Hourly Demand Response in Day-ahead Scheduling for Managing the Variability of Renewable Energy

Transcription

1 Hourly emad Repoe i ay-ahead Schedulig for Maagig he Variabiliy of Reewable Eergy Hogyu Wu, Mohammad Shahidehpour, ad Ahmed Al-Abdulwahab The fir auhor i wih he Rober W. alvi Ceer for Elecriciy Iovaio a Illioi Iiue of Techology. The ecod auhor i wih he Rober W. alvi Ceer for Elecriciy Iovaio a Illioi Iiue of Techology ad he ECE eparme a Kig Abdulaziz Uiveriy, Jeddah, Saudi Arabia. The hird auhor i wih he ECE eparme a Kig Abdulaziz Uiveriy. Thi udy wa fuded i par by he OE Award # E-FC26-08T Abrac Thi paper propoe a ochaic opimizaio model for he day-ahead chedulig i power yem, which icorporae he hourly demad repoe (R) for maagig he variabiliy of reewable eergy ource (RES). R coider phyical ad operaig corai of he hourly demad for ecoomic ad reliabiliy repoe. The propoed ochaic day-ahead chedulig algorihm coider radom ouage of yem compoe ad foreca error for hourly load ad RES. The Moe Carlo imulaio (MCS) i applied o creae ochaic ecuriy-coraied ui commime (SCUC) ceario for he day-ahead chedulig. A geeral purpoe MILP ofware i employed o olve he ochaic SCUC problem. umerical reul i he paper demorae he beefi of applyig R o he propoed day-ahead chedulig wih variable reewable eergy ource. Idex Term - Hourly demad repoe, day-ahead chedulig, variable reewable eergy ource, load foreca error, ework coigecie, ochaic SCUC. Parameer: T umber of ime period umber of available geeraor B umber of bue umber of reewable eergy ource J umber of baerie S umber of ceario Idex for ime period, 1, 2,, T. OMECLATURE i Idex for geeraor, i 1, 2,,. b Idex for bue, b 1, 2,, B k Idex for reewable ource, k 1, 2,,. Idex for baerie, 1, 2,, J. Idex for ceario, 1, 2,, S. l Idex for available ramiio lie B b, umber of block of eergy demad by bu b a ime B i, umber of block of upply bid offered by geeraor i a ime P Probabiliy of ceario L o-load co of geeraor i, i $ i, b, m, i, Margial beefi of he -h block of he bid a bu b ad ime, i $/MW Margial producio co of he m-h block of geeraor i a ime, i $/MW V O L L Value of lo load a bu b a ime, i $ R C A P Syem reerve requireme a ime, i MW

2 m a x P Upper geeraio limi of ui i, i MW i ( ) ( ) Shif facor m i R Miimum curailed load a bu b ad ime, i MW R m ax m a x Maximum curailed load a bu b ad ime, i MW Maximum load a bu b a ime, i MW i Maximum ramp up/dow rae of geeraor i, i MW/mi b Pick-up or drop-off rae of load a bu b o X O ime of load a bu b a ime -1, i hour 1 o ff X OFF ime of load a bu b a ime -1, i hour 1 UT b T b Miimum O ime of load a bu i hour Miimum OFF ime of load a bu i hour m a x E Maximum eergy chage a bu b i he chedulig horizo, i MW b c q c q d q d q e e Miimum charge of orage, i MW Maximum charge of orage, i MW Miimum dicharge of orage, i MW Maximum dicharge of orage, i MW Miimum ae of orage, i MW Capaciy of orage, i MW Reerve repoive ime, uually i 10 miue Period pa, uually i hour ( Mea ime o failure for yem compoe, i hour ) ( Mea ime o repair for yem compoe, i hour ) Variable: d, emad i he -h block of he epwie demad bid a bu b a ime i ceario, i MWh p m, i, eeraio i he m-h block of piecewie liear oupu by geeraor i a ime i ceario, i MW S i, () Sar-up or hu-dow co of ui i a ime, i $ X i, Time period whe ui i ha bee O or OFF a ime, i hour L Lo of load a bu b a ime i ceario, i MW i, p ipach of geeraor i a ime i ceario, i MW k, g ipach of reewable ource k a ime i ceario, i MW, q Charge (-) or dicharge (+) of orage a ime i ceario, i MW, C Sae of charge (SOC) of orage a ime i ceario, i % E B R Expeced price-repoive load a bu b a ime, i MW Cuomer bae load a bu b a ime i ceario, i MW Aduable load of bu b a ime i ceario, i MW

3 RU i, RB, Reerve provided by geeraor i a ime i ceario, i MW Reerve provided by orage a ime i ceario, i MW z i, Commime Sau of hermal geeraor i a ime ; 1 for O ad 0 for OFF y Sae of curailme a bu b a ime i ceario ; 1 whe curailed ad 0 oherwie I. ITROUCTIO The hourly demad repoe (R) program i elecriciy marke could provide igifica beefi o marke paricipa ad cuomer. Such beefi iclude lower hourly marke price, lower volailiy i hourly marke price, ehaced yem reliabiliy, ad a maller chace for he marke power exerio by geeraig compaie (ECO), a cuomer play a more acive role i power yem operaio. R offer iceive for lowerig elecriciy uage a ime whe elecriciy price are high or whe he power yem reliabiliy i i queio [1]-[3]. R become more aracive o cuomer ad ISO a elecriciy demad, fuel price, ad he que for achievig a higher yem reliabiliy icreae. The R program iclude reliabiliy ad ecoomic coideraio. I he reliabiliy R program, paricipaig cuomer are paid iceive for meaured baelie load reducio durig coigecy codiio [2]. I he ecoomic R program, paricipaig coumer would curail hourly load voluarily i repoe o marke price. I hi cae, cuomer would hif heir le criical hourly load o period which would balace poeial co avig agai cuomer icoveiece [4]-[8]. The efficie marke dyamic are repreeed by icorporaig boh R program io he marke clearig proce. The iegraio of reewable eergy ource (RES) io power yem could reduce ramiio loe ad cogeio by diperig power geeraio, improve he yem reliabiliy, defer ifrarucure upgrade by he iallaio of local power upply, reduce carbo foopri by cuomizig he ue of RES, ad improve he yem efficiecy by ehacig he power qualiy accordig o cuomer requireme [9]-[11]. However, he widepread uage of variable RES could be problemaic for power yem operaio [12],[13]. The imulaio-baed approach i geerally applied whe coiderig RES. A e of power producio ceario wih heir probabiliie i iroduced o hadle uceraiie [14]. The ochaic ui commime ad dipach wih high wid peeraio are examied for rollig plaig wih ceario ree [15]. Rollig plaig i carried ou for rechedulig which i baed o he mo up-o-dae wid foreca ad exiig chedule [16]. A mehodology i propoed o deermie he required level of piig ad o-piig reerve wih a high peeraio of wid power [17]. The Moe Carlo imulaio (MCS) mehod i applied o evaluae he performace of grid-coeced wid urbie geeraor (WT) [18],[19]. WT are modeled a eergy limied ui by uig a load modificaio echique [20]. Reliabiliy idice are developed for hybrid olar-wid geeraio yem [21]. Thi paper propoe a hor-erm ochaic SCUC model for day-ahead marke which icorporae a coordiaed R ad orage program for maagig variable RES, radom ouage of geeraig ui ad ramiio lie, ad load ad wid foreca error. Boh ecoomic ad reliabiliy R program are coidered i he preeed R model. The operaig characeriic of load iclude epwie price bid ad phyical corai of load. The ceario reducio i adoped i MCS a a radeoff bewee calculaio peed ad oluio accuracy. A geeral purpoe MILP ofware i employed o olve he ochaic SCUC problem. The re of paper i orgaized a follow. The marke clearig mechaim i provided i Secio II. The Moe Carlo imulaio mehod for imulaig he ochaic SCUC i decribed i Secio III. The mahemaical formulaio of he ochaic SCUC problem i propoed i Secio IV. umerical eig reul are preeed ad aalyzed i Secio V. The obervaio ad he cocludig remark are provided i Secio VI ad Secio VII, repecively. A. ay-ahead Marke II. PROPOSE MARKET CLEARI MECHAISM The ISO received bid from marke paricipa icludig load aggregaor ad R provider (RP), ad clear he marke by opimizig he hourly dipach of idividual geeraig ui over a chedulig horizo. The day-ahead chedule will maximize he ocial welfare while aifyig yem-wide limi ad operaig corai of idividual marke paricipa. B. R Program I he propoed R model, load iclude he cuomer bae load (CBL) ad he price repoive load (PRL). CBL i forecaed baed o he hiorical daa; for example, he cuomer average elecriciy uage i he curailme bid period durig he 10 day prior o he day whe he bid wa ubmied [22]. The ecoomic R may iclude block of hourly PRL bid wih correpodig price. The hourly corai may iclude expeced price-repoive load, miimum/maximum curailable load, maximum load pick-up/drop-off rae ad miimum up/dow ime of load curailme. PRL ca be curailed or hifed o oher ime period for ecoomic reao a cheduled by ISO i he day-ahead marke. The propoed model allow cuomer o paricipae i reliabiliy R program. The CBL of paricipaig cuomer could be curailed i he cae of a yem emergecy. Cuomer are required o ubmi he maximum lo of load ad he value of lo load (VOLL) o he A marke ad he load curailme will be cheduled by ISO. Ulike he PRL i ecoomic R, he lo of load i ivoluary [23],[24]. If load heddig occur, cuomer will ge

4 compeaed equivale o he amou of lo load muliplied by he correpodig VOLL. Boh R program offer operaio reerve o he acillary ervice marke. The eergy ad reerve marke are cheduled ad cleared imulaeouly hrough MILP i he propoed model. III. MOTE CARLO SIMULATIO FOR STOCHASTIC SCUC The ochaic SCUC i our propoed model iclude he followig: A. Reewable Eergy Source We diregard for impliciy he correlaio of load ad RES ad reaed hem idepedely i he chedulig horizo. Suppoe he radom phoovolaic array (PVA) oupu follow a Bea diribuio ad he radom WT oupu follow a Weibull diribuio a each ime period [25]. The coiuou probabiliy diribuio fucio (PF) are approximaed by a dicree diribuio. Le PVA ad W T deoe dicree probabiliy diribuio for PVA ad WT oupu a ime, repecively. The: P V A [{, P ( )} ], 1, 2,..., S (1) W T [{ w, P ( w )} ], 1, 2,..., W where (2) S ad W are he oal umber of dicree oupu level i level of PVA ad WT oupu a ime age, repecively; ( ) ad w PVA ad P ad P ( w ), which ca be calculaed baed o heir probabiliy deiy fucio (PF). W T, repecively; ad w are he -h dicree are probabiliie of occurrece wih repec o We divide he eire chedulig horizo io everal ime age i which each age pa everal hour. For each ime age, everal ceario are creaed baed o hiorical daa i which PVA ad WT oupu are differe from he correpodig foreca. The probabiliy of each ceario a each age i calculaed a i weigh baed o he PF. The weigh for he fial-age ceario i obaied by muliplyig correpodig weigh alog he ceario ree. The ochaic oupu of PVA or WT i he repreeed by poible ceario wih heir correpodig probabiliy. B. Moe Carlo Simulaio The umber of ample eeded for a give accuracy level i irreleva o he yem ize; o he Moe Carlo imulaio mehod i uiable for repreeig he uceraiy i large-cale opimizaio problem. MCS iclude radom ouage of geeraig ui ad ramiio lie [26],[27] a well a CBL foreca error which repree variaio aroud he foreca a each ime age. The CBL foreca error are repreeed by ormal diribuio fucio i which he mea value are he foreca ad he adard deviaio are perceage of he mea value. The ouage of geeraor ad ramiio lie are imulaed baed o forced ouage rae ad repair rae [27]. I each ceario, a amplig mehod [26] i ued o deermie he 0/1 value of yem compoe availabiliy. Sceario reducio i adoped a a radeoff bewee compuaioal burde ad modelig accuracy i large-cale R chedulig problem [28]. The probabiliy meric baed o he ceario reducio mehod i applied. IV. STOCHASTIC PROBLEM FORMULATIO A COSTRAITS We aume elecriciy marke paricipa are idepede bidder who bid a heir repecive margial co. ISO calculae he hourly SCUC ad R chedule, ad hourly locaioal margial price (LMP). The problem obecive ad corai are formulaed a follow: A. Obecive Fucio The obecive of he propoed SCUC problem i o deermie he day-ahead hourly chedule of geeraig ui ad hourly R chedule uch ha he expeced oal ocial welfare i maximized. The ocial welfare i defied a he um of coumer urplu ad he producer urplu a how i Fig. 1. The obecive fucio i expreed a follow: S T B B, P, b, d, b, m a x { 1 1 b 1 1 T Bi, 1 i 1 m 1 1 b1 m, i, m, i, i i, i, i, i, [ p L z S ( X, z )] T B V O L L b, L b, * } (3) The fir erm i he obecive fucio (3) i he cuomer gro urplu ad he ecod erm i he geeraio co of hermal ui, which iclude fuel co, o-load co, ad piecewie liear ar-up ad hu-dow co. The hird erm repree he co of load curailme. The obecive i ubec o he followig idividual ceario corai. B. Syem ad Ui Corai Corai (4), (6) ad (8) are o power balace, yem reerve, ad ramiio flow, repecively. Corai (5) ad (7)

5 how ui piig reerve ad lie flow, repecively. Oher phyical corai of geeraig ui are geeraig ui limi, ramp rae limi, ad mi up/dow ime limi [1],[29],[30]. Bi, J B m, i, k,, b, b, p g q ( E R ) 0,,. (4) i 1 m 1 k 1 1 b 1 m ax i, i, i i, i R U z m i{ P p, }, i,,. (5) J B i,, b, R U R B R R C A P,,. (6) i 1 1 b 1 B i, J B J L (7) F p g q ( E R ), l,,. l, l, i m, i, l, k k, l,, l, b b, b, i 1 m 1 k 1 1 b 1 F F F, l,,. (8) l l, l C. R Corai Fig. 1. e ocial welfare ad marke equilibrium Fig. 2. Sepwie demad repoe bid Fig. 2 how a epwie R bid i which OA, OC, ad O repree he cuomer bae load, he expeced price-repoive load, ad he maximum hourly load, repecively. CB ad CF are he miimum ad maximum load curailme, repecively. OE deoe he cuomer load cheduled by ISO i he day-ahead marke. Poi E (ed poi of he cheduled load) would be locaed wihi wo zoe of FB ad C a highlighed i Fig. 2. The price-repoive load ca be curailed or hifed o aoher ime period for aifyig yem ecoomic or reliabiliy corai. The raio of available price-repoive load o he expeced price-repoive load i defied a load paricipaio facor (LPF), which i expreed a L P F A C / O C i Fig. 2. A higher LPF idicae a higher price elaiciy of demad ad more curailable load. R i he aduable load of bu b a ime i ceario which i calculaed a he differece bewee he expeced price-repoive load ad he cheduled load a how i Fig. 2. eciio variable i he propoed R model are R ad i 0-1 ae. R i poiive whe he load i hifed ou from bu b a ime, ad egaive b, whe he load i hifed o bu b a ime. The demad repoe corai are lied i (9)-(15). The correlaio bewee block demad ad oal demad i give i (9). The limi o curailable load i provided i (10), which may eiher reflec phyical load limi or be impoed by ISO. The lo of load corai i how i (11), which idicae ha lo of load could occur if ad oly if all price-repoive load are compleely curailed. Limi o pick-up/drop-off rae of load, mi up/dow ime for load curailme ad allowable chage of bu load acro chedule horizo are give i (12)-(15), repecively. Corai (12) would reric he rae of cuomer load chage bewee ay wo ucceive hour. Corai (13) idicae he miimum umber of hour ha a load would be curailed. Corai (14) how he miimum umber of hour whe he load would be upplied. Corai (15) would limi he oal m a x umber of load curailme i he chedulig horizo. By eig E o 0 i (15), he curailed load a cerai ime period will b be fully hifed o oher period. B, d, b, E b, R b,, b,,. (9) 1 m i m a x R y R R y, if R 0 b, b, b, b, b, b, m a x R E, e le b, b, b, b, b, b, b, b,,. (10) L m ax{ B ( E R ), 0 },,. (11) ( E R ) ( E R ), b, 2, 3,...,,. (12) b, b, b, 1 b, 1 b T

6 ( X, o U T )( y y ) 0, b, 2, 3,...,,. (13) b, 1 b b, 1 b, T ( X, o ff T )( y y ) 0, b, 2, 3,...,,. (14) b, 1 b b, b, 1 T T m a x R E b, b b (15) 1 0,,,.. Sorage Corai We aume he power yem i equipped wih a orage wih he followig corai: ipu ad oupu limi of orage, SOC dyamic, SOC limi, iiial/fial SOC, ad reerve coribuio of orage are give i (16)-(20), repecively [31]. I (16), q, i egaive whe orage i chargig, poiive whe he orage i dichargig, ad 0 whe he orage i o fucioal. Corai (20) idicae ha reerve provided by orage i he miimum of i exiig capaciy ad he maximum dicharge. c c d d q, {0, [ q, q ], [ q, q ]},,,. (16) C, C, 1 q, / e,, 2, 3,..., T,. (17) e C C, 1,,,. (18) e 0 T,0, T C C, C C,,. (19) d,, R B m i { C e, q },,,. (20) Here, (4)-(20) are corai ha are relaed o idividual ceario. I each ceario, he availabiliy of yem compoe i repreeed by a e of ipu parameer i he propoed opimizaio formulaio. For he purpoe of preeaio, hi addiioal e of variable i o iroduced i he SCUC formulaio. Thermal ui are formulaed a o-quick ar ui wih hourly ceario commime which are he ame a hoe i he bae cae. However, he dipach of idividual commied hermal ui i ceario could be alered i repoe o ceario realizaio. The fial dipach of a hermal ui i i expeced dipach which i he correpodig weighed average oluio of all poible ceario. V. UMERICAL SOLUTIO FOR THE PROPOSE PROBLEM umerical cae are udied for a modified 6-bu yem ad a modified IEEE 118-bu yem. The MILP model (3)-(20) i olved uig he ILO CPLEX 11.0 [32] i Microof Viual C#.ET o a Iel Xeo Sever wih 64B RAM. The R program i implemeed a all load bue ad curailed load will be hifed o oher period. The hourly price-repoive load coi of a igle eergy block wih a biddig price of 20$/MWh. The yem reerve requireme i e a he large geeraig ui capaciy. A. The Modified 6-bu Syem The modified 6-bu yem, how i Fig. 3, ha hree hermal ui, oe WT, ad eve ramiio lie. The characeriic of geeraor, ramiio lie ad he expeced hourly load are lied i Table I, Table II ad III, repecively. U Pmax TABLE I EERATORS' ATA FOR 6-BUS SYSTEM Pmi Iiial Sau Mi ow Mi Up Ramp (MW /h) i i Lie o. TABLE II TRASMISSIO LIE ATA FOR 6-BUS SYSTEM From Bu To Bu X (pu) Flow Limi l l H TABLE III EXPECTE HOURLY LOA FOR 6-BUS SYSTEM Load H Load H Load H (MWh) (MWh) (MWh) Load (MWh)

7 Fig.3. Oe lie diagram of 6-bu yem Fig 4. Acual ad hifed load Three cae are udied o illurae he impac of R program o he RES variabiliy i he day-ahead chedulig: Cae 1: R i coidered a all load bue. Cae 2: Combied R ad WT variabiliy i coidered. Cae 3: Effec of R, WT variabiliy, ad orage o hourly LMP i compared. Thee cae are dicued a follow: Cae 1: Ecoomic R program i coidered a all load bue. Fig. 4 how he hourly yem demad wih everal LPF. A peak hour, he hourly load profile will be more fla a LPF icreae. I Fig. 4, he load profile wih LPF=0.3 i almo fla durig Hour 6-24, ad he adard deviaio of hourly load i reduced from 101 MW o 18 MW a 0.3 LPF. A fla load profile correpod o lower LMP, lower ramiio cogeio, ad lower yem producio co. Alo, power yem operaio will be more efficie ice he hourly demad flucuaio are le freque [2]. We aume a large WT i locaed a Bu 5 wih i deermiiic hourly profile how i Fig. 5. Wih a higher LPF, he yem load profile will be icreaigly cloe o he WT profile. I a exreme cae, whe LPF=0.9, he yem load profile would almo mach ha of WT i which he peak load i hifed o oher hour whe he WT oupu reache i peak. Cae 2: I hi cae, ecoomic R a all load bue ad variable WT oupu a Bu 5 are icluded. The forecaed hourly WT oupu i baed o hp:// The 24-hour chedulig horizo i divided io 4 ime age whe each ime age pa 6 hour. For each ime age, 5 ceario icludig he forecaed oupu are coidered i which he probabiliy of each ceario i calculaed accordig o he PF of Weibull diribuio. For impliciy, he variace i fixed durig he horizo. There are 5 4 =625 ceario ad each ceario repree a poible WT oupu. The ceario reducio mehod i o applied o hi mall yem. The MCS covergece characeriic for he WT oupu ad he value of obecive fucio i he 625 ceario are how i Fig. 6. The relaive error i give a (1.9 6 S Y / M ) / Y %, where SY, M ad Y are adard deviaio, umber of ceario, ad expeced value of variable Y uder 95% cofidece ierval, repecively. I Fig. 6, he relaive error of he oal WT oupu wih 625 imulaio i le ha 1.5%, while he relaive error of obecive fucio i le ha 0.2%. Moreover, he relaive error are wihi 2% afer he iiial 250 imulaio. Fig. 5 Compario of WT oupu Fig. 6. Covergece characeriic of MCS Cae 3: I hi cae, he effec of coiderig R, WT variabiliy, ad orage o he hourly LMP are dicued. We udy he

8 followig four ceario i hi cae: Sceario 3.1: Bae cae wihou coiderig WT or R. Sceario 3.2: A variable WT i coidered a Bu 5. The MCS wih 625 ceario ued i Cae 2 i adoped here. Sceario 3.3: A aggregaed ad large orage (e.g., pumped orage hydro) locaed a Bu 5 i added o Sceario 3.2 i order o how explicily he effec of he orage o hourly LMP profile. The orage parameer are lied i Table IV. Sceario 3.4: R i coidered a Bu 5 baed o Sceario 3.2. For compario, he upper boud of hourly price-repoive load i e o he maximum charge/dicharge i Table IV. The pick-up/drop-off rae limi of load ad he miimum up/dow ime are o coidered for load curailme. LMP a bu 5 i he four ceario are compared i Fig. 7. Here, he LMP i Sceario 3.1 pike a Hour I Sceario 3.2, he ime period i horeed o Hour However, he peak-valley differece of LMP become larger due o he WT variabiliy. The price pike i Sceario 3.3 i miigaed a he orage hif peak load o off-peak hour. Sceario 3.4 how a mooher LMP profile wih 1.20$/MWh of peak-valley LMP differece by hifig load o off-peak hour. The LMP flucuaio i Sceario 3.4 are reduced a compared o hoe i Sceario 3.3. A large orage i le effecive ha R i reducig he volailiy of hourly LMP becaue he chargig of orage may be limied a off-peak hour. Fig. 8 how he expeced hourly orage oupu veru he expeced LMP i Sceario 3.3. Here, he orage i chargig durig low LMP hour ad dichargig whe he LMP i high. TABLE IV STORAE ATA FOR 6-BUS SYSTEM Capaciy (MWh) Max Charge Mi Charge Max icharge Mi icharge Iiial SOC (%) Fial SOC (%) Fig. 7. LMP a Bu 5 Fig. 8. Hourly orage charge veru LMP a Bu 5 B. The Modified IEEE 118-Bu Syem The IEEE-118 bu yem ha 54 hermal geeraor, 186 brache, 91 load bue. The parameer of geeraor, ramiio ework, ad load profile are give i [1]. Ecoomic ad reliabiliy R program a all load bue, radom ouage of geeraig ui ad ramiio lie, load foreca error, ad variable RES, ad aggregaed orage yem are coidered. There are 3 RES icludig 2 WT (a Bue 15,54) ad 1 PVA (a Bu 96). A orage wih parameer lied i Table IV i ialled a bue wih RES. The hourly WT foreca i provided a hp:// VOLL i e a 100$/MWh. The hourly load foreca error i repreeed by ±5% of he CBL foreca. We geerae 1800 ceario ad reduce he umber o 185 by ceario reducio. Table V li he reul i which EXP i he expeced value ad RERR i he relaive error. Here, he expeced average LMP i 19.06±0.23 $/MWh wih a 0.2 LPF ad 20% load heddig. oe ha he 19.06±0.23 how ha 5% of LMP will be beyod he give ierval of ±0.23. The maller he cofidece ierval, he more accurae he expecaio will be. I pie of high VOLL, he load heddig occur a cerai ceario wih ramiio lie ouage. I uch ceario, he average LMP i much higher ha ha of he bae cae. I Table V, he expeced average LMP decreae from $/MWh o $/MWh a LPF icreae from 0.2 o 0.3. I hi cae, more operaig reerve are made available wih a higher LPF. The reul ugge ha he beefi of larger ecoomic R i more igifica whe coiderig yem coigecie. The oal CPU ime i 6.2 hour whe 185 ceario are applied. The relaive error of operaig co ad average LMP are le ha 2% a lied i Table V. The relaive error will be maller ad he accuracy will be higher if more ceario are iroduced. I uch cae, parallel compuaio ca be furher adoped i each ceario o reduce he oal CPU ime. TABLE V R RESULTS WITH 3 RES (95% COFIECE ITERVAL) 20% Load LPF=0.2 LPF=0.3

9 Sheddig Operaig Co ($) Average LMP ($/MWh) Operaig Co ($) Average LMP ($/MWh) EXP ± ± ± ±0.11 RERR 1.38% 1.21% 1.52% 0.59% Fig. 9 how he reducio i operaig co, average LMP, ad load payme a a fucio of RES coribuio, which are compared wih he bae SCUC (wihou R or RES.) I Fig. 9, he reducio i ecoomic meric icreae almo liearly a RES coribuio icreae. Whe icorporaig a 3.7% RES coribuio ad a 20% R, he yem operaig co, average LMP ad load payme are reduced by 6.93%, 17.77% ad 20.71%, repecively. Fig. 10 how he variaio of ecoomic meric wih LPF whe he RES coribuio i 3.7%. Comparig Fig. 9 ad 10, i i ee R ha a higher impac o he reducio of average LMP ad load payme, bu RES ha a higher impac o he reducio of operaig co. The coribuio of R, RES ad orage o he average LMP reducio i how i Fig. 11. I hi cae, R i he leadig facor i coribuig o he 64.3% reducio i he average LMP, which i followed by hoe of WT (18.2%), orage (10.4%) ad PVA (7.1%). Fig. 9. Ecoomic meric veru RES Fig. 10. Ecoomic meric veru LPF Fig. 11. Coribuio perceage o average LMP reducio Fig. 12. Expeced dipach of WT a bu 54 TABLE VI EFFECT OF R O WI EERY I THE SYSTEM Wih R EXP Wihou R (LPF=0.2) Toal Wid Curailme (MWh) Wid Peeraio (%) I Fig. 12, WT curailme wih or wihou R a bu 54 are compared. The expeced available wid eergy i hi cae i 24,631 MWh, which i 21.7% of he oal daily eergy demad. The available wid geeraio repree he upper limi of acual wid dipach ad he differece bewee he upper limi ad he acual dipach i defied a wid curailme. I Fig. 12, he available wid geeraio i dipached wihou ay curailme a Hour 1-13, 18 whe he hourly available wid geeraio i below 232 MW. The lighly haded area i Fig. 12 how wid curailme whe coiderig a 20% R a Bu 54. Here, wid curailme i higher a Hour 14-17, whe he available wid geeraio i higher ha 256MW. The flow o Lie 77 ad 78, which coec Bue ad Bue 54-56, reach heir repecive limi durig hoe curailme hour. However, whe R i applied, Bu 54 face a higher wid curailme wihou R, which i repreeed by darker hade i Fig. 12. Thi i becaue he correpodig load ca be hifed bewee hour. Table VI how he R effec o reducig he yem wid curailme. Here, a 20% R a every load bu would reduce he wid curailme from 6,948 MWh o 4,958 MWh, while he wid peeraio i icreaed from 13.4% o 17.3%.

10 We li he obervaio below baed o our umerical reul. VI. OBSERVATIOS 1. Ecoomic R offer a fla load profile which lead o lower LMP, lower ramiio cogeio, ad lower yem operaig co. Ecoomic R beefi are more igifica whe coiderig yem coigecie. Reliabiliy R provide a chace o maiai he yem ecuriy. 2. R ha a more igifica impac ha RES o lowerig average LMP ad load payme; RES ha a more igifica impac ha R o reducig operaig co. R icreae he wid peeraio by reducig wid curailme. 3. The orage yem i le effecive ha R o lowerig he hourly LMP flucuaio which i due o he phyical limiaio of orage. Whe compared wih RES ad orage yem, R i more effecive i reducig average LMP. VII. COCLUSIOS I hi paper, we propoe a ochaic opimizaio model for he day-ahead power yem chedulig which icorporae he hourly R for maagig he variabiliy of RES. Phyical ad operaig corai of hourly demad are coidered i R for ecoomic ad reliabiliy repoe. The MCS creae muliple ceario for repreeig poible realizaio of uceraiy. Radom ouage of yem compoe ad foreca error for hourly load ad RES are icluded i MCS. umerical reul demorae ha R offer a fla load profile which lead o lower ramiio cogeio, lower yem operaig co ad lower LMP. I addiio, R i he leadig facor for lowerig LMP, which ouperform he uilizaio of geeraio reource uch a RES ad orage. R icreae wid peeraio i erm of reducig wid curailme, which make R a effecive ool for maagig he variabiliy of RES. REFERECES [1] M. Shahidehpour, H. Yami, ad Z. Y. Li, Marke Operaio i Elecric Power Syem. ew York: Wiley, [2] M.H. Albadi, E.F. El-Saaday. A ummary of demad repoe i elecriciy marke, Elec. Power. Sy. Re., vol. 78, o. 11, pp , ov [3] U.S. eparme of Eergy, Beefi of emad Repoe i Elecriciy Marke ad Recommedaio for Achievig Them, [4] A. J. Coeo, J. M. Morale, ad L. Barigo. Real-ime demad repoe model, IEEE Tra. Smar rid, vol. 1, o. 3, pp , ec [5] J. Wag, C. Bloyd, Z. Hu ad Z. Ta, emad repoe i Chia, I. J. Eergy, vol. 35, o. 4, pp , April [6] A. Khodaei, M. Shahidehpour, ad S. Bahramirad, SCUC wih hourly demad repoe coiderig ieremporal load characeriic, IEEE Tra. Smar rid, vol. 2, o. 3, pp , Sep [7] K. Herer, P. McAuliffe, ad A. Roefeld, A exploraory aalyi of Califoria reideial cuomer repoe o criical peak pricig of elecriciy, Eergy, vol. 32, o. 1, pp , Ja [8] S. Valero, M. Oriz, C. Seabre, e al. Mehod for cuomer ad demad repoe policie elecio i ew elecriciy marke, IET e. Tram. irib., vol. 1, o. 1, pp , Ja [9] B.C. Ummel, M. ibecu, E. Pelgrum, W.L. Klig, ad A.J. Brad, Impac of wid power o hermal geeraio ui commime ad dipach, IEEE Tra. o Eergy Coverio, vol. 22, o. 1, pp , [10] Y. M. Awa, E. F. El-Saaday, M. M. A. Salama, e al, Opimal reewable reource mix for diribuio yem eergy lo miimizaio, IEEE Tra. Power Sy., vol. 25, o. 1, pp , Feb [11] L. F. Ochoa ad. P. Harrio, Miimizig eergy loe: opimal accommodaio ad mar operaio of reewable diribued geeraio, IEEE Tra. Power Sy., vol. 26, o. 1, pp , Feb [12] H.H.. Magueira, O.R. Saavedra, ad J.E.O. Peaha, Impac of wid geeraio o he dipach of he yem: A fuzzy approach, Ieraioal Joural of Elecrical Power & Eergy Syem, vol. 30, o. 1, pp , [13] A.. Tikalaki,.. Haziargyriou, Y.A. Kaigiai, ad P.S. eorgilaki, Impac of Wid Power Forecaig Error Bia o he Ecoomic Operaio of Auoomou Power Syem, Wid Eergy, vol. 12, o. 4, pp , [14]. Celli ad F. Pilo, MV ework plaig uder uceraiie o diribued geeraio peeraio, i Proc IEEE PES Summer Meeig, vol. 1, pp [15] A. Tuohy, P. Meibom, E. ey, ad M. O'Malley, Ui commime for yem wih igifica wid peeraio, IEEE Tra. o Power Syem, vol. 24, o. 2, pp , May [16] P. Meibom, R. Barh, B. Hache, e al, Sochaic opimizaio model o udy he operaioal impac of high wid peeraio i Irelad, IEEE Tra. o Power Syem, vol. 26, o. 3, pp , Aug [17] J. M. Morale, A. J. Coeo, J. Perez Ruiz, Ecoomic valuaio of reerve i power yem wih high peeraio of wid power, IEEE Tra. o Power Syem. vol. 24, o. 2, pp , May [18]. erocher, M. Blachard, ad S. Sud, A Moe Carlo imulaio mehod for he ecoomic aeme of he coribuio of wid eergy o power yem, IEEE Tra. Eergy Cover., vol. EC-1, o. 4, pp , ec [19] R. Billio, H. Che, ad R. haar, A equeial imulaio echique for adequacy evaluaio of geeraig yem icludig wid eergy, IEEE Tra. Eergy Cover., vol. 11, o. 4, pp , ec

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