Wilmar Deliverable D6.2 (b) Wilmar Joint Market Model Documentation. Peter Meibom, Helge V. Larsen, Risoe National Laboratory

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1 Rsø-R-1552(EN) Wlmar Delverable D6.2 (b) Wlmar Jon Marke Model Documenaon Peer Mebom, Helge V. Larsen, Rsoe Naonal Laboraory Rüdger Barh, Heke Brand, IER, Unversy of Sugar Chrsoph Weber, Olver Voll, Unversy of Dusburg-Essen Rsø Naonal Laboraory Rosklde Denmark January 2006

2 Auhor: Peer Mebom, Helge V. Larsen, Rsoe Naonal Laboraory, Rüdger Barh, Heke Brand, IER, Unversy of Sugar, Chrsoph Weber, Olver Voll, Unversy of Dusburg- Essen Tle: Wlmar Jon Marke Model, Documenaon Rsø-R-1552(EN) January 2006 Absrac: The Wlmar Plannng Tool s developed n he projec Wnd Power Inegraon n Lberalsed Elecrcy Markes (WILMAR) suppored by EU (Conrac No. ENK5-CT ). A User Shell mplemened n an Excel workbook conrols he Wlmar Plannng Tool. All daa are conaned n Access daabases ha communcae wh varous sub-models hrough ex fles ha are expored from or mpored o he daabases. The Jon Marke Model (JMM) consues one of hese sub-models. Ths repor documens he Jon Marke model (JMM). The documenaon descrbes: ISSN ISBN Conrac no.: ENK5-CT Group's own reg. no.: The fle srucure of he JMM. 2. The ses, parameers and varables n he JMM. 3. The equaons n he JMM. 4. The loopng srucure n he JMM. Pages: 59 Tables: appendces References: 7 Rsø Naonal Laboraory Informaon Servce Deparmen P.O.Box 49 DK-4000 Rosklde Denmark Telephone bbl@rsoe.dk Fax

3 Conens Preface 4 1 Inroducon Objecves of he Jon marke model Fle srucure of he Jon Marke Model 6 2 Daa npu fles Ses Parameers 7 3 Fles defnng Ses and Parameers 8 4 Oupu generaon fles 8 5 Oupu fles 9 6 Saus fles 10 7 Conrol fles 10 8 Communcaon wh he LTM model 10 9 Model descrpon Ses, parameers and decson varables Objecve funcon and resrcons Rollng plannng Loopng srucure Calculaon of shadow values Specfcaon of he model used Deermnsc verson of he model References 34 Appendx A : Ses n he model 35 Appendx B : Parameers n he model 41 Appendx C : Decson Varables n he model 47 Appendx D : Inpu daa fles, Se defnons 49 Appendx E : Daa npu fles, Parameers 51 Appendx F : Oupu fles 57 Rsø-R

4 Preface The Wlmar Plannng Tool s developed n he projec Wnd Power Inegraon n Lberalsed Elecrcy Markes (WILMAR) suppored by EU (Conrac No. ENK5-CT ). A User Shell mplemened n an Excel workbook conrols he Wlmar Plannng Tool. All daa are conaned n Access daabases ha communcae wh varous sub-models hrough ex fles ha are expored from or mpored o he daabases. The Jon Marke Model (JMM) consues one of hese sub-models as shown n Fgure 1. Ths repor documens he Jon Marke model (JMM). The documenaon descrbes: 1. The fle srucure of he JMM. 2. The ses, parameers and varables n he JMM. 3. The equaons n he JMM. 4. The loopng srucure n he JMM. Fgure 1: Overvew of Wlmar Plannng ool. The green cylnders are daabases, he red parallelograms ndcae exchange of nformaon beween submodels or daabases, he blue squares are models. The user shell conrollng he execuon of he Wlmar Plannng ool s shown n black. Table 1: Basc nformaon abou he Jon Marke model. Auhors Heke Brand (frs versons and supervson), Peer Mebom, Rüdger Barh, Chrsoph Weber (supervson), Juha Kvluoma Developmen perod November 2002 December 2005 Relaon o oher programs See Fgure 1. Program language GAMS * (General Algebrac Modelng Sysem) wh CPLEX 9.0 Locaon hp:// * see for furher nformaon. 4 Rsø-R-1552(EN)

5 1 Inroducon 1.1 Objecves of he Jon marke model The negraon of subsanal amouns of wnd power n a lberalzed elecrcy sysem wll mpac boh he echncal operaon of he elecrcy sysem and he elecrcy marke. In order o cope wh he flucuaons and he paral unpredcably n he wnd power producon, oher uns n he power sysem have o be operaed more flexbly o manan he sably of he power sysem. Techncally hs means ha larger amouns of wnd power wll requre ncreased capaces of spnnng and non-spnnng power reserves and an ncreased use of hese reserves. Moreover, f wnd power s concenraed n ceran regons, ncreased wnd power generaon may lead o bolenecks n he ransmsson neworks. Economcally, hese changes n sysem operaon have ceranly cos and consequenly prce mplcaons. Moreover hey may also mpac he funconng and he effcency of ceran marke desgns. Even f he wnd power producon s no bded no he spo marke, he feed-n of he wnd power wll affec he spo marke prces, snce nfluences he balance of demand and supply. As subsanal amouns of wnd power wll requre ncreased reserves, he prces on he regulang power markes are furhermore expeced o ncrease. Ye hs s no prmarly due o he flucuaons of wnd power self bu raher due o he paral unpredcably of wnd power. If wnd power were flucuang bu perfecly predcable, he convenonal power plans would have o operae also n a more varable way, bu hs operaon could be scheduled on a day-ahead bass and seled on convenonal dayahead spo markes. I s he unpredcably of wnd power whch requres an ncreased use of reserves wh correspondng prce mplcaons. In order o analyse adequaely he marke mpacs of wnd power s herefore essenal o model explcly he sochasc behavour of wnd generaon and o ake he forecas errors no accoun. In an deal, effcen marke seng, all power plan operaors wll ake no accoun he predcon uncerany when decdng on he un commmen and dspach. Ths wll lead o changes n he power plan operaon compared o an operaon schedulng based on deermnsc expecaons, snce he cos funcons for power producon are usually non-lnear and no separable n me. E.g. even whou flucuang wnd power, sar-up coss and reduced par-load effcency lead o a rade-off for power plan operaon n low demand suaons,.e. noably durng he ngh. Eher he power plan operaor chooses o shu down some power plans durng he ngh o save fuel coss whle operang he remanng plans a full oupu and hence opmal effcency. Or he operaes a larger number of power plans a par load n order o avod sar-up coss n he nex mornng. Ths rade-off s modfed f he nex ncrease n demand s no known wh (almos) cerany. So n an deal world, where nformaon s gahered and processed a no cos, power plan operaors wll ancpae possble fuure wnd developmens and adjus her power plan operaon accordngly. The model presened n he followng descrbes such an deal and effcen marke operaon by usng a sochasc lnear programmng model, whch depcs real world opmzaon on he power marke on an hourly bass wh rollng plannng. Wh effcen markes,.e. also whou marke power, he marke resuls wll correspond o he oucomes of a sysem-wde opmzaon as descrbed n he followng. The cos and prce effecs derved for he negraon of wnd energy n hs model should hen provde a lower bound o he magnude of hese effecs n he real, mperfec world. Rsø-R

6 1.2 Fle srucure of he Jon Marke Model The Jon Marke model consss of a large number of fles, whch can be classfed as follows: 1. Inpu daa fles: conanng he daa npu o he JMM. When he generaon of npu fles o he JMM model s acvaed, all queres n he npu daabase wh names sarng wh O Se or are run and he resuls of hese queres are expored o ex fles wh names <Query name>.nc, cf. Chaper 2. The fles are saved n folder base\model\nc_daabase. 2. Fles conanng he GAMS defnons of ses and parameers conanng npu daa n he JMM (see Chaper 3). The fles are saved n folder base\model\nc_srucure_de. The npu daa fles menoned n pon 1 above are ncluded no hese fles. 3. Fles conanng GAMS code ha generaes he oupu fles of he JMM (see Chaper 4). The fles are saved n folder base\prnnc. 4. The JMM model wres a seres of oupu fles conanng he resuls of a JMM run named OUT_Xyz.csv where Xyz gves some nformaon on he conen of he fle, cf. Chaper 5. These fles are mpored o he oupu daabase. The fles are saved n folder base\model\prnou. 5. Durng he opmsaon n he JMM model wo saus fles SolveSaus.x and ISolveSaus.x are wren, see Chaper Opons fles conanng sengs nfluencng he JMM run (Chaper 7). The seng of some of he opons s done from he user shell and wren n fle Choce.gms. The fles are saved n folder base\model. 7. The JMM model communcaes wh he Long Term Model LTM hrough several fles (Chaper 8). 8. The man model fle Wlmar1_12.gms conanng he specfcaon of he equaons and loopng srucure of he JMM. Also nernal ses and parameers (no holdng npu daa) are defned n hs fle. The fle s saved n folder base\model. The equaons of he JMM are descrbed n Chaper 9 and he loopng srucure of he JMM n Chaper 10. Fnally he choces nvolved n he specfcaon of he model used are descrbed n Chaper Daa npu fles When he generaon of npu fles o he JMM model s acvaed, all queres n he npu daabase wh names sarng wh O Se or are run and he resuls of hese queres are expored o ex fles wh names <Query name>.nc. The synax of hese fles s desgned so ha he fles can be used drecly as nclude fles n a GAMS source fle. The fles are placed n folder Base\Model\Inc_Daabase. 2.1 Ses There are 30 fles O Se *.nc as lsed n Appendx D. These fles specfy he se elemens n he GAMS model. The able n Appendx D has he columns shown n Table 2. 6 Rsø-R-1552(EN)

7 Table 2: Conen of able n Appendx D. Headng Conen Example Fle Name of he JMM npu fle. O Se C.nc 1 GAMS se SET(s) n he GAMS model defned by hs fle. CCC & C (CCC) Type Type of daa. Geography Source able The name of he able n he npu daabase from whch he daa are quered. Base Counres Descrpon A shor descrpon of he daa. Counres 1 : Fle O Se Abc.nc s expored from query O Se Abc n he npu daabase. 2.2 Parameers There are 49 fles *.nc as lsed n Appendx E. These fles hold all daa needed o descrbe he energy sysem ha s o be smulaed by he JMM model. In Appendx E here are wo ables descrbng he fles. The conen of he frs able n Appendx E s shown n Table 3. Table 3: Conen of frs able n Appendx E. Headng Conen Example Fle Name of he JMM npu fle. FUELPRICE_GJ.nc 1 Gams parameer The GAMS parameer ha receves he daa. FUELPRICE_PER_GJ GAMS dependency The se(s) ha he GAMS parameer depends on. YYY, AAA, FFF Descrpon A shor descrpon of he daa. Fuel prce for areas wh own fuel prce scenaros. Un The un for he daa. EUR2002/GJ 1 : Fle Abc.nc s expored from query Abc n he npu daabase. The second able n Appendx E has he columns shown n Table 4. Table 4: Conen of second able n Appendx E. Headng Conen Example Fle Name of he JMM npu fle. FUELPRICE_GJ.nc Source able The man able n he npu daabase from whch he daa are quered. Daa AAA YYY FFF Fuel Prces Source feld The feld n hs daabase able. AnnualFuelPrce Rsø-R

8 3 Fles defnng Ses and Parameers Fles defnng GAMS defnon of ses and parameers are conaned n folder base\model\nc_srucure_de. The npu daa fles menoned n Chaper 2 are ncluded n hese fles. Table 5: Fles conanng GAMS defnon of ses and parameers. Fle basevar.nc fuel.nc fuelp.nc geogr.nc gkfx_all.nc parameer_soch.nc ses.nc ses_soch.nc STARTVALUES.INC ech.nc rans.nc Var.nc Descrpon Defnon of parameers conanng hourly me seres Fuel daa Annually specfed fuel prces Geographcally specfc values Annually specfed generaon capaces Defnon of sochasc parameers Ses used n he program Sochasc ses n he program Sar values of he JMM run (hydro reservor fllng degree) Technology daa Transmsson daa Prce-elasc demand 4 Oupu generaon fles Folder base\prnnc conans fles used o generae he oupu fles from a JMM run. For each oupu parameer, varable or margnal value of an equaon, a fle wres he values of he oupu n queson o a specfc oupu fle. The conen of he oupu fles s descrbed n Chaper 5 and Appendx F. Normally only roo node values are wren ou (.e. sage 1 values), because hese values are he fnal ones beng deermned n he opmsaon run closes o he hours n queson. Furhermore, he sze of he oupu coverng he whole scenaro ree s very large. Table 6 shows he fle names of he oupu generaon fles ha are conaned n folder base\prnnc. Fle prn_fle_defnon.nc conans he defnon of fle names and defnon of ses used o generae he oupu. Fle prn_resuls_node_.nc selecs he oupu o be wren ou by ncluson or excluson of he fles generang he oupu. Table 6: Fles conanng GAMS code ha generaes he oupu fles. Fle names prn_fle_defnon.nc prn_resuls_node_.nc prn-solvesaus.nc prn-out_basetime.nc prn-out_casename.nc prn-out_elec_cons_t.nc prn-out_fuelprce.nc prn-out_heat_cons_t.nc prn-out_igeleccapacity_y.nc prn-out_velec_contentstorage.nc prn-out_vge_ancneg.nc prn-out_vge_ancpos.nc prn-out_vge_consumed_ancneg.nc prn-out_vge_consumed_ancpos.nc Prn-OUT_VGE_CONSUMED_NONSP_ANCNEG.nc Prn-OUT_VGE_CONSUMED_NONSP_ANCPOS.nc prn-out_vge_nonspin_ancneg.nc prn-out_vge_nonspin_ancpos.nc 8 Rsø-R-1552(EN)

9 Fle names prn-out_isdp_hydrores.nc prn-out_isdp_online.nc prn-out_isdp_storage.nc prn-out_iwind_avg_ir.nc prn-out_iwind_realised_ir.nc prn-out_ix3country_t_y.nc prn-out_qancnegeq_m.nc prn-out_qancposeq_m.nc prn-out_qeeqday_m.nc prn-out_qeeqint_m.nc prn-out_qestovolt_m.nc prn-out_qgonlstart_m.nc prn-out_qhequrban_m.nc prn-out_qhstovolt_m.nc prn-out_qnonsp_ancposeq_m.nc prn-out_technologydaa.nc prn-out_unitgroups_in_case.nc prn-out_vcontenthydrores_nt.nc prn-out_vdemandelecflexible.nc prn-out_vgelec.nc prn-out_vgelec_consumed.nc prn-out_vgelec_consumed_dneg.nc prn-out_vgelec_consumed_dpos.nc prn-out_vgelec_dneg.nc prn-out_vgelec_dpos.nc prn-out_vgfuelusage.nc prn-out_vgheat.nc prn-out_vgheat_consumed.nc prn-out_vgonline.nc prn-out_vgstartup.nc prn-out_vheat_contentstorage.nc prn-out_vhydrospillage.nc prn-out_vobj.nc Prn-OUT_VOBJ_R_T.nc Prn-OUT_VXE_NONSPIN_ANCPOS_T.nc Prn-OUT_VXELEC_DNEG_T.nc Prn-OUT_VXELEC_DPOS_T.nc Prn-OUT_VXELEC_T.nc 5 Oupu fles The JMM model wres a seres of oupu fles (comma-separaed ex fles) wh a header row wh varable names. These fles are named OUT_Xyz.csv where Xyz gves some nformaon on he conen of he fle. The fles are placed n folder Base\PrnOu. When mpor of hese fles o he oupu daabase s acvaed, folder Base\PrnOu s searched for all fles complyng wh he fle mask OUT_*.csv. When a parcular fle, say OUT_Abcd.csv, has been found s mpored o daabase able Abcd usng he names n he frs row as feld names. The JMM generaes 53 oupu fles OUT_*.csv as lsed n Appendx F. The able n Appendx F has he followng columns shown n Table 7. Table 7: Conen of able n Appendx F. Headng Conen Example OUT fle Name of he JMM oupu fle. OUT_FuelPrce.csv 1 Ou fle header The header lne. CaseID, AreaID, FuelName, 2 Un The un for he daa. EUR2002/MWh Descrpon A shor descrpon of he daa. Fuel prce for curren smulaon year. 1 : Fle OUT_Abc.csv s mpored o able Abc n he oupu daabase. 2 : The comma separaed ex srngs correspond o feld names n he daabase able. Rsø-R

10 6 Saus fles The JMM model wres wo saus fles SolveSaus.x and ISolveSaus.x o he folder Base\PrnOu. SolveSaus.x gves nformaon on he progress of he opmsaon and a shor ndcaon of possble errors. ISolveSaus.x conans he same nformaon supplemened wh dealed nformaon on any errors. 7 Conrol fles A conrol fle Choce.gms s wren by he User Shell. Ths fle conans some GAMS saemens reflecng he user s choces regardng he deermnsc or sochasc opmsaon run as well as regardng he number of loops n he opmsaon. The fle s placed n folder Base\Model. The conrol fle Choce.gms s a smple GAMS nclude fle. The synax of hs fle can bes be descrbed by an example : * Choce of sochasc or deermnsc model. * Yes = Deermnsc, No = Sochasc. $SeGlobal JMM_De Yes * Number of loops ncluded n one run. SCALAR LOOPRUNS /8/; * The number of nfomes ha are skpped * before solvng he model. Should be equal * o 2+4*N wh N beng a posve neger. SCALAR STARTLOOP /4/; The fle Cplex.op conans sengs nfluencng he runnng of he solver CLPEX used o solve he opmsaon problem. The fle s placed n folder Base\Model. The fle wlmargams.op conans sengs nfluencng he oupu wren n he GAMS ls fle. The fle s placed n folder Base\Model. 8 Communcaon wh he LTM model The JMM model communcaes wh he Long Term Model LTM hrough hree fles placed n folder Base\Model\LTM\LTMmed : WV1reg.med ResFllWsar.med WVcalb.med Fle WV1reg.med gves waer values as funcon of hydro reservor fllng and week number, assumng a one regon hydro reservor model. The un s EUR2002/MWh. The fle s recalculaed once a day by he LTM. Fle ResFllWsar.med gves he relave fllng of hydro reservors for each regon and for he week n queson. I s wren by he JMM each me a day has been smulaed, and s used by he JMM o lookup waer values n fle WV1reg.med. Fle WVcalb.med holds weekly hydro power producon as calculaed by he LTM. I s used by he JMM o calbrae waer values read from fle WV1reg.med. The LTM s acvaed from a JMM run by callng he fle base\model\ltm2.gms. 10 Rsø-R-1552(EN)

11 9 Model descrpon In a lberalzed marke envronmen s possble no only o change he un commmen and dspach, bu even o rade elecrcy a dfferen markes. The fundamenal model analyses power markes based on a hourly descrpon of generaon, ransmsson and demand, combnng he echncal and economcal aspecs, and derves hourly elecrcy marke prces from margnal sysem operaon coss. Ths s done on he bass of an opmsaon of he un commmen and dspach akng no accoun he radng acves of he dfferen acors on he consdered energy markes. In hs model four elecrcy markes and one marke for hea are ncluded: 1. A day-ahead marke for physcal delvery of elecrcy where he EEX marke a Lepzg s aken as he sarng pon. Ths marke s cleared a 12 o clock for he followng day and s called he day-ahead marke. The nomnal elecrcy demand s gven exogenously. 2. An nra-day marke for handlng devaons beween expeced producon agreed upon he day-ahead marke and he realzed values of producon n he acual operaon hour. Regulang power can be raded up o one hour before delvery. In hs model he demand for regulang power s caused by he forecas errors conneced o he wnd power producon. 3. A day-ahead marke for auomacally acvaed reserve power (frequency acvaed or load-flow acvaed). The demand for hese ancllary servces s deermned exogenously o he model. 4. An nra-day marke for posve secondary reserve power (mnue reserve) manly o mee he N-1 creron and o cover he mos exreme wnd power forecas scenaros ha are negleced by he scenaro reducon process. Hence, he demand for hs marke s gven exogenously o he model. 5. Due o he neracons of CHP plans wh he day-ahead and he nra-day marke, an nra-day marke for dsrc heang and process hea s also ncluded n model. Thereby he hea demand s gven exogenously. The model s defned as a sochasc lnear programmng model (Brge and Louveaux, 2000), (Kall and Wallace, 1994). The sochasc par s presened by a scenaro ree for possble wnd power generaon forecass for he ndvdual hours. The echncal consequences of he consderaon of he sochasc behavour of he wnd power generaon s he paronng of he decson varables for power oupu, for he ransmed power and for he loadng of elecrcy and hea sorages: one par descrbes he dfferen quanes a he day-ahead marke (hus hey are fxed and do no vary for dfferen scenaros). The oher par descrbes conrbuons a he nra-day-marke boh for up- and down-regulaon. The laer consequenly depends on he scenaros. So for he power oupu of he un group a me n scenaro s we fnd DAY _ AHEAD + P + P P. The varable DAY _ AHEAD denoes he energy sold a he P, s, =,, s,, s, + day-ahead marke and has o be fxed he day before. and denoe he posve and negave conrbuons o he nra-day marke. Analogously he decson varables for he ransmed power and he loadng of elecrcy and hea sorages are defned accordngly. P, P, s, P, s, Furher he model s defned as a mul-regonal model (cf. Fgure 2). Each counry s sub-dvded no dfferen regons, and he regons are furher sub-dvded no dfferen Rsø-R

12 areas. Thus, regonal concenraons of nsalled wnd power capacy, regons wh comparable low demand and occurrng bolenecks beween he model regons can be consdered. The subdvson no areas allows consderng ndvdual dsrc heang grds. Counres Regons Areas Elecrcal Transmsson Fgure 2: Illusraon of he geographcal enes and he ransmsson possbles 9.1 Ses, parameers and decson varables The used labellng of ses, parameers and decson varables for he documenaon of he objecve funcon and resrcons s lsed n Table 8, Table 9 and Table 10, respecvely. The name n he programme code of he se, parameer or varable (compare appendx A, B and C) s ndcaed n he end of he descrpon of each se, parameer or varable. Table 8: Ses n he model. Ses Descrpon a, A Index/ se of areas. IA, AAA F Se of used fuels. FFF, I Index/ se of un groups. G BACKPRESSURE I Se of un groups wh backpressure urbnes. IGBACKPR CHP I Se of combned hea and power producng un groups. IGELECANDHEAT ELEC ELEC I, I Se of power producng un groups, se of power producng un r groups n regon r. IGELEC _ ONLY Se of un groups producng only power. IGELECONLY ELEC I ELECSTORAGE I Se of elecrcy sorages (e. g. pumped hydro sorages). IGELECTSTORAGE EXTRACTION I Se of un groups wh exracon-condensng urbnes. IGEXTRACTION HEAT I Se of hea producng un groups, se of hea producng un groups a n area a. IGHEAT(G) HEATONLY I Se of un groups producng only hea (. e. hea boler, hea pump, hea sorage). IGHEATONLY(G) HEAT I, 12 Rsø-R-1552(EN)

13 Ses Descrpon HEATPUMP I Se of elecrc hea pumps. IGHEATPUMP HEATSTORAG E I Se of hea sorages. IGHEATSTORAGE HYDRO HYDRO I, I Se of hydro sorages, se of hydro sorages n regon r. r IGHYDRORES ONLINE I Se of un groups wh mnmum resrcon for power producon. IGONLINE RAMP I Se of un groups for whch a ramp rae < 1 s defned. IGRAMP SPIN I Se of spnnng un groups. IGSPINNING STORAGE I Se of sorages wh loadng capacy,.e. elecrcy and hea sorages. IGSTORAGE USING _ FUEL I Se of un groups usng fuel. IGUSINGFUEL UP DOWN k, K, K Se of prce flexble power demand seps on he day-ahead marke, K UP seps ha ncrease demand relavely o nomnal power demand, K DOWN downward seps. DEF_U/DEF_D r, R Index/ se of regons. IR, RRR NEIGHBOUR R r Se of regons, whch are he neghbour regons of regon r s, S Index/ se of scenaros. NODE,T Se of me seps whn a scenaro ree, T descrbes he las me sep whn a scenaro ree. T, IENDTIME(T) NOT _ FIXED T Tme seps where he decson varables of he day-ahead marke are no fxed. ITSPOTPERIOD(T) Table 9: Parameers n he model. Parameers Descrpon START _UP c Cos parameer of un group for he sar-up of addonal capacy. GDATA(IA,G,'GDSTARTUPCOST') ANC, UP ANC, DOWN d r,, d r Demand for ancllary reserve (up/down regulaon)., IDEMAND_ANCPOS/IDEMAND_ANCNEG ELEC d r, Nomnal demand for me sep n regon r. IDEMANDELEC ELEC,EXPORT d r, Elecrcy expor from regon r o hrd counres a me sep HEAT d a, Hea demand for me sep n area a. IDEMANDHEAT DISLOSS _ H Hea dsrbuon loss. DISLOSS_H NONSP, ANC, UP d, Demand for non-spnnng secondary reserve (up regulaon). rs,, IDEMAND_NONSPIN_ANCPOS NONSP,ANC,DOWN d r, e Fuel consumpon parameer for un group when onlne. GDATA(IA,G, GDSECTION ) f Fuel consumpon parameer for un group when producng power dependng on he effcency a he acual load. GDATA(IA,G, GDSLOPE ) EMISSION f Emsson of CO 2 or SO 2 when burnng fuel F. F FDATA(FFF,'FDCO2') or FDATA(FFF,'FDSO2') PRICE f Fuel prce of fuel F n regon r. IFUELPRICE_Y F,r SUBSIDY f Subsdy for power produced on plans usng bomass or wase. Fr, ELEC_SUBSIDY(C,FFF) TAX f Tax on emsson of CO 2 or SO 2 from power plans. EMISSION M_POL('TAX_CO2',C) or M_POL('TAX_SO2',C) f Tax of usng fuel F n un group. GDATA(IA,G,'GDFUELTAX') TAX F,r Rsø-R

14 Parameers TAX HEATPUMP, r Descrpon f Tax of usng elecrcy n hea pumps. TAX_HEATPUMP MIN _ BOUND H Mnmum bound on hea producon., IHEATGEN_LOWBOUND_VAR_T INFLOW, Naural nflow no hydro sorage a me sep. IHYDROINFLOW_T_Y RUNRIVER Producon of run-of-rver power plan a me sep., IRUNRIVER_VAR_T SOLAR Producon of solar plan a me sep. ISOLAR_VAR_T, LOADLOSS Facor consderng he load loss of elecrcy and hea sorages. GDATA(IA,G,'GDLOADLOSS') TRANS,COST l Transmsson cos per MWh. XCOST r,r TRANS,MAX l Maxmum ransmsson capacy from regon r o r. r,r IXCAPACITY_Y o Operaon and manenance cos parameer for un group. GDATA(IA,G,'GDOMVCOST') ACTUAL _WIND p Acual wnd power producon capacy n regon r, n scenaro s a r,s, me sep. IWIND_REALISED_IR BID _WIND p Expeced wnd power producon n regon r a me sep when he r, day-ahead marke s cleared (12 o clock). IWIND_BID_IR EXPECTED _WIND p Expeced wnd power producon n regon r a me sep. r, IWIND_AVG_IR FLEXIBLE _ PRICE p Prce of flexble demand sep. IDEFLEXIBLEPRICE_T rk,, p Avalably facor for un group. IGKDERATE _ Maxmum elecrcy capacy of un group. IGELECCAPACITY_Y MIN _ PROD p Mnmum elecrcy capacy facor of un group, when un group s onlne. GDATA(IA,G,'GDMINLOADFACTOR') WATERVALUE p r, of waer n hydro sorages n regon r a me sep. ISDP_HYDRORES _ PROD Maxmum hea capacy of un group (only for hea generang un groups). IGHEATCAPACITY_Y RAMPRATE Maxmum ncrease of power producon whn an hour relave o he nsalled capacy. GDATA(IA,G,'GDRAMP') ELECSTORAGE Sp Shadow value for elecrcy sorage conen a he end of a scenaro ELECSTORAGE I, s, T ree. ISDP_STORAGE HEATSTORAGE Sp Shadow value for hea sorage conen a he end of a scenaro ree. HEATSTORAGE I, s, T ISDP_STORAGE HYDRO Sp Shadow value for hydro sorage conen a he end of a scenaro HYDRO I,s,T ree. ISDP_HYDRORES ONLINE Sp Shadow value for un group beng onlne a he end of a scenaro ONLINE I,s,T ree. ISDP_ONLINE Leadme of un group. GDATA(IA,G,'GDLEADTIME') GKDERATE MAX PROD p MAX q LEADTIME MIN MIN _ OP Mnmum operaon me of un group. GDATA(IA,G,'GDMINOPERATION') _ SD Mnmum shu down mes of un group. GDATA(IA,G,'GDMINSHUTDOWN') MAX w Maxmum loadng capacy of elecrcy or hea sorage. IGSTOLOADCAPACITY_Y XLOSS Transmsson loss proporonal o ransmed energy. XLOSS(IRE,IR) 14 Rsø-R-1552(EN)

15 Parameers Descrpon CB δ Hea rao of CHP urbne. GDATA(IA,G,'GDCB') FULLLOAD η Effcency of un group a full load. GDATA(IA,G, GDFULLLOAD ) Reducon of elecrc power producon due o hea producon of CHP urbne. GDATA(IA,G,'GDCV') ELECSTORAGE,MAX v Maxmum sorage conen of elecrcy sorage. IGSTOCONTENTCAPACITY_Y HEAT,MAX v Maxmum sorage conen of hea sorage. IGSTOCONTENTCAPACITY_Y HYDRO,MAX v Maxmum sorage conen of hydro sorage. IGHYDRORESCONTENTCAPACITY_Y HYDRO,MIN v Mnmum sorage conen of hydro sorage. IGHYDRORESMINCONTENT_Y Occurrence probably of scenaro s. IPROBREACHNODE γ π s Table 10: Decson varables n he model. Decson varables Descrpon FLEX _ DAY AHEAD D Amoun of flexble demand acvaed for prce sep k. rk,, VDEMANDELECFLEXIBLE_T F Fuel usage n regon r n scenaro s a me sep. r,s, VGFUELUSAGE_NT P, s, Realsed power oupu of un group n scenaro s a me sep. No name + P, s,, P, s, Down / up-regulaon for balancng marke of urbne n scenaro s a me sep. VGELEC_DPOS_NT/ VGELEC_DNEG_NT P r, r, s, Realsed ransmsson of power from regon r o regon r n scenaro s a me sep. No name ANC,+ ANC, P,, P Conrbuon of un group o ancllary reserve (up/down, regulaon) a me sep. VGE_ANCPOS/VGE_ANCNEG DAY _ AHEAD P Power of urbne sold o day-ahead marke a me sep., VGELEC_T DAY _ AHEAD,WINDSHED P Wnd power sheddng of wnd power plan a he day-ahead, marke for me sep. VWINDSHEDDING_DAY_AHEAD NONSP,ANC,+ P,,s, Conrbuon of un group o non-spnnng secondary reserve (up/down regulaon) n scenaro s a me sep. VGE_NONSPIN_ANCPOS ONLINE, Onlne capacy of un group a me sep. VGONLINE_NT s NONSP,ANC P,s, P, STARTUP P Sared capacy of un group n scenaro s a me sep.,s, VGSTARTUP_NT TRANS,+ TRANS, P, r, r, s, P Conrbuon o up / down regulaon a balancng marke n regon r, r, s, r by ncreased/decreased ransmsson of power from regon r o regon r n scenaro s a me sep. VXELEC_DPOS_NT/VXELEC_DNEG_NT TRANS, DAY AHEAD Planned ransmsson from regon r o regon r when bddng on P r, r, he day-ahead marke. VXELEC_T Reservaon of up / down regulaon a non-spnnng secondary reserve marke n regon r by ncreased/decreased ransmsson of power from regon r o regon r n scenaro s a me sep. VXE_NONSPIN_ANCPOS P Wnd sheddng of wnd power plan a he nra-day marke n P, TRANS,NONSP,ANC,+ r,r,s, TRANS,NONSP,ANC, P r,r,s, WIND, r,s, scenaro s a me sep. VGELEC_DNEG_NT(IA,IGWIND,NODE,T) Rsø-R

16 Decson varables Descrpon Q, s, Realsed hea oupu of un group n scenaro s, a me sep. VGHEAT_NT ELECSTORAG E V Conen of elecrcy sorage n scenaro s a me sep.,s, VCONTENTSTORAGE_NT HEATSTORAG E V Conen of hea sorage n scenaro s a me sep.,s, VCONTENTSTORAGE_NT HYDRO V Conen of hydro sorage n scenaro s a me sep.,s, VCONTENTHYDRORES_NT W, s, Realsed loadng of elecrcy sorage or elecrcy consumpon of hea pump n scenaro s a me sep. No name + W, s,, W, s, Down / up regulaon a nra-day marke of elecrcy sorage n scenaro s a me sep. VGELEC_CONSUMED_DPOS_NT /VGELEC_CONSUMED_DNEG_NT ANC,+ ANC, W,, W Conrbuon of elecrcy sorage o ancllary reserve (down/up, regulaon). VGE_CONSUMED_ANCPOS/ VGE_CONSUMED_ANCNEG DAY AHEAD W Fxed loadng capacy of elecrcy sorage a he day-ahead, marke. VGELEC_CONSUMED_NT HEAT W Loadng of hea sorage n scenaro s a me sep.,s, VGHEAT_CONSUMED_NT NONSP,ANC + W,,s, NONSP,ANC W,s, Conrbuon of elecrcy sorage o non-spnnng secondary reserve (down / up regulaon) n scenaro s a me sep. VGE_CONSUMED_NONSP_ANCPOS 9.2 Objecve funcon and resrcons In he followng equaons he name of he equaon n he model code s gven n he sar of he equaon. The objecve funcon (1) mnmzes he oal operaon coss Vobj n he whole consdered sysem. The frs summand of he objecve funcon descrbes he fuel coss. The followng hree summands consder he operaon and manenance coss of elecrcy and hea producon. The nex summand deermnes he coss due o sarng addonal capacy and n he followng summand ransmsson coss are consdered. Nex fuel axes are deermned followed by he ax on power used n hea pumps. The acual mplemenaon of he fuel axes n he model s more complcaed han shown n (1), because he ax schemes dffer beween counres. The emsson axes on CO 2 and SO 2 are consdered n he nex lne. The effec of SO 2 emsson reducon equpmen s aken no accoun n he model when calculang he SO 2 ax. The subsdy for power producon based on bomass or wase s aken no accoun by he nex summand. The value of power plan uns beng onlne, he value of sored waer n hydro sorages and he value of he conen of elecrcy and hea sorages a he las me sep T of a scenaro ree reduces he oal operaon coss. The values for un groups beng onlne and for elecrcy and hea sorages are deermned by he shadow values of he respecvely equaons (28), (40) and (45) n a prevous plannng loop (see Chaper 10 for an explanaon of he calculaon of hese shadow values). The values for he conen of hydro sorages are derved wh a furher model ha opmzes he fll level of hydro sorages n he long-erm over a year, cf. (Mebom e al, 2004). Prce flexble power demand on he day-ahead marke s represened by he wo las summands wh he ncrease n consumer surplus when consumpon s ncreased and he decreased n consumer surplus when demand s reduced. 16 Rsø-R-1552(EN)

17 In he acual model code he ncrease n sysem coss when slack varables are acvaed s also ncluded n QOBJ alhough no shown n (1). QOBJ: mn Vobj = I USING _ FUEL I I I I ELEC CHP HEATONLY ONLINE s S T s S T s S T s S T s S T π F π op PRICE s r, s, F, r s, s, π oγ Q rr, s S T I I I I I I I I T USING _ FUEL HEATPUMP USING _ FUEL USINFG _ FUEL ONLINE HYDRO STORAGE STORAGE π l s, s, π oq π c s, s, STARTUP STARTUP s, s, TRANS, COST s rr, rrs,,, s S T s S T s S T s S T π F π f f P P TAX s r, s, F, r TAX s HEATPUMP, r, s, EMISSION TAX s r, s, F EMISSION SUBSIDY s F, r, s, ONLINE ONLINE π ssp ONLINE P ONLINE I, s, T I, s, T s S T s S T = 1 r R k K T = 1 r R k K s S T π Sp f W π F f f π f P HYDRO HYDRO s HYDRO I, s, T HYDRO I, s, T π Sp ELECSTORAGE ELECSTORAGE s ELECSTORAGE I, s, T STORAGE I, s, T HEATSTORAGE HEATSTORAGE π ssp HEATSTORAGE V STORAGE I, s, T I, s, T s S T UP D DOWN V V FLEX _ DAY AHEAD FLEXIBLE _ PRICE rk,, rk,, D p FLEX _ DAY AHEAD FLEXIBLE _ PRICE rk,, rk,, p Objecve funcon Fuel coss. Varable O&M coss. Varable O&M coss. Varable O&M coss. Sar-up coss. Transmsson coss. Fuel ax. Elecrcy ax for hea pumps. Tax on emsson of CO 2 and SO 2. Subsdy for power produced on plans usng bomass or wase. Shadow prce for uns beng onlne a he end of a scen. ree. Shadow prce for hydro sorage conen a he end of a scen. ree. Shadow prce for elec. sorage conen a he end of a scen. ree. Shadow prce for hea sorage conen a he end of a scen. ree. Increase n consumer surplus due o ncreased demand. Decrease n consumer surplus due o decreased demand. (1) Marke resrcons for he balance of supply and demand Rsø-R

18 The demand consran s spl up no wo consrans: one balance equaon for he power sold a he day-ahead marke and one balance equaon for he power sold a he nra-day marke. The consran for he me seps, where he day-ahead marke s opmsed (.e. a 12 o clock), s defned n (2). The equaon requres ha he sum of he power produced ncludng he expeced wnd power producon plus he mpored power mnus he planned wnd power sheddng equals he sum of he expored power o hrd counres ha are no consdered n he model plus he power used for loadng elecrcy sorages and elecrc hea pumps plus he expored power o oher regons plus he elecrcy demand modfed wh he amouns of prce flexble consumpon acvaed. The varable consderng wnd power sheddng a he day-ahead marke can be urned off wh he use of a bnary parameer no shown n (2). The same apples for he prce flexble demand (See Chaper 11 for an explanaon of he model selecons ha can be done usng bnary parameers). QEEQDAY: I ELEC r DAY _ AHEAD RUNRIVER SOLAR BID _ WIND DAY _ AHEAD, WIND _ SHED,,, r, r, + (1 XLOSS) P r TRANS, DAY AHEAD r, r, ELEC, EXPORT DAY _ AHEAD r,, r ELECSTORAGE HEATPUMP I I r TRANS ELEC FLEX, + FLEX, P + d rr,, r, + Drk,, Drk,, NEIGHBOUR UP DOWN r R k K k K r P p P = d + + r W NOT _ FIXED T, r R If he expeced wnd power producon s hgher han he acual wnd power producon, a demand for up regulaon exss. Conversely, here exss a demand for down regulaon f he expeced wnd power producon s lower han he acual one. The balance equaon for he balancng marke s descrbed by he followng equaon (3). The up and down regulaon of he un groups and he up and down regulaon of he loadng of elecrcy sorages as well as he up and down regulaon by ncreased / decreased mpor has o be equal o he dfference beween he expeced wnd power producon a he bddng hour of he day-ahead marke (hereby he possble wnd sheddng a he day-ahead marke has o be consdered) and he acual wnd power producon mnus he decreased / ncreased expor. As he model allows wnd sheddng also a he nra-day marke, he WIND, erm s added o he equaon. Furher he consderaon of ncreased / decreased P r, s, mpor or expor can be urned off usng a bnary parameer,.e. a model run ha do no allow ransmsson of regulang power can be run. (2) 18 Rsø-R-1552(EN)

19 QEEQINT: + + s,, s,, s,, s,, ELEC I ELECSTORAGE HEATPUMP I I rr, ( P P ) + ( W W r r r + (1 XLOSS)( P P ) P = p P TRANS, + TRANS, WIND, rr,, rr,, rs,, BID _ WIND DAY _ AHEAD, WIND _ SHED r, r, p + ( P P ACTUAL _ WIND TRANS, rs,, rr,, r, r TRANS, + ) rr,, r R, s S, T The balance on he hea marke s gven as he hea producon on CHP plans, hea bolers, hea pumps and unloadng of hea sorages equal o he loadng of hea sorages and an exogenously gven hea demand dvded wh he hea dsrbuon loss for each area (4). The GAMS code for havng prce flexble hea demand s mplemened bu due o lack of daa hs possbly s no used presenly. ) (3),s,, s, a, 1 SS _ H HEAT HEAT QHEQ: Q = W + d ( DISLO ) HEAT Ia HEATSOTRAGE I a A, s S, T The represenaon of each ndvdual dsrc heang grd exsng n realy as a separae hea area n he model s no feasble due o calculaon me and daa resrcons. Therefore he dsrc heang grds are aggregaed n he model. When aggregang wo CHP plans wh dfferen margnal producon coss, ha n realy produce n separae hea grds, he rsk s ha he CHP plan wh he cheapes producon coss produce relavely o much and he expensve CHP plan produce o lle due o he aggregaon. For Germany hs problem has been reduced by usng mnmum bounds on he hea producon from dfferen CHP plans (5). The mnmum bounds are calculaed wh a separae mehodology descrbng he hea generang uns n Germany (Weber & Barh 2004). (4) QGHEATMIN: Q HEAT H I, s S, T (5) MIN _ BOUND,s,, Demand for ancllary and non-spnnng secondary reserves The day-ahead marke for ancllary servces (.e. prmary reserves) s descrbed by demand resrcons for up (6) and down regulaon (7). The exogenously gven demand for up regulaon can be suppled eher by ncreased power producon of he power producng un groups or by reduced loadng of elecrcy sorages and use of hea pumps, whereas he exogenously gven demand for down regulaon can be mee by decreasng he power producon or by ncreasng he loadng of elecrcy sorages and use of hea pumps. The equaon (8) ensures ha only spnnng un groups can provde SPIN prmary reserves. Currenly hs equaon s replaced by usng he subse I n equaon (6) und (7). Rsø-R

20 QANCPOSEQ: I ELEC r P ANC, +, + I ELECSTORAGE I HEATPUMP W ANC, +, d ANC,UP r, r R, T (6) QANCNEGEQ: I ELEC r P ANC,, + I ELECSTORAGE I HEATPUMP W ANC,, d ANC,DOWN r, r R, T (7) QANC0: 1 ( 1) P MIN _ PROD p,s, P ANC, +, SPIN I r R, s S, T (8) The marke for non-spnnng secondary reserves (mnue reserves) s descrbed by demand resrcon for up regulaon (9). The exogenously gven demand for up regulaon n a regon can be suppled eher by ncreased power producon of he power producng un groups, by reduced loadng of elecrcy sorages as well as use of hea pumps or can be mpored from anoher regon, whch requres reservaon of ransmsson capacy. The oal demand for posve secondary reserve n a gven me perod and sae s me parly by he varables n (9) and parly by reservaon of onlne capacy usng he up regulaon varables n (3) for provdng up regulaon n he case of he expeced wnd power producon beng hgher han he wnd power forecas n a gven sae. Therefore he demand for secondary reserve n (9) s reduced n he case ha he acual wnd power producon s lower han expeced. QNONSP_ANCPOSEQ: NONSP, ANC, + NONSP, ANC, +,, ELEC Ir ELECSTORAGE HEATPUMP I I + (1 XLOSS ) P d r NONSP, ANC, UP rs,, max 0, TRANS, NONSP, ANC, + rrs,,, EXPECTED _ WIND ACTUAL _ WIND { pr, prs,, } + (1 XLOSS ) P r P Capacy resrcons + TRANS, NONSP, ANC, + rrs,,, W r R, T, s S The capacy resrcons for he un groups generang elecrcy are defned n he followng equaons for maxmum and mnmum elecrc power oupu. The realsed power producon,.e. he sum of he producon commed o he day-ahead marke and he regulaon of he producon sold a he nraday marke, plus he conrbuon o he ancllary and non-spnnng secondary reserve have o be lower han he avalable capacy equal o he nsalled capacy mes he avalably facor (10). The avalably facor s equal o 1 mnus he ouage facor: (9) 20 Rsø-R-1552(EN)

21 QGCAPELEC1: P + P + P p p ANC, + NONSP, ANC, + GKDERATE MAX _ PROD s,,, s,,, ELEC I, s S, T (10) For un groups wh sar-up coss,.e. hermal un groups, hs s laer resrced o ONLINE beng lower han, he capacy onlne for he un group a me sep. P, s, To ensure ha he power whch s commed o he day-ahead marke does no become unreasonable bg, equaon (11) has o be consdered: QGCAPELEC3: P p p DAY _ AHEAD GKDERATE MAX _ PROD, I ELEC, T (11) ONLINE P s,, s an addonal varable nroduced n order o descrbe sar-up coss, reduced par-load effcency and he resrcons for mnmum shu down and mnmum operaon mes as well as lead mes n a lnear programmng model. In he ypcal un commmen models he resrcons for e. g. he mnmum operaon me and mnmum down me nclude neger varables. However, hs s hardly feasble for a model represenng a naonal marke. Therefore (Weber & Barh 2004) proposes an approxmaon o model he resrcons n a lnear way, whch makes necessary o ONLINE nroduce hs addonal decson varable P,,. The dea s llusraed n Fgure 3. s MW P max P Onlne ANC,+ P,s, + P,s, P,s, DAY _ AHEAD P, ANC, P,s, P mn Fgure 3: Tme Illusraon of he conrbuon of a power generang urbne o he dfferen markes. Compared o usng neger varables he man dfference wh he lnear approxmaon s ha we can brng any amoun of addonal capacy onlne, as long as he amoun s smaller han he avalable capacy, e.g. brng 0.1 MW onlne f s opmal o do so. Ths s no as problemac as sounds n a model where ndvdual power plans anyhow Rsø-R

22 are aggregaed no un groups. The capacy onlne mulpled wh he mnmum oupu facor p forms a lower bound o he possble power oupu (12): MIN _ PROD QGONLCND2: P P p P ANC, MIN _ PROD ONLINE s,,, s,, ELEC I, s S, T R (12) The value of he decson varable ONLINE P, s, GKDERATE capacy of he un group ncludng he avalably facor QGONLCAP: P p p ONLINE GKDERATE MAX _ PROD s,, self has o be lower han he maxmum I p (13): ELEC,s S, T CHP un groups are dsngushed no exracon condensng un groups and backpressure un groups. The used PQ-chars (elecrc power - hermal power chars) show n a smplfed verson he possble operaon modes of he un groups represenng he possble combnaons of elecrc and hermal power produced. In Fgure 4 examples of PQ-chars for he wo dfferen ypes of CHP urbnes ncluded n he model are shown. Hence, addonal equaons o mach hese echncal resrcons are requred. (13) Fgure 4: Smplfed PQ-char for a) exracon-condensng urbnes and b) back pressure urbnes For exracon urbnes he oupu of hea and power s resrced by he followng equaons represenng he upper lne (14), he lower lne of he PQ-char (15) and he lne accordng o he hea rao CB δ (16), respecvely: QGEXTRACT1: ANC, + NONSP, ANC, + ONLINE P + P + P P γ Q s,,, s,, s,, s,, EXTRACTION I, s S, T (14) QGEXTRACT2: ANC, MIN _ PROD ONLINE P P p P γ Q s,,, s,, s,, EXTRACTION I, s S, T (15) 22 Rsø-R-1552(EN)

23 QGCBGEXT: ANC, CB P P δ Q s,,, s,, EXTRACTION I, s S, T (16) Where γ corresponds o he elecrc power reducon due o hea producon. For gas- urbnes ha are used as CHP uns, γ s se o zero. Backpressure urbnes produce hea and power wh he consan hea rao CB δ. Hence, he followng equaons for backpressure urbnes are used accordngly (17), (18), (19): QGBACKPR1:, +,, + P + P + P P ANC NONSP ANC ONLINE s,,, s,, s,, BACKPRESSU RE I, s S, T (17) QGBACKPR2:, _ P P p P ANC MIN PROD ONLINE s,,, s,, BACKPRESSU RE I, s S, T (18) QGCBGBPR: P BACKPRESSU RE = δ Q I, s S, T (19) CB s,, s,, Equaon QGONLCND1 s he same equaon as QGBACKPR1 excep ha apples for condensng ype of hermal uns. Generally, he maxmum hea producon of he hea generang un groups o be resrced o he hea generaon capacy (20): HEAT I has QGCAPHEAT: HEAT Q q I, s S, T (20),s, MAX _ PROD As he model s defned as a mul-regon model, he capacy resrcons of he ransmsson lnes are defned n (21). QXK: TRANS, DAY AHEAD TRANS, P + P + rr,, rrs,,, TRANS, TRANS, NONSP, ANC, + TRANS, MAX P P l rrs,,, rrs,,, rr, + r,r R, T, s S To ensure ha he ransmsson planned a he day-ahead marke does no exceed he avalable ransmsson capacy, equaon (22) has o be appled: (21) QXK2: P TRANS,DAY AHEAD r,r, l TRANS,MAX r,r r,r R, T, s S (22) Resrcons for down regulaon The model has a possbly for allowng wnd power sheddng on he day-ahead marke. In hs case he amoun of possble wnd sheddng has o be lower han he wnd power producon ha has been expeced a he hour when he day-ahead s cleared (.e. a 12 o clock) (23): QWINDSHED: DAY _ AHEAD, WINDSHED BID _ WIND Pr, p r R, T r, (23) Rsø-R

24 Realsed wnd power sheddng s also ncluded n he model. Here he sheddng of he wnd power producon has o be smaller han he acual wnd power producon: QGCAPELEC2: WIND, Prs,, r R, s S, T (24) WIND prs,, The down regulaon for elecrcy producng un groups can no be larger han he commed producon (25): QGNEGDEV: P, DAY _ AHEAD s,, P s,, ANC + P, + P s +,, ELEC I, s S, T (25) And also he down regulaon by he ransmsson lnes has o be lower han he planned ransmsson (26): QXNEGDEV: P r P TRANS,,r,s, TRANS,DAY AHEAD r,r, r, r R, s S, T (26) Fuel consumpon Equaon (27) deermnes he fuel used by convenonal power plans for producng power and hea. In order o avod ha un groups are always kep onlne and o accoun for ha he effcency a par load s lower han a full load, he fuel consumpon of he ONLINE sared capacy s ncluded: P, s, QGFUELUSE: ONLINE Fs, = e P FUEL + f ( P FUEL + γ Q CHP + Q I USING _,s, I USING _,s, I,s, r I USING _ FUEL I HEATONLY,s, ), s S, T Where e s he fuel consumpon parameer for he capacy onlne, f he fuel consumpon parameer when un group produces power accordng o he full load effcency. γ sands for he elecrc power reducon due o hea producon. Accordngly he amoun of hea producon mulpled wh he facor γ corresponds o he ncreased fuel consumpon caused by hea producon of exracon CHP plans. γ s se o 1 for backpressure plans, because f for backpressure plans s defned as he rao beween he sum of he power and hea producon dvded wh he fuel consumpon Sared capacy Addonal coss due o power plan sar-ups nfluence consderably he un commmen decsons of plan operaors. Therefore he sared capacy has o be defned wh he followng equaon (28): (27) QGONLSTART: STARTUP ONLINE ONLINE P,s, P,s, P,s, 1 I ONLINE, s S, T (28) Mnmum operaon and shu down mes, lead-mes 24 Rsø-R-1552(EN)

25 Lke power plan sar-ups, mnmum operaon mes and mnmum shu down mes nfluence he un commmen decsons of plan operaors. The ypcal formulaon of he mnmum operaon mes resrcons says, ha a un group can be shu down only f MIN _ OP was onlne durng he las me seps. In he lnear approxmaon he requremen s, ha he reducon n he capacy onlne of un group beween me sep _ OP and me sep -1 canno exceed he capacy onlne durng he las me seps MIN (29). These me seps correspond o he mnmum operaon hours of he correspondng power plan. QGONLOP: P ONLINE ONLINE, s, 1 P, s, I ELEC ONLINE P, s, τ MIN _ OP τ wh τ 1 MIN _ OP OPTIM _ PERIOD, s S, [,..., T ] Conversely he maxmum sar-up capacy s lmed o be he capacy shu-down durng he las QGONLSD: MIN P _ SD me seps (30). ONLINE ONLINE,s, P,s, 1 τ I ELEC ONLINE ONLINE P,s, P,s, MIN _ SD τ wh τ 1 MIN _ SD OPTIM _ PERIOD, s S, [,..., T ] In he curren verson of he model, he equaons for he mnmum operaon and shu down mes are negleced. Insead, he un commmen s resrced by he use of leadmes ha descrbe he needed me o change he capacy onlne of a un group. Accordngly he model s only able o reac on dfferen wnd power scenaros afer he leadme of he un group has passed (31): (29) (30) ONLINE QLEADTIME: Ps,, τ = Ps, ', ONLINE τ I, s S, s' Sτ wh τ < + LEADTIME (31) To save calculaon me and o ake no accoun ha some uns produce a a consan level whou akng wnd power producon flucuaons no accoun, e.g. power producng wase ncneraon plans, he followng equaon do he same as QLEADTIME, bu for all me seps: ONLINE QGONLMEDIU: Ps,, = P, ', ONLINE s I INFLEXIBLE, s S, s' S, T (32) Furhermore he possbly of havng some power plans ha only change her onlne capacy accordng o planned revsons s ncluded by he followng equaons: QGONLSLOW: P = p p ONLINE GKDERATE MAX _ PROD s,, CONSTANT_ CAPACITY I, s S, T (33) Ramp raes Rsø-R

26 Equaon (34) resrcs he ncrease of he power producon of an un group. As all un groups are expeced o ncrease her power producon from mnmal o maxmal capacy whn an hour, hs equaon s no used n he model. QGRAMP: P,s, P,s, 1 P ONLINE,s, RAMPRATE RAMP I, s S, T (34) Elecrc hea pumps Elecrc hea pumps are descrbed by he equaon (35). Thereby he varables descrbng he consumed elecrcy producon and he full load effcency are used: W,s, FULLLOAD η QGGETOH: W,s, HEATPUMPS = Q η I, s S, T (35),s, FULLLOAD Hydro power The equaons for he hydro power plans wh reservors are summarzed n he followng: Equaon (36) resrcs he maxmum reservor capacy, whereas (37) represens he mnmum reservor capacy. Equaon (38) deermnes he acual conen of he reservor capacy by akng no accoun he preceden conen, he power producon and he naural waer nflow. QHYRSSEQ: V HYDRO,s, HYDRO v I, s S, T (36) HYDRO, MAX QHYRSMAXCON: V HYDRO,s, HYDRO v I, s S, T (37) HYDRO, MIN QHYRSMINCON: HYDRO HYDRO INFLOW V,s, = V,s, 1 P,s, +, HYDRO I, s S, T (38) The equaon (39) ensures ha he sum of power producon by hydro sorage and run-ofrver power plans s lower han he nsalled capacy: QHYRSMAXPROD: NONSP, ANC, + ANC, + RUNRIVER Ps,, + Ps,, + Ps,, +, HYDRO HYDRO HYDRO I I I I HYDRO MAX _ PROD MAX _ PROD p RUNRIVER I p + s S, T (39) Elecrcy and hea sorages For elecrcy sorages lke pumped hydro sorages, he followng equaons are used: The elecrcy sorage dynamc equaon (40) deermnes he acual sorage conen by akng no accoun he preceden conen, he used capacy for loadng he elecrcy sorage mulpled wh he load loss and he power producon: 26 Rsø-R-1552(EN)

27 QESTOVOLT: V V LOADLOSS W P ELECSTORAGE ELECSTORAGE s,, = s,, 1 + s,, s,, s ELECSTORAGE I, s S, T (40) The capacy for he loadng process of elecrcy sorages s resrced by equaon (41) ha also consders elecrc hea pumps. The sum of he loadng process plus he conrbuon of elecrcy sorages o he up regulang a he ancllary and non-spnnng secondary marke has o be lower or equal han he loadng capacy plus he hea capacy of he elecrc hea pumps mulpled wh he ouage facor: QESTOLOADC: ANC, NONSP, ANC,, s, +, s, +, s, W W W M AX MAX _ PROD FULLLOAD GKDERATE η ELECSTORAGE HEATPUMP ( w + q / ) (1 p I I, s S, T ) (41) To ensure ha he planned capacy consumpon for he loadng of elecrcy sorages and for he use of hea pumps a he day-ahead marke does no become unreasonable bg, equaon (42) has o be consdered: QGCAPELEC4: DAY _ AHEAD MAX MAX _ PROD FULLLOAD GKDERATE + η W, ( w q / ) (1 p ) I ELECSTORAGE I HEATPUMP, T (42) The maxmal conrbuon of elecrc sorages o he down regulaon s deermned by equaon (43) conversely. Thereby he equaon also consders elecrc hea pumps: QESTOLOADA: NONSP, ANC, + ANC, + DAY AHEAD + s,, + s,, + s,,, + s,, ELECSTORAGE HEATPUMP W W W W W I I, s S, T (43) The maxmum elecrcy sorage conen s resrced by equaon (44): QESTOMAXCO: V v ELECSTORAGE,s, ELECSTORAGE,MAX ELECSTORAGE I, s S, T (44) The equaons for hea sorages show a smlar srucure. The hea sorage dynamc equaon (45), he resrcon for he maxmal loadng process of hea sorages (46) and he maxmum hea sorage conen (47) are defned as follows: Rsø-R

28 QHSTOVOLT: STORAGE STORAGE HEAT s,, = s,, 1 + s,, Qs,, s V V LOADLOSS W HEATSTORAGE I, s S, T (45) QHSTOLOADC: W w I, s S, T (46) HEAT,s, MAX HEATSTORAGE QHSTOMAXCO: V v STORAGE,s, HEATSTORAG E,MAX HEATSTORAGE I, s S, T (47) 10 Rollng plannng The ncluson of uncerany abou he wnd power producon n he opmsaon model s consdered by usng a scenaro ree. The scenaro ree represens wnd power producon forecass wh dfferen forecas horzons correspondng o each hour n he opmsaon perod. For a gven forecas horzon he scenaros of wnd power producon forecass n he scenaro ree are represened as a number of wnd power producon oucomes wh assocaed probables,.e. as a dsrbuon of fuure wnd power producon levels. The mehodology o generae hs scenaro ree s descrbed n delverable 6.2 (d). As s no possble o cover he whole smulaed me perod wh only one sngle scenaro ree, he model s formulaed by nroducng a mul-sage recurson usng rollng plannng. In sochasc mul-sage lnear recourse models, here exs wo ypes of decsons: roo decsons ha have o be aken before he oucome of unceran evens (sochasc parameers) s known and hence mus be robus owards he dfferen possble oucomes of he unceran evens, and recourse decsons ha can be aken afer he oucome of unceran evens s resolved. Wh hese recourse decsons acons can be sared whch mgh possbly revse he frs decsons. In he case of a power sysem wh wnd power, he power generaors have o decde on he amoun of elecrcy hey wan o sell a he day-ahead marke before he precse wnd power producon s known (roo decson). In mos European counres hs decson has o be aken a leas hours before he delvery perod. And as he wnd power predcon s no very accurae, recourse acons n he form of up or down regulaons of power producon s necessary n mos cases. In general, new nformaon arrves on a connuous bass and provdes updaed nformaon abou wnd power producon and forecass, he operaonal saus of oher producon and sorage uns, he operaonal saus of he ransmsson and dsrbuon grd, hea and elecrcy demand as well as updaed nformaon abou day-ahead marke and regulang power marke prces. Thus, an hourly bass for updang nformaon would be mos adequae. However, sochasc opmsaon models quckly become nracable, snce he oal number of scenaros has a double exponenal dependency n he sense ha a model wh k+1 sages, m sochasc parameers, and n scenaros for each m k parameer (a each sage) leads o a scenaro ree wh a oal of s = n scenaros (assumng ha scenaro reducon echnques s no appled). I s herefore necessary o smplfy he nformaon arrval and decson srucure n he sochasc model. 28 Rsø-R-1552(EN)