue ha ome iveme may oly be made i ceai dicee ize EQ(l)FLMRK Exee fo a give commodiy ha he amou oduced/coumed by a oce i ied o he oal amou oduced/coumed of ha commodiy EQ(l)FLOBND Boud o he um ove a commodiy gou of he commodiy flow of a oce EQ(l)FLOFR Relaiohi bewee a flow i oe imelice ad he aual flow fo a give oce EQIRE Exee ha imo of a commodiy by egio mu be equal o all exo by ohe egio o egio 172

173 Equaio Name EQIREBND EQXBND EQ(l)INSHR EQ(l)OUTSHR EQPEAK EQPTRANS EQSTGTSS EQSTGIPS EQ(l)STGIN EQ(l)STGOUT Ue Coai of he LHS ye Ue Coai of he Dyamic ye Ue Coai of he Gowh ye Sho deciio Boud o exchage of a commodiy bewee wo egio Boud o oal exchage of a commodiy by oe egio Fo a give oce exee ha he iflow of a commodiy i ied o he oal iflow of all commodiie i a ceai gou Fo a give oce exee ha he ouflow of a commodiy i ied o he oal ouflow of all commodiie i a ceai gou Exee ha caaciy available mu exceed demad of a eleced commodiy i ay ime lice by a ceai magi Eablihe a equaliy elaiohi bewee (gou of) iu ad ceai (gou of) ouu of a oce Eue he oage of a commodiy bewee wo imelice Eue he oage of a commodiy bewee wo ime eiod Boud he iu io a oage oce Boud he ouu of a oage oce Ue defied coai ha have a ue defied RHS Ue defied coai ha ivolve moe ha oe eiod Ue defied coai ha exe a limi o he gowh 173

174 5.3.1 Equaio: EQACTFLO Idice: egio (); iveme yea (v); model yea () oce () ime lice () Tye: = Relaed vaiable: VARACT; VARFLO Relaed equaio: EQCOMBAL; EQCAPACT; EQPTRANS Puoe: Thi equaio defie he VARACT aciviy vaiable i em of he imay flow of a oce. The imay flow ae defied by he ue hough he cacu e aibue. Remak: The ieal e viy eue ha (v) exeio ae geeaed fo he viaged ocee ad () fo he o-viaged oe. The coai defie he aciviy of a oce. The aciviy of a oce i limied i he equaio EQ(l)CAPACT by he available caaciy. vaa() cool valid eiod i which he oce ca oeae. If he aciviy of a oce i defied by a igle flow he flow vaiable i elaced by he aciviy vaiable i cae ha he educio algoihm i acivaed. The i all equaio whee he flow occu he aciviy vaiable i ued iead. I hi cae he equaio EQACTFLO i o geeaed. Equaio: EQ ACTFLO v viy v c vaa IF NOT cie VAR ACT v = c cacu VAR FLO v c PRC ACTFLO v c The oce i o a ieegioal oce IF cie VAR ACT v = c cacu VAR IRE v c im VAR IRE PRC ACTFLO v c v c ex The oce i a ieegioal ade oce. 174

175 5.3.2 Equaio EQ(l)ACTBND Idice: egio (); model yea () oce () ime lice () Tye: Ay ye a deemied by he idex bd of ACTBND: l = G fo bd = LO (lowe boud) yield. l = E fo bd = FX (fixed boud) yield =. l = L fo bd = UP (ue boud) yield. Relaed vaiable: VARACT Relaed equaio: EQCOMBAL; EQACTFLO; EQPTRANS Puoe: Thi equaio boud he oal aciviy of a oce i a eiod ideedely of he viage yea of he ialled caaciie. The equaio will eihe be geeaed whe he aciviy boud i ecified fo a imelice beig a a imelice level above he imelice level of he oce (cl) e.g. ACTBND i ecified fo a ANNUAL imelice bu he oce oeae o a DAYNITE imelice level o ieecively of he imelice whe he oce i chaaceized a a viaged oe (cvi). If aciviy boud ae ecified fo imelice below he oce imelice level (cl) he boud will be aggegaed o he oce imelice level by adad aggegaio (ee aa 3.1.2) ad he diecly alied o he aciviy vaiable fo o-viaged ocee. The ame i ue fo aciviy boud ecified a he oce imelice level of o-viaged ocee. Remak: The equaio i equied becaue fo he wo cae decibed above (boud ecified fo a imellice above he oce imelice level o oce i chaaceized a a viaged oe) o igle vaiable exi which ca be bouded diecly. The boud i oly diecly alied o VARACT fo o-viaged ocee whe ACTBND i alied a he level c(). Ieeaio of he eul: Pimal: The level value of he equaio decibe he aciviy of he oce i he coideed eiod ad imelice. Dual: The dual vaiable decibe i he cae of a lowe (ue) boud he co iceae (deceae) caued by a iceae of he aciviy boud by oe ui. Equaio: EQ( l) ACTBND ACT BND Aciviy mu exi ad oce i available i eiod bd All imelice a o above cl ( cvi ) vaa c c v viy 2 c VAR ACT v 2 { = ; ; } ACT BND l 2: all imelice o oce imelice level(c) ha ae decede of i he imelice ee; deemied by he ieal e ma(2). eihe i viaged o he boud i alied fo a exac lice of 175

176 5.3.3 Equaio: EQ(l)BLND Idice: egio (); yea (); efiey oduc (ble); ecificaio (e) Tye: Ay ye a deemied by he value of he iu aamee BLTYPE(blee): l = L fo a value of 1 yield. l = G fo a value of 2 yield. l = E fo a value of 3 yield =. Relaed vaiable: VARBLND Relaed equaio: EQCOMBAL Puoe: The bledig equaio eue ha he chaaceiic of eoleum oduc (e.g. ulfu coe deiy ocae umbe ec.) lie wihi ecified limi if deied. Remak: Paamee BLCOM coai he value of he bledig ecificaio e fo he bledig eam o. Paamee BLSPEC coai he value of he ecificaio e of he bledig oduc ble. The bledig vaiable VARBLND ae exeed i volume ui. If he chaaceiic of he bledig eam o ad he oduc ble ae o give i volume ui (idicaed by iu aamee REFUNIT) he ue ha o ovide a coveio aamee CONVERT which coai he deiy ad eegy coe (by weigh o by volume) of each bledig eam. The coveio aamee ae ued o deive he coefficie RUCVT of he bledig eam i he bledig equaio. Equaio: EQ( l) BLND ble e bl ye ble e o ble o ble o { ; = ; } o ble o ble o BL COM BL SPEC ble o e ble o e RU CVT RU CVT ble e o ble e o VAR BLND VAR BLND ble o ble o 176

177 5.3.4 Boud: BNDELAST Idice: egio (); yea (); commodiy (c); ime lice (); lieaizaio e (j); diecio of elaic demad chage (l) Tye: Relaed vaiable: VARELAST Relaed equaio: EQ(l)COMBAL EQOBJELS EQOBJ Puoe: Ue Boud o he e vaiable ued o eee he demad whe he elaiciy i o zeo. Remak: Thee boud ae alied wheeve a demad i ice elaic i.e. whe he COMELAST (elaiciy) ad COMVOC (oal age) aamee ae ecified ad o zeo. If COMELAST ad COMVOC ae ecified ad COMSTEP (umbe of e) i o he lae defaul o 1 (igle e diceizaio) Aibue COMVOC ad COMSTEP do o have a imelice idex. The ue ca ill cool elaiciie i each ime lice hough COMELAST. Boud: BND ELAST c j l COM STEP c l ( com c ) VAR ELAST c j l COM PROJ c COM FR c COM STEP c l COM VOC c l 177

178 5.3.5 Equaio: EQ(l)BNDNET/PRD Idice: egio () eiod () commodiy (c) imelice () Tye: Ay ye a deemied by he boud idex bd of COMBNDNET/PRD: l = G fo bd = LO (lowe boud) yield. l = E fo bd = FX (fixed boud) yield =. l = L fo bd = UP (ue boud) yield. Puoe: If he boud o he e o go oducio of a commodiy i ecified fo a imelice beig above he imelice level of he commodiy he equaio decibed hee i geeaed. The boud o he e o go oducio of a commodiy i diecly alied o he vaiable (VARCOMNET VARCOMPRD) if he boud aamee i ecified fo a commodiy imelice (com). Remak: The ieal e ccom ued i he equaio coai all imelice a o above he imelice level beig defied fo he commodiy. The ieal e cvac ued i he ummaio a of he equaio coai all imelice (ou of com) ad eiod fo which he commodiy i available. The ieal e ma() ued i he ummaio a of he equaio coai fo a give imelice () all imelice () beig a o below i he imelice ee. Ieeaio of he eul: Pimal: Value of he e oducio of a commodiy (oducio miu coumio) Dual: magial co of iceaig he boud by oe ui Equaio EQ( I) BND( NET / PRD) c { ccom ( NOT com ) COM BND( NET / PRD) } c c c bd cvac ma c VAR COM ( NET / PRD) c COM ( / / = ) BND( NET / PRD) c bd Sig accodig o he l equaio idex (mu coicide wih he bd idex i aamee COMBNDNET/PRD). 178

179 5.3.6 Equaio: EQ(l)CAPACT Idice: egio (); viage yea (v) yea (); oce (); ime lice () Tye: Deemied by he boud idex bd of NCAPAF NCAPAFS o NCAPAFA: l = E fo bd = FX (fixed boud) yield =. l = L fo bd = UP (ue boud) yield. Relaed vaiable: VARACT; VARNCAP; VARFLO Relaed equaio: EQACTFLO; EQCOMBAL; EQINSHR; EQOUTSHR; EQPTRANS Puoe: The caaciy-aciviy equaio elae he aciviy of a oce o i available exiig caaciy of a oce i a eiod. The exiig caaciy coi of iveme made i he cue eiod (VARNCAP) iveme made i eviou eiod (VARNCAP) ad iveme ha have bee made befoe he begiig of he model hoizo (NCAPPASTI). The availabiliy of he exiig caaciy i a ecific eiod ad imelice i ecified by he availabiliy faco. Thee availabiliy faco exi: NCAPAF(vbd): Availabiliy faco ecified fo a ecific eiod ad imelice. If hi availabiliy faco i o ecified fo he oce imelice (c) he availabiliie ae aggegaed/iheied accodig o he imelice ee. Thu fo a oce oeaig o he DAYNITE level i i ufficie o ecify oly oe availabiliy fo he ANNUAL imelice which i he iheied o he DAYNITE imelice. NCAPAFS(vbd): Availabiliy faco ecified fo a ecific eiod ad imelice. I coa o NCAPAF hi availabiliy i o iheied/aggegaed alog he imelice ee. If hi availabiliy i ecified fo a eaoal imelice fo a oce oeaig o he DAYNITE level he caaciy-aciviy coai i geeaed fo he eaoal imelice ad um ove he DAYNITE aciviie. Thi give he oce flexibiliy how o oeae wihi he eaoal imelice a log a he oveall eaoal availabiliy eicio i fulfilled. NCAPAFA(vbd): Aual availabiliy faco imila o NCAPAFS beig ecified fo he ANNUAL imelice wih he diffeece ha NCAPAFA i alway alied i uch a way a if he oce i o-viage deede eve if i i ecified a a viaged oe (cvi). Thu he aual availabiliy faco i eecially ueful o calibae he aciviy of a oce i he fi eiod() o he aiic ieecively of i viage ucue ad he viage deede aciviie (NCAPAFS) which ca be ecified i addiio o NCAPAFA. If he oce i defied a a viage oe (cvi) fo each viage yea (v) of he exiig caaciy ock i eiod () a eaae caaciy-aciviy coai will be geeaed (exceio NCAPAFA) while fo a o-viaged oce oe caaciy- 179

180 aciviy coai i geeaed ha um ove all viage yea. I he lae cae he viage idex of he equaio (EQ(l)CAPACT(v)) alway equal he eiod idex (v = ). The caaciy-aciviy coai Remak: Fo all oce imelice (c) NCAPAF( UP ) i by defaul e o 1. Thu i i eued ha he aciviy of a oce ca eve exceed i caaciy. If fo examle oly NCAPAFA i ecified by he modele a aual availabiliy fo a oce wih a DAYNITE imelice eoluio i addiio o he aual aciviy-caaciy coai aciviy-caaciy coai wih a availabiliy of 100% ae geeaed fo he oce imelice. A aveage value of he availabiliy faco (NCAPAF/S/A) i ued whe a Shae i ecified. cy ideifie he caaciie ialled i eiod v ill available i eiod. Thi e ake io accou ha iveme may be ued-off fo ceai eiod (by PRCNOFF). The codiio i a ude: v uch ha B(v) B() - (COEFRPTI*TL) - IL 1 ad B(v) E() - IL cvi i a e of ocee fo which aibue ae chagig ove ime ad viagig i equied. Eie i viy ae coolled by he ame logic a alied o COEFCPT combied wih he viagig coideaio. Noe v = whe o viagig i equied o viagig i ued off fo a aicula ocee whee he um ove he eviou iveme i ued iead of idividual vaiable. COEFAF vbd will be ead off a e-oceed able afe alicaio of SHAPE ad MULTI o he ue ovided availabiliie (NCAPAF/A/S). COEFAF i calculaed i he followig mae: 1) aly MULTI o NCAPAF/A/S 2) aggegae if oible (lvlbd.mod) ohewie ihei (i mai.mod) 3) aly SHAPE Fo oage ocee he caaciy decibe he volume of he oage ad he aciviy he oage coe. Fo oage ocee bewee imelice (cg c) aamee RSSTGPRD i ued iead of GYRFR. RSSTGPRD() equal he umbe of oage eiod fo he imelice i a yea mulilied wih he duaio of i ae imelice which i he duaio of oe oage eiod. Thu he oage level VARACT (ad idiecly he oage i- ad ouu flow VARSIN ad VARSOUT) ae caled-u fo he eie yea. RSSTGPRD() i: o 1 fo a eaoal oage o 365/7*GYRFR() fo a weekly oage whee i he ae ode of o 365*GYRFR() fo a weekly oage whee i he ae ode of. 180

181 Ieeaio of he eul: Pimal: I cae of a iequaliy coai ad o a iveme (i.e. RHS i zeo) he imal value decibe he diffeece bewee he aciviy level ad he maximum oible aciviy due o he ialled caaciy i he coideed eiod ad imelice. If he imal value i egaive i mea ha he caaciy i o fully uilized. I cae of a iveme he RHS i o zeo 36 bu ha a oiive value ad coeod o he oible aciviy due o he a iveme. If he imal value equal he RHS value he caaciy i fully uilized. If o he diffeece (RHS miu imal value) whee he imal value may alo be egaive decibe he oible uued aciviy oducio. Dual: The dual value i i cae of a iequaliy coai a egaive umbe whe he coai i bidig. I decibe he co educio caued by a addiioal caaciy ui ad ca hu be ieeed a he value of he caaciy. Fo a owe la fo examle i ca be viewed a he a of he eleciciy ice ha ca be ued fo coveig he fixed oeaig ad iveme co of he caaciy (mulilied by he accodig coefficie i he dual equaio of he eleciciy flow vaiable). If NCAPAFS o NCAPAFA ae alied fo imelice beig above he oce imelice level i addiio caaciy-aciviy coai (wih a defaul value fo NCAPAF of 1 a ue boud) ae geeaed fo he oce imelice. The dual value of he coai elaed o NCAPAFS o NCAPAFA eve a bechmak value of he caaciy bewee he oce imelice. If fo examle NCAPAFA i give fo a owe la wih a DAYNITE imelice eoluio (e.g. WD WN SD SN) he NCAPAF elaed caaciy coai wih a availabiliy of 1 ae uually bidig oly i oe oce imelice level e.g. WD. Now he dual vaiable of NCAPAFA ca be ee a e ha mu be coveed i ohe oce imelice (WN SD SN) by he he evailig eleciciy ice o ha he model would decide o hif he cace aual caaciy fom WD o aohe imelice. 36 GAMS move all coa (e.g. a iveme) o he RHS ad he vaiable o he LHS of he equaio. I he liig file he imal value of he equaio ca be foud i he oluio eo ude he LEVEL colum. The RHS value i give ude he colum UPPER colum i cae of a <= iequaliy ad i he LOWER colum fo a >= iequaliy. Fo a equaliy LOWER LEVEL ad UPPER value ae he ame. 181

182 182 Equaio: ( ) ( ) { } ( ) ( ) [ ] ) ( ) ( ) ( ) o he eiod idex i equal EQ(l)CAPACT of he viage idex cae hi (i ) ( ; ; ) ( ] [ STG STG cy ma c v cma cma cvi cvi vaa c viy v = STGPRD RS YRFR G PASTI NCAP NCAP VAR CAPACT PRC CPT COEF AF COEF v PASTI NCAP NCAP VAR CAPACT PRC CPT COEF AF COEF ACT VAR AFA NCAP AFS NCAP AF NCAP CAPACT EQ l v v v bd v v v v v bd v v v

183 COEF CPT v : if v = D( ) NCAP ILED = Max D( ) 0 If v ha bee a log ime eiod ad i cloe eough o ecoue a caaciy ceaed a he ed of v. ele if v D( v) > IL TL B( ) < E( v) TL Mi = Max 0 ele edif ( B( v) IL COEF RPTI TL E( ) 1) D( ) v ( B( v) IL TL E( ) 1) Max( B( v) IL B( ) ) Mi = Max D( ) 0 edif B( ) Numbe of yea of exiece wihi eiod divided by he eiod duaio Thi e block ou he iveme ha have aleady eied which may be evaluaed wih a egaive emaiig life Whee COEF RPTI v = D( v) IL TL Simly cou he umbe of iveme i a log ime eiod. Exeio a i equal o he malle iege a. whee: IL = NCAPILED v TL = NCAPTLIFE v B() = 1 yea of he eiod coaiig E() = La yea of he eiod coaiig D() = Duaio of he eiod coaiig 183

184 5.3.7 Equaio: EQ(l)CPT Idice: egio (); yea (); oce () Tye: Ay ye a deemied eihe by he boud idex bd of CAPBND o he eed o have a caaciy vaiable (leaig echology o caaciy vaiable ued i ue coai): l = G fo bd = LO (lowe boud) yield if o ue boud a he ame ime l = E fo bd = FX (fixed boud) o fo lowe ad ue caaciy boud a he ame ime o fo leaig echology o fo caaciy vaiable ued i ue coai yield =. l = L fo bd = UP (ue boud) yield if o lowe boud a he ame ime. Relaed vaiable: VARNCAP VARCAP Relaed equaio: EQ(l)CAPACT Puoe: Thi equaio add u he iveme (VARNCAP) which have bee made i he cue ad eviou eiod ad ill exi i he cue eiod ad a iveme beig made befoe he begiig of he model hoizo ad eihe aig i o he caaciy vaiable VARCAP o alie diecly lowe o ue caaciy boud o i. Remak: I i geeaed oly fo hoe mileoe yea & oce combiaio ha have a coeodig CAPBND ecificaio fo ocee whee hee i a ue coai ivolvig a caaciy vaiable ad fo ocee beig a leaig echology (eg). I cae ha oly a lowe o a ue caaciy boud i ecified he caaciy boud ae diecly ued a RHS coa. I he ohe cae he caaciy vaiable i ued iead. The e va() decibe he cae whee a caaciy vaiable i eeded: Caaciy vaiable i ued i a ue coai Lowe ad ue caaciy boud ae ecified fo he ame eiod. I hi cae i i moe efficie o geeae oe caaciy vaiable by oe EQECPT equaio ad boud he vaiable iead of geeaig he wo equaio EQLCPT ad EQGCPT. 184

185 185 Equaio: ( ) ( ) [ ] ( ) [ ] { } CAPACT EQ l equaio i defied a CPT COEF whee PASTYEAR v PASTI NCAP PASTYEAR v MILESTONYR v NCAP VAR CPT COEF BND CAP NOT BND CAP BND CAP NOT BND CAP BND CAP CAP VAR BND CAP CPT EQ l v v v v v UP UP LO LO FX bd ) ( ) ( ) ( ) ( ; ; ) ( = cy v va va eg va va eg

186 5.3.8 Equaio: EQ(l)COMBAL Idice: egio (); yea () commodiy (c); imelice () Tye: Deemied by he ue-ulied e comlim. Defaul ae: l = G (lim = LO i comlim) fo eegy caie (comma(c NRG )) demad (comma(c DEM ))ad emiio (comma(c ENV )); yield ye of equaio; oducio ha o be geae o equal coumio if o ue boud a he ame ime l = E (lim = FX i comlim) fo maeial (comma(c MAT )) ad fiacial commodiie (comma(c FIN )); yield = ye of equaio; oducio ha o be equal coumio if o ue boud a he ame ime Relaed vaiable: VARACT; VARFLO; VARCOMNET; VARCOMPRD; VARIRE; VARNCAP; VARSIN/OUT; VARBLND; VARELAST Puoe: Thi equaio eue ha a each eiod ad ime-lice he oal ocueme of a commodiy balace i oal dioiio. A commodiy may be ocued i eveal diffee way: imoed oduced by echologie (aciviy ad caaciy baed) eleaed a eieme of ome iveme. A commodiy may be dioed of i eveal ohe way: exoed coumed by echologie (aciviy o caaciy baed) o by a demad o uk a iveme ime of a oce. The defaul ye fo he balace coai of a eegy caie ad fo a emiio i which allow ocueme o exceed dioiio. Thi may be imoa i ode o avoid ome ifeaibiliie due o igid ocee wih may ouu o iu. The defaul ig i = fo maeial. Boh defaul may be modified by he ue by he e comlim. Remak: The commodiy balace i geeaed fo he imelice () accodig o he ue defied e coml o com. Whe hee ae oe o moe of he aibue BND/CST/SUB/TAX/CUM elaig o oducio of he commodiy EQECOMPRD i geeaed i addiio o hi equaio. EQECOMPRD imly ceae a ew vaiable (VARCOMPRD) equal o he oducio a of he LHS of he balace coai (ee exeio COMSUP below) Similaly if hee ae eleva coefficie fo he e oducio of he commodiy he exeio VARCOMNET i ceaed coaiig he e oducio ad ued i he RHS (ee below). Noe ha CALFLOFLO(cio) able oe he comlee exeio (coefficie ad vaiable) givig he flow of each commodiy. The iveme elaed iu flow ae aumed o be ead uifomly houghou he commodiy lead-ime NCAPCLED edig exacly a he ed of NCAPILED (defaul value fo NCAPCLED i NCAPILED). Commodiy ouu flow elaed o dimalig ae aumed o occu uifomly ove NCAPDLIFE ad o a igh afe NCAPDLAG (defaul value: NCAPDLIFE =1). 186

187 NCAPCOM have a io o hould i be ju o he uly ide fo accouig uoe? Examle exi fo (hyical) coumio a well a eleae lad ue by hydo dam ad mehae emiio fom hem eecively. EQCOMBAL ead chemaically a follow: Pocueme Dioiio { o = } COEFFBRHS Whee COEFFBRHS i 0 fo all balace equaio exce fo demad balace whee i i equal o a oiive aamee. I addiio COEFFBRHS i equal o a vaiable whe he equaio i ued o defie he vaiable VARCOMPRD o VARCOMNET. Thi i exeed mahemaically a he followig equaio whoe coefficie will be fuhe develoed i wha follow. Ieeaio of he eul: Pimal: I cae of a iequaliy coai of he commodiy balace he imal value coeod o he value which i obaied whe all em wih vaiable ae moved o he LHS of he equaio ad all coa e.g. em wih he demad aamee COMPROJ o fixed flow vaiable VARFLO ae moved o he RHS ide. The imal value equal he value of he LHS ide. Thu he commodiy balace i bidig whe i imal value equal i RHS coa i i o-bidig i.e. oducio exceed coumio if he imal value i geae ha he RHS coa 37. Dual: The dual vaiable (hadow ice) of he commodiy balace decibe he ieal value of he commodiy. If he commodiy balace i bidig i.e. coumio equal oducio he hadow ice decibe he co chage i he objecive fucio iduced by a iceae of he commodiy demad by oe ui. Sice he LHS of he commodiy balace decibe he diffeece bewee oducio ad coumio hi addiioal demad may be coveed by a iceae i oducio o by a deceae i coumio. I he fi cae he hadow ice i deemied by aciviie o he uly ide of he commodiy while i he lae cae avig meaue o he demad ide of he commodiy ae eig he hadow ice. Noe ha whe a eakig coai (EQPEAK) fo he coideed commodiy exi he ice coume mu ay duig eak hou deed o oly o he hadow ice of he commodiy balace bu alo o he hadow of he eakig coai (i he cae ha he flow vaiable of he coumig echology ha he ame imelice eoluio a he commodiy ad ha he eakig aamee COMPKFLX=0 ad FLOPKCOI=1 i i imly he um of he wo hadow ice; i ohe cae he dual coai of he flow vaiable hould be ieced o ideify he coec coefficie fo he wo hadow ice). 37 The imal value ad he RHS coa of a equaio ca be foud i he GAMS liig file i oluio eo a. The LEVEL value colum coeod o he imal value he LOWER level value equal he RHS of a coai of ye >= ad he UPPER level value equal he RHS of a coai of a ye <=. 187

188 188 Equaio: [ ] ( ) ( ) ) ( ) ( ) ( ohewie if 1 ) ( 1 1. ) ( ) ( ) ( age coiued o ex u l ELAST VAR lo l ELAST VAR YRFR G PASTYEAR v PASTI NCAP MILESTONYR v NCAP VAR OCOM COEF YRFR G PASTYEAR v PASTI NCAP MILESTONYR v NCAP VAR CPT COEF COM NCAP TSFR RTCS BLND VAR BAL BLE EFF STG YRFR G YRFR G SOUT VAR IRE AUX IRE CAL FLOFLO CAL IE COM COMBAL l EQ l l c v OUT c v c v STEP COM j l j c STEP COM j l j c OCOM COEF if v v v c v COM NCAP if v v v v OUT c v o ANNUAL c o c o c v v OUT c v IMP c c v v OUT c v c c = = = = vc v vc co v 1 cimp v cout v ccaflo cy ccaflo bleo viy c 1 cie viy o viy cbd ma ccombal Flow oduced by Techology Ivme/Dimalig Flow oduced by Techology Caaciy Ne educio i demad Thi eie exeio i deoed: COMSUP Ouu of bledig oce; he aamee BLEBAL cove he bledig eam o eegy ui Ouu flow of odiay ocee Imo of he commodiy

189 Soage of commodiy o cie ( v ) viy 1 c ( BLE BAL ble c VAR BLND ble c RTCS TSFR c ANNUAL ) ble bleo ( v) ccaflo if ( cyv NCAP COM ( v) ccaflo if COEF ICOM v viy { ; = } COEF FBRHS CAL FLOFLO v viy c EXP v cout v blec vc v c IN ) vc v c v 1 CAL IRE VAR SIN v c IN v c c2 EXP v c 1 AUX IRE 1 G YRFR G YRFR NCAP COM v c IN COEF CPT v VAR NCAP v v MILESTONYR NCAP PASTI v v PASTYEAR Thi ieal e give he eiod a which he commodiy i available (uually all eiod bu he ue ca u-off eiod by he e comoff) ad he imelice a defied by he ue i coml o com. Iu flow of odiay ocee c IN if ma ohewie G YRFR COEF ICOM v c VAR NCAP v v MILESTONYR G YRFR NCAP PASTI v v PASTYEAR 1 Commodiy coumed by Techology Ivme/Dimalig 1 Exo of he commodiy Iu flow io oage ocee di Ouu of bledig oce; he aamee BLEBAL cove he bledig eam o eegy ui Iu flow of echology caacviy = ig if (comye = MAT o FIN) o if ue defied equaio ye by comlim i give 189

190 We ow how he deailed calculaio of he Righ-had-ide COEF FBRHS : Do Cae Cae COM BNDNET COM CUMNET COM CSTNET COM SUBNET COM TAXNET COEF FBRHS = VAR COMNET Cae COM BNDPRD COM CUMPRD COM CSTPRD COM SUBPRD COM TAXPRD COEF FBRHS = VAR COMPRD Cae COM PROJ COEF FBRHS = COM PROJ COM FR Ohewie Edcae COEF FBRHS = 0 190

191 Flow Coefficie elaed o oce aciviy (VARFLO) CAL FLOFLO v c io flo NOT ccoly c The oce ha egula flow vaiable (VARFLO). = 1 cvaf c1 VAR FLO v c 1 RTCS TSFR c 1 RPCCONLY coai commodiie ONLY ivolved i NCAPI/O/COM wih RTCSTSFR defied i he followig way: The TS eoluio of VARFLO i deemied by he oce-commodiy combiaio ad o by he commodiy aloe (ee EQPTRANS). The e cvaf coai he valid eiod () ad imelice (1) fo which he flow vaiable exi. RTCS TSFR( c 1) IF ELSE ma 1 = 1 COM FR = COM FR G YRFR c = G YRFR c c 1 c 1 if c i a demad commodiy ad COMFR i ecified ohewie. The aamee RTCSTSFR i ued o mach he imelice eoluio of flow vaiable (VARFLO/VARIRE) ad commodiie. RTCSTSFR i he coefficie of he flow vaiable which i oducig o coumig commodiy (c) i he commodiy balace of c. If imelice coeod o he commodiy imelice eoluio of c ad imelice 1 o he imelice eoluio of he flow vaiable wo cae may occu: 1) The flow vaiable ae o a fie imelice level ha he commodiy balace (fi cae i he fomula above ma(1) i ue): i hi cae he flow vaiable wih imelice beig below i he imelice ee ae ummed o give he aggegaed flow wihi imelice 1. RTCSTSFR ha he value 1. 2) The flow vaiable ae o coae imelice level ha he commodiy balace: i hi cae he flow vaiable i li-u o he fie imelice level of he commodiy balace accodig o he aio of he imelice duaio of o 1: RTCSTSFR ha he value = COMFR() / COMFR(1) fo demad commodiie ad GYRFR() / GYRFR(1) ohewie. Whe COMFR i ued he demad load cuve i moved o he demad oce. Thu i i oible o model demad ocee o a ANNUAL level ad eue a he ame ime ha he oce follow he give load cuve COMFR. Ie-egioal Flow Coefficie 191

192 CAL IRE = v c ie 1 cvafc1 cie VAR IRE cie v c 1 ie NOT ccoly RTCS TSFR c c 1 Ieal e idicaig ha commodiy (c) i imoed/exoed (ie) via oce () i/fom egio (). Adju he ime-lice of IRE fo COMBAL AUX IRE = c io Comue he Auxiliay flow aociaed wih a ie-egioal oce = cie comie v viy v 1 cvafcom 1 ( com ie) IRE FLOSUM com ie c io IRE FLOSUM if ma1 1 ele G YRFR G YRFR 1 com 1 ie c io VAR IRE v c 1 ie The imelice (1) of he flow vaiable VARIRE i below () i he imelice ee. Sice he imelice (1) of he flow vaiable VARIRE i above () i he imelice ee VARIRE i aoioed accodig o he imelice duaio. 192

193 Iveme Relaed Flow Coefficie Iemediae Noaio: BCF = B( v) NCAP ILED NCAP CLED Begiig yea of commodiy flow ECF = B( v) NCAP ILED 1 Edig yea of commodiy flow Noe ha hee flow eve eed o be caied aco log eiod becaue he coucio eve exceed he ed of eiod v if v i log COEF ICOM : if ( v = ) ( IL TL < D( )) NCAP ICOM = COEF RPTINV D( ) whee COEF RPTINV = ele 1 Mi = Max edif ( ECF E( ) ) Max( BCF B( ) ) D( ) D( ) ILED v TLIFE NCAP ICOM NCAP CLED v v 0 Cae IV Cou he umbe of iveme i a log eiod Cae I II III Cae I Cae II NCAPCLED Cae III Cae IV 193

194 Dimalig Relaed Flow Coefficie Iemediae Noaio: BCF = B( v) NCAP ILED NCAP TLIFE NCAP DLAG Sa yea of commodiy flow. ECF = B( v) NCAP ILED NCAP TLIFE NCAP DLAG NCAP DLIFE 1 Ed yea of commodiy flow. COEF OCOM : Eihe he cue eiod i log o hee wa a log eiod ha could have iveme lae eough o be dimaled i. if v D( v) > IL TL B( ) < E( v) TL DLAG DLIFE = COEF RPTINV ele i= 1 Mi Max Max 0 ( B( v) IL ( i TL) DLAG DLIFE 1 E( ) ) ( B( v) IL ( i TL) DLAG B( ) ) D( ) D( ) NCAP OCOM NCAP DLIFE v v Mi ECF E Max BCF B NCAP OCOM Max 1 ( ( )) ( ( )) = D( ) NCAP DLIFE 0 edif v v 194

195 5.3.9 Equaio: EQECOMPRD Idice: egio (); yea () commodiy (c); imelice () Tye: = Relaed vaiable: VARACT; VARFLO; VARCOMNET; VARCOMPRD; VARIRE; VARNCAP; VARSOUT; VARBLND; VARELAST Relaed equaio: EQ(l)COMBAL; EQ(l)BNDPRD; EQ(l)CUMPRD; EQOBJVAR Puoe: Thi equaio geeae a vaiable VARCOMPRD equal o he oal uly of he commodiy i.e. imo oducio (aciviy ad caaciy baed) iveme-ime ouflow dimalig elaed ouflow i each eiod ad ime lice. Noe ha hi exclude demad educio (i he cae of a demad commodiy) Remak: Eable he alicaio of boud o he aual o cumulaive oducio of commodiie. Thi i alo eeded o icooae co/ub/ax aibue o commodiy oducio. Equaio: EQE COMPRD c COM BNDPRD COM CUMPRD COM CSTPRD COM SUBPRD COM TAXPRD COMSUP = VAR COMPRD c Thi efe o he em maked COMSUP o equaio EQCOMBAL 195

196 Equaio: EQ(l)CUMNET/PRD Idice: egio (); yea1 (y1); yea2 (y2); commodiy (c) Tye: Ay ye a deemied by he boud idex bd of COMCUMNET/PRD: l = G fo bd = LO (lowe boud) yield. l = E fo bd = FX (fixed boud) yield =. l = L fo bd = UP (ue boud) yield. Relaed vaiable: VARCOMNET/PRD Relaed equaio: EQ(l)COMBAL; EQECOMPRD Puoe: Thi equaio geeae a cumulaive boud fo e eleae o oal go oducio of a commodiy. The coai coce e eleae/oducio ove a abiay umbe of coecuive yea bewee he yea (y1) ad yea (y2) a give i he boud aamee COMCUMNET/PRD. Remak: I i oible o have mulile cumulaive boud of ay ye. The oal ime a fo calculaig he cumulaive oducio eed o coi of a exac umbe of eiod. The cumulaive boud ae exeed aually oly. The ig of he boud i idicaed by he l equaio idex. Ieeaio of he eul: Pimal: The imal value decibe he cumulaive e eleae/he cumulaive oducio of commodiy c bewee he yea y1 ad y2. Dual: The dual value of he coai decibe he chage i he objecive fucio if he boud aamee i iceaed by oe ui. The iceae of a ue boud yield a educio of he oal co (dual value i egaive) ice he yem wa o ue moe of hi commodiy. The iceae of a lowe boud yield a iceae of he oal co (dual value i oiive) ice he yem ha o be foced o ue moe of a ucomeiive commodiy (he commodiy ielf o he echologie uilizig i maybe oo exeive). The dual value of a cumulaive oducio coai ca alo be ieeed a a ax/ubidy ha i alied bewee he yea y1 ad y2 o each he ame cumulaive oducio a ecified i he boud (he ax/ubidy ha o be adjued by he dicou ae). 196

197 Equaio: EQ( l) CUMNET y1 y2 c COM CUMNET y1 y2 c l = T ( y2) = T ( y1) cvac c [ Mi{ E( ) y2} Max{ B( ) y2} 1] VAR COMNET c { = ; ; } COM CUMNET y1 y2 c l EQ( l) CUMPRD y1 y2 c COM CUMPRD y1 y2 c l The ieal e cvac give he eiod a which he commodiy i available (uually all eiod bu he ue ca u-off eiod by he e comoff) ad he imelice a defied by he ue i coml o com. = T ( y2) = T ( y1) cvac c [ Mi{ E( ) y2} Max{ B( ) y2} 1] VAR COMPRD { = ; ; } COM CUMPRD y1 y2 c l c 197

198 Equaio EQDSCNCAP Idice: egio () mileoeyea () oce () Tye: = Relaed vaiable: VARDNCAP VARNCAP Relaed equaio: EQDSCONE Puoe: The iveme vaiable of he echology i eiod ad egio ca ake oly ecific ui ize give by he aamee NCAPDISC. Thi equaio defie he iveme vaiable o be equal o he um ove he diffee ui ize each mulilied by he coeodig deciio vaiable VARDNCAP. Howeve he ie equaio EQDSCONE eic hi um o a igle em oly (i.e. a igle ui of a ecific ize i allowed o be iveed i a eiod ). Remak: The e ui coai he ame of caaciy block/ui ha ca be added he e coai iege umbe goig fom 0 o 100. The ui ame 0 i ued o decibe he deciio ha o caaciy hould be added. The e dca() coai he ocee (i egio ) fo which he dicee caaciy fomulaio hould be ued The aamee NCAPDISC(u) i he allowed caaciy ize of ui u; e.g. he ize of ui 1 could be 50 MW ui MW ad ui MW. The ize of ui 0 i auomaically e o zeo (EPS). If all ui ize ae ake equal he fomulaio allow he eeaed iveme of a baic ui (a may a 100 ime i iege umbe). VARDNCAP(u) i a biay deciio vaiable decibig whehe he caaciy ui ui of echology hould be added i eiod o o. Some olve fo mixed-iege oblem a CPLEX o XPRESS allow he defiiio of vaiable a o-called SOS1 e (ecial odeed e) i ode o imove he oluio oce. A SOS1 e i defied a a e of vaiable of which oly oe vaiable ca ake a o-zeo value. VARDNCAP i cuely defied a SOS1 vaiable. No all olve uo hi oio i hee cae he vaiable ye hould be chaged o a biay vaiable i he file modva.dc. Equaio EQ DSCNCAP dcca VAR NCAP = ( VAR DNCAP u NCAP DSC u ) u ui 198

199 Equaio: EQDSCONE Idice: egio () mileoeyea () oce () Tye: = Relaed vaiable: VARDNCAP VARNCAP Relaed equaio: EQDSCNCAP Puoe: The equaio eue ha oly oe of he mulile ui ize allowed fo echology (decibed by NCAPDSC(u)) ca be added i eiod. Equaio EQ DSCONE dcca u ui VAR DNCAP u = 1 Noe ha VAR DNCAP mu be declaed a a biay vaiable ( akig value 0 o 1 oly) 199

200 Equaio: EQ(l)FLMRK Idice: egio (); eiod (); oce (); commodiy (c) ime-lice () Tye: Ay ye a deemied by he boud idex bd of FLOMARK: l = G fo bd = LO (lowe boud) yield. l = E fo bd = FX (fixed boud) yield =. l = L fo bd = UP (ue boud) yield. Relaed vaiable: VARFLO; VARCOMPRD Relaed equaio: EQ(l)COMBAL; EQECOMPRD Puoe: Relaiohi o faciliae coai o he make hae of oce () i he oal oducio of commodiy (c). Idicae ha he flow of commodiy (c) fom/o oce () i bouded by he give facio of he oal oducio of commodiy (c). The ime-lice level of he coai i ha of he commodiy (c). I he ee imlemeaio he ame give facio i alied o all imelice (hi could be geealized o allow ime-lice-ecific facio if deemed ueful). Vaiable ivolved VARFLO(vcom) he aveage flow o/fom a oce buil i eiod v duig ime-lice duig each yea of eiod. The vaiable fo a iu flow aea o he coumio ide of he balace equaio wihou ay coefficie ad he vaiable fo a ouu flow o he oducio ide mulilied wih he commodiy efficiecy (COMIE). VARIRE(vcomie) he aveage flow o/fom a exchage oce buil i eiod v duig ime-lice duig each yea of eiod. The exo vaiable aea o he coumio ide of he balace equaio wihou ay coefficie ad he imo vaiable o he oducio ide mulilied by he commodiy efficiecy (COMIE). VARSIN/SOUT(vc) flow eeig/leavig a oage oce oig a commodiy c. The vaiable fo chagig aea o he coumio ide of he balace equaio wihou ay coefficie; he imo vaiable o he oducio ide mulilied by boh he oage efficiecy ad commodiy efficiecy (SGTEFF COMIE). VARCOMPRD(com) vaiable equal o he oal imo oducio (aciviy ad caaciy baed) iveme eieme elaed flow i each eiod ad ime lice. Thi balace i defied by he equaio EQECOMPRD which i auomaically geeaed fo all commodiie ued i FLOMARK aamee. Paamee FLOMARK(cl) Make hae of oce i oal commodiy oducio. Remak 200

201 1. Make-hae coai ca be ecified fo odiay ocee a well a fo exchage ad oage ocee. Fo odiay ocee he FLOMARK aamee value hould alway be o-egaive. Howeve becaue exchage ad oage ocee ca have boh iu ad ouu flow of he ame commodiy fo hee ocee egaive value ca alo be ecified. Deedig o he aamee value he coai i i hee cae alied eihe o he iu o ouu flow by uig he followig imle coveioal ule: Value > 0: Coai i alied o he ouu flow (imo o oage dichage) Value < 0: Coai i alied o he egaive of iu flow (exo o oage chage) Value=EPS: Coai i alied o he e ouu flow (ouu iu flow) Thee imle ule ovide eaoable flexibiliy fo ecifyig make hae boud alo fo exchage ad oage ocee i addiio o odiay ocee. Alhough hee ule eclude idividually boudig he iu o ouu flow o zeo hi could alway be accomlihed by uig he IREBND STGOUTBND ad STGINBND aamee whe eceay. 2. I mo cae he commodiy c o be ecified i he FLOMARK aamee i diecly he commodiy of he oce flow. All commodiie defied i he oology ca alway be diecly ued i he FLOMARK aamee whe aifacoy. Howeve he commodiy ued i he aamee doe o acually eed o be i he oology bu i hould coai ome commodiy ha doe exi i he oce oology. Thi feaue ca be uilized fo defiig make-hae equaio a he ANNUAL level fo eaoal commodiie. Fo examle if ELC i a eaoal commodiy he ue could defie a ew commodiy ELCANN ha iclude ELC a a gou membe (hough COMGMAP membehi) ad ue he ELCANN commodiy i he FLOMARK aamee iead of ELC. If o imelice level i defied fo ELCANN he coai will he by defaul be defied a he ANNUAL level. Examle: Defie a ue make hae boud of 5% fo echology WIND1 i oal ELC oducio i he 2010 eiod. Defie a ue make hae of 25% fo dieel exo (hough exchage oce DSLXHG) of oal DSL oducio i he 2010 eiod. Noe ha becaue he boud i fo exo i hi cae he aamee value hould be egaive ad he boud ye LO iead of UP. PARAMETER FLOMARK / REG.2010.WIND1.ELC.UP 0.05 REG.2010.DSLXHG.DSL.LO 0.25 /; Ieeaio of he eul: Pimal: If he imal value i zeo he coai i bidig. If he imal value i oiive fo a lowe FLOMARK boud o egaive fo a ue boud he coai i o-bidig. Dual: The dual value decibe fo examle fo a lowe boud he ubidy eeded o guaaee he make hae of he echology beig foced io he make. The ubidy i eeded ice he oducio of he echology i oo exeive comaed o ohe comeig echologie. The value of he ubidy which he echology eceive i equal o (1-FLOMARK)*(dual vaiable). Thi ubidy 201

202 ha o be aid by he ohe echologie oducig he ame commodiy. Thu he co of hee echologie ae iceaed by he amou FLOMARK*(dual vaiable). The coai ca heefoe be ieeed a a quoe yem fo he oducio of a ecific echology e.g. a ceificae yem fo eleciciy by a wid echology: each o-wid oduce ha o buy ceificae accodig o he quoa. The ice of he ceificae equal he dual value of he coai. Equaio: EQ( l) FLMRK c ( c ) RTP FLO MARK c l COM TS c ( com v ) RPC COM GMAPc RTP VINTYR RPCS VAR VAR { = ; ; } VAR FLO VAR IRE SOUT v v com v com COM IE 1 com if ouu if iu COM IE com im com if FLO MARK c l 0 STG EFFv 0 if FLO MARK c l < 0 VAR IRE v com ex 1 if FLO MARK c l 0 VAR SIN v com 0 if FLO MARK c l > 0 1 if TS MAP( ) FR( ) if RS BELOW ( ) FR( ) com RPC COM GMAP c RHS COMPRD com FLO MARK 1 FR( ) FR( ) c l VAR COMPRD com if TS MAP( ) if RS BELOW ( ) 202

203 Equaio: EQ(l)FLOBND Idice: egio () eiod () oce () commodiy gou (cg) imelice () Tye: Ay ye a deemied by he boud idex bd of FLOBND: l = G fo bd = LO (lowe boud) yield. l = E fo bd = FX (fixed boud) yield =. l = L fo bd = UP (ue boud) yield. Puoe: Boud o he um of oce flow i a give commodiy gou (cg) fo a aicula oce () i eiod () ad imelice (). Remak: The coai boud he flow i a ecific eiod () ieecively of he viage yea of he oce caaciy. The boud ca be defied fo a igle commodiy o a gou of commodiie liked o he oce (). I he lae cae a commodiy gou (cg) mu be defied by he ue (hough comgma). The coai i geeaed if oe of he followig codiio i ue: o Poce () i viaged o o he um of eveal oce flow give by he commodiy gou (cg) ad o oly a igle oce flow hould be bouded o o he imelice eoluio of he flow vaiable ae below he imelice () of he boud aamee. I he ohe cae he boud ca be diecly alied o he coeodig flow vaiable o ha o exa equaio i eeded. The imelice level () of he boud mu be a o highe ha he imelice level of he oce flow (cvaf). Ieeaio of he eul: Pimal: If he imal value equal he boud aamee he coai i bidig. Dual: The dual value decibe fo a lowe/ue boud he co iceae/deceae i he objecive fucio if he boud i iceaed by oe ui. I may alo be ieeed a ubidy/ax eeded o each he give boud value. 203

204 Equaio EQ( l) FLOBND The oce i viaged. cg FLO BND cg bd cg i a gou of commodiie ad cvi o oly a igle commodiy The boud i alied o a um of oce flow. c comgma cgc cvafc below c comgma cgc cvaf c v viyv ( / / = ) FLO BND VAR FLO cg bd v c The imelice eoluio () of he oce flow() i below he imelice eoluio () of he boud. whee he equaio ig i idicaed by equaio idex l baed o he boud ye bd. 204

205 Equaio: EQ(l)FLOFR Idice: egio () eiod () oce () commodiy (c) imelice () Tye: Ay ye a deemied by he boud idex bd of FLOFR: l = G fo bd = LO (lowe boud) yield. l = E fo bd = FX (fixed boud) yield =. l = L fo bd = UP (ue boud) yield. Puoe: Relaiohi i eiod () bewee he oal aual flow ad he flow i a aicula imelice () fo a ecific oce (). The aamee FLOFR may be ued o defie a load cuve fo a oce flow. Remak: The ig of he equaio deemie whehe he flow i a give imelice i igidly (=) o flexibly ( ; ) liked o he aual flow. The coai boud he flow ieecively of he viage yea of he oce caaciy. Equaio EQ( l) FLOFR ( / / = ) c cvaf c v viyv ma cvac FLO FR ( VAR FLO v c RTCS TSFR c ) c bd The imelice of he oce flow () have o be below he imelice () of he boud. cvaf c v viyv [ VAR FLO v c FLO FR c bd ] See ude EQ(l)COMBAL fo he defiiio of he ieal aamee RTCSTSFR. whee he equaio ig i idicaed by equaio idex l. 205

206 Equaio elaed o exchage (EQIRE EQIREBND EQXBND) The hee equaio i hi ecio coce ade bewee egio. Sice hee equaio ivolve (diecly o idiecly) moe ha oe egio we a hei eeaio by a comlee deciio of he modelig aoach ued which a we hall ee ivolve vaiou cheme fo eeeig diffee ye of ade. The deciio aleady give i chae 2 i alo eleva o hee equaio. Sucue ad ye of edogeou ade I TIMES he ie-egioal adig ucue of a give commodiy baically coi of oe o eveal exchage ocee (called IRE ocee) each of which defie a oio of he adig ewok fo he commodiy. The idividual ub-ewok ca be liked ogehe hough commo iemediaig egio. A a examle eleciciy ade ca be coveiely decibed by bi-laeal exchage ocee (figue 5.2). Bu bi-laeal adig bewee all ai of egio may become oeou i em of daa ad model ize. I i heefoe ueful o coide he ohe ade ucue of TIMES called muli-laeal ade whee egio ade wih a commo make (figue 5.3). Fo eihe ucue he oology of he adig oibiliie ae all defied via he e oie of quiule {1c12c2} whee 1 2 ae he exoig ad imoig egio eecively c1 c2 ae he ame of he aded commodiy i egio 1 ad 2 eecively ad i he oce ideifie. Poce i a oce i boh egio. I ha o be defied oly oce bu oe ca add aamee o i i boh egio (e.g. co boud ec.). (Nealy evey iece of ifomaio i TIMES ha o be aiged o a egio.) TIMES ovide coideable flexibiliy i he defiiio of adig ucue. Each ub-ewok defied fo a igle exchage oce ca have he geeal ucue how i Figue 5.1 a adig ucue ha ivolve boh eveal uly (exo) egio ad eveal demad (imo) egio cao be defied wihou ioducig a iemediaig make egio (R M ). Wheeve uch a iemediae egio i defied bewee (a lea) wo diffee egio he model geeao will aume ha he ucue i acually mea o igoe he iemediae ode-egio how i Figue 5.1. If he iemediae e hould oehele be icluded hi ca be accomlihed by dividig he ub-ewok io wo a by uig wo exchage ocee. Coequely deedig o he ue choice he adig elaiohi how i Figue 5.1 ca be modeled boh wih ad wihou he iemediae aoaio e how i he Figue. 206

207 Suly egio Demad egio R S1 Exo Imo R D1 R S2 Imo/Exo R D2 R S3 R M R D3 R Sm Suly ad demad e may coai ame egio; oe of hem may alo be emy R D Figue 5.1. Geeal ucue of he ai-wie ecificaio of he adig ubewok allowed i TIMES fo a igle exchage oce. The geeal ucue allowed fo he adig ub-ewok ca be fuhe divided io fou cae which will be dicued below i moe deail: Cae 1: Cae 2: Cae 3: egio Cae 4: Bi-laeal adig. Uidiecioal ade fom ome exo egio io a igle imoig egio Muli-diecioal ade fom a igle exo egio o eveal imoig Geeal muli-laeal adig ucue Tadig wihou eed fo exlici makelace defiiio Cae 1 2 ad 3 fall i hi caegoy. Bi-laeal ade ake lace bewee ai of egio. A odeed ai of egio ogehe wih a exchage oce i fi ideified R 1 Exo Imo R 2 Imo Exo R 1 R 2 =R M R 1 Figue 5.2. Cae 1: Bi-laeal ade (boh R 1 ad R 2 qualify a R M ). 207

208 ad he ade hough he exchage oce i balaced bewee hee wo egio. Whaeve amou i exoed fom egio i o egio j i imoed by egio j fom egio i (oibly wih a adjume fo aoaio loe). The baic ucue i how i Figue 5.2. Bi-laeal adig ca be fully decibed i TIMES by ecifyig he wo ai-wie coecio i oie. The caaciy ad iveme co of he exchage oce ca be decibed idividually fo boh egio. Fo Cae 2 ad 3 he geeal ucue of he ade elaiohi i how i Figue 5.4. Alo i hee cae he defiiio of he adig ucue i eay becaue he elaiohi ca be uambiguouly decibed by ai-wie oie ecificaio bewee wo egio. Tadig baed o makelace Cae 4 i coveed by he geeic ucue how i Figue 5.1. Tadig occu i hi cae bewee a lea hee egio ad ivolve boh eveal exoig egio ad eveal imoig egio. I hi ye of ade he commodiy i u o he make by each egio aiciaig i he uly ide of he make ad may be bough by ay egio aiciaig i he demad ide of he make. Thi cae i coveie fo global commodiie uch a emiio emi o cude oil whee he aoaio co fom i o j may be aoximaed by CoiCoj (ahe ha a moe accuae co uch a Cij). Whe he exac co (o loe) ae icly deede o he ai ij of adig egio i may be moe accuae o ue bilaeal ade. I geeal hee ae may diffee oibiliie fo defiig he muli-laeal ucue by uig he ai-wie oie ecificaio. I ode o comly wih he ucue allowed i TIMES he ue ha o decide which of he egio eee he makelace i.e. i choe o be he R M how i Figue 5.2. Noe ha he make egio will aiciae boh i he uly ad demad ide of he make. The TIMES model geeao auomaically ideifie hi geeal ye of adig o he bai of he oie oology defied by he ue. Theefoe he ue oly eed o defie he oible adig elaiohi bewee egio Suly egio Demad egio R S1 Exo Imo R D1 R S2 Imo Exo R D2 R S3 R M R M R D3 R Sm R D Figue 5.3. Geeal ucue of uidiecioal ade io a igle imo egio (Cae 2 o he lef) ad mulidiecioal ade fom a igle exo egio (Cae 3 o he igh). 208

209 io he oie e. If hee ae uly egio ad m demad egio he oal umbe of eie eeded i oie fo defiig all he ade oibiliie i m 2 (couig he make egio o be icluded i boh he uly ad demad egio. Alhough he make egio ha o be defied o be a iemediae ode i he ucue he model geeao will acually o ioduce ay iemediae e bewee he exo ad imo egio. The imelice level of he aded commodiy may be diffee i each egio (a well a he commodiy ame). Howeve ome aoiae commo imelice level mu be choe fo wiig he make balace equaio. Tha commo level i he level aached o he exchage oce i he make egio. I all ohe eec he make egio i o eaed i ay way diffeely fom he ohe egio aiciaig i he make. Nevehele he ue ca of coue ovide diffee daa fo he diffee egio fo examle iveme co o efficiecie fo he exchage oce ca be diffeeiaed by egio. If he e of uly ad demad egio aiciaig i he make hould acually be dijoi eve i ha cae he ue ha o chooe oe of he egio o be ued a he iemediae make egio. The imo o o exo fom he make egio ca he be wiched off by uig a IREXBND aamee if ha i coideed eceay. Remak o flexibiliy 1. Ay umbe of exchage ocee ca be defied fo decibig he oal ade elaiohi of a igle commodiy (bu ee waig 1 below). 2. The ame of aded commodiie ca be diffee i each egio aiciaig i he ade. I addiio alo he imo ad exo ame of he aded commodiie ca be diffee (bu ee waig 2 below). Thi could be ueful e.g. i he cae of eleciciy fo which i i commo o aume ha he exo commodiy i ake fom he yem afe gid ao while he imo commodiy i ioduced io he yem befoe he gid. 3. Ay umbe of commodiie ca be i geeal imoed o a egio o exoed fom a egio hough he ame oce (bu ee waig 2 below). Waig 1. Fo each exchage oce of ay aded commodiy he oal ucue of he adig ub-ewok a defied i oie mu comly wih oe of he baic ucue uoed by TIMES (Cae 1 4). If fo examle eveal bi-laeal adig elaiohi ae defied fo he ame commodiy hey hould of coue o be defied ude he ame oce bu each ude a diffee oce. 2. If he exo ad imo ame fo a make-baed commodiy (c) ae diffee i he make egio o ohe commodiie hould be imoed o he make egio hough he ame exchage oce a commodiy c. 3. The model geeao combie he adig elaiohi of a igle oce io a igle make wheeve hee i a iemediae egio bewee wo diffee egio. If howeve he iemediae exchage e hould be exlicily icluded i he model he adig ub-ewok hould be divided bewee wo diffee exchage ocee. 209

210 Examle Aume ha we wa o e u a make-baed adig whee he commodiy CRUD ca be exoed by egio A B C ad D ad ha i ca be imoed by egio C D E ad F. Fi he exchage oce ad makelace hould be defied. Fo examle we may chooe (CXPCRUD) a he makelace whee XP ha bee choe o be he ame of he exchage oce (ecall ha oce XP i declaed oly oce bu exi i all adig egio oibly wih diffee aamee). The ade oibiliie ca he be defied imly by he followig ix oie eie: SET PRC / XP /; SET TOPIRE / A.CRUD.C.CRUD.XP B.CRUD.C.CRUD.XP D.CRUD.C.CRUD.XP C.CRUD.D.CRUD.XP C.CRUD.E.CRUD.XP C.CRUD.F.CRUD.XP /; To comlee he RES defiiio eeded fo he exchage oce i addiio oly he e cacu(cu) eed be defied fo he exchage oce XP: SET PRCACTUNT / A.XP.CRUD.PJ B.XP.CRUD.PJ C.XP.CRUD.PJ D.XP.CRUD.PJ E.XP.CRUD.PJ F.XP.CRUD.PJ /; Thee defiiio ae ufficie fo eig u of he make-baed ade. Addiioally he ue ca of coue ecify vaiou ohe daa fo he exchage ocee fo examle iveme ad diibuio co ad efficiecie. TIMES SET elaed o edogeou ade oie(1c12c2): Fo bi-laeal ade uidiecioal ade io a igle deiaio egio ad mulidiecioal ade fom a igle ouce egio oie hould coai he coeodig eie fom he exoig egio() 1 o he imoig egio() 2. Fo make-baed ade oie mu coai eie fo each exoig egio o he iemediae make egio ad fom he make egio o each imoig egio. Each egio may be boh exoig ad imoig. cmake(c): Thi e ecifie he makelace() fo he commodiie ha ae aded hough make-baed ade. The makelace ae auomaically e by he model geeao fo ay ade ha ivolve a iemediae egio bewee wo diffee egio fo he ame exchage oce () ad ame commodiy (c) o if hee ae mulile deiaio 210

211 (imoig) egio fo he ame exoig egio. Howeve he ue ca alo maually ecify a makelace eve fo a bidiecioal bi-laeal exchage. Thi ca be doe maually by ecifyig oe of he wo demad egio o be he makelace fo he exoed commodiy. Iead of wo ade balace equaio oly oe make balace equaio i he geeaed. caoff(y1y2): Oveide ued o cool i wha yea (o eiod) a oce i o available. Thi e i o ecifically elaed o exchage ocee. Howeve i he cae of make-baed adig i ca be ued o wich off he eie commodiy make fo eiod ha fall wihi he age of yea give by caoff. The make will be cloed fo all commodiie exchaged hough he oce (). I i alo oible o ecify mulile eie of caoff if fo examle adig hould be oible oly bewee eleced yea. Remak I make-baed ade he exo egio aiciaig i he make coi of all hoe egio ha exo commodiy c io egio hough oce (a defied i oie). Similaly he imo egio aiciaig i he make coi of hoe egio ha imo commodiy c fom egio hough oce (a defied i oie). I addiio he make egio by ielf alway aiciae i he make boh a a imo ad exo egio. Howeve he imo/exo of commodiy (c) o/fom he make egio () ca be wiched off by uig a IREXBND aamee if eceay. Paamee IREFLO(1vc12c22): Coefficie ha eee he efficiecy of exchage fom 1 o 2 iide a ie-egioal oce whee boh egio ae ieal. Noe ha eaae IREFLO ae equied fo imo ad exo. Defaul =1 fo each oie diecio ecified. Time lice 2 efe o he egio whee he commodiy aive. Ui: oe IREFLOSUM(c1iec2io): Secial aibue o eee auxiliay coumio (io = IN owig o he commodiy eeig he oce) o oducio/ emiio (io = OUT owig o he commodiy leavig he oce) of commodiy c2 due o he IMPo / EXPo (idex ie) of he commodiy c1 i egio by a ie-egioal oce 38. I i a fixed FLOSUM wih (oe of) he cg i ha egio. Thee elae commodiie o he ame ide of he oce. 38 The idexig of auxiliay coumio flow o emiio of ie-egioal exchage ocee i illuaed i he figue below. 211

212 IREBND(1c2iel): To boud he oal imo/exo i ieal egio 1 o/fom egio 2 whee egio 2 may be ieal o exeal 39 ; c i he ame of commodiy i egio 1. Defaul oe. IREXBND(ciel): Limi o oal imo/exo of commodiy c i egio o/fom all deiaio/ouce whee may be a ieal o exeal egio (Defaul: oe IRECCVT(1c12c2) Coveio of commodiie a a of ie-egioal exchage boh ieal ad exeal. Defaul = 1 whe exchage emied. Ui: oe IRETSCVT(1122): A maix ha afom ime lice of egio 1 o egio 2 a a of ie-egioal exchage icludig boh ieal ad exeal. Defaul = 1 whe exchage emied. Ui: oe Remak: I make-baed adig he IREFLO aamee i ake io accou o he exo ide oly (eeeig he efficiecy fom he exo egio o he commo makelace). By uig hi coveio ay bi-laeal exchage ca be eeeed by a fully equivale make-baed exchage imly by chooig oe of he wo egio o be he makelace ad addig he coeodig ey o he e cmake(c). The efficiecy of he exo fom he make egio ielf o he makelace hould alo be ecified wih a IREFLO aamee whe eceay (1=2=make egio). If he ue wa o ecify efficiecy o he imo ide of a make-baed exchage hi ca be doe by uig a IREFLOSUM aamee o he imo ide. Similaly o ay ohe ai of egio he oal amou of commodiy imoed o a egio fom he commodiy make ca be coaied by he IREBND aamee by ecifyig he make egio a he exo egio. Coeodigly he oal amou of commodiy exoed fom a uly egio o he makelace ca be coaied by he IREBND aamee by ecifyig he make egio a he imo egio. Vaiable VARIRE( v c ie) Deciio: The oal amou of aded commodiy (c) imoed/exoed (ie) o/fom egio () hough oce () viage (v) i each ime eiod () Puoe: The ade vaiable faciliae ade of commodiie bewee exoig ad imoig egio Boud: The amou of commodiy imoed o a egio fom each exoig egio ca be diecly coaied by he IREBND aamee. Remak: 39 The equaio EQ(l)XBND may have a exeal egioal a egio idex (boudig he imo fom oe exeal egio o all ohe egio). 212

213 Noe ha hee i a oe-o-oe coeodece bewee he VARIRE vaiable ad he m ac how i Figue 5.1 (oe vaiable fo each uly egio ad oe vaiable fo each demad egio). I make-baed ade he VARIRE vaiable fo he make egio ill oly decibe he e imo o ad exo fom he make egio o he oal make volume. Thee i o vaiable fo he oal volume of he commodiy make i makebaed ade. The oal volume ca oly be addeed by mea of UCIRE aamee (ummig ove all imo o o exo fom he make). I make-baed ade oly he amou of commodiy imoed o a egio fom he make o exoed fom he egio o he make ca be coaied by he IREBND aamee. The imo ad exo hu cao be aibued o a ecific uly o demad egio o he ohe ide of he ade. The amou of commodiy exoed fom / imoed o a egio may alo be limied by boud ecified o gowh ae bewee eiod (dyamic UCIRE wih GROWTH aibue) a well a cumulaive limi imoed o he eouce ove he eie ime hoizo (cumulaive UCIRE). Howeve i hee cae he boud ca oly aly o he oal exo fom o imo o a egio ad cao aly o e.g. imo fom a ecific egio. Thee ae oly hee ade equaio amely a geeic ade balace equaio EQIRE ad wo boud EQ(l)IREBND ad EQ(l)XBND. The geeic balace equaio EQIRE ca be fuhe divided io wo flavo: A. Balace equaio fo bilaeal ad ohe uidiecioal ade io a igle deiaio egio (Cae 1 ad 2). B. Balace equaio fo mulidiecioal ade fom igle exo egio ad mulilaeal make-baed ade (Cae 3 ad 4) Equaio EQIRE Idice: Tye: = egio () yea () oce () commodiy (c) imelice () Relaed vaiable: VARIRE Relaed equaio: EQ(l)IREBND; EQ(l)XBND; EQ(l)COMBAL; EQACTFLO Puoe: Thi equaio defie he balace bewee he imo of each aded commodiy (c) io egio () ad he coeodig exo ough each exchage oce () i each ime eiod () ad imelice () of he oce. Ui: Ui of commodiy aded. Nomally PJ fo eegy Mo o ko fo maeial o emiio. 213

214 Remak: Flow io idividual egio may be limied by he IREBND ad IREXBND aamee. The equaio ha wo flavo: The fi oe i fo bilaeal ad uidiecioal ade wih a igle deiaio egio ad he ecod i fo make-baed ade ad mulidiecioal ade fom a igle ouce egio Cae A. Bi-laeal o mulilaeal uidiecioal ade o a igle imo egio EQ IRE Equaio c { c ( cva )} ceqie c c : v viyv VAR IRE v c IMP = Thi i he efficiecy of oce fo he ai of egio ad commodiy c. ( 2 c2) oie2 c2c v viy2v 2 IRE TSCVT 2 2 cvaf2c2 ee2 2 i he imelice i egio 2 ha coeod o imelice i egio. The coveio able IRETSCVT coai he coveio coefficie. The imelice () of he exo flow i egio 2 ae decibed by he e cvaf. VAR IRE 2 v c IRE TSCVT 2 RTCS TSFR 2 2 EXP 2 c 2 Coefficie fo maig imelice of VARIRE wih he imelice 2. See EQ(l)COMBAL fo he defiiio of RTCSTSFR. IRE FLO IRE CCVT 2 v c2 c 2 c2 c Thi cove he ui. Remak: The IRETSCVT coveio coefficie ae i acice ovided oly fo ome ai of maed imelice bewee 2 ad. Theefoe he imelice coveio i acually doe i wo age: Fi he imelice of he VARIRE vaiable ae coveed o he maed imelice ad he he maed imelice i 2 o hoe i a follow: The maig coefficie IRETSCVT do o have o be ovided by he ue if he imelice defiiio i boh egio ae ideical. If he imelice defiiio ae diffee he ue ovide he maig coefficie IRETSCVT o cove he imelice 2 i egio 2 o he imelice i egio. Sice he imelice level of 2 maybe diffee o he imelice 214

215 level of he exchage vaiable i egio 2 he aamee RTCSTSFR i ued o mach ad 2. Noe ha he equaio i geeaed fo each eiod i oly o fo each viage i viy a i he oigial code. Thi i becaue cvi i egio-ecific. If cvi i e o YES i oe egio ad o NO i aohe ha would ceae eiou yc oblem if he equaio wee geeaed fo each viage i viy. I addiio diffeece i e.g. NCAPPASTI NCAPTLIFE ad NCAPAF could ceae yc oblem eve if cvi would be e o YES i all egio Cae B. Mulidiecioal ad make-baed ade bewee egio. EQ IRE c Equaio: { c ( cva )} c ceqiec : ( 2 c1 c2) v viy2v 2 IRE TSCVT 2 2 cvaf2c2 ( oie c12c2 oiec1c cmake ee c1 ) 2 VAR IRE2 v c IRE CCVT 2 c RTCS TSFR 2 2 IMP 2 c1 2 c 2 IRE CCVT IRE TSCVT c1 c 2 2 = ( 2 c2) oie2 c2c v viy2v 2 IRE TSCVT 2 2 cvaf2c2 ee2 VAR IRE2 v IRE TSCVT RTCS TSFR c2 EXP c 2 IRE FLO IRE CCVT 2 v c2 c 2 c2 c Remak: The IRETSCVT coveio coefficie ae i acice ovided oly fo ome ai of maed imelice bewee 2 ad. Theefoe he imelice coveio i acually doe i wo age: Fi he imelice of he VARIRE vaiable ae coveed o he maed imelice ad he he maed imelice i 2 o hoe i. I he cae of make-baed adig caoff ca be ued o wich off he eie commodiy make fo eiod ha fall wihi a age of yea. I i alo oible o ecify mulile eie of caoff if fo examle adig hould be oible oly bewee eleced yea. The oie ey bewee he exo ad imo commodiy i he make egio ielf i auomaically defied by he TIMES model geeao whe eceay i.e. hee i o eed o ovide i by he ue. 215

216 Equaio: EQ(l)IREBND Idice: egio () yea () commodiy (c) imelice () egio2 (all) imo/exo (ie) Tye: Ay ye a deemied by he boud idex bd of IREBND: l = G fo bd = LO (lowe boud) yield. l = E fo bd = FX (fixed boud) yield =. l = L fo bd = UP (ue boud) yield. Relaed vaiable: VARIRE Relaed equaio: EQIRE; EQ(l)XBND; EQ(l)COMBAL Deciio: Se a boud fo he amou of commodiy (c) imoed/exoed (ie) o/fom egio () fom/o aohe egio (all) i ime eiod () ad imelice (). Puoe: The equaio i oioal ad ca be ued o e a boud fo a ai-wie ieegioal exchage. The geeaio of he equaio i iggeed by he ue-ecified aamee IREBND. Ui: Ui of commodiy aded. Nomally PJ fo eegy Mo o ko fo maeial o emiio. Tye: Se accodig o he l idex i IREBND. Remak: Toal ade flow io/fom idividual egio may be limied by uig he IREXBND aamee. Ieeaio of he eul: Pimal: If he imal value equal he boud aamee he coai i bidig. Dual: The dual value decibe fo a lowe/ue boud he co iceae/deceae i he objecive fucio if he boud i iceaed by oe ui. I may alo be ieeed a ubidy/ax eeded o each he give boud value. 216

217 217 Equaio: Cae A. Imo fom a exeal egio o make egio { } ie all c IRE TOP c VINTYR RTP v ex c v ie all c ie c c ie all c BND IRE BELOW RS if FR FR MAP TS if IRE VAR BND IRE IE RPC COMTS RCS ie all c IREBND l EQ c c all v ) 2: ( : 2 2 ; ; ) 2 ( 2 2) ( ) ( 2) ( 2 1 : ) ) : ( ( : ) ( 2 = Cae B. Imo fom a ieal o-make egio { } ie all c all c c all c c v all VAR RPCS IRE TOP c VINTYR RTP v ex c v all ie all c ie c c ie all c BND IRE BELOW RS if FR FR MAP TS if TSCVT IRE CCVT IRE FLO IRE IRE VAR BND IRE IE RPC COMTS RCS ie all c IREBND l EQ c c c all v all ) 2 ( ; ; ) 1 ( 1 1) ( ) ( 1) ( 1 1 : ) ) ( ( : ) ( 1 2 =

218 Cae C. Exo fom a o-make egio o a ieal o exeal egio c all ie : ( RCS COMTS c EQ( l) IREBND c all ie : ( : RPC IE c ie) IRE BND c all ie) : ( c2: TOP IRE c all c 2 ) v RTP VINTYR v 2 VAR IRE v c 2 ex { ; = ; } IRE BND ie c all 1 if 2 TS MAP( 2) FR( ) if 2 RS BELOW ( 2 ) FR( 2) Cae D. Exo fom a make egio o a ieal egio EQ( l) IREBND c all ie c all ie : ( RCS COMTS ( : RPC IE c ie) IRE BND c c all ie : ) ( c2 ) TOP IRE c all c 2 v RTP VINTYRall v 2 VAR IRE all v c2 2 ex IRE CCVT all c2 c IRE TSCVT all 2 1 if 2 TS MAP( 2) FR( ) if 2 RS BELOW ( 2 ) FR( 2) { ; = ; } IRE BND c all ie Remak: The IRETSCVT coveio coefficie ae i acice ovided oly fo ome ai of maed imelice bewee all ad. Theefoe he imelice coveio i acually doe i wo age: Fi he imelice of he VARIRE vaiable ae coveed o he maed imelice ad he he maed imelice i all o hoe i. 218

219 Equaio: EQ(l)XBND Idice: egio () yea () commodiy (c) imelice () im/ex (ie) Tye: Ay ye a deemied by he boud idex bd of IREXBND: l = G fo bd = LO (lowe boud) yield. l = E fo bd = FX (fixed boud) yield =. l = L fo bd = UP (ue boud) yield. Relaed vaiable: VARIRE Relaed equaio: EQ(l)IRE; EQ(l)IREBND; EQ(l)COMBAL Deciio: Boud o he oal amou of aded commodiy (c) imoed/exoed (ie) o/fom egio (all) i a eiod () ad imelice (). Puoe: Ui: Remak: aamee. Thi equaio boud ie-egioal o exogeou exchage i a aicula egio aco all ohe egio. Ui of commodiy aded. Nomally PJ fo eegy Mo o ko fo maeial o emiio. Flow io/fom idividual egio may be limied by he IREBND Ieeaio of he eul: Pimal: If he imal value equal he boud aamee he coai i bidig. Dual: The dual value decibe fo a lowe/ue boud he co iceae/deceae i he objecive fucio if he boud i iceaed by oe ui. I may alo be ieeed a ubidy/ax eeded o each he give boud value. 219

220 Equaio: EQ( l) XBND all cie IRE XBND all cie bd { = ; ; } ( cvaf ee ) cie 2 v viy all cie all i a ieal all c2 IRE XBND all 2 all cie bd all i a exeal allv VAR IREall v c 2 ie 1 if 2 maall2 G YRFR( ) if 2 below G YRFR( 2) all2 cie ( 2) ( ee cvaf IRE TSCVT ) v viy comimex 2 com 2 all v VAR IRE v com 2 imex IRE CCVT IRE TSCVT( all ) com all c { = ; ; } IRE XBNDall cie bd All egio wih imex ie Havig imo/exo fom/o all 220

221 Equaio: EQ(l)INSHR EQ(l)OUTSHR Idice: egio (); yea (); oce (); commodiy (c); commodiy gou (cg); ime-lice () Tye: Ay ye a deemied by he boud idex bd of FLOSHAR: l = G fo bd = LO (lowe boud) yield. l = E fo bd = FX (fixed boud) yield =. l = L fo bd = UP (ue boud) yield. Relaed vaiable: VARFLO; VARACT Relaed equaio: EQ(l)COMBAL; EQPTRANS; EQACTFLO Puoe: A make/oduc allocaio coai equaio i geeaed fo each oce () fo each ime eiod () ad each ime-lice () i each egio (if deied). I eue ha he hae of a iflow/ouflow of a commodiy (c) i lowe/highe/equal a ceai eceage of he oal coumio/oducio of hi oce fo a ecified commodiy gou (cg). Qualiy Cool Check: c cg c cg FLO SHAR FLO SHAR v c cg LO v c cg UP ( FLO SHAR ( FLO SHAR v c cg LO v c cg UP l = " ") 1 l = " ") 1 c cg c cg FLO SHAR FLO SHAR v c cg FX c cg FX FLO SHAR > 0 Remak: Exchagig o(c IN )=Iu v. o(c OUT ) = Ouu i hi equaio yield EQ(l)OUTSHR ice c i oly membe of oe cg. The eiod idex of he aamee FLOSHAR i elaed o he viage eiod (v) of he oce i.e. if he oce i viaged (cvi) a coai will be geeaed fo each eiod () he iallaio made i he viage eiod (v) ill exi (hee eiod ai ae ieally ovided by he e viy). Ieeaio of he eul: Pimal: If he imal value i zeo he coai i bidig. If he imal value i oiive fo a lowe FLOSHAR boud o egaive fo a ue boud he coai i o-bidig. Dual: The dual value decibe fo a lowe boud he ubidy eeded o guaaee ha he flow i a he give lowe boud. The ubidy i eeded ice fo a ouu 221

222 Equaio: flow he hadow ice of he oduced commodiy i oo low o cove he oducio co of he flow vaiable (fo a iu flow he ooie i ue he commodiy i oo exeive o be ued i he oce). The value of he ubidy which he flow eceive i equal o (1-FLOSHAR)*(dual vaiable). Thi ubidy ha o be aid by he ohe flow fomig he deomiao i FLOSHAR coai hu he co fo hee flow ae iceaed by he amou FLOSHAR*(dual vaiable). I a imila way a ue boud FLOSHAR ca be ieeed a a ax beig added o he co of a flow. EQ( l) IN / OUTSHR FLO SHAR { = ; ; } v c cg v c cg bd ( 1 ( c cg) com cg 2 cvafcom2 ( viy ) ) FLO SHAR v v c cg bd o c IN / OUT [ VAR FLO v com 2 RTCS TSFR com 2 ] 2 cvafc2 VAR FLO v c 2 RTCS TSFR c 2 See EQ(l)COMBAL fo he defiiio of RTCSTSFR. The e 1 coai he imelice of he imelice level which i defied o be he fie imelice level of he oce (cl)ad all commodiie (coml) liked o he oce. 222

223 Equaio: EQPEAK Tye: Relaed vaiable: VARACT; VARNCAP; VARFLO Relaed equaio: EQ(l)COMBAL; EQ(l)CAPACT Puoe: The commodiy eakig coai eue ha he caaciy ialled i eough o mee he highe demad i ay imelice akig io coideaio boh adjume o he aveage demad acked by he model ad a eeve magi equiig exce caaciy o be ialled. Remak: I he deciio below efeece i made o exiig comoe of he oducio ad coumio a of he EQ(l)COMBAL commodiy balace equaio whee a eak coibuio/co-icide faco i alied o he em. Thee faco ae oce deede ad a uch ae acually alied wihi he efeeced exeio duig he ummig oeaio. COMBALu efe o all he comoe of oducio ohe ha hoe elaed o caaciy a eleae fom he caaciy ae o o be ake io coideaio fo aifyig he eakig coai. New e ad aamee: comeak(cg) i a flag ha a eakig coai i deied. I i oioal if comk(cg) i ovided comk(cg) ae he exlici ime lice fo which eakig coai ae o be couced. A o-oimizaio QC check will be doe o eue ha he imelice wih highe demad i i aid li. Defaul i all com(c). COMPKRSV(c) i he eak eeve magi. Defaul 0. COMPKFLX(c) i he diffeece (flucuaio) bewee he aveage calculaed demad ad he acual hae of he eak. Defaul 0 FLOPKCOI(c) i a faco ha emi iceaig he aveage demad calculaed by he model o hadle he iuaio whee eak uage i yically highe due o coicideal uage a eak mome (e.g. ai codiio). Defaul 1 fo each oce coumig c. Ue ca eve a oce fom coibuig o he calculaio of he eak by ecifyig = 0 NCAPPKCNT() i he amou of caaciy (aciviy) o coibue o he eak. Defaul 1 fo each oce oducig commodiy c. Ue ca eve a oce fom coibuig o he eak by ecifyig = EPS eak(c) ae hoe ocee which coibue o ceae/aifyig he eak. Deived by he eoceo fom all hoe oce coumig/oducig commodiy c wih o-zeo FLOPKCOI/NCAPPKCNT. 223

224 ckaf() wich o e NCAPPKCNT=NCAPAF/1 a defaul. Defaul: o Ieeaio of he eul: Pimal: Dual: The dual value of he eakig equaio decibe he emium coume have o ay i addiio o he commodiy ice (dual vaiable of EQ(l)COMBAL) duig he eak imelice. The emium equal (1COMPKFLX)*FLOPKCOI*RTCSTSFR*(dual vaiable). Equaio: EQ PEAK cg comeak cg comk cg 1/(1 COM PKRSV c ) COM IE c c cg ( ocout ciecimp ) ( NOT cko ) if gc NCAP PKCNT v COEF CPT v if v cyv PRC CAPACT PRC ACTFLO if ciecimp CAL IRE v c IMP v viyv ele CAL FLOFLO v c OUT NCAP PKCNT v v viyv CAL IRE v c IMP v viyv ( NOT cie ) cimp G YRFR ( VAR NCAP v NCAP PASTI v ) v c 224

225 225 ( ) ( ) = = = = Edcae Ohewie u l ELAST VAR lo l ELAST VAR FR COM PROJ COM DM COM Cae Cae YRFR G PASTYEAR v PASTI NCAP MILESTONYR v NCAP VAR ICOM COEF YRFR G PASTYEAR v PASTI NCAP MILESTONYR v NCAP VAR CPT COEF COM NCAP PKCOI FLO IRE CAL PKCOI FLO FLOFLO CAL PKFLX COM l l c v IN c v STEP COM j l j STEP COM j l j c c c NOT ICOM COEF if v v v c v COM NCAP if v v v v IN c v v c EXP c v v c OUT c v cg c c 0 ) ( ) ( ) (1 1 1 ) ( ) ( ) ( cexp cin vc v vc cexp v v cko cie o ccaflo cy ccaflo cie viy viy

226 Equaio: EQPTRANS Idice: egio (); yea (y); oce (); commodiy gou1 (cg1); commodiy gou2 (cg2) ime-lice () Tye: "=" Relaed vaiable: VARFLO; VARACT Relaed equaio: EQ(l)COMBAL; EQ(l)INSHR; EQ(l)OUTSHR; EQACTFLO Puoe: Allow ecifyig a equaliy elaiohi bewee ceai iu ad ceai ouu of a oce e.g. efficiecie a he flow level o he modelig of emiio ha ae ied o he iu. I i geeaed fo each oce fo each ime eiod ad each ime-lice i each egio. Remak: Ieal e 1(): The fie of (e of ime lice of he mo fiely divided membe of he he commodiie wihi he hadow imay gou (commodiie beig o a of imay commodiy gou ad ae o he oce ie ooie o he imay commodiy gou) ad he oce imelice level (cl)). The flow vaiable of he commodiie wihi he imay commodiy gou ae modelled o he oce level (cl). All ohe flow vaiable o he imelice level of 1. The ieal aamee COEFPTRAN(vcg1ccg2) i he coefficie of he flow vaiable of commodiy c belogig o he commodiy gou cg2. While FLOFUNC(vcg1cg2) eablihe a elaiohi bewee he wo commodiy gou cg1 ad cg2 FLOSUM(vcg1ccg2) ca be i addiio ecified a mulilie fo he flow vaiable of c i cg2. COEFPTRAN i deived fom he ue ecified FLOFUNC ad FLOSUM aamee baed o he followig ule: o If FLOFUNC i give bewee cg1 ad cg2 bu o FLOSUM fo he commodiie c i cg2 i i aumed ha he FLOSUM ae 1. o If FLOSUM i ecified bu o FLOFUNC he miig FLOFUNC i e o 1. o If FLOSUM(vcg1ccg2) ad FLOFUNC(vcg2cg1) ae ecified he eciocal of FLOFUNC i ake o calculae COEFPTRAN. FLOSUM ca oly be ecified fo he flow wihi oe commodiy gou cg1 o cg2 of EQPTRANS bewee hee wo commodiy gou bu o fo boh commodiy gou a he ame ime. By ecifyig a SHAPE cuve hough he aamee FLOFUNCX(vcg1cg2) he efficiecie FLOFUNC ad FLOSUM ca be decibed a fucio of he age of he iallaio. The ieal aamee RTPFFCX coai he aveage SHAPE mulilie fo he eleva yea i a eiod (hoe yea i which he ialled caaciy exi). 226

227 Ieeaio of he eul: Pimal: The imal value of he afomaio i uually zeo. Dual: Due o he flexibiliy of he afomaio equaio he ieeaio of i dual value deed o he ecific cae. Fo a imle cae a oce wih oe iu flow c1 ad oe ouu flow c2 beig liked by a efficiecy FLOFUNC(c1c2) he dual vaiable which i beig defied a he co chage whe he RHS i iceaed by oe ui ca be ieeed a co chage whe he efficiecy of he oce i iceaed by 1/VARFLO(vc1): VAR FLO. v c2 VAR FLO VAR FLO v c2 FLO FUNC v c2 FLO FUNC FLO FUNC v c1 c2 1 VAR FLO v c1 c2 v c1 c2 v c1 VAR FLO VAR FLO v c1 VAR FLO v c1 v c1 = 1 1 = 0 = 0 Equaio: EQ PTRANS v cg1 cg 2 1 ( v ) 2 ma ( flo viy ) 21 FLO SUM FLO FUNC v cg1 c cg 2 2 cg1 cg NOT 1 ( FLO SUM FLO SUM ) cg1 c cg 2 2 cg 2 c cg1 2 c cg 2 VAR FLO ( ma cvaf ) 1 c v c RTCS TSFR c 1 = c cg1 ( COEF PTRAN v cg1 c cg 2 VAR FLO v c RTCS TSFR c 1 ) ( ma cvaf ) 1 c ( 1 RTP FFCX ( if cvi ) v cg1 cg 2 227

228 COEF PTRAN = c 1 FLO FUNC v cg1 c cg 2 ( ) if ma ( if below ) FLO FUNC v cg 2 cg1 cvac G YRFR G YRFR v cg1 cg 2 c ( if FLO SUM ) v cg1 c cg 2 if FLO FUNC FLO FUNC v cg1 cg 2 v cg 2 cg1 ( 1 ( if NOT FLO SUM ) FLO SUM ) v cg1 c cg 2 v cg1 c cg 2 Calculaio of SHAPE aamee RTPFFCX Cae A: Lifeime miu coucio ime i loge ha he coucio eiod PRC YMIN v = Bv NCAP ILED v PRC YMAX PRC YMIN NCAP TLIFE 1 RTP FFCX = v viyv v = v v y v cg1 c cg 2 FLO FUNCX v cg1 cg 2 SHAPE v ( eiodyy [ y MAX ( B( ) PRC YMAX v )]) MAX 1 MIN ( E( ) PRC YMAX ( FLO FUNCX 1 MIN ( y PRC YMAX ) PRC YMIN ) cg1 cg 2 [ ) MAX ( B( ) PRC YMIN ) 1] v v v v 1 Cae B: Lifeime miu coucio ime i hoe ha he coucio eiod => Iveme i eeaed i coucio eiod PRC YMAX v NCAP TLIFE v RTP FFCX v cg = SHAPE v viy v = 1 c cg 2 1 FLO FUNCX ( FLO FUNCX PRC YMAX ) v cg1 cg 2 PRC YMAX v cg1 cg 2 v v 1 228

229 Equaio: EQSTGTSS/IPS Idice: egio (); yea (y); oce (); ime-lice () Tye: "=" Relaed vaiable: VARFLO; VARACT Relaed equaio: EQ(l)COMBAL; EQ(l)CAPACT; EQ(l)STGIN/OUT Puoe The model allow wo kid of oage: ie-eiod oage (IPS) ad oage aco ime-lice (o ime-lice oage TSS). A ecial ye of he TSS oage i a igh-oage device which may have a iu commodiy beig diffee fom i ouu commodiy. The iu ad ouu commodiy of a igh-oage device ae beig give by he oology e o. Soage ocee ae ecial a hey have he ame commodiy a iu ad ouu. Alo all ohe ocee afom eegy wihi hei ime-lice ad ime eiod. Sice oology (wih he exceio of igh-oage device) doe o deemie i/ou diffee vaiable have o be ued fo hi uoe. Similaly ice he afomaio i ecial EQPTRANS i elaced by ew equaio fo he wo ye of oage. Se: cgi(c): The e of ie-eiod oage ocee. They ae foced o oeae aually. cg(c): The e of ime-lice oage ocee. A oage oce ca oeae oly a oe aicula ime lice level. c(): The e coai he allowed chagig imelice fo a igh-oage device. Vaiable: VARSIN(vc) - he aveage i flow o a oce buil i eiod v duig ime-lice duig each yea of eiod. Thi vaiable would aea o he coumio ide of he balace equaio wihou ay coefficie. VARSOUT(vc) - he aveage ou flow fom a oce buil i eiod v duig ime-lice duig each yea of eiod. Thi vaiable would aea o he uly ide of he balace equaio mulilied by STGEFF ad COMIE. VARACT(v) - he eegy oed i a oage oce a he begiig of ime-lice (fo a imelice oage)o ed of eiod (fo a ieeiod oage). Noe ha hi i a ecial ieeaio of aciviy o eee oage level. Theefoe EQACTFLO will o be geeaed fo oage ocee. I EQSTGIPS oly aual flow ae allowed; he imelice idex i e o ANNUAL i hi cae. 229

230 Equaio: EQSTGTSS() - afom iu o ouu fo he imelice oage ocee. EQSTGIPS() - afom iu o ouu fo he ieeiod oage ocee. Paamee: STGLOSS(v) - aual eegy lo fom a oage echology e ui of (aveage) eegy oed. STGCHRG() - exogeou chagig of a oage echology. Fo imelice oage hi aamee ca be ecified fo each eiod while fo ieeiod oage hi aamee ca oly be ecified fo he fi eiod o decibe he iiial coe of he oage EQSRGTSS: Soage bewee imelice (icludig igh-oage device): EQ STGTSS v viy v VAR ACT ( ) v ( cg cma ) PRC ACTFLO c v cg NST c ( cg i he imay commodiy gou) = v viy v VAR ACT v 1 PRC ACTFLO if i a igh - oage device : 1 VAR SIN v c if i o a igh - oage device VAR SIN v c 1 VAR SOUT VAR ACT v VAR ACT 2 PRC ACTFLO v cg v cg ( cg i he imay commodiy gou) ( if 1 c o ) VAR SOUT ( if o ) v c 1 v 1 1 cin ( cg i he imay commodiy gou) STG LOSS v com 1 v G YRFR cout STG CHRG 1 230

231 EQSTGIPS: Soage bewee eiod ( ) ( ) 1) ) ( ( ) (1 ) ( ) (1 he imay commodiy gou cg i he imay commodiy gou cg i ) ( 0.5) ) ( ( ) ( 1 = = wheord CHRG STG LOSS STG SOUT VAR SIN VAR LOSS STG ACTFLO PRC ACT VAR ACTFLO PRC ACT VAR STGIPS EQ ANNUAL v y y E ANNUAL v ANNUAL c v ANNUAL c v v D ANNUAL v c v ANNUAL v v c v ANNUAL v v y 1 v v viy eiody viy viy c cgi

232 Equaio: EQ(l)STGIN / EQ(l)STGOUT Idice: egio () eiod () oce () commodiy (c) imelice () Tye: Ay ye a deemied by he boud idex bd of STGIN/OUTBND: l = G fo bd = LO (lowe boud) yield. l = E fo bd = FX (fixed boud) yield =. l = L fo bd = UP (ue boud) yield. Relaed vaiable: VARSIN; VARSOUT Relaed equaio: EQSTGTSS; EQSTGIPS Puoe: Boud o he iu/ouu flow of a oage oce of commodiy (c) fo a aicula oce () i eiod () ad imelice (). Remak: The coai boud he flow i a ecific eiod () ieecively of he viage yea of he oce caaciy. The coai i geeaed if oe of he followig codiio i ue: o Poce () i viaged o o he imelice eoluio of he flow vaiable (VARSIN/OUT) ae below he imelice () of he boud aamee. I he ohe cae he boud ca be diecly alied o he flow vaiable (VARSIN/SOUT) o ha o exa equaio i eeded. The imelice level () of he boud mu be a o highe ha he imelice level a which he oage oeae. Ieeaio of he eul: Pimal: If he imal value equal he boud aamee he coai i bidig. Dual: The dual value decibe fo a lowe/ue boud he co iceae/deceae i he objecive fucio if he boud i iceaed by oe ui. I may alo be ieeed a ubidy/ax eeded o each he give boud value. Equaio: EQ( l) STGIN / OUT c ( c) c STGIN / OUT BND ( cvi ( NOT c ) c c bd c ( c ma ) v viyv ( / / = ) VAR SIN / SOUT STGIN / OUT BND v c c bd All imelice a o above he imelice level of he oce (cl). whee he equaio ig i idicaed by equaio idex l baed o he boud ye bd. 232

233 Ue Coai Idexe: egio () ime eiod () ime lice () ue coai (uc) Tye: Ay ye a deemied by he boud idex bd of UC RHS( R)( T )( ) ( ) uc ( )( ) bd : l = G fo bd = LO (lowe boud) yield. l = E fo bd = FX (fixed boud) yield =. l = L fo bd = UP (ue boud) yield. Relaed vaiable: VARACT; VARCAP; VARFLO; VARNCAP; VARCOMPRD; VARCOMCON Relaed equaio: EQ(l)COMBAL; EQ(l)CPT Puoe: The ue coai i TIMES ovide a modele wih a flexible famewok o add cae-udy ecific coai o he adad equaio e embedded i TIMES. Wih he hel of he ue coai viually ay oible liea elaiohi bewee vaiable i TIMES ca be fomulaed. Examle of ue coai ae quoa fo eewable i eleciciy geeaio o imay eegy coumio GHG educio age abolue boud o he miimum amou of eleciciy geeaed by vaiou bioma echologie ec. Thee ye of ue coai ca be diiguihed: LHS (lef had ide) ue coai Dyamic ue coai ad Gowh coai. I he followig hee ubecio he diffee ye of ue coai ae holy eeed. Thei mahemaical fomulaio ae he eeed i a ew ecio. LHS ue coai The o-called LHS ue coai have he followig mai ucue: EQ( l) UC ( R)( T )( S) ( ) uc ( )( ) UC RHS( R)( T )( S) ( ) uc ( )( ) bd ( uceachuc ) ( uceach ) ( uceach ) uc uc ucum uc ucumuc ucum uc LHS { = / / } UC RHS( R)( T )( S) ( ) uc ( )( ) bd 233

234 To ideify he ue coai he modelle ha o give i a uique ame uc. The LHS exeio LHS coi of he um of vaiou TIMES vaiable (VARACT VARFLO VARCOMPRD VARCOMNET VARNCAP VARCAP) mulilied by coeodig coefficie (UCACT UCFLO UCCOMPRD UCCOMCON UCNCAP UCCAP). The coefficie ae iu daa give by he modelle ad eve hu alo a a idicao of which vaiable ae beig comoe of he ue coai. Wih eec o egio ime eiod ad imelice he ue coai i eihe ecified fo ecific egio eiod o imelice o he exeio wihi he ue coai i ummed ove ube of egio eiod ad imelice. I he fi cae he egio eiod o imelice fo which he ue coai hould be geeaed ae give by he e uceach uceach o uceach while i he lae cae ummaio e ae ecified by he e ucum ucum ad ucum. The coeodig e ucxeach/um ae excluive o ha fo examle if uceach ha bee ecified he e ucum cao be ecified ad vice vea. By chooig ucxeach/um alo he ame ad he idex domai of he ue coai ae ecified e.g. if uceach uceach ad ucum ae give he ue coai ha he ame ad idex domai EQ ( l) UCRT uc. I i geeaed fo each egio ad eiod ecified by uceach ad uceach eecively ad i ummig wihi he ue coai ove he imelice give i uceach. The ame of he RHS coai deed i he ame way o he choice of ucxeach/um. I he eviou examle he RHS coa ha he ame ad idex domai UC RHSRT uc bd. The kowledge of hee amig ule i imoa ice he modelle ha o give he coec RHS aamee ame deedig o he choice of ucxeach/um whe defiig a ue coai. Sice fo each of he hee dimeio (egio eiod imelice) wo oio (EACH o SUM) exi hi would eul i 8 oible combiaio of ue coai equaio (Figue 5.6). Howeve he combiaio EQ(l)UCS ad EQ(l)UCRS which would lead o a coai beig geeaed fo ecific imelice while ummig ove ime eiod a he ame ime have bee coideed uealiic o ha 6 vaia emai. I hould be oed ha he e uceach/um uceach/um ad uceach/um ca coai a abiay combiaio of eleme e.g. he eiod ecified i uceach/um do o have o be coecuive. 234

235 Ue coai uc Each Regio Summig ove egio Each Peiod Summig ove eiod Each Peiod Summig ove eiod EQlUCRTS EQlUCRT EQlUCRS EQlUCR EQlUCTS EQlUCT EQlUCS EQlUC Each imelice Summig ove imelice Each imelice Summig ove imelice Each imelice Summig ove imelice Each imelice Summig ove imelice Figue 5.6: The allowed combiaio of egio eiod ad imelice fo ue coai. The RHS (igh had ide) of hi caegoy of ue coai coi of a coa UC RHS( R)( T )( S )( ) uc ( )( ) bd which i ovided by he modelle. The RHS coa alo defie he equaio ye of he ue coai. If he RHS coa ha he idex FX he ue coai i geeaed a ic equaliy (=). If he RHS idex i LO (eecively UP) he coai ha (eecively ) iequaliy ig. I hould be oed ha a RHS ue coai i oly geeaed whe a RHS coa i ecified (hi feaue may be ued o eaily u-o/off ue coai bewee diffee ceaio). I addiio o he coefficie UCACT UCFLO ec. alo ome model iu aibue may be ued a coefficie fo he vaiable i a ue coai. The model aibue beig ued a coefficie i a ue coai i ecified by he e UC ATTR uc LHS VAR ATTR wih he idicao VAR fo he vaiable (ACT FLO NCAP CAP) ad he idex ATTR eeeig he aibue beig ued (ACTBND FLOCOST FLODELIV FLOTAX FLOSUB NCAPCOST NCAPISUB NCAPITAX CAPBND). 235

236 Iead of defiig diffee equaliy ye of ue coai deedig o he boud RHS R T S a aleaive fomulaio ca be ued i ye of UC ( )( )( )( ) uc ( )( ) bd TIMES. I hi fomulaio a vaiable UC( R)( T )( S )( ) uc ( )( ) VAR i ceaed ha i e equal o he LHS exeio. The RHS boud ae he alied o hee vaiable. EQE UC ( R)( T )( S ) ( ) uc ( )( ) UC RHS( R)( T )( S )( ) uc ( )( ) bd ( uceachuc ) ( uceach ) ( uceach ) uc uc uc um uc uc um uc uc um uc LHS = VAR UC ( R)( T )( S ) ( ) uc ( )( ) VAR UC VAR UC VAR UC ( R)( T )( S ). LO( ) uc ( )( ) = UC RHS( R)( T )( S )( ) uc ( )( ) LO ( R)( T )( S ). UP( ) uc ( )( ) = UC RHS( R)( T )( S )( ) uc ( )( ) UP ( R)( T )( S ). FX ( ) uc ( )( ) = UC RHS( R)( T )( S )( ) ( )( ) uc FX The aleaive fomulaio i ceaed whe he dolla cool aamee VARUC (ee Pa III fo he ue of dolla cool aamee) i e o YES by he modelle while i he defaul cae he fi fomulaio i ued. 236

237 EQ( l) UC Dyamic ue coai Dyamic ue coai eablih a elaiohi bewee wo coecuive eiod. The LHS exeio LHS i geeaed fo eiod wheea he RHS exeio em RHS 1 coeod o he eiod 1. ( R) SU ( S) ( ) uc ( ) UC RHS( R) T ( S )( ) uc ( ) bd ( uceachuc ) ( ucucc ) ( uceach ) uc uc uc um uc uc um uc LHS { = / / } RHS 1 UC RHS( R) T ( S ) uc bd uc um uc uc um uc ( ) ( ) To build a dyamic ue coai bewee he eiod ad 1 he modelle ideifie he deied e of ime eiod ha will be ued a fi eiod i he ai ( 1). Thi e i amed ucucc (oe ha he e ucum ad uceach ae o ued i he coex of dyamic ue coai ad ae eeved fo he LHS ue coai decibed i he eviou ecio). Oly fou combiaio wih eec o he egio ad imelice domai ae oible: EQ(l)UCSU: dyamic ue coai ummig ove ucum ad ove ucum EQ(l)UCRSU: dyamic ue coai beig geeaed fo each egio uceach ad ummig ove ucum EQ(l)UCRSUS: dyamic ue coai beig geeaed fo each egio uceach ad imelice uceach ad EQ(l)UCSUS: dyamic ue coai ummig ove ucum ad beig geeaed fo each imelice i e uceach. The coefficie UCACT UCFLO UCIRE UCCOMCON UCCOMPRD UCNCAP ad UCCAP have a idex SIDE which ca be eihe LHS o RHS o ideify o which ide of he ue coai he coeodig vaiable hould aea. The LHS idex coeod alway o he eiod while he RHS idex i elaed o he 1 em. A fo LHS ue coai eig he dolla cool aamee VARUC o YES yield a ic equaliy ye of dyamic ue coai (EQEUCSU EQEUCRSU EQEUCRSUS EQEUCSUS) wih he RHS coa elaced by a ue coai vaiable (VARUCSU VARUCRSU VARUCRSUS VARUCSUS). The boud give by he RHS coa i he alied o he ue coai vaiable. 237

238 Gowh coai Gowh (o decay) coai ae a ecial ye of dyamic coai. A gowh coai may fo examle exe ha he caaciy iceae bewee wo eiod i limied by a aual gowh ae. So gowh coai elae vaiable i oe eiod o he oe i he eviou o followig eiod a i dyamic coai decibed i he eviou ecio. I gowh coai howeve i addiio ome of he vaiable coefficie UCACT UCFLO UCIRE UCCOMCON UCCOMPRD UCNCAP UCCAP ca eee aual gowh (o decay) ae 40 by ecifyig he e UC ATTR uc LHS VAR ATTR wih he idex ATTR beig e o GROWTH. Thi will caue he coefficie of he coeodig vaiable beig ieeed a a aual gowh ae. If fo examle he iu ifomaio UC ATTR REG 1 G 1 LHS CAP GROWTH i give fo he ue coai G1 he coefficie UC CAP G 1 LHS REG1 LHS P of he caaciy vaiable of echology will be ieeed a aual gowh ae ad he fial coefficie of he vaiable VARCAP i he ue coai will be calculaed i he followig way: M ( 1) M ( ) ( UC ) CAP G 1 LHS REG1 LHS T P. Wih he hel of he iu e UCATTR gowh coefficie ca be defied fo vaiable i LHS exeio (a i he examle) o fo vaiable i RHS exeio. If a gowh ae i defied fo vaiable o he LHS he exoe i M(1)-M() wheea fo RHS vaiable he exoe i equal o M()-M(1). If a lea oe gowh coefficie i defied fo a LHS vaiable he ucue of he dyamic coai i imila o he dyamic coai decibed i he eviou ecio. I hee cae gowh coai ae geeaed fo he eiod ai ad 1 fo all eiod of he model hoizo wih he exceio of he la eiod. Thee ye of gowh coai ae called of ye (1). If howeve all gowh coefficie ae ecified fo RHS vaiable he gowh coai will have he followig fom: EQ( l) UC ( R) T ( S ) ( ) uc ( ) UC RHS( R) T ( S )( ) uc ( ) bd ( uceachuc ) ( ucucc ) ( uceach ) uc uc ucum uc ucumuc LHS { = / / } R UC R SUM UC RHS S UC TS SUM RHS ( R) T ( S )( ) uc ( ) bd 1 40 If he coefficie UCACT UCFLO ec. i geae ha oe i eee a aual gowh ae while a coefficie malle ha oe decibe a aual decay ae. 238

239 The gowh coai ae ow geeaed fo he eiod ai -1 ad fo all eiod of he model hoizo. The exoe i he calculaio of he gowh coefficie o he RHS i i hee cae equal o he em M()-M(-1). I hi aleaive RHS fomulaio i i oible o ioduce bouday codiio ha ae uually eeded fo he fi eiod. Thee gowh coai ae called of ye (-1). The ue of he gowh coai i illuaed by he followig examle. Examle: The aual caaciy iceae of echology E01 bewee wo eiod hould o exceed 2% fo model coveig he hee e-yea eiod ad So oe wa o ceae ue coai exeig: VAR CAP VAR CAP REG11990 E01 REG12000 E01 1 VAR CAP 1 VAR CAP REG12000 E01 REG12010 E01 The ummad 1 oe he LHS exee a iiial caaciy value o ha caaciy gowh ca a fom hi aig oi e.g. if VAR CAP REG E01 i zeo he model ca ive a mo 1 caaciy ui i he yea 2000: 1 VAR CAP REG E01. Sice gowh coai hould be geeaed fo he fi wo eiod bu o he la oe he gowh coai hould be of ye (1). The ecificaio of he gowh coai called G1 i GAMS look like: SET UCN / G1 / SET UCRREACH / REG1.G1 / SET UCTSREACH / REG1.G1.ANNUAL / * Secify gowh of caaciy o LHS SET UCATTR / REG1.G1.LHS.CAP.GROWTH / * Secify gowh coefficie fo E01 o LHS (eiod 1) ad coefficie * fo caaciy o RHS (eiod 1) PARAMETER UCCAP / * o LHS G1.LHS.REG E

240 G1.LHS.REG E * o RHS G1.RHS.REG E01 1 G1.RHS.REG E01 1 / * Secify RHS coa PARAMETER UCRHSRTS / REG1.G ANNUAL.LO -1 REG1.G ANNUAL.LO -1 /; Oe hould oe ha he eiod idex ued fo he UCCAP o he LHS i elaed o he eiod while he eiod idex o he RHS i elaed o he eiod 1. The RHS UCRHSRTS coa i ovided fo he ime eiod of he LHS. Sice a gowh coefficie i ecified fo he LHS he ue coai i auomaically ideified a a dyamic gowh coai o ha he e ucucc doe o eed o be ovided by he ue. The coai will be geeaed fo all eiod fo which he RHS aamee UCRHSRTS i give. I he followig ecio we give he full deciio of he available ue coai i each caegoy alog wih a emide of he coeodig vaiable. Mahemaical deciio of ue coai Li of ue coai ad vaiable We fi how he comlee li of ue coai i he hee caegoie. The followig ye of LHS ue coai exi: EQ ( l) UC uc : ue coai ummig ove egio ucum eiod ucum ad imelice ucum EQ ( l) UCR uc : ue coai geeaed fo egio uceach ad ummig ove eiod ucum ad imelice ucum EQ ( l) UCT uc : ue coai geeaed fo eiod uceach ad ummig ove egio ucum ad imelice ucum EQ ( l) UCRT uc : ue coai geeaed fo egio uceach ad eiod uceach ad ummig ove imelice ucum EQ ( l) UCTS uc : ue coai geeaed fo eiod uceach imelice uceach ad ummig ove egio ucum EQ ( l) UCRTS uc : ue coai geeaed fo egio uceach eiod uceach ad imelice uceach. The laceholde l eflec he equaio ye of he ue coai (l=e G o L) coeodig o he boud ye of he RHS coa. I cae he dolla cool aamee 240

241 VARUC i e o YES he ue coai ae alway ic equaliie (l=e) wih he RHS coa elaced by he followig ue coai vaiable: VAR UC uc VAR UCR uc VAR UCT uc VAR UCRT uc VAR UCTS uc VAR UCRTS uc : ue coai vaiable fo EQEUC : ue coai vaiable fo EQEUCR : ue coai vaiable fo EQEUCT : ue coai vaiable fo EQEUCRT : ue coai vaiable fo EQEUCTS : ue coai vaiable EQEUCRTS. The followig ye of dyamic ue coai ad gowh coai exi: EQ ( l) UCSU uc : ue coai geeaed fo eiod ucucc ad ummig ove egio ucum ad imelice ucum EQ ( l) UCRSU uc : ue coai geeaed fo egio uceach ad eiod ucucc ad ummig ove imelice ucum EQ ( l) UCSUS uc : ue coai geeaed fo eiod ucucc imelice uceach ad ummig ove egio ucum EQ ( l) UCRSUS uc : ue coai geeaed fo egio uceach eiod ucucc ad imelice uceach. The laceholde l eflec he equaio ye of he ue coai (l=e G o L) coeodig o he boud ye of he RHS coa. I cae he dolla cool aamee VARUC i e o YES he ue coai ae alway ic equaliie (l=e) wih he RHS coa elaced by he followig ue coai vaiable: VAR UCSU uc VAR UCRSU uc VAR UCSUS uc VAR UCRSUS uc : ue coai vaiable fo EQEUCSU : ue coai vaiable fo EQEUCRSU : ue coai vaiable fo EQEUCSUS : ue coai vaiable EQEUCRSUS. Se ad aamee elaed o ue coai The followig e ad aamee ae elaed o he ue coai famewok i TIMES. Se Ieal e: ide : e havig he wo eleme LHS ad RHS (eleme ae fixed ad o ude ue cool) 241

242 ucgye : e havig he eleme ACT FLO IRE COMCON COMPRD NCAP CAP ued i he muli-dimeioal e UCATTR (eleme ae fixed ad o ude ue cool) ucame : e havig he followig aibue ame a eleme: ACTBNDUP ACTBNDLO ACTBNDFX ACTCOST FLOCOST FLODELIV FLOSUB FLOTAX NCAPCOST NCAPISUB NCAPITAX CAPBNDUP CAPBNDLO CAPBNDFX ad GROWTH ued i he muli-dimeioal e UCATTR (eleme ae fixed ad o ude ue cool). Ue-ecified e: uc : uique ame of he ue coai uceach uc : egio fo which he ue coai uc i geeaed ucum uc : egio beig ummed ove i he ue coai uc uceach uc : eiod fo which he ue coai uc i geeaed ucum uc : eiod beig ummed ove i he ue coai uc uceach uc : imelice fo which he ue coai uc i geeaed ucum uc : imelice beig ummed ove i he ue coai uc uca ucideucgye ucame : idicao ha he aibue ucame o he RHS o LHS ide of he ue coai uc a coefficie of he vaiable give by ucgye. If eihe uceach o ucum ae give he defaul i e o all uceach coaiig all ieal egio. I a imila fahio uceach beig e o all mileoeyea i he defaul if eihe uceach o ucum ae ecified. The defaul fo he imelice dimeio i uceach beig e o all imelice fo which he RHS coa UCRHSRS o UCRHSRTS ae beig ecified. Paamee Ue-ecified coefficie of vaiable: UC ACT uc ide : coefficie of he aciviy vaiable VAR ACT v i he ue coai uc o he LHS o RHS ide UC FLO uc ide c : coefficie of he flow vaiable VAR FLO v c i he ue coai uc o he LHS o RHS ide UC IRE uc ide c : coefficie of he ie-egioal exchage vaiable VAR IRE v c ie i he ue coai uc o he LHS o RHS ide UC COMCON uc ide c : coefficie of he commodiy coumio vaiable VAR COMCON c i he ue coai uc o he LHS o RHS ide ie 242

243 UC COMPRD uc ide c : coefficie of he e commodiy oducio vaiable VAR COMPRD c i he ue coai uc o he LHS o RHS ide UC NCAP uc ide : coefficie of he iveme vaiable VAR NCAP i he ue coai uc o he LHS o RHS ide UC CAP uc ide : coefficie of he caaciy vaiable VAR CAP i he ue coai uc o he LHS o RHS ide. Ue-ecified RHS coa: UC RHS uc bd : RHS coa wih boud ye bd of he ue coai UC RHSR uc bd EQl of ye l UC uc : RHS coa wih boud ye bd of he ue coai EQl UCR uc of ye l UC RHST uc : RHS coa wih boud ye bd of he ue coai EQl UCT uc of ye l UC RHSRT uc : RHS coa wih boud ye bd of he ue coai EQl UCRT uc of ye l UC RHSTS uc : RHS coa wih boud ye bd of he ue coai EQl UCTS uc of ye l UC RHSRTS uc : RHS coa wih boud ye bd of he ue coai EQl UCRTS uc of ye l. bd bd bd bd 243

244 = Mahemaical fomulaio of LHS ue coai I he mahemaical deciio of he diffee vaia of LHS ue coai he followig laceholde ae ued fo claiy eao: ACT LHS FLO LHS IRE LHS COMPRD LHS COMCON LHS NCAP LHS CAP LHS. Fo examle he laceholde ACT iclude he a of he ue coai elaed o ACT he aciviy vaiable. LHS v viy v c LHS 1 if ibelow VAR ACT v UC ACTuc LHS v G YRFR( ) if i above G YRFT( ) ( ACT BND X ) if UC ATTR uc LHS ACT ACT BNDX i give OBJ ACOST cu if UC ATTR uc LHS ACT ACT COST i give cu dcu cu 244

245 245 = cu c v dcu cvaf viy cu TAX FLO FLO LHS uc cu c SUB FLO FLO LHS uc cu c DELIV FLO FLO LHS uc cu c COST FLO FLO LHS uc cu c c v LHS uc c v c v LHS give i ATTR UC if FTAX OBJ give i ATTR UC if FSUB OBJ give i ATTR UC if FDELV OBJ give i ATTR UC if FCOST OBJ i above if TSFR RTCS ibelow if FLO UC FLO VAR FLO ) ( 1 ( ) = c v ie cvaf viy cie c c v ie ie c v LHS uc ie c v LHS i above if TSFR RTCS ibelow if IRE UC IRE VAR IRE 1 ( ) = cvac c c c LHS uc c LHS i above if YRFT G YRFR G ibelow if COMPRD UC COMPRD VAR COMPRD ) ( ) ( 1

246 246 ( ) = cvac c c c LHS uc c LHS i above if YRFT G YRFR G ibelow if COMCON UC COMCON VAR COMCON ) ( ) ( 1 = give i ATTR UC if ITAX OBJ give i ATTR UC if ISUB OBJ give i ATTR UC if ICOST OBJ NCAP UC NCAP VAR NCAP ITAX NCAP NCAP LHS uc cu cu ISUB NCAP NCAP LHS uc cu cu COST NCAP NCAP LHS uc cu cu LHS uc LHS cu cu cu dcu dcu dcu give i ATTR UC if BND CAP CAP UC CAP VAR CAP BNDX CAP CAP LHS uc X LHS uc LHS =

247 Equaio: EQ(l)UC / EQEUC Idice: ue coai (uc) Relaed vaiable: VARFLO; VARNCAP; VARCAP; VARACT; VARCOMPRD; VARCOMCON; VARIRE Puoe: The ue coai EQ(l)UC i a ue coai which i ummig ove ecified egio (ucum) eiod (ucum) ad imelice (ucum). Equaio: EQ ( l) UCuc UC RHSuc ucum uc bd ucum uc ucum uc ucum ucum ucum LHS LHS ( NCAP LHS CAP LHS ) ucum ucum ACT LHS FLO LHS IRE COMCON COMPRD LHS whe cool aamee VARUC i e o NO by he ue o i miig: { ; = ; } UC RHS uc l Whe cool aamee VARUC=YES he ue coai i ceaed a ic equaliy ad he LHS i e equal o he vaiable VARUC. The boud UCRHS ae he alied o he vaiable VARUC. = VAR UC uc wih VAR UC. LO = UC RHS uc VAR UC. UP = UC RHS uc VAR UC. FX = UC RHS uc uc LO uc UP uc FX 247

248 Equaio: EQ(l)UCR / EQEUCR Idice: ue coai (uc) egio () Relaed vaiable: VARFLO; VARNCAP; VARCAP; VARACT; VARCOMPRD; VARCOMCON; VARIRE Puoe: The ue coai EQ(l)UCR i a ue coai which i ceaed fo each egio of uceach ad i ummig ove eiod (ucum) ad imelice (ucum). Equaio: EQ ( l) UCR uc UC RHSR uc ucum uc bd ucum uc uceach uc ucum ucum LHS LHS ( NCAP LHS CAP LHS ) ucum ACT LHS FLO LHS IRE COMCON COMPRD whe cool aamee VARUC=NO: { ; = ; } UC RHSR uc l LHS Whe cool aamee VARUC=YES he ue coai i ceaed a ic equaliy ad he LHS i e equal o he vaiable VARUCR. The boud UCRHSR ae he alied o he vaiable VARUCR. = VAR UCR uc wih VAR UCR. LO = uc UC VAR UCRUP. = uc UC VAR UCR. FX = UC uc RHSR RHSR RHSR uc LO uc UP uc FX 248

249 Equaio: EQ(l)UCT / EQEUCT Idice: ue coai (uc) eiod () Relaed vaiable: VARFLO; VARNCAP; VARCAP; VARACT; VARCOMPRD; VARCOMCON; VARIRE Puoe: The ue coai EQ(l)UCT i a ue coai which i ceaed fo each eiod of uceach ad i ummig ove egio (ucum) ad imelice (ucum). Equaio: EQ ( l) UCTuc UC RHSTuc uceach uc bd ucum uc ucum uc ucum ucum LHS LHS ( NCAP LHS CAP LHS ) ucum ACT LHS FLO LHS IRE COMCON COMPRD LHS whe cool aamee VARUC=NO: { ; = ; } UC RHST uc l Whe cool aamee VARUC=YES he ue coai i ceaed a ic equaliy ad he LHS i e equal o he vaiable VARUCT. The boud UCRHST ae he alied o he vaiable VARUCT. = VAR UCT uc wih VAR UCT. LOuc = UC RHST VAR UCT. UPuc = UC RHST VAR UCT. FX = UC RHST uc uc LO uc UP uc FX 249

250 Equaio: EQ(l)UCRT / EQEUCRT Idice: ue coai (uc) egio () eiod () Relaed vaiable: VARFLO; VARNCAP; VARCAP; VARACT; VARCOMPRD; VARCOMCON; VARIRE Puoe: The ue coai EQ(l)UCRT i a ue coai which i ceaed fo each egio of uceach ad each eiod of uceach ad i ummig ove imelice (ucum). Equaio: EQ ( l) UCRT UC RHSRT uceach uc uc uc bd ucum uc uceach uc ucum ACT COMCON ( NCAP CAP ) LHS LHS FLO LHS LHS LHS IRE COMPRD whe cool aamee VARUC=NO: { ; = ; } UC RHSRT uc l LHS LHS Whe cool aamee VARUC=YES he ue coai i ceaed a ic equaliy ad he LHS i e equal o he vaiable VARUCRT. The boud UCRHSRT ae he alied o he vaiable VARUCRT. = VAR UCRT uc wih VAR UCRT. LO uc = UC VAR UCRT. UP uc = UC VAR UCRT. FX = UC uc RHSRT RHSRT RHSRT uc LO uc UP uc FX 250

251 Equaio: EQ(l)UCRTS / EQEUCRTS Idice: ue coai (uc) egio () eiod () imelice () Relaed vaiable: VARFLO; VARNCAP; VARCAP; VARACT; VARCOMPRD; VARCOMCON; VARIRE Puoe: The ue coai EQ(l)UCRTS i a ue coai which i ceaed fo each egio of uceach each eiod of uceach ad each imelice of uceach. Equaio: EQ ( l) UCRTS uc UC RHSRTS uc uceach uc bd uceach uc uceach uc ACT COMCON LHS ( NCAP CAP ) LHS FLO LHS LHS COMPRD LHS IRE LHS LHS whe cool aamee VARUC=NO: { ; = ; } UC RHSRTS uc l Whe cool aamee VARUC=YES he ue coai i ceaed a ic equaliy ad he LHS i e equal o he vaiable VARUCRTS. The boud UCRHSRTS ae he alied o he vaiable VARUCRTS. = VAR UCRTS uc wih VAR UCRTS. LO uc = UC VAR UCRTS. UP uc = UC VAR UCRTS. FX = UC uc RHSRTS RHSRTS RHSRTS uc LO uc UP uc FX 251

252 Equaio: EQ(l)UCTS / EQEUCTS Idice: ue coai (uc) eiod () imelice () Relaed vaiable: VARFLO; VARNCAP; VARCAP; VARACT; VARCOMPRD; VARCOMCON; VARIRE Puoe: The ue coai EQ(l)UCTS i a ue coai which i ceaed fo each eiod of uceach ad each imelice of uceach ad i ummig ove egio (ucum). Equaio: EQE UCTS UC RHSRTS uceach uc uc uc bd uceach uc ucum uc ucum ( NCAP LHS CAP LHS ) ucum ACT LHS FLO LHS IRE COMCON LHS COMPRD whe cool aamee VARUC=NO: { ; = ; } UC RHSTS uc l LHS Whe cool aamee VARUC=YES he ue coai i ceaed a ic equaliy ad he LHS i e equal o he vaiable VARUCTS. The boud UCRHSTS ae he alied o he vaiable VARUCTS. = VAR UCTS uc wih VAR UCTS. LOuc = UC RHSTS VAR UCTS. UPuc = UC RHSTS VAR UCTS. FX = UC RHSTS uc LHS uc LO uc UP uc FX 252

253 = Mahemaical fomulaio of dyamic ue coai ad gowh coai of ye (1) I he mahemaical deciio of he dyamic ue coai ad he gowh coai of ye ( 1) he followig laceholde ae ued fo vaiable em o he LHS (eiod ): ACT GROW LHS FLO GROW LHS IRE GROW LHS COMPRD GROW LHS COMCON GROW LHS NCAP GROW LHS CAP GROW LHS ad o he RHS (eiod T1): ACT GROW 1 RHS FLO GROW 1 RHS IRE GROW 1 RHS COMPRD GROW 1 RHS COMCON GROW 1 RHS NCAP GROW 1 RHS CAP GROW 1 RHS. ACT GROW v viy LHS c v 1 if ibelow VAR ACT v UC ACTuc LHS v G YRFR( ) if i above G YRFT( ) ( ACT BND X ) if UC ATTR uc LHS ACT ACT BNDX i give OBJ ACOST cu if UC ATTR uc LHS ACT ACT COST i give cu dcu cu M ( 1) M ( ) 1 ( ) UC ACTuc LHS v if UC ATTR uc LHS ACT GROWTH i give 253

254 254 ( ) ( ) = give i ATTR UC if FLO UC give i ATTR UC if FTAX OBJ give i ATTR UC if FSUB OBJ give i ATTR UC if FDELV OBJ give i ATTR UC if FCOST OBJ i above if TSFR RTCS ibelow if FLO UC FLO VAR GROW FLO GROWTH FLO LHS uc M M c v LHS uc cu TAX FLO FLO LHS uc cu c SUB FLO FLO LHS uc cu c DELIV FLO FLO LHS uc cu c COST FLO FLO LHS uc cu c c v LHS uc c v c v LHS 1 ) ( 1) ( 1 cu c v dcu cvaf viy ( ) ( ) = give i ATTR UC if IRE UC i above if TSFR RTCS ibelow if IRE UC IRE VAR GROW IRE GROWTH IRE LHS uc M M ie c v LHS uc ie c v LHS uc ie c v c v ie LHS 1 ) ( 1) ( 1 c v ie cvaf viy cie c

255 255 ( ) ( ) = cvac c c GROWTH COMPRD LHS uc M M c LHS uc c LHS uc c LHS give i ATTR UC if COMPRD UC i above if YRFT G YRFR G ibelow if COMPRD UC COMPRD VAR GROW COMPRD 1 ) ( 1) ( ) ( ) ( 1 ( ) ( ) = give i ATTR UC if COMCON UC i above if YRFT G YRFR G ibelow if COMCON UC COMCON VAR GROW COMCON GROWTH COMCON LHS uc M M c LHS uc c LHS uc c c LHS 1 ) ( 1) ( ) ( ) ( 1 cvac c

256 256 ( ) = give i ATTR UC if NCAP UC give i ATTR UC if ITAX OBJ give i ATTR UC if ISUB OBJ give i ATTR UC if ICOST OBJ NCAP UC NCAP VAR GROW NCAP GROWTH NCAP LHS uc M M LHS uc ITAX NCAP NCAP LHS uc cu cu ISUB NCAP NCAP LHS uc cu cu COST NCAP NCAP LHS uc cu cu LHS uc LHS 1 ) ( 1) ( cu cu cu dcu dcu dcu ( ) = give i ATTR UC if CAP UC give i ATTR UC if BND CAP CAP UC CAP VAR GROW CAP GROWTH CAP LHS uc M M LHS uc BNDX CAP CAP LHS uc X LHS uc LHS 1 ) ( 1) (

257 257 ( ) ( ) = 1 v cu viy c dcu v GROWTH ACT RHS uc M M v RHS uc COST ACT ACT RHS uc cu cu BNDX ACT ACT RHS uc X v RHS uc v RHS give i ATTR UC if ACT UC give i ATTR UC if ACOST OBJ give i ATTR UC if BND ACT i above if YRFT G YRFR G ibelow if ACT UC ACT VAR GROW ACT 1 1) ( ) ( ) ( ) ( 1 ( ) ( ) = give i ATTR UC if FLO UC give i ATTR UC if FTAX OBJ give i ATTR UC if FSUB OBJ give i ATTR UC if FDELV OBJ give i ATTR UC if FCOST OBJ i above if TSFR RTCS ibelow if FLO UC FLO VAR GROW FLO GROWTH FLO RHS uc M M c v RHS uc cu TAX FLO FLO RHS uc cu c SUB FLO FLO RHS uc cu c DELIV FLO FLO RHS uc cu c COST FLO FLO RHS uc cu c c v RHS uc c v c v RHS 1 1) ( ) ( cu 1c 1 v dcu cvaf viy

258 258 ( ) ( ) = give i ATTR UC if IRE UC i above if TSFR RTCS ibelow if IRE UC IRE VAR GROW IRE GROWTH IRE LHS uc M M ie c v LHS uc ie c v LHS uc ie c v c v ie RHS 1 ) ( 1) ( c 1 v ie cvaf viy cie c ( ) ( ) = 1c cvac c GROWTH COMPRD RHS uc M M c RHS uc c RHS uc c RHS give i ATTR UC if COMPRD UC i above if YRFT G YRFR G ibelow if COMPRD UC COMPRD VAR GROW COMPRD 1 1) ( ) ( ) ( ) ( 1 ( ) ( ) = give i ATTR UC if COMCON UC i above if YRFT G YRFR G ibelow if COMCON UC COMCON VAR COMCON GROWTH COMCON RHS uc M M c RHS uc c RHS uc c c RHS 1 1) ( ) ( ) ( ) ( 1 cvac c

259 259 ( ) = give i ATTR UC if NCAP UC give i ATTR UC if ITAX OBJ give i ATTR UC if ISUB OBJ give i ATTR UC if ICOST OBJ NCAP UC NCAP VAR GROW NCAP GROWTH NCAP RHS uc M M RHS uc ITAX NCAP NCAP RHS uc cu cu ISUB NCAP NCAP RHS uc cu cu COST NCAP NCAP RHS uc cu cu RHS uc RHS 1 1) ( ) ( cu cu cu dcu dcu dcu ( ) = give i ATTR UC if CAP UC give i ATTR UC if BND CAP CAP UC CAP VAR GROW CAP GROWTH CAP RHS uc M M RHS uc BNDX CAP CAP RHS uc X RHS uc RHS 1 ) ( 1) (

260 Equaio: EQ(l)UCSU / EQEUCSU Idice: ue coai (uc) eiod () Relaed vaiable: VARFLO; VARNCAP; VARCAP; VARACT; VARCOMPRD; VARCOMCON; VARIRE Puoe: The dyamic ue coai o gowh coai of ye (1) EQ(l)UCSU eablihe a coai bewee wo ucceive eiod ad 1. Fo dyamic ue coai he eiod i ecified by he e ucucc gowh coai ae geeaed fo all eiod bu he la. The coai i ummig ove egio (ucum) ad imelice (ucum). Equaio: EQ ( l) UCSU UC RHST ucucc uc uc uc bd ucum uc ucum uc ucum ucum LHS LHS ( NCAP GROW LHS CAP GROW LHS ) ucum ACT GROW LHS FLO GROW LHS IRE GROW COMCON GROW COMPRD GROW Whe cool aamee VARUC=NO: { ; = ; } UC RHST ucum ucum 1 RHS 1 RHS ( NCAP GROW 1 RHS CAP GROW 1 RHS ) ucum uc l ACT GROW COMCON GROW 1 RHS FLO GROW 1 RHS COMPRD GROW LHS IRE GROW Whe cool aamee VARUC=YES he ue coai i ceaed a ic equaliy ad he RHS coa UCRHST i elaced by he vaiable VARUCT. The boud UCRHST ae he alied o he vaiable VARUCT. = 1 RHS 260

261 261 ( ) ucum ucum ucum RHS RHS RHS RHS RHS RHS RHS uc CAP NCAP COMPRD COMCON IRE FLO ACT UCT VAR wih. LO uc uc RHST UC LO UCT VAR =. UP uc uc RHST UC UCT UP VAR =. FX uc uc RHST UC FX UCT VAR =

262 Equaio: EQ(l)UCRSU / EQEUCRSU Idice: egio () ue coai (uc) eiod () Relaed vaiable: VARFLO; VARNCAP; VARCAP; VARACT; VARCOMPRD; VARCOMCON; VARIRE Puoe: The dyamic ue coai o gowh coai of ye (1) EQ(l)UCSU eablihe a coai bewee wo ucceive eiod ad 1. Fo dyamic ue coai he eiod i ecified by he e ucucc gowh coai ae geeaed fo all eiod bu he la. The coai i geeaed fo each egio of he e uceach ad i ummig ove imelice (ucum). Equaio: EQ ( l) UCRSU uc UC RHSRT uc ucucc uc bd ucum uc uceach uc ucum ACT GROW COMCON GROW ( NCAP GROW CAP GROW ) LHS LHS FLO GROW LHS Whe cool aamee VARUC=NO: { ; = ; } UC RHSRT uc l ACT GROW COMCON GROW LHS LHS COMPRD GROW ( NCAP GROW CAP GROW ) 1 RHS 1 RHS FLO GROW 1 RHS IRE GROW LHS 1 RHS COMPRD GROW ucum 1 RHS 1 RHS LHS IRE GROW 1 RHS Whe cool aamee VARUC=YES he ue coai i ceaed a ic equaliy ad he RHS coa UCRHSRT i elaced by he vaiable VARUCRT. The boud UCRHSRT ae he alied o he vaiable VARUCRT. = 262

263 263 ( ) RHS RHS RHS RHS RHS RHS RHS uc CAP NCAP COMPRD COMCON IRE FLO ACT UCRT VAR ucum wih. LO uc uc RHSRT UC LO UCRT VAR =. UP uc uc RHSRT UC UCRT UP VAR =. FX uc uc RHSRT UC FX UCRT VAR =

264 Equaio: EQ(l)UCRSUS / EQEUCRSU Idice: egio () ue coai (uc) eiod () imelice () Relaed vaiable: VARFLO; VARNCAP; VARCAP; VARACT; VARCOMPRD; VARCOMCON; VARIRE Puoe: The dyamic ue coai o gowh coai of ye (1) EQ(l)UCSUS eablihe a coai bewee wo ucceive eiod ad 1. Fo dyamic ue coai he eiod i ecified by he e ucucc gowh coai ae geeaed fo all eiod bu he la. The coai i geeaed fo each egio of he e uceach ad each imelice of he e uceach. Equaio: EQ ( l) UCRSUS uc UC RHSRTS uc ucucc uc bd uceach uc uceach uc ACT GROW COMCON GROW LHS ( NCAP GROW CAP GROW ) LHS FLO GROW LHS Whe cool aamee VARUC=NO: { ; = ; } UC RHSRTS uc l ACT GROW COMCON GROW 1 RHS LHS COMPRD GROW LHS IRE GROW LHS ( NCAP GROW CAP GROW ) 1 RHS FLO GROW 1 RHS 1 RHS COMPRD GROW 1 RHS 1 RHS LHS IRE GROW 1 RHS Whe cool aamee VARUC=YES he ue coai i ceaed a ic equaliy ad he RHS coa UCRHSRTS i elaced by he vaiable VARUCRTS. The boud UCRHSRTS ae he alied o he vaiable VARUCRTS. = 264

265 265 ( ) RHS RHS RHS RHS RHS RHS RHS uc CAP NCAP COMPRD COMCON IRE FLO ACT UCRTS VAR wih. LO uc uc RHSRTS UC LO UCRTS VAR =. UP uc uc RHSRTS UC UCRTS UP VAR =. FX uc uc RHSRTS UC FX UCRTS VAR =

266 Equaio: EQ(l)UCSUS / EQEUCSUS Idice: ue coai (uc) eiod () imelice () Relaed vaiable: VARFLO; VARNCAP; VARCAP; VARACT; VARCOMPRD; VARCOMCON; VARIRE Puoe: The dyamic ue coai o gowh coai of ye (1) EQ(l)UCSUS eablihe a coai bewee wo ucceive eiod ad 1. Fo dyamic ue coai he eiod i ecified by he e ucucc gowh coai ae geeaed fo all eiod bu he la. The coai geeaed fo each imelice uceach ad i ummig ove egio (ucum). Equaio: EQ ( l) UCSUS UC RHSTS ucucc uc uc uc bd uceach uc ucum uc ucum ( NCAP GROW LHS CAP GROW LHS ) ucum ACT GROW LHS FLO GROW LHS IRE GROW COMCON GROW LHS COMPRD GROW LHS Whe cool aamee VARUC=NO: { ; = ; } UC RHSTS ucum 1 RHS 1 RHS ( NCAP GROW 1 RHS CAP GROW 1 RHS ) ucum uc l ACT GROW COMCON GROW 1 RHS FLO GROW 1 RHS COMPRD GROW LHS IRE GROW 1 RHS Whe cool aamee VARUC=YES he ue coai i ceaed a ic equaliy ad he RHS coa UCRHSTS i elaced by he vaiable VARUCTS. The boud UCRHSTS ae he alied o he vaiable VARUCTS. = 266

267 VAR UCTS ucum 1 RHS 1 RHS ( NCAP 1 RHS CAP 1 RHS ) ucum uc ACT COMCON 1 RHS FLO 1 RHS COMPRD wih VAR UCTS. LOuc = UC RHSTS VAR UCTS. UPuc = UC RHSTS VAR UCTS. FX = UC RHSTS uc IRE uc LO uc UP uc FX 1 RHS Mahemaical fomulaio of gowh coai of ye (-1 ) I he mahemaical deciio of gowh coai of ye (-1 ) he followig laceholde ae ued fo vaiable em o he RHS (eiod -1): ACT GROW 1 RHS FLO GROW 1 RHS IRE GROW 1 RHS COMPRD GROW 1 RHS COMCON GROW 1 RHS NCAP GROW 1 RHS CAP GROW 1 RHS. Fo he LHS em he laceholde ae he ame oe a defied fo he LHS ue coai. ACT GROW = 1 RHS v viy v 1 c 1 if ibelow VAR ACT v 1 UC ACTuc RHS v 1 G YRFR( ) if i above G YRFT( ) ( ACT BND 1 X ) if UC ATTR uc RHS ACT ACT BNDX i give OBJ ACOST 1 cu if UC ATTR uc RHS ACT ACT COST i give cu dcu cu M ( ) M ( 1) 1 ( ) UC ACTuc RHS v 1 if UC ATTR uc RHS ACT GROWTH i give 267

268 268 ( ) ( ) = give i ATTR UC if FLO UC give i ATTR UC if FTAX OBJ give i ATTR UC if FSUB OBJ give i ATTR UC if FDELV OBJ give i ATTR UC if FCOST OBJ i above if TSFR RTCS ibelow if FLO UC FLO VAR GROW FLO GROWTH FLO RHS uc M M c v RHS uc cu TAX FLO FLO RHS uc cu c SUB FLO FLO RHS uc cu c DELIV FLO FLO RHS uc cu c COST FLO FLO RHS uc cu c c v RHS uc c v c v RHS 1 1) ( ) ( cu 1c 1 v dcu cvaf viy ( ) ( ) = give i ATTR UC if IRE UC i above if TSFR RTCS ibelow if IRE UC IRE VAR GROW IRE GROWTH IRE LHS uc M M ie c v RHS uc ie c v RHS uc ie c v c v ie RHS 1 1) ( ) ( c 1 v ie cvaf viy cie c

269 269 ( ) ( ) = 1c cvac c GROWTH COMPRD RHS uc M M c RHS uc c RHS uc c RHS give i ATTR UC if COMPRD UC i above if YRFT G YRFR G ibelow if COMPRD UC COMPRD VAR GROW COMPRD 1 1) ( ) ( ) ( ) ( 1 ( ) ( ) = give i ATTR UC if COMCON UC i above if YRFT G YRFR G ibelow if COMCON UC COMCON VAR GROW COMCON GROWTH COMCON RHS uc M M c RHS uc c RHS uc c c RHS 1 1) ( ) ( ) ( ) ( 1 1c cvac

270 270 ( ) = give i ATTR UC if NCAP UC give i ATTR UC if ITAX OBJ give i ATTR UC if ISUB OBJ give i ATTR UC if ICOST OBJ NCAP UC NCAP VAR GROW NCAP GROWTH NCAP RHS uc M M RHS uc ITAX NCAP NCAP RHS uc cu cu ISUB NCAP NCAP RHS uc cu cu COST NCAP NCAP RHS uc cu cu RHS uc RHS 1 1) ( ) ( cu cu cu dcu dcu dcu ( ) = give i ATTR UC if CAP UC give i ATTR UC if BND CAP CAP UC CAP VAR GROW CAP GROWTH CAP RHS uc M M RHS uc BNDX CAP CAP RHS uc X RHS uc RHS 1 ) ( 1) (

271 Equaio: EQ(l)UCSU / EQEUCSU Idice: ue coai (uc) eiod () Relaed vaiable: VARFLO; VARNCAP; VARCAP; VARACT; VARCOMPRD; VARCOMCON; VARIRE Puoe: The gowh coai of ye (-1) EQ(l)UCSU eablihe a coai bewee wo ucceive eiod -1 ad. The gowh coai i geeaed fo all eiod. The coai i ummig ove egio (ucum) ad imelice (ucum). Equaio: EQ ( l) UCSU UC RHST ucucc uc uc uc bd ucum uc ucum uc ucum ucum LHS LHS ( NCAP GROW LHS CAP GROW LHS ) ucum ACT GROW LHS FLO GROW LHS IRE GROW COMCON GROW COMPRD GROW Whe cool aamee VARUC=NO: { ; = ; } UC RHST ucum ucum 1 RHS 1 RHS ( NCAP GROW 1 RHS CAP GROW 1 RHS ) ucum uc l ACT GROW COMCON GROW 1 RHS FLO GROW 1 RHS COMPRD GROW IRE GROW LHS 1 RHS Whe cool aamee VARUC=YES he ue coai i ceaed a ic equaliy ad he RHS coa UCRHST i elaced by he vaiable VARUCT. The boud UCRHST ae he alied o he vaiable VARUCT. = 271

272 272 ( ) ucum ucum ucum RHS RHS RHS RHS RHS RHS RHS uc CAP NCAP COMPRD COMCON IRE FLO ACT UCT VAR wih. LO uc uc RHST UC LO UCT VAR =. UP uc uc RHST UC UCT UP VAR =. FX uc uc RHST UC FX UCT VAR =

273 Equaio: EQ(l)UCRSU / EQEUCRSU Idice: egio () ue coai (uc) eiod () Relaed vaiable: VARFLO; VARNCAP; VARCAP; VARACT; VARCOMPRD; VARCOMCON; VARIRE Puoe: The gowh coai of ye (-1) EQ(l)UCSU eablihe a coai bewee wo ucceive eiod -1 ad. The gowh coai i geeaed fo all eiod. The coai i geeaed fo each egio of he e uceach ad i ummig ove imelice (ucum). Equaio: EQ ( l) UCRSU uc UC RHSRT uc ucucc uc bd ucum uc uceach uc ucum ACT GROW COMCON GROW ( NCAP GROW CAP GROW ) LHS LHS FLO GROW LHS Whe cool aamee VARUC=NO: { ; = ; } UC RHSRT ucum uc l ACT GROW COMCON GROW LHS LHS COMPRD GROW ( NCAP GROW CAP GROW ) 1 RHS 1 RHS FLO GROW 1 RHS 1 RHS IRE GROW LHS 1 RHS COMPRD GROW 1 RHS LHS IRE GROW 1 RHS Whe cool aamee VARUC=YES he ue coai i ceaed a ic equaliy ad he RHS coa UCRHSRT i elaced by he vaiable VARUCRT. The boud UCRHSRT ae he alied o he vaiable VARUCRT. = 273

274 274 ( ) RHS RHS RHS RHS RHS RHS RHS uc CAP NCAP COMPRD COMCON IRE FLO ACT UCRT VAR ucum wih. LO uc uc RHSRT UC LO UCRT VAR =. UP uc uc RHSRT UC UCRT UP VAR =. FX uc uc RHSRT UC FX UCRT VAR =

275 Equaio: EQ(l)UCRSUS / EQEUCRSU Idice: egio () ue coai (uc) eiod () imelice () Relaed vaiable: VARFLO; VARNCAP; VARCAP; VARACT; VARCOMPRD; VARCOMCON; VARIRE Puoe: The gowh coai of ye (-1) EQ(l)UCSUS eablihe a coai bewee wo ucceive eiod -1 ad. The gowh coai i geeaed fo all eiod. The coai i geeaed fo each egio of he e uceach ad each imelice of he e uceach. Equaio: EQ ( l) UCRSUS uc UC RHSRTS uc ucucc uc bd uceach uc uceach uc ACT GROW COMCON GROW LHS ( NCAP GROW CAP GROW ) LHS FLO GROW LHS Whe cool aamee VARUC=NO: { ; = ; } UC RHSRTS uc l ACT GROW COMCON GROW 1 RHS LHS COMPRD GROW LHS ( NCAP GROW CAP GROW ) 1 RHS FLO GROW 1 RHS IRE GROW 1 RHS LHS 1 RHS COMPRD GROW 1 RHS LHS IRE GROW 1 RHS Whe cool aamee VARUC=YES he ue coai i ceaed a ic equaliy ad he RHS coa UCRHSRTS i elaced by he vaiable VARUCRTS. The boud UCRHSRTS ae he alied o he vaiable VARUCRTS. = 275

276 276 ( ) RHS RHS RHS RHS RHS RHS RHS uc CAP NCAP COMPRD COMCON IRE FLO ACT UCRTS VAR wih. LO uc uc RHSRTS UC LO UCRTS VAR =. UP uc uc RHSRTS UC UCRTS UP VAR =. FX uc uc RHSRTS UC FX UCRTS VAR =

277 Equaio: EQ(l)UCSUS / EQEUCSUS Idice: ue coai (uc) eiod () imelice () Relaed vaiable: VARFLO; VARNCAP; VARCAP; VARACT; VARCOMPRD; VARCOMCON; VARIRE Puoe: The gowh coai of ye (-1) EQ(l)UCSUS eablihe a coai bewee wo ucceive eiod -1 ad. The gowh coai i geeaed fo all eiod. The coai geeaed fo each imelice uceach ad i ummig ove egio (ucum). Equaio: EQ ( l) UCSUSuc UC RHSTS úcucc uc uc bd uceach uc ucum uc ucum ( NCAP GROW LHS CAP GROW LHS ) ucum ACT GROW LHS FLO GROW LHS IRE GROW COMCON GROW LHS COMPRD GROW LHS Whe cool aamee VARUC=NO: { ; = ; } UC RHSTS ucum ( NCAP GROW 1 RHS CAP GROW 1 RHS ) ucum uc l ACT GROW COMCON GROW 1 RHS FLO GROW 1 RHS 1 RHS COMPRD GROW 1 RHS LHS IRE GROW 1 RHS Whe cool aamee VARUC=YES he ue coai i ceaed a ic equaliy ad he RHS coa UCRHSTS i elaced by he vaiable VARUCTS. The boud UCRHSTS ae he alied o he vaiable VARUCTS. = 277

278 278 ( ) ucum ucum RHS RHS RHS RHS RHS RHS RHS uc CAP NCAP COMPRD COMCON IRE FLO ACT UCTS VAR wih. LO uc uc RHSTS UC LO UCTS VAR =. UP uc uc RHSTS UC UCTS UP VAR =. FX uc uc RHSTS UC FX UCTS VAR =

279 6 The Edogeou Techological Leaig (ETL) oio A dicued i chae 8 of PART I hee ae iuaio i which he ae a which a echology ui iveme co chage ove ime i a fucio of cumulaive iveme i he echology. I hee iuaio echological leaig i called edogeou. Mixed Iege Pogammig (MIP) i emloyed i ode o model Edogeou Techological Leaig (ETL) i TIMES. A ha aleady bee oed i he cae of Lumy Iveme (ee ecio ) MIP oblem ae much moe difficul o olve ha adad LP oblem ad o he ETL feaue hould be alied oly whee i i deemed eceay o model a limied umbe of echologie a cadidae fo Edogeou Techological Leaig. Thi cauio i eecially equied fo lage cale TIMES iace. Aohe imoa cavea i ha ETL i eleva whe he modelig coe i boad e.g. whe a lage oio of (o eha he eie) wold eegy yem i beig modeled ice he echological leaig heomeo e o global cumulaive caaciy of a echology ad o o he caaciy imlemeed i a mall oio of he wold. I hi chae we ovide he daa ad modelig deail aociaed wih modelig Edogeou Techological Leaig (ETL) i TIMES. The imlemeaio of ETL i TIMES i baed o he ealizaio i he MARKAL model geeao. The majo a of he MARKAL code fo ETL could be afeed o TIMES. Accodigly he deciio of ETL eeed hee follow he MARKAL documeaio of ETL. To hi ed he ex hee ecio will adde he Se Paamee Vaiable ad Equaio elaed o he Edogeou Techological Leaig oio icludig he ecial clueed leaig ETL oio whee a comoe commo o eveal echologie lea heeby beefiig all he elaed (clueed) echologie. 6.1 Se Swiche ad Paamee Like all ohe aec of TIMES he ue decibe he ETL comoe of he eegy yem by mea of a Se ad he Paamee ad Swiche decibed i hi chae. Table 6.1 ad Table 6.2 below decibe he Ue Iu Paamee ad he Maix Coefficie ad Ieal Model Se ad Paamee eecively ha ae aociaed wih he Edogeou Techological Leaig oio. Noe ha he ecial clueed leaig ETL oio equie oe addiioal Ue Iu Paamee (ETL-CLUSTER) ad wo addiioal Maix Coefficie/Ieal Model Paamee (CLUSTER ad NTCHTEG). Beide he baic daa decibed i Table 6.1 he ue cool whehe o o he ETL comoe i acivaed by mea of he $SET ETL YES wich. Thi wich i ovided by he daa hadlig yem whe he ue idicae ha he ETL oio i o be icluded i a u. Thi emi he eay excluio of he feaue if he ue doe o wa o efom a MIP olve wihou havig o emove he ETL daa. 279

280 Table 6.1. Defiiio of ETL ue iu aamee Iu Paamee (Idexe) CCAP0 () CCAPM () TEG () Alia/Ieal Name CCAP0 Relaed Paamee PAT CCOST0 Ui/Rage & Defaul Ui of caaciy (e.g. GW PJa). [oe]; o defaul. CCAPM CCOSTM Ui of caaciy (e.g. GW PJa). [oe]; o defaul TEG ETL-CUMCAP0 ETL- CUMCAPMAX ETL-INVCOST0 ETL-NUMSEG ETL- PROGRATIO Idicao. [1]; o defaul. Iace (Requied/Omi/ Secial Codiio) Requied alog wih he ohe ETL iu aamee fo each leaig echology (TEG). Requied alog wih he ohe ETL iu aamee fo each leaig echology (TEG). Requied o ideify he leaig echologie. Fo each TEG he ohe ETL iu aamee ae equied. Deciio The iiial cumulaive caaciy (aig oi o he leaig cuve) fo a (o-eouce) echology ha i modeled a oe fo which edogeou echology leaig (ETL) alie. Leaig oly begi oce hi level of ialled caaciy i ealized. The CCAP0 aamee aea a he igh-had-ide of he cumulaive caaciy defiiio coai (EQCUINV). Noe ha if he NCAPPASTI aamee i ecified fo a ETL echology he i value i he fi eiod hould mach he value of CCAP0 ohewie a ifeaibiliy will occu. The maximum cumulaive caaciy (edig oi o he leaig cuve) fo a (o-eouce) echology ha i modeled a oe fo which edogeou echology leaig (ETL) alie. The aamee CCAPM doe o aea i ay of he ETL coai bu i value affec he value of a umbe of ieal aamee ha diecly coibue o oe o moe of he ETL coai. A idicao (alway 1) ha a oce i modeled a oe fo which edogeou echology leaig (ETL) alie. The e TEG cool he geeaio of he ETL coai. Each of he ETL coai i geeaed oly fo hoe echologie ha ae i e TEG. 280

281 Iu Paamee (Idexe) SC0 () SEG () PRAT () Alia/Ieal Name Relaed Paamee Ui/Rage & Defaul SC0 PAT Bae yea moeay ui e ui of caaciy (e.g M$/GW o PJa). [oe]; o defaul. SEG PRAT ALPH BETA CCAPK CCOSTK CCAPK CCOST0 CCOSTM PAT PBT Numbe of e. [1-6]; o defaul. Decimal facio. [0-1]; o defaul. Iace (Requied/Omi/ Secial Codiio) Requied alog wih he ohe ETL iu aamee fo each leaig echology (TEG).. Requied alog wih he ohe ETL iu aamee fo each leaig echology (TEG).. Requied alog wih he ohe ETL iu aamee fo each leaig echology (TEG). Deciio The iveme co coeodig o he aig oi o he leaig cuve fo a echology ha i modeled a oe fo which edogeou echology leaig (ETL) alie. The aamee SC0 doe o aea i ay of he ETL coai bu i value affec he value of a umbe of ieal aamee ha diecly coibue o oe o moe of he ETL coai. The umbe of egme o be ued i aoximaig he leaig cuve fo a echology ha i modeled a oe fo which edogeou echology leaig (ETL) alie. The SEG aamee aea i all of he ETL coai ha ae elaed o iecewie liea aoximaio of he leaig cuve (EQCC EQCOS EQEXPE1 EQEXPE2 EQLA1 EQLA2). The oge aio fo a echology ha i modeled a oe fo which edogeou echology leaig (ETL) alie. The oge aio which i efeed o a he leaig ae i defied a he aio of he chage i ui iveme co each ime cumulaive iveme i a ETL echology double. Tha i if he iiial ui iveme co i SC0 ad he oge aio i PRAT he afe cumulaive iveme i doubled he ui iveme co will be PRAT * SC0. The aamee PRAT doe o aea i ay of he ETL coai bu i value affec he value of a umbe of ieal aamee (ALPH BETA CCAPK CCOST0) ha diecly coibue o oe o 281

282 Iu Paamee (Idexe) CLUSTER () Alia/Ieal Name CLUSTER NCLUSTER Relaed Paamee Ui/Rage & Defaul Decimal facio. [0-1]; o defaul. Iace (Requied/Omi/ Secial Codiio) Povided o model clueed edogeou echology leaig. Each of he leaig aamee mu alo be ecified fo he key leaig echology. Deciio moe of he ETL coai. The clue maig ad coulig faco fo a echology ha i modeled a a clueed echology i aociaed wih a key leaig echology o which edogeou echology leaig (ETL) alie. Clueed echologie ue he key ETL echology ad ae ubjec o leaig via he key echology. The fi idex of he CLUSTER aamee i a key leaig echology. The ecod idex of he CLUSTER aamee i a clueed echology ha i aociaed wih hi key leaig echology. I geeal hee may be eveal clueed echologie each of which i aociaed wih he ame key leaig echology ad hece hee may be eveal iace of he CLUSTER aamee each of which ha he ame key leaig echology a i fi idex. The umeical value of he CLUSTER aamee idicae he exe of coulig bewee he clueed echology ad he key leaig echology o which i i aociaed. 282

283 Table 6.2. ETL-ecific maix coefficie ad ieal model aamee 41 Maix Cool & Coefficie (idexe) ALPH (k) BETA (k) CCAP0 () CCAPK (k) CCOST0 () Tye Deciio & Calculaio I ALPH ae he iece o he veical axi of he lie egme i he iecewie liea aoximaio of he cumulaive co cuve. They ae calculaed i COEFETL.ETL fom he aig ad edig oi of he cumulaive co cuve i aumed fom he umbe of egme ued i i iecewie liea aoximaio ad he choice of ucceive ieval legh o he veical axi o be uch ha each ieval i wice a wide a he ecedig oe. The aamee ALPH occu i he ETL equaio EQCOS ha defie he iecewie liea aoximaio o he cumulaive co cuve. I BETA ae he loe of he lie egme i he iecewie liea aoximaio of he cumulaive co cuve. They ae calculaed i COEFETL.ETL fom he aig ad edig oi of he cumulaive co cuve i aumed fom he umbe of egme ued i i iecewie liea aoximaio ad he choice of ucceive ieval legh o he veical axi o be uch ha each ieval i wice a wide a he ecedig oe. The aamee BETA occu i he ETL equaio EQCOS ha defie he iecewie liea aoximaio o he cumulaive co cuve. A CCAP0 i he iiial cumulaive caaciy (aig oi o he leaig cuve). The aamee CCAP0 occu i he ETL equaio EQCUINV ha defie cumulaive caaciy i each eiod. I CCAPK ae he beak oi o he hoizoal axi i he iecewie liea aoximaio of he cumulaive co cuve. They ae calculaed i COEFETL.ETL fom he aig ad edig oi of he cumulaive co cuve i aumed fom he umbe of egme ued i i iecewie liea aoximaio ad he choice of ucceive ieval legh o he veical axi o be uch ha each ieval i wice a wide a he ecedig oe. The aamee CCAPK occu i he ETL equaio EQLA1 ad EQLA2 whoe ole i o eue ha vaiable RLAMB(k) lie i he k h ieval i.e. bewee CCAPK(k-1) ad CCAPK(k) whe i aociaed biay vaiable RDELTA(k) = 1. I CCOST0 i he iiial cumulaive co (aig oi o he leaig cuve). I i calculaed i COEFETL.ETL fom he iiial cumulaive caaciy (CCAP0) ad coeodig iiial iveme co (ue iu aamee SC0) ad he oge aio (ue iu aamee PRAT). The aamee CCOST0 occu i he ETL equaio EQIC1 ha defie fi eiod iveme co (io o dicouig). 41 Paamee ha occu i he ETL-ecific equaio bu ha alo occu i o-etl equaio (e.g. TCHLIFE) ae o lied i hi able. 283

284 Maix Cool & Coefficie (idexe) SEG () TEG () CLUSTER () NTCHTEG () PBT () PAT () K WEIG (kc) SALETLINV () Tye Deciio & Calculaio A The ue iu aamee SEG i he umbe of egme i he cumulaive co cuve. The aamee SEG occu i all of hoe ETL equaio ha ae elaed o he iecewie liea aoximaio of he cumulaive co cuve. S TEG i he e of echologie o which edogeou echology leaig (ETL) alie. Each of he ETL equaio ha e TEG a a idex. I The clue maig ad coulig faco ue iu aamee CLUSTER i oly eleva whe modelig clueed edogeou echology leaig. The aamee CLUSTER occu i he ecial ETL clue equaio EQCLU ha defie iveme i ew caaciy (VARNCAP) i he key leaig echology a he weighed um of iveme i ew caaciy of he clueed echologie ha ae aached o he key echology. (The weigh ued ae he umeic value of he CLUSTER aamee.) I The aamee NTCHTEG i oly eleva whe modelig clueed edogeou echology leaig. If TEG i a ETL echology he NTCHTEG(RTEG) i he umbe of clueed echologie ha ae aached o key echology TEG. NTCHTEG i calculaed i COEFETL.ETL fom he clue maig ad coulig faco (CLUSTER). I occu i he ecial ETL clue equaio EQCLU. The leaig idex PBT i a ieal aamee calculaed i COEFETL.ETL. I i deived fom he oge aio PRAT uig he fomula: PBT() = -log(prat())/log(2). PBT doe o occu diecly i he equaio bu i ued i he calculaio of equaio coefficie. The ieal aamee PAT decibe he ecific iveme co of he fi ui. I i deived i COEFETL.ETL uig PBT SC0 ad CCAP0. PAT doe o occu diecly i he equaio bu i ued i he calculaio of equaio coefficie. The e K ha he membe 1-6 ad i ued a idicao fo he kik oi of he iecewie liea aoximaio of he cumulaive co cuve. The umbe of eleme ca be chaged i he *u file if deied. I The ieal aamee WEIG i calculaed i COEFETL.ETL ad i ued a a faco i he calculaio of he legh of he ieval beig ued i he iecewie liea aoximaio of he cumulaive co cuve. The ieval legh o he veical axi ae choe i uch a way ha each ieval i wice a wide a he ecedig oe. I Thi aamee cedi back o he egioal objecive fucio (MRPRICE) he dicoued alvage co of leaig echology iveme ha emai available a he ed of he modelig hoizo. [Noe ha hi aamee doe o ecifically exi i he code bu ahe he exeio i exlicily wie i MMEQTEG.ML. See MRSV i he equaio ecio.] 284

285 6.2 Vaiable The vaiable ha ae ued o model he Edogeou Techological Leaig oio i TIMES ae eeed i Table 6.3 below. A i he cae wih he modelig of lumy iveme he imay ole of he vaiable ad equaio ued o model ETL i o cool he adad TIMES iveme vaiable (VARNCAP) ad he aociaed dyamic co of hee iveme o ETL i ahe elf-coaied. Tha i he VARNCAP vaiable lik he ETL deciio o he e of he model ad he VARIC iveme co vaiable deemie he aociaed coibuio o he egioal iveme co (VAROBJINV). Noe ha he ecial clueed leaig ETL oio doe o equie ay addiioal vaiable a comaed wih he modelig of edogeou echology leaig whe hee ae o clue. Table 6.3. ETL-ecific model vaiable Vaiable (Idexe) VARCC AP () VARCC OST () VARDE LTA (k) VARIC () VARLA MBD (k) Vaiable Deciio The cumulaive iveme i caaciy fo a ETL echology. Thi vaiable eee he iiial cumulaive caaciy (CCAP0) lu iveme i ew caaciy made u o ad icludig he cue eiod. Thi vaiable diffe fom he oal ialled caaciy fo a echology (VARCAP) i ha i iclude all iveme i ew caaciy made u o ad icludig he cue eiod wheea he lae oly iclude iveme ha ae ill available (i.e. whoe life ha o exied ye). The cumulaive co of iveme i caaciy fo a ETL echology. The cumulaive co i ieolaed fom he iecewie liea aoximaio of he cumulaive co cuve. Biay vaiable (ake he value 0 o 1) ued fo a ETL echology o idicae i which ieval of he iecewie liea aoximaio of he cumulaive co cuve he cumulaive iveme i caaciy (VARCCAP) lie. A value of 1 fo hi vaiable fo exacly oe ieval k idicae ha VARCCAP lie i he k h ieval. The oio of he cumulaive co of iveme i caaciy fo a ETL echology (VARCCOST) ha i icued i eiod ad o ubjec o he ame dicouig ha alie o ohe eiod iveme co. Thi vaiable i calculaed a he diffeece bewee he cumulaive co of iveme i caaciy fo eiod ad -1 ad ee he egioal iveme co a of he objecive fucio (EQOBJINV) Coiuou vaiable ued fo a ETL echology o eee he oio of cumulaive iveme i caaciy (VARCCAP) ha lie i he k h ieval of he iecewie liea aoximaio of he cumulaive co cuve. Fo a give ETL echology ad give ime eiod ETL model coai ivolvig hi vaiable ad he aociaed biay vaiable VARDELTA eue ha VARLAMBD i oiive fo exacly oe ieval k. 285

286 6.2.1 VARCCAP() Deciio: Puoe ad Occuece: The cumulaive iveme i caaciy fo a ETL echology. Thi vaiable ack he cumulaive iveme i caaciy fo a ETL echology which he deemie alog wih he oge aio how much he iveme co i o be adjued fo he leaig gai. Thi vaiable i geeaed fo each ETL echology i all ime eiod begiig fom he eiod ha he echology i fi available. I aea i he cumulaive caaciy defiiio coai (EQCUINV) ha defie i a he iiial cumulaive caaciy (CCAP0) lu iveme i ew caaciy (VARNCAP) made u o ad icludig he cue eiod. I alo aea i he cumulaive caaciy ieolaio coai (EQCC). Thi coai equae VARCCAP() o he um ove k of he vaiable VARLAMBD(k) ued o eee he cumulaive iveme i caaciy lyig i he k h ieval of he iecewie liea aoximaio of he cumulaive co cuve. Ui: Boud: PJ/a Gw o Bvkm/a o ay ohe ui defied by he aaly o eee echology caaciy. Thi vaiable i o diecly bouded. I may be idiecly bouded by ecifyig a boud (NCAPBND) o he level of iveme i ew caaciy (VARNCAP) VARCCOST() Deciio: Puoe ad Occuece: The cumulaive co of iveme i caaciy fo a ETL echology. Thi vaiable defie he ieolaed cumulaive co of iveme i caaciy i em of he coiuou vaiable VARLAMBD ad he biay vaiable VARDELTA ad he ieal model aamee ALPH ad BETA. ALPH ad BETA eee he iece o he veical axi ad he loe eecively of he lie egme i he iecewie liea aoximaio of he cumulaive co cuve. Thi vaiable i geeaed fo each ETL echology i all ime eiod begiig fom he eiod ha he echology i fi available. I aea i he cumulaive co ieolaio equaio (EQCOS) ha defie i. I alo aea i he equaio EQIC1 ad EQIC2 ha defie he VARIC vaiable ha eee he oio of he cumulaive co of iveme i caaciy ha ae icued i eiod. Ui: Boud: Millio 2000 US$ o ay ohe ui i which co ae acked. Noe. 286

287 6.2.3 VARDELTA(k) Deciio: Biay vaiable (ake he value 0 o 1) ued fo a ETL echology o idicae i which ieval of he iecewie liea aoximaio of he cumulaive co cuve he cumulaive iveme i caaciy (VARCCAP) lie. Puoe ad To idicae which e o he leaig cuve a echology achieve. A value of 1 fo Occuece: hi vaiable fo ieval k ad zeo value fo ieval k imly ha he cumulaive iveme i caaciy (VARCCAP) lie i he k h ieval of he iecewie liea aoximaio of he cumulaive co cuve. Thi biay vaiable alog wih he aociaed coiuou vaiable VARLAMBD ae geeaed fo each ETL echology i all ime eiod begiig fom he eiod ha he echology i fi available ad fo each ieval i he iecewie liea aoximaio. I aea i he coai EQDEL whoe uoe i o eue ha fo each ETL echology i each eiod i ha a value of 1 fo exacly oe ieval k (wih zeo value fo ieval k); ad i he cumulaive co ieolaio coai (MRCOS). I alo aea i he ai of coai EQLA1 ad EQLA2 whoe uoe i o eue ha VARLAMBD if oiive fo ieval k i bewee he wo beak oi o he hoizoal axi fo ieval k i he iecewie liea aoximaio. (See below ude Puoe ad Occuece fo he vaiable VARLAMBD.) Fially hi biay vaiable aea i wo coai EQEXPE1 ad EQEXPE2 whoe uoe i o educe he domai of feaibiliy of he biay vaiable ad heeby imove oluio ime fo he Mixed Iege Pogam (MIP). Ui: Noe. Thi i a biay vaiable ha ake he value 0 o 1. Boud: Thi biay vaiable i o diecly bouded VARIC() Deciio: Puoe ad Occuece: The oio of he cumulaive co of iveme i caaciy fo a ETL echology (VARCCOST) ha i icued i eiod. Thi vaiable eee he oio of he cumulaive co of iveme i caaciy fo a ETL echology ha i icued i eiod ad o i ubjec o he ame dicouig i he iveme co a of he objecive fucio (EQOBJINV) ha alie o ohe eiod iveme co. Thi vaiable i calculaed a he diffeece bewee he cumulaive co of iveme i caaciy fo eiod ad -1 ad i geeaed fo each ETL echology i all ime eiod begiig fom he eiod ha he echology i 287

288 fi available. Aa fom i aeaace i he objecive fucio hi vaiable aea i he coai EQIC1 ad EQIC2 ha defie i i he fi eiod ha he echology i available ad i ubeque eiod eecively. I alo aea i he alvage of iveme coai (EQOBJSALV) which calculae he amou o be cedied back o he objecive fucio fo leaig caaciy emaiig a he modelig hoizo. Ui: Boud: Millio 2000 US$ o ay ohe ui i which co ae acked. Noe VARLAMBD(k) Deciio: Coiuou vaiable ued fo a ETL echology o eee he oio of cumulaive iveme i caaciy (VARCCAP) ha lie i he k h ieval of he iecewie liea aoximaio of he cumulaive co cuve. Puoe ad A oiive value fo hi vaiable fo ieval k ad zeo value fo ieval k Occuece: imly ha he cumulaive iveme i caaciy (VARCCAP) lie i he k h ieval of he iecewie liea aoximaio of he cumulaive co cuve. Thi coiuou vaiable alog wih he aociaed biay vaiable VARDELTA ae geeaed fo each ETL echology i all ime eiod begiig fom he eiod ha he echology i fi available (START) ad fo each ieval i he iecewie liea aoximaio. Sice hi vaiable eee he oio of he cumulaive iveme i caaciy (VARCCAP) ha lie i he k h ieval of he iecewie liea aoximaio of he cumulaive co cuve he value of EQLAMBD if oiive i equied o be bewee CCAPK(k-1) ad CCAP(k) whee he ieal model aamee CCAPK ae he beak oi o he hoizoal axi i he iecewie liea aoximaio of he cumulaive co cuve. A zeo value fo VARLAMBD i alo allowed. Thee equieme o he value of VARLAMBD ae imoed via he ai of coai EQLA1 ad EQLA2 i which he value fo VARLAMBD i ubjec o lowe ad ue boud of CCAPK(k-1) * VARDELTA ad CCAP(k) * VARDELTA eecively whee VARDELTA = VARDELTA(k) i he biay vaiable aociaed wih VARLAMBD = VARLAMBD(k). Thi vaiable alo aea i he cumulaive caaciy ieolaio coai (EQCC) ad he cumulaive co ieolaio coai (EQCOS). Ui: Boud: PJ/a Gw o Bvkm/a o ay ohe ui defied by he aaly o eee echology caaciy. The ai of coai EQLA1 ad EQLA2 ha ae dicued above have he effec of eihe boudig VARLAMBD bewee CCAPK(k-1) ad CCAP(k) o focig VARLAMBD o be zeo. 288

289 6.3 Equaio The equaio ha ae ued o model he Edogeou Techological Leaig oio i TIMES ae eeed i Table 6.4 below. Sice he imay ole of he vaiable ad equaio ued o model ETL i o cool he adad TIMES iveme vaiable (VARNCAP) ad he aociaed dyamic co of hee iveme ETL i ahe elfcoaied. Tha i he VARNCAP vaiable lik he ETL deciio o he e of he model ad he VARIC iveme co vaiable deemie he aociaed coibuio o he egioal iveme co a objecive fucio (EQOBJINV). Noe ha he ecial clueed leaig ETL oio ivolve oe addiioal equaio (EQCLU) a comaed wih he modelig of edogeou echology leaig whee hee ae o clue. Remide: he ETL fomulaio i acivaed a u ime fom he daa hadlig yem (VEDA-FE) which i u e he $SET ETL YES wich. Table 6.4. ETL-ecific model coai Coai (Idexe) EQCC () EQCLU () EQCOS () EQCUINV () Coai Deciio The Cumulaive Caaciy Ieolaio coai fo a ETL echology. Thi coai defie he cumulaive iveme i caaciy fo a echology (VARCCAP) i a eiod a he um ove all ieval k of he coiuou vaiable RLAMBD(k) ha eee cumulaive iveme i caaciy a lyig i he k h ieval of he iecewie liea aoximaio of he cumulaive co cuve. Coai ha i geeaed oly fo he ecial clueed leaig ETL oio (CLUSTER). Fo a key leaig ETL echology i defie iveme i ew caaciy (VARNCAP) a he weighed um of iveme i ew caaciy of he aociaed clueed echologie. The Cumulaive Co Ieolaio coai fo a ETL echology. Thi coai defie he ieolaed cumulaive co of iveme i caaciy fo a echology (VARCCOST) i a eiod i em of he biay vaiable VARDELTA ad he coiuou vaiable VARLAMBD ad he ieal model aamee ALPH ad BETA. The Cumulaive Caaciy Defiiio coai fo a ETL echology. Defie he cumulaive iveme i caaciy fo a echology i a eiod a he iiial cumulaive caaciy (CCAP0) lu he um of iveme i ew caaciy (VARNCAP) made u o ad icludig hi eiod. GAMS Ref EQETL.ETL EQETL.ETL EQETL.ETL EQETL.ETL 289

290 Coai (Idexe) EQDEL () EQEXPE1 (k) EQEXPE2 (k) EQIC1 () EQIC2 () EQLA1 (k) EQLA2 (k) EQOBJSAL (cu) EQOBJINV (cu) Coai Deciio The coai fo a ETL echology ha eue ha i each eiod hee i exacly oe ieval k fo which he biay vaiable RDELTA(k) ha value 1 (wih zeo value fo ieval k). Oe of wo coai fo a ETL echology o imove MIP oluio ime by educig he domai of feaibiliy of he biay vaiable VARDELTA. Secod of wo coai fo a ETL echology o imove MIP oluio ime by educig he domai of feaibiliy of he biay vaiable VARDELTA. The coai fo a ETL echology ha defie he oio of he cumulaive co of iveme i caaciy (VARIC) ha i icued i he fi eiod of he model hoizo. The coai fo a ETL echology ha defie he oio of he cumulaive co of iveme i caaciy (VARIC) ha i icued i each eiod bu he fi oe. The coai fo a ETL echology ha e a lowe boud o he coiuou vaiable VARLAMBD(k). The coai fo a ETL echology ha e a ue boud o he coiuou vaiable VARLAMBD(k). Fo a ETL echology i eiod aoiaely cloe o he model hoizo a of he iveme co (VARIC) exceed he model hoizo. Thi a of he iveme co i efleced i he calculaio of he alvage value vaiable VAROBJSAL. The edogeouly calculaed co of iveme fo leaig echologie (VARIC) eed o be dicoued ad icluded i he egioal iveme co a of he objecive fucio (EQOBJINV) i lace of he adiioal iveme calculaio uig vaiable VARNCAP. GAMS Ref EQETL.ETL EQETL.ETL EQETL.ETL EQETL.ETL EQETL.ETL EQETL.ETL EQETL.ETL EQOBJSAL.M OD EQOBJINV.M OD 290

291 6.3.1 EQCC() Deciio: The Cumulaive Caaciy Ieolaio coai fo a ETL echology. Puoe ad Occuece: Thi coai defie he cumulaive iveme i caaciy fo a echology i a eiod (VARCCAP) a he um ove all ieval k of he coiuou vaiable VARLAMBD(k) ha eee cumulaive iveme i caaciy a lyig i he k h ieval of he iecewie liea aoximaio of he cumulaive co cuve. Thi coai lik he cumulaive caaciy iveme vaiable (VARCCAP) o he vaiable VARLAMBD. I combiaio wih ohe ETL coai i i fudameal o euig he validiy of he iecewie liea aoximaio of he cumulaive co cuve. Thi equaio i geeaed i each ime eiod fo which he ETL echology i available. Ui: Tye: Techology caaciy ui. Bidig. The equaio i a equaliy (=) coai. Ieeaio of he eul: Pimal: The level of hi coai mu be zeo i a feaible oluio. Dual vaiable: The dual vaiable of mixed iege oblem have limied uefule a dicued i chae 7 of PART I. Equaio EQ CC [( eg) (( ) ) ] Cumulaive iveme i caaciy i he cue eiod { = } VAR CCAP Sum ove all ieval k (i he iecewie liea aoximaio of he cumulaive co cuve) of he coiuou vaiable VARLAMBD i he cue eiod. VAR LAMBD k k 291

292 6.3.2 EQCLU() Deciio: Fo a key leaig ETL echology i defie iveme i ew caaciy (VARNCAP) a he weighed um of iveme i ew caaciy of he aached clueed echologie. The weigh ued ae he umeic value of he CLUSTER aamee. Puoe ad Defie he elaiohi bewee iveme i ew caaciy fo a key leaig Occuece: ETL echology ad iveme i ew caaciy fo he aociaed clueed echologie. Thi equaio i geeaed i each ime eiod fo which he ETL echology i available. I i a key leaig echology ha i ha ha aociaed clueed echologie. Ui: Tye: Moey ui e.g. millio 2000 US$ o ay ohe ui i which co ae acked. Bidig. The equaio i a equaliy (=) coai. Ieeaio of he eul: Pimal: The level of hi coai mu be zeo i a feaible oluio. Dual vaiable: The dual vaiable (DVRCLU) of hi coai i he MIP oluio i of lile iee. Remak: Acivaio of he ecial clueed leaig ETL oio occu auomaically if daa i icluded fo he CLUSTER aamee. Equaio EQ CLU ( eg) ( NTCHTEG > 0) (( ) ) Iveme i ew caaciy (fo key leaig echology eg) i eiod { = } VAR NCAP The weighed um of he iveme i ew caaciy i eiod of he clueed echologie aached o he key leaig echology eg ad whoe START eiod i le ha o equal o. The weigh ued ae he umeic value of he CLUSTER aamee. 292

293 ( > 0) $ CLUSTER ( ) ( CLUSTER * VAR NCAP ) EQCOS() Deciio: The Cumulaive Co Ieolaio coai fo a ETL echology. Puoe ad Occuece Ui: Tye: Thi coai defie he ieolaed cumulaive co of iveme i caaciy fo a echology i a eiod (VARCCOST) i em of he biay vaiable VARDELTA ad he coiuou vaiable VARLAMBD ad he ieal model aamee ALPH ad BETA whee ALPH ad BETA eee he iece o he veical axi ad he loe eecively of he lie egme i he iecewie liea aoximaio of he cumulaive co cuve. Fo a moe ecie defiiio ee Equaio below. I combiaio wih ohe ETL coai i i fudameal o euig he validiy of he iecewie liea aoximaio of he cumulaive co cuve. Thi equaio i geeaed i each ime fo which he ETL echology i available. Moey ui e.g. millio 2000 US$ o ay ohe ui i which co ae acked. Bidig. The equaio i a equaliy (=) coai. Ieeaio of he eul: Pimal: The level of hi coai mu be zeo i a feaible oluio. Dual vaiable: The dual vaiable of mixed iege oblem have limied uefule a dicued i chae 7 of PART I. Equaio EQ COS [( eg) (( ) ) ] Ieolaed cumulaive co of iveme i caaciy i he cue eiod { = } VAR CCOST Sum ove all ieval k (i he iecewie liea aoximaio of he cumulaive co cuve) of ALPH ime he biay vaiable VARDELTA lu BETA ime he coiuou vaiable VARLAMBD fo he cue eiod whee ALPH ad BETA eee he iece o he veical axi ad he loe eecively of he k h ieval. 293

294 ( ALPH k * VAR DELTA k BETA k * VAR LAMBD k ) k 294

295 6.3.4 EQCUINV() Deciio: The Cumulaive Caaciy Defiiio coai fo a ETL echology. Puoe ad Occuece: Ui: Tye: Thi coai defie he cumulaive iveme i caaciy of a echology i a eiod (VARCCAP) a he iiial cumulaive caaciy (CCAP0) lu he um of iveme i ew caaciy made u o ad icludig hi eiod. Thi equaio i geeaed i each ime eiod fo which he ETL echology i available. Techology caaciy ui. Bidig. The equaio i a equaliy (=) coai. Ieeaio of he eul: Pimal: The level of hi coai mu be zeo i a feaible oluio. Dual vaiable: The dual vaiable of mixed iege oblem have limied uefule a meioed above. Equaio EQ CUINV [( eg) (( ) ) ] Cumulaive iveme i caaciy i he cue eiod { = } VAR CCAP Cumulaive iveme i caaciy a he a of he leaig oce. CCAP 0 Sum of he iveme made ice he echology i fi available. u u VAR NCAP u u 295

296 6.3.5 EQDEL() Deciio: The coai fo a ETL echology ha eue ha i each ime eiod hee i exacly oe ieval k fo which he biay vaiable VARDELTA(k) ha value 1 (wih zeo value fo ieval k). Puoe ad To eue ha oly oe of he biay vaiable VARDELTA(k) ha value 1 Occuece: fo each echology. Thi coai i combiaio wih ohe ETL coai i fudameal o euig he validiy of he iecewie liea aoximaio of he cumulaive co cuve. Thi equaio i geeaed i each ime eiod fo which he ETL echology i available. Ui: Tye: Noe. Bidig. The equaio i a equaliy (=) coai. Ieeaio of he eul: Pimal: The level of hi coai mu be 1 i a feaible oluio. Dual vaiable: The dual vaiable of mixed iege oblem have limied uefule a aleady meioed. Equaio EQ DEL [( eg) (( ) ) ] Sum ove all ieval k (i he iecewie liea aoximaio of he cumulaive co cuve) of he biay vaiable VARDELTA i he cue eiod. k VAR DELTA k { = } 1 296

297 6.3.6 EQEXPE1(k) Deciio: Oe of wo coai fo a ETL echology o imove MIP oluio ime by educig he domai of feaibiliy of he biay vaiable VARDELTA. Puoe ad Occuece: Ui: Tye: To imove MIP oluio ime hi coai ake advaage of he obevaio ha cumulaive iveme i iceaig wih ime hu euig ha if he cumulaive iveme i eiod lie i egme k he i will o lie i egme k-1 k-2 1 i eiod 1. Thi equaio i geeaed fo each ETL echology i each ime eiod fo which he echology i available ad excludig he fial eiod (TLAST) ad fo each ieval k i he iecewie liea aoximaio of he cumulaive co cuve. Noe. Bidig. The equaio i a geae ha o equal o ( ) coai. Ieeaio of he eul: Pimal: The level of hi coai mu be geae ha o equal o zeo i a feaible oluio. Dual vaiable: The dual vaiable of mixed iege oblem have limied uefule a aleady meioed. Equaio [( eg) (( ) ) ( )] EQ EXPE1 k < TLAST Sum ove ieval j k of biay vaiable VARDELTA(j) fo he k h ieval i eiod. { } ( VAR DELTA j ) j k Sum ove ieval j k of biay vaiable VARDELTA(j) fo he k h ieval i eiod 1. ( VAR DELTA 1 j ) j k 297

298 6.3.7 EQEXPE2(k) Deciio: Secod of wo coai fo a ETL echology o imove MIP oluio ime by educig he domai of feaibiliy of he biay vaiable VARDELTA. Boh coai ely o he obevaio ha cumulaive iveme i iceaig a ime goe o. Puoe ad Occuece: To imove MIP oluio ime hi coai i deived fom he obevaio ha if cumulaive iveme i eiod lie i egme k he i mu lie i egme k o k1 o k2 ec i eiod 1. Thi equaio i geeaed fo each ETL echology i each ime eiod fo which he echology i available ad excludig he fial eiod (TLAST) ad fo each ieval k i he iecewie liea aoximaio of he cumulaive co cuve. Ui: Tye: Noe. Bidig. The equaio i a le ha o equal o ( ) coai. Ieeaio of he eul: Pimal: The level of hi coai mu be le ha o equal o zeo i a feaible oluio. Dual vaiable: The dual vaiable of mixed iege oblem have limied uefule a aleady meioed. Equaio [( eg) (( ) ) ( )] EQ EXPE2 k < TLAST Sum ove ieval j k of biay vaiable VARDELTA(j) fo he k h ieval i eiod. { } j k ( VAR DELTA j ) Sum ove ieval j k of biay vaiable VARDELTA(j) fo he k h ieval i eiod 1. ( VAR DELTA 1 j ) j k 298

299 6.3.8 EQIC1() Deciio: The coai fo a ETL echology ha defie he oio of he cumulaive co of iveme i caaciy (VARIC) ha i icued i eiod whee = fi eiod of model hoizo. Puoe ad Occuece: Ui: Tye: To deemie he vaiable VARIC which eee he cue iveme co icued i he fi eiod a leaig echology i available accodig o he cumulaive iveme made i ha eiod. whee VARIC he ee he egioal iveme co a of he objecive fucio (EQOBJINV) ubjec o he ame dicouig ha alie o ohe eiod iveme co. Thi equaio i geeaed fo he fi eiod of he model hoizo. Moey ui e.g. millio 2000 US$ o ay ohe ui i which co ae acked. Bidig. The equaio i a equaliy (=) coai. Ieeaio of he eul: Pimal: The level of hi coai mu be zeo i a feaible oluio. Dual vaiable: The dual vaiable of mixed iege oblem have limied uefule a aleady meioed. Equaio EQ IC1 ( eg) ( MIYR = V The oio of he cumulaive co of iveme i caaciy ha i icued i eiod i hi cae he fi eiod he echology i available. 1) { = } VAR IC The cumulaive co of iveme i ew caaciy i he fi eiod ( = MIYRV1). VAR CCOST The iiial cumulaive co of iveme i ew caaciy fo a leaig echology. CCOST 0 299

300 6.3.9 EQIC2() Deciio: The coai fo a ETL echology ha defie he oio of he cumulaive co of iveme i caaciy ha i icued i each eiod beig o he fi eiod. Puoe ad Occuece: Ui: Tye: To deemie he vaiable VARIC which eee he cue iveme co icued i eiod accodig o he cumulaive iveme made hu fa whee VARIC he ee he egioal iveme co a of he objecive fucio (EQOBJINV) ubjec o he ame dicouig ha alie o ohe eiod iveme co. Thi equaio i geeaed i each ime eiod beig o he fi eiod of he model hoizo. Moey ui e.g. millio 2000 US$ o ay ohe ui i which co ae acked. Bidig. The equaio i a equaliy (=) coai. Ieeaio of he eul: Pimal: The level of hi coai mu be zeo i a feaible oluio. Dual vaiable: The dual vaiable of mixed iege oblem have limied uefule a aleady meioed. Equaio EQ > IC2 ( eg) ( MIYR V1) The oio of he cumulaive co of iveme i caaciy ha i icued i eiod. { = } VAR IC The cumulaive co of iveme i ew caaciy a of eiod. VAR CCOST The cumulaive co of iveme i ew caaciy a of he eviou eiod -1. VAR CCOST 1 300

301 EQLA1(k) Deciio: The coai fo a ETL echology ha e a lowe boud o he coiuou vaiable VARLAMBD(k). Puoe ad To e he lowe boud fo VARLAMBD(k) o CCAPK(k-1) * Occuece: VARDELTA whee CCAPK(k-1) i he lef had ed of he k h ieval ad VARDELTA = VARDELTA(k) i he biay vaiable aociaed wih VARLAMBD(k). If biay vaiable VARDELTA = 1 he effec i o e a lowe boud o vaiable VARLAMBD(k) of CCAPK(k-1) wheea if VARDELTA = 0 he effec i o e a lowe boud of 0.Thi coai i combiaio wih ohe ETL coai i fudameal o euig he validiy of he iecewie liea aoximaio of he cumulaive co cuve. Thi equaio i geeaed i each ime eiod fo which he ETL echology i available ad fo each ieval k i he iecewie liea aoximaio of he cumulaive co cuve. Ui: Tye: Techology caaciy ui. Bidig. The equaio i a geae ha o equal o ( ) coai. Ieeaio of he eul: Pimal: The level of hi coai mu be geae ha o equal o zeo i a feaible oluio. Dual vaiable: The dual vaiable of mixed iege oblem have limied uefule a aleady meioed. Equaio EQ LA1 k [( eg) (( ) ) ] Poio of he cumulaive iveme i caaciy ha lie i he k h ieval (of he iecewie liea aoximaio of he cumulaive co cuve) i he cue eiod. { } VAR LAMBD k Lef had ed of he k h ieval (CCAPK(k-1)) ime biay vaiable VARDELTA(k) i he cue eiod. CCAPK k 1 * VAR DELTA k 301

302 EQLA2(k) Deciio: The coai fo a ETL echology ha e a ue boud o he coiuou vaiable VARLAMBD(k). Puoe ad To e he ue boud of VARLAMBD(k) o CCAPK(k) * Occuece: VARDELTA whee CCAPK(k) i he igh had ed of he k h ieval ad VARDELTA = VARDELTA(k) i he biay vaiable aociaed wih VARLAMBD(k). If biay vaiable VARDELTA = 1 he effec i o e a ue boud o vaiable VARLAMBD(k) of CCAPK(k) wheea if VARDELTA = 0 he effec i o e a ue boud of 0.Thi coai i combiaio wih ohe ETL coai i fudameal o euig he validiy of he iecewie liea aoximaio of he cumulaive co cuve. Thi equaio i geeaed i each ime eiod fo which he ETL echology i available ad fo each ieval k i he iecewie liea aoximaio of he cumulaive co cuve. Ui: Tye: Techology caaciy ui. Bidig. The equaio i a le ha o equal o ( ) coai. Ieeaio of he eul: Pimal: The level of hi coai mu be le ha o equal o zeo i a feaible oluio. Dual vaiable: The dual vaiable (DVRLA2) of hi coai i he MIP oluio i of lile iee. Equaio MR LA2 k [( eg) (( ) ) ] Poio of he cumulaive iveme i caaciy ha lie i he k h ieval (of he iecewie liea aoximaio of he cumulaive co cuve) i he cue eiod. { } VAR LAMBD k Righ had ed of he k h ieval (CCAPK(k)) ime biay vaiable RDELTA(k) i he cue eiod. CCAPK k * VAR DELTA k 302

303 EQOBJSAL(cu) Deciio: Regioal alvage value a of objecive fucio adjued o iclude he alvage value of edogeouly deemied iveme (VARIC) i leaig echologie. A alvage value fo a leaig echology iveme exi whe he echical lifeime of he iveme exceed he model hoizo. Puoe ad Ocuece: Ui: Tye: The objecive fucio a calculaig he alvage value i chaged (fo leaig echologie oly) by elacig he adiioal calculaio of he alvage value of iveme wih oe baed o he iveme co of leaig echologie (VARIC). Moey ui e.g. millio 2000 US$ o ay ohe ui i which co ae acked. Bidig. The equaio i a equaliy (=) coai. Equaio EQ OBJSAL cu All he baic objecive fucio em fo calculaig he alvage value (ecio 5.2.8) The calculaed alvage value aociaed wih he ETL echologie. The ieally deived aamee coefficie OBJSIC decibig he oio of he iveme co ha ha o be alvaged. I ake io accou he dicouig of he alvage value. [ * VAR ] eg OBJSIC IC 303

304 EQOBJINV(cu) - ee EQOBJINV i ecio fo a geeal deciio wihou ETL Deciio: Regioal iveme co a of objecive fucio adjued o iclude he edogeouly deemied iveme co (VARIC) fo ew iveme i leaig echologie. Puoe ad Occuece: The objecive fucio a calculaig he iveme co i chaged (fo leaig echologie oly) by elacig he adiioal calculaio of dicoued co of iveme i ew caaciy wih ha of he edogeouly deemied value. Thi equaio i geeaed fo each egio whee he leaig iveme co occu i each ime eiod begiig fom he eiod fo which he ETL echology i available. Equaio EQ OBJINV cu All he baic objecive fucio em fo iveme co (ecio 5.2.2) The calculaed iveme co aociaed wih he ETL echologie. [ * VAR ] eg DISC IC 304

305 7 The TIMES Climae Module Thi chae coai he full documeaio o he Climae Module oio fo he TIMES model. The chae i divided i 8 ecio: ecio 7.1 coai a deailed deciio of he heoeical aoach ake ecio 7.2 o 7.6 ee he aamee vaiable ad equaio equied by he Climae Module. Secio 7.7 dicue he GAMS imlemeaio of he Climae Oio ad ecio 7.8 give ueful efeece fo he chae maeial Fomulaio of he TIMES Climae Module Aoach ake The Climae Module a fom global emiio a geeaed by he TIMES global model ad oceed o comue ucceively: - he chage i CO2 coceaio i hee eevoi - he oal chage (ove e-iduial ime) i amoheic adiaive focig fom ahoogeic caue ad - he emeaue chage (ove e-iduial ime) i wo eevoi. The Climae Equaio ued o efom hee calculaio ae adaed fom Nodhau ad Boye (1999) who ooed liea ecuive equaio fo calculaig coceaio ad emeaue chage. Thee liea equaio give eul ha ae good aoximaio of hoe obaied fom moe comlex climae model (Doue e al. 2004; Nodhau ad Boye 1999). I addiio he o-liea adiaive focig equaio ued by hee auho i he ame a he oe ued i mo model. The choice of he Nodhau ad Boye climae equaio i moivaed by he imliciy of hei aoach ad by he fac ha hei climae module i well-documeed ad acceably accuae. The equaio ued i he module ae heoeically alicable oly o he o-called cabo cycle ad heefoe he coec eame of ohe geehoue gae hould be doe uig diffee e of equaio fo each GHG o aeool (mehae N2O ozoe ulfae ec.). Howeve followig a aoach ued by may eeache (ef ) i i alo oible o ue he CO2 equaio o calculae he imac of ohe gae o climae. To do o i i eceay o fi cove he emiio of each ga io a CO2-equivale quaiy ad o add hee CO2-equivale o fom a ficiiou emiio of oal CO2- equivale which i he eaed a if i wee eal CO2 emiio. The coefficie ued fo coveig emiio of ohe gae io CO2-equivale ae hoe ecommeded by 42 A eaae eo i alo available uo eque coaiig a examle of alicaio of he Climae Module fo a iace of he Global muliegioal TIMES model. 305

306 he IPCC (ef) ad eoduced i he Aedix. Theefoe i wha follow he em CO2 hould eally be hough a CO2-equivale. We ow decibe he mahemaical equaio ued a each of he hee e of he climae module Coceaio (accumulaio of CO2) CO2 accumulaio i eeeed a he liea hee-eevoi model below: he amohee he quickly mixig ue ocea biohee ad he dee ocea. CO2 flow i boh diecio bewee adjace eevoi. The 3-eevoi model i eeeed by he followig 3 equaio whe he e of he ecuio i equal o oe yea: M am (y) = E(y-1) (1 φ am-u ) M am (y-1) φ u-am M u (y-1) (1) M u (y) = (1 φ u-am φ u-lo ) M u (y-1) φ am-u M am (y-1) φ lo-u M lo (y-1) (2) M lo (y) = (1 φ lo-u ) M lo (y-1) φ u-lo M u (y-1) (3) wih M am (y) M u (y) M lo (y): mae of CO 2 i amohee i a quicly mixig eevoi eeeig he ue level of he ocea ad he biohee ad i dee ocea (GC) eecively a eiod (GC) E(y-1) = CO 2 emiio i eviou yea (GC) φ ij ao ae fom eevoi i o eevoi j (i j = am u lo) fom yea y-1 o y Radiaive focig The elaiohi bewee GHG accumulaio ad iceaed adiaive focig F() i deived fom emiical meaueme ad climae model. F() = γ * l (M am () M 0 ) O() l 2 whee: M 0 (i.e.co2atmpreind) i he e-iduial (cica 1750) efeece amoheic coceaio of CO2 = GC γ i he adiaive focig eiiviy o amoheic CO 2 coceaio doublig = 4.1 W/m 2 O() (i.e. EXOFORCING()) i he iceae i oal adiaive focig a eiod elaive o e-iduial level due o ahoogeic GHG o accoued fo i he comuaio of CO2 emiio. Ui = W/m 2. I Nodhau ad Boye (1999) oly emiio of CO2 wee exlicily modeled ad heefoe O() accoued fo all ohe GHG. I TIMES oly ome ohe gae ae fully accoued fo bu ome ae o (e.g. CFC aeool ozoe). I i he modele eoibiliy o 306

307 iclude i he calculaio of O() oly hoe gae o icluded i he CO2- equivale emiio. The aameeizaio of he focig equaio i o cooveial ad elie o he IPCC Secod Aeme Reo by Wokig Gou I (1996). The majo aumio made i RICE i alo made hee: a doublig of CO2 coceaio lead o a iceae i adiaive focig γ = 4.1 W/m 2. The IPCC Thid Aeme Reo by Wokig Gou I (2001) ovide a lighly malle value of 3.7 W/m 2 (baed o Table chae 6). Ue may wa o exeime wih ohe value of he γ aamee Temeaue iceae I he TIMES Climae Module a i may ohe iegaed model climae chage i eeeed by he global mea uface emeaue. The idea behid he wo-eevoi model i ha a highe adiaive focig wam he amoheic laye which he quickly wam he ue ocea. I hi model he amohee ad ue ocea fom a igle laye which lowly wam he ecod laye coiig of he dee ocea. ΔT u (y) = ΔT u (y-1) σ 1 { F(y) λ ΔT u (y-1) σ 2 [ΔT u (y-1) ΔT low (y-1)]} (5) ΔT low (y) = ΔT low (y-1) σ 3 [ΔT u (y-1) ΔT low (y-1)] (6) wih ΔT u = globally aveaged uface emeaue iceae above e-iduial level ΔT low = dee-ocea emeaue iceae above e-iduial level σ 1 = 1-yea eed of adjume aamee fo amoheic emeaue σ 2 = coefficie of hea lo fom amohee o dee ocea σ 3 = 1-yea coefficie of hea gai by dee ocea λ = imaic feedback eoacio) aamee (λ = (cl 4.1/C C beig he emeaue eiiviy o CO 2 coceaio doublig). Remak: i coa wih mo ohe aamee he value of C he emeaue eiiviy o CO 2 coceaio doublig i highly uceai ad may age fom 1 o C o 10 o C. Thi aamee i heefoe a ime cadidae fo eiiviy aalyi o fo eame by obabliliic mehod. 307

308 7.2 Iu aamee of he Climae Module Thi ad he ex 4 ecio decibe he aamee vaiable ad equaio of he climae module. Thi ecio ee he iu aamee ecio 7.3 ee he vaiable ecio 7.4 he equaio ad ecio 7.5 he eoig aamee (i.e. exeio calculaed i ode o be eoed a a of he oluio bu o ue GAMS equaio). Secio 7.6 how he defaul value of he iu aamee. The diicio bewee vaiable ad eoig aamee i imoa: while he fome may be coaied o bouded he lae ae exeio ha may coai ue vaiable bu hemelve may o be bouded. They may oly be ued fo aive eoig uoe. I ou imlemeaio oly he coceaio of CO2 i he hee eevoi ae ue vaiable wheea adiaive focig ad emeaue chage ae eaed a eoig aamee 43. Iu aamee All iu aamee ae ime-ideede exce EXOFOR. Defaul value fo all aamee ae dicued i ecio 7.6. PHIATUP PHIUPAT PHIUPLO PHILOUP (alo deoed φ am-u φ u-am ec): aual CO2 flow coefficie bewee he hee eevoi (AT=Amohee UP=Ue ocea laye LO=Dee ocea laye). Thee ae ime-ideede coefficie. Ui: oe CO2ATM0 CO2UP0 CO2LOW0: Value i iiial eiod (1995 by defaul) of he mae of CO2 i he amohee he ue ocea laye ad he dee ocea laye eecively. Ui: GC CO2ATPREIND: Pe-iduial amoheic ma of CO2. Ui = GC GAMMA (alo deoed γ): adiaive focig eiiviy o a doublig of he amoheic CO 2 ma. Ui: Wa/m 2 LAMBDA (alo deoed λ): a feedback aamee eeeig he equilibium imac of CO 2 coceaio doublig o climae. C beig he emeaue eiiviy o CO 2 coceaio doublig ( o C) ad γ he adiaive focig eiiviy o CO 2 coceaio doublig (W/m 2 ) he: λ = γ / C SIGMA1 (alo deoed σ 1 ): eed of adjume aamee fo amoheic emeaue. 1/σ 1 eee he hemal caaciy of he amoheic ue ocea laye (W-y/m 2 / o C) SIGMA2 (alo deoed σ 2 ): aio of he hemal caaciy of he dee ocea o he afe ae fom hallow o dee ocea (W/m 2 / o C) SIGMA3 (alo deoed σ 3 ): 1/σ 3 i he afe ae (e yea) fom he ue level of he ocea o he dee ocea (y -1 ) DTATM0 DTLOW0: value i iiial eiod (1995 by defaul) of he emeaue chage (w o e-iduial ime) i amohee ad dee laye eecively. Ui: o C 43 Allowig boud ad coai o hee aamee would eul i a o-liea o-covex oimiaio model 308

309 EXOFOR(y): adiaive focig fom No-CO2 gae i each yea fom Ui: Wa/m 2 DTFORC() i he oal chage i focig i eiod. Ui: W/m2. DTTATM() ad DTTLOW(): aveage global emeaue chage i he amohee ad i dee ocea eecively i eiod elaive o he aveage global emeaue i eiduial ime. Ui: o C Ieal aamee I ode o faciliae he wiig of he equaio eveal iemediae quaiie ae couced. Thee ae decibed i each equaio ecio. A addiioal ieal aamee CMDEFAULT i ued o oe he defaul value fo he calibaio quaiie (ee chae 2) Reoig aamee Thee ae hee eoig aamee whoe exeio ae give i ecio 7.5 DTFORC() DTATM() DTLOW() Ohe geeal TIMES aamee (ee chae 3 ) D(): duaio of eiod =1 o T m(): mileoe yea of eiod (aoximae middle of eiod) y deigae a yea while deigae a eiod (agig fom 1 o T) Thee ae a may mileoe yea a hee ae eiod (i.e. T). 309

310 7.3 Climae elaed Vaiable Thee ae fou Climae vaiable each idexed by oly (ime eiod) VARCO2TOT() Deciio: Global aual amoheic CO2 emiio i eiod. Ui: GC VARCO2ATM() VARCO2UP() VARCO2LOW() Deciio: Mae i eiod of CO 2 i he hee quickly mixig eevoi eecively eeeig he amohee he ue level of he ocea ad he dee oceaic laye. Ui: GC 7.4 Climae Equaio Thee ae five equaio: he fi equaio calculae he global emiio of CO2 he ex hee equaio calculae he coceaio of CO2 i he hee eevoi ad he fifh equaio oioally e a ueboud o amoheic coceaio. I addiio hee ae hee addiioal exeio ha calculae he oal adiaive focig ad he emeaue chage i he wo eevoi. Thee exeio ae equaed o hee eoig aamee a how i ecio Equaio: EQCO2TOT Idice: mileoeyea () Tye: = Relaed vaiable: VARCOMNET(CO2) Puoe: Thi equaio defie he global emiio io he amohee o amoheic CO2 emiio i each egio i eiod. Remak: A ue ovided coveio faco (CO2GTC) i equied o cove emiio ui ued i he TIMES model o Gigaoe of cabo. Fo iace if CO2 emiio ae i M CO2 he coveio coefficie mu be ake equal o: Equaio EQ CO2TOT ( MILESTONEYEARS) VAR CO2TOT ( ) CO2GCTC VAR COMNET( CO2 ) = 0 whee R i he e of egio R 310

311 7.4.2 Equaio: EQCO2ATM Idice: mileoeyea () Tye: = Relaed vaiable: VARCO2ATM VARCO2UP VARCO2LOW VARCO2TOT Puoe: Thi equaio defie he ma of CO2 i he global amohee i eiod a a fucio of he mae of CO2 i he hee eevoi a he eviou mileoeyea ad of he CO2 emiio fom eviou o cue mileoeyea. Remak: The coefficie goveig hi equaio deed o he legh of eiod ad -1 ad heefoe equie he comuaio of iemediae quaiie. We follow he TIMES coveio ha each eiod i eeeed by i mileoe yea m() iuaed a o ea he middle of he eiod. Thi exlai he fac ha he coceaio a eiod deed o emiio a eiod -1 ad. The coeodig equaio of he RICE-99 model ae imle fo wo eao: fi RICE ha coa eiod legh ad ecod i RICE he coceaio vaiable eee he fi yea of he eiod ahe ha he middle yea a i TIMES. Equaio: EQ CO2ATM ( MILESTONEYEARS) ( 1) : VAR CO2ATM( ) A11 VAR CO2ATM( 1) A12 VAR CO2UP( 1) A13 VAR CO2LOW ( 1) BB11 VAR CO2TOT ( ) CC11 VAR CO2TOT ( 1) = 0 EQ CO2ATM ( = 1) VAR CO2ATM( ) = CO2ATM 0 whee : { A11 A12 A13} PHI BB11 i he 3 3 maix i he fi ow of i he fi coefficie of : maix : (1 PHI AT UP) PHI AT UP 0 PHI PHI UP AT (1 PHI UP AT PHI UP LO) PHI UP LO he fi colum of maix : BB = CC11 i he fi coefficie of he fi colum of maix : CC = i equal o D()/2 D( ) i he umbe of yea i eiod i equal o y()-y(-1 ) alo equal o D()/ 2 D( 1)/ 2 y( )i he mileoe yea of eiod x deoe he malle iege lage ha o equal o x x deoe he lage iege malle ha o equal o x 0 PHI LO UP (1 PHI LO UP) 2 ( PHI PHI PHI ) 1 ( PHI PHI ) 311

312 7.4.3 Equaio: EQCO2UP Idice: mileoeyea () Tye: = Relaed vaiable: VARCO2ATM() VARCO2UP() VARCO2LOW() VARCO2TOT() VARCO2TOT(-1) Puoe: Thi equaio defie he ma of CO2 i he ue ocea laye i eiod a a fucio of he mae of CO2 i he hee eevoi a he eviou mileoeyea ad of he CO2 emiio fom eviou o cue mileoeyea. Remak: The coefficie goveig hi equaio deed o he legh of eiod ad -1 ad heefoe equie he comuaio of iemediae quaiie. We follow he TIMES coveio ha each eiod i eeeed by i mileoe yea m() iuaed a o ea he middle of he eiod. Thi exlai he fac ha he coceaio a eiod deed o emiio a eiod -1 ad. The coeodig equaio of he RICE-99 model ae imle fo wo eao: fi RICE ha coa eiod legh ad ecod i RICE he coceaio vaiable eee he fi yea of he eiod ahe ha he middle yea a i TIMES. Equaio: EQ CO2UP ( MODELYEARS) ( 1) : VAR CO2UP( ) A21 VAR CO2ATM( 1) A22 VAR CO2UP( 1) A23 VAR CO2LOW ( 1) BB21 VAR CO2TOT ( ) CC21 VAR CO2TOT ( 1) = 0 EQ CO2UP ( = 1) VAR CO2UP( ) = CO2UP 0 whee : { A21 A22 A23} i he ecod ow of maix : PHI (1 PHI AT UP) PHI UP AT PHI i he 3 3 maix : PHI AT UP (1 PHI UP AT PHI UP 0 PHI UP LO BB21 i he ecod coefficie of he fi colum of maix : BB = CC21 i he ecod coefficie of he fi colum of maix : CC = i equal o D()/2 D( ) i he umbe of yea i eiod i equal o y()-y(-1 ) alo equal o D()/ 2 D( 1)/ 2 y( )i he mileoe yea of eiod x deoe he malle iege lage ha o equal o x x deoe he lage iege malle ha o equal o x LO) 0 PHI LO UP (1 PHI LO UP ) 2 ( PHI PHI PHI ) 1 ( PHI PHI ) 312

313 7.4.4 Equaio: EQCO2LOW Idice: mileoeyea () Tye: = Relaed vaiable: VARCO2ATM() VARCO2UP() VARCO2LOW() VARCO2TOT () VARCO2TOT(-1) Puoe: Thi equaio defie he ma of CO2 i he lowe ocea laye i eiod a a fucio of he mae of CO2 i he hee eevoi a he eviou mileoeyea ad of he CO2 emiio fom eviou o cue mileoeyea. Remak: The coefficie goveig hi equaio deed o he legh of eiod ad -1 ad heefoe equie he comuaio of iemediae quaiie. We follow he TIMES coveio ha each eiod i eeeed by i mileoe yea m() iuaed a o ea he middle of he eiod. Thi exlai he fac ha he coceaio a eiod deed o emiio a eiod -1 ad. The coeodig equaio of he RICE-99 model ae imle fo wo eao: fi RICE ha coa eiod legh ad ecod i RICE he coceaio vaiable eee he fi yea of he eiod ahe ha he middle yea a i TIMES. Equaio: 313

314 EQ CO2LOW ( MODELYEARS) ( 1) : VAR CO2LOW ( ) A31 VAR CO2ATM( 1) A32 VAR CO2UP( 1) A33 VAR CO2LOW ( 1) BB31 VAR CO2TOT ( ) CC31 VAR CO2TOT ( 1) = 0 EQ CO2LOW ( = 1) VAR CO2LO( ) = CO2LOW 0 whee : { A31 A32 A33} PHI BB31 i he 3 3 maix i he hod ow of i he hid coefficie of : maix : (1 PHI AT UP) PHI AT UP 0 PHI PHI UP AT (1 PHI UP AT PHI UP LO) PHI UP LO he fi colum of maix : BB = PHI LO UP (1 PHI LO UP) 2 ( PHI PHI PHI ) 1 ( PHI PHI ) CC31 i he hid coefficie of he fi colum of maix : CC = i equal o D()/2 D( ) i he umbe of yea i eiod i equal o y()-y(-1 ) alo equal o D()/ 2 D( 1)/ 2 y( )i he mileoe yea of eiod x deoe he malle iege lage ha o equal o x x deoe he lage iege malle ha o equal o x Remak: The hee coceaio equaio may be wie a a igle veco equaio a follow uig he oaio decibed above: VAR CO21ATM( ) VAR CO2UP( ) PHI VAR CO2LOW ( ) VAR CO21ATM( 1) 2 ( ) 2 ( 1) 2 ( 1) 0 0 VAR CO TOT VAR CO TOT VAR CO UP BB CC = 0 VAR CO2LOW ( 1) 0 0 I i ieeig o comae hi o he RICE-99 veco equaio (Nodhau ad Boye 1999) which wie: 0 VAR CO21ATM( ) VAR CO21ATM( 1) VAR CO2TOT ( 1) 2 ( ) 10 2 ( 1) 10 0 VAR CO UP PHI VAR CO UP = 0 VAR CO2LOW ( ) VAR CO2LOW ( 1) 0 whee PHI10 i he 10-yea aiio maix adoed i RICE-99. A exlaied befoe he imle RICE equaio i due o he coa eiod legh (10 yea) ad he fac ha he mileoe yea of RICE eee he fi yea of a eiod. 314

315 7.4.5 Equaio: EQMXCONC Idice: mileoeyea () Tye: Relaed vaiable: VARCO2ATM Puoe: Thi equaio i acually a ue boud o vaiable VARCO2ATM. I allow he modele o imoe a limi o he amoheic coceaio of CO2 a ay ime eiod. Remak: The ame may be achieved via a ue boud o VARCO2ATM. Equaio: EQ CO2MXCONC ( MODELYEARS) VAR CO2ATM( ) MAXCO2( ) whee MAXCO2( ) i a ue defied ajecoy of maximum allowable amoheic coceaio value (GC) 315

316 7.5 Reoig Paamee DTFORC Idice: mileoeyea () Puoe: Thi eoig aamee defie he oal iceae i adiaive focig due o ahoogeic gae i he amohee elaive o e-iduial ime. I decomoe io wo mai em: focig due o CO2 coceaio (which i edogeou i TIMES) ad focig due o ohe ouce (which i coideed exogeou i TIMES). Exeio DT FORC ( MODELYEARS) DT FORC( ) = GAMMA VAR CO2ATM ( ) l l 2 CO2 PREIND EXOFORC( ) whee : GAMMA i he focig eiiviy o a doublig i amoheic CO2 coceaio CO2 PREIND i he ma of amoheic CO2 a e - iduial ime EXOFORC() i he coibuio of ouce ohe ha CO2 o he chage i focig a eiod 316

317 7.5.2 DTATM Idice: mileoeyea () Puoe: Thi eoig aamee defie he emeaue chage of he amoheic laye (icludig ue ocea) ove he e-iduial emeaue a fucio of he emeaue chage i he wo laye a he eviou eiod ad of he chage i adiaive focig a eviou eiod. Remak: The coefficie goveig hi exeio deed o he legh of eiod ad -1 ad heefoe equie he comuaio of iemediae quaiie. We follow he TIMES coveio ha each eiod i eeeed by i mileoe yea m() iuaed a o ea he middle of he eiod. Thi exlai he fac ha he emeaue chage a eiod deed o focig chage a eiod -1 ad. The coeodig equaio of he RICE-99 model ae imle fo wo eao: fi RICE ha coa eiod legh ad ecod i RICE he emeaue chage vaiable eee he fi yea of he eiod ahe ha he middle yea a i TIMES. Exeio DT ATM ( MODELYEARS) ( 1) DT TATM ( ) = DD11 DT TATM ( 1) DD12 DT TLOW ( 1) EE11 SIGMA1 DT FORC( ) FF11 SIGMA1 DT FORC( 1) DTATM ( = 1) DT TATM ( ) = DT TATM 0 whee : DD11i he fi eleme of he fi ow of he 2 2 maix DD = SIG DD12 i he ecod eleme of he fi ow of he 2 2 maix DD = SIG 1 LAMBDA SIGMA1 SIGMA1 SIGMA2 SIG = SIGMA3 SIGMA1 SIGMA2 1 SIGMA3 1/ SIGMA1 i he oe - yea hemal caaciy coefficie of he amoheic laye 1/SIGMA3 i he oe - yea emeaue afe ae fom amoheic laye o he lowe ocea laye SIGMA3 i he (dimeiole) aio of he hemal caaciy of he lowe ocea laye o he afe ae fom amoheic o lowe ocea laye LAMBDA i a aamee eeeig he equilibium imac of amoheic CO2 coceaio doublig o global amoheic emeaue. Noe ha if C eee he eiiviy of global emeaue o a doublig i CO2 coceaio he followig elaiohi hold : LAMBDA = GAMMA/ C EE11 i he fi eleme of he fi colum of 2 he 2 2 maix EE = SIG SIG SIG FF11 i he fi eleme of he fi colum of 1 2 he 2 2 maiix FF = SIG SIG SIG a defied i he coceaio equaio 317

318 7.5.3 DTLOW Idice: mileoeyea () Puoe: Thi aamee defie he emeaue chage of he lowe ocea laye ove i e-iduial emeaue a a fucio of he emeaue chage i he wo laye a he eviou eiod ad of he chage i adiaive focig a eviou eiod. Remak: The coefficie goveig hi exeio deed o he legh of eiod ad -1 ad heefoe equie he comuaio of iemediae quaiie. We follow he TIMES coveio ha each eiod i eeeed by i mileoe yea m() iuaed a o ea he middle of he eiod. Thi exlai he fac ha he emeaue chage a eiod deed o focig a eiod -1 ad. The coeodig equaio of he RICE-99 model ae imle fo wo eao: fi RICE ha coa eiod legh ad ecod i RICE he emeaue chage vaiable eee he fi yea of he eiod ahe ha he middle yea a i TIMES. Exeio DT LOW ( MODELYEARS) ( 1) DT LOW ( ) = DD21 DT TATM ( 1) DD22 DT TLOW ( 1) EE21 SIGMA1 DT FORC( ) FF21 SIGMA1 DT FORC( 1) DT LOW ( = 1) DT TLOW ( ) = DT TLOW 0 whee : DD21 i he fi eleme of he ecod ow of DD22 i he ecod eleme of he ecod ow he 2 2 maix of he 2 2 maix DD = SIG DD = SIG 1 LAMBDA SIGMA1 SIGMA1 SIGMA2 SIG = SIGMA3 SIGMA1 SIGMA2 1 SIGMA3 1/ SIGMA1 i he oe - yea hemal caaciy coefficie of he amoheic laye 1/SIGMA3 i he oe - yea emeaue afe ae fom amoheic laye o he lowe ocea laye SIGMA3 i he (dimeiole) aio of he hemal caaciy of he lowe ocea laye o he afe ae fom amoheic o lowe ocea laye LAMBDA i a aamee eeeig he equilibium imac of amoheic CO2 coceaio doublig o global amoheic emeaue. Noe ha if C eee he eiiviy of global emeaue o a doublig i CO2 coceaio he followig elaiohi hold : LAMBDA = GAMMA/ C EE21 i he ecod eleme of he fi colum of 2 he 2 2 maix EE = SIG SIG SIG FF21 i he ecod eleme of he fi colum of 1 2 he 2 2 maiix FF = SIG SIG SIG a defied i he coceaio equaio 318

319 Remak: The wo emeaue chage eexeio may be wie a a igle veco equaio a follow uig he oaio decibed above: DT TATM ( ) DT TATM ( 1) DT FORC ( ) SIG SIGMA1 EE SIGMA1 FF DT TLOW ( ) DT TLOW ( 1) 0 DT FORC ( ) 0 = 0 I i ieeig o comae hi o he coeodig RICE-99 equaio i veco fom (Nodhau ad Boye 1999) which ead: DT TATM ( ) DT TLOW ( ) DT TATM ( 1) SIG10 DT TLOW ( 1) SIGMA1 DT FORC( 1) 0 = 0 whee SIG10 i he 10-yea aiio maix adoed i RICE-99. A meioed befoe he imle RICE equaio i due o he coa eiod legh (10 yea) ad he fac ha he mileoe yea of RICE eee he fi yea of a eiod. 319

320 7.6 Defaul value of he climae aamee Table 7.1 how he aumed value of all aamee of he Climae Module exce exogeou focig. Table 7.1. Paamee of he climaic module (defaul value) (GAMS oaio) Paamee Defaul value Gamma 4.1 W/m 2 PHIUPAT e yea PHIATUP e yea PHILOUP e yea PHIUPLO e yea C o diecly eeded 2.91 C LAMBDA SIGMA1 SIGMA2 SIGMA3 CO2ATMPREIND CO2ATM0 CO2UP0 CO2LO0 DELTATATM0 DELTATLOW0 DELTAFORCING0 o diecly eeded e yea 0.44 (o ime dimeio) e yea GC (e-iduial equilibium) 735 GC (i 1995) 781 GC (i 1995) GC (i 1995) 0.43 o C (1995) 0.06 o C (1995) (1995) Imoa Noe : The la 6 aamee ae give fo yea Ue whoe aig mileoe yea i diffee fom 1995 mu ovide aoiae value. Nodhau ad Boye ue he followig fomula o calculae he adiaive focig due o all GHG exce CO2. I he cae of he TIMES global model he eegy elaed mehae ad N2O emiio ae aleady accoued fo i he calculaio of CO2 equivale emiio. Theefoe he fomula below coiue a ue boud fo he adiaive focig due o ohe gae. EXOFORCING() = x (m()-1995) if 1995<=m()<= if m() > 2095 I Nodhau ad Boye (1999) he focig of ohe GHG (CFC CH4 N2O ozoe) ad fom aeool ae coideed o be exogeou. Some of hee gae ae ooly udeood. Moeove ome of hem ae coolled by o-climae olicie (e.g. CFC ozoe aeool). Thee value ae iied by he MAGICC model (Wigley e al. 1994). The IPCC TAR (2001) ovide eimaed age of he focig of o-co 2 GHG i 1998 (chae 6) a well a imlified equaio (Table chae 6). Howeve o aveage value i ovided fo eveal of he gae which make i difficul o comae he exogeou focig ooed by Nodhau ad Boye (1999) o hee udaed eimaio. 320

321 7.7 GAMS imlemeaio All equied GAMS module have bee added o he code. The Climae Module i imlemeed a a TIMES exeio module which i a modula way of addig code o he adad TIMES code. The Climae Module i acivaed by addig he ho ame of he climae exeio (amely: CLI) o he agume of he call fo iimy.mod. Thu he Climae Module i acivaed by he followig call aeme i he u file: $ BATINCLUDE iimy.mod CLI. All he equied climae aamee mu alo be ecified a exlaied i ecio 2.1 ad he climae eul ae made available o he VEDA-BE eo geeao a exlaied i ecio Secificaio of aamee Ue iu aamee All aamee ae alo available fom he VEDA-FE hell whee hey may be modified. The Aedix o chae 2 how he excel emlae ued by VEDA o iiially imo he aamee value. Theeafe hee value may be modified via he VEDA-FE bowe. If hi i doe he modified value oveide he had coded defaul value (if ay). All aamee ame have a efix CM i he GAMS ogam. They ae dicued i fou gou below: PARAMETER CMCO2GTC(REGCOM) Coveio faco bewee ue-defied CO2 commodiie ad GC PARAMETER CMEXOFORC(ALLYEAR) Radiaive focig fom exogeou ouce PARAMETER CMMAXCO2C(ALLYEAR) Maximum allowable amoheic CO2 coceaio PARAMETER CMHISTORY(ALLYEARCMHISTS) Calibaio value fo CO2 ad focig PARAMETER CMCONST(*) Climae module coa 1. The aamee CMCO2GTC i eeded o cove vaiou emiio io he oal CO2-equivale exeed i G of cabo. I a ue model he commodiie ha decibe CO2 o ohe GHG emiio ca have diffee ame ad ui. Eve CO2 emiio may have diffee ui i diffee egio. I addiio i ome model he oal CO2 emiio could be divided io e.g. eegy-elaed emiio ad o-eegy-elaed emiio which ae decibed by eaae commodiie. 321

322 2. The aamee CMEXOFORC ad CMMAXCO2C ae ideical o hoe decibed i chae 1. CMEXOFORC i auomaically ad CMMAXCO2C oioally ieolaed ad exaolaed. 3. The aamee CMHISTORY i ued fo he calibaio value. To imove ideedece of daa fom model yea a yea idex i alo icluded i hi aamee. The e CMHISTS iclude he quaiy ye fo which he calibaio value ae o be give: CO2-ATM Ma of CO2 i he amohee (i GC) CO2-UP Ma of CO2 i he ue ocea laye (i GC) CO2-LO Ma of CO2 i he lowe ocea laye (i GC) DELTA-ATM Temeaue chage i he uface DELTA-LO Temeaue chage i he dee ocea laye If he ue ovide o value fo he CMEXOFORC o CMHISTORY quaiie had-coded defaul value ae alied. The defaul fo CMHISTORY ae coded i INITMTY.CLI ad he defaul fo CMEXOFORC ae coded i RPTEXT.CLI. The value i CMHISTORY ae auomaically deely ie/exaolaed ad he aoiae bae yea calibaio value ae icked u ad ued i he equaio. 4. PARAMETER CMCONST(*) Climae module coa Thi aamee coai he ime-ideede coa ued i he Climae Module: PARAMETER CMCONST(*) / GAMMA 4.1 PHI-UP-AT PHI-AT-UP PHI-LO-UP PHI-UP-LO LAMBDA 1.41 SIGMA SIGMA SIGMA CO2-PREIND /; Ue-ovided value (via he hell) will auomaically oveide he had-coded defaul value how above. Ieal aamee Thee ae equivale o hoe ued i wiig he equaio ad eoig aamee i Chae 1. A addiioal ieal aamee CMDEFAULT i ued o oe he defaul value fo he calibaio quaiie (ee INITMTY.CLI). 322

323 Reoig aamee PARAMETER CMDTFORC(ALLYEAR) Dela focig PARAMETER CMDTTATM(ALLYEAR) Temeaue chage i uface PARAMETER CMDTTLOW(ALLYEAR) Temeaue chage i dee laye Thee eoig aamee coeod o he ame oe i chae 1 wih he adjocio of he efix CM Climae elaed Vaiable VARCO2TOT(): global aual amoheic CO2 emiio i eiod (i GC). VARCO2ATM() VARCO2UP() VARCO2LOW(): mae i eiod of CO 2 i amohee i a quickly mixig eevoi eeeig he ue level of he ocea ad he biohee ad i dee ocea eecively. Ui: GC Thee vaiable ae equivale o hoe decibed i Richad docume. Howeve he eoig aamee decibed above elace he vaiable VARFORCING() VARDELTATATM() ad VARDELTATLOW() i Richad docume Equaio EQCO2TOT(T) Balace fo he oal CO2 emiio i GC EQCO2ATM(T) Balace fo he ma of CO2 i he amohee EQCO2UP(T) Balace fo he ma of CO2 i he ue ocea laye EQCO2LO(T) Balace fo he ma of CO2 i he lowe ocea laye EQCO2MXCONC(T) Coai fo maximum CO2 coceaio The equaio EQCO2TOT(T) ha bee added (i i o icluded i chae 1 deciio of equaio). I combie all egioal CO 2 emiio io he vaiable VARCO2TOT(). All he ohe fou equaio ae equivale o hoe decibed i chae 1. I addiio he ma balace equaio ca be calibaed fo he fi eiod by uig wo aoache of which he defaul i equivale o he mehod decibed i chae 1. I he aleaive calibaio aoach calibaio value fo he yea B(MIYR1) ae ued iead of value fo he mileoe yea. The aleaive aoach ca be acivaed by uig he followig eig i he u-file: $SET CMCALIB B The equaio ad 3.6 have bee elaced by aamee calculaio which ae doe i he file RPTEXT.CLI. 323

324 7.7.4 Examle of ue Becaue all he coa ad calibaio value have had-coded defaul value you ca e he imlemeaio i a vey imle way. Ju add io you daa ecificaio he coveio faco fom CO2 commodiie o he amou of CO2 i GC. Fo examle if CO2 emiio ae decibed by a commodiy amed CO2SUM i egio REG ad ae exeed i M CO2 add he followig aamee iace o you dd-file (o diecly io he u-file): PARAMETER CMCO2GTC / REG.CO2SUM /; Moeove becaue he cue imlemeaio of he Climae Module ha bee imlemeed a a exeio module he CLI exeio module eed o be acivaed e.g. by addig a CLI agume o he call of iimy.mod i he u file a follow: $ BATINCLUDE iimy.mod CLI Fially a decibed above he aleaive calibaio aoach ca be acivaed by icludig he followig eig i he u-file: $ SET CMCALIB B Exoig eul o VEDA4 Fo eoig he eul of he climae module he followig aibue have bee added ad aea i VEDABE: CMdfoc: Dela focig CMdam: Temeaue chage i uface CMdlow: Temeaue chage i dee laye VARco2o: Toal CO2 emiio by mileoe yea (i GC) VARco2am: Ma of CO2 i he amohee (i GC) VARco2u: Ma of CO2 i he ue ocea laye (i GC) VARco2lo: Ma of CO2 i he dee ocea laye (i GC) EQco2cocM: Udicoued aual hadow ice of maximum CO2 coceaio coai. 324

325 Sice hee aibue ae oly ceaed by he model whe he climae module exeio CLI i ued a ecial vdd file called ime2vedaclim.vdd ha o be alied i coecio wih gdx2veda. 7.8 Refeece fo chae 7 Doue L. Edwad N.R. ad A. Hauie (2004). Coulig Climae ad Ecoomic Model i a Co-Beefi Famewok: A Covex Oimizaio Aoach. Submied o Eviomeal Modelig ad Aeme. IPCC Climaic chage 1995: The Sciece of Climae Chage. Iegovemeal Pael o Climae Chage Secod Aeme Reo Wokig Gou I. Cambidge : Cambidge Uiveiy Pe IPCC Climaic chage 2001: The Scieific Bai. Iegovemeal Pael o Climae Chage Thid Aeme Reo Wokig Gou I. Cambidge : Cambidge Uiveiy Pe Nodhau W. D. ad J. Boye Roll he DICE Agai: Ecoomic Model of Global Wamig. Yale Uiveiy mauci ediio. Wigley T.M.L. Solomo M. ad S.C.B. Rae Model fo he Aeme of Geehoue-Ga Iduced Climae Chage. Veio 1.2. Climae Reeach Ui Uiveiy of Ea Aglia UK. 325