A Bilevel Optimization Model and a PSO-based Algorithm in Day-ahead Electricity Markets

Transcription

1 roceedngs o he 009 IEEE Inernaona Conerence on Sysems Man and Cybernecs San Anono X USA - Ocober 009 A Beve Opmzaon Mode and a SO-based Agorhm n Day-ahead Eecrcy Markes Guo Zhang Deparmen o Mahemacs and hyscs orh Chna Eecrc ower Unversy Baodng Hebe.R.Chna zhangguo@ncepu.edu.cn Guangquan Zhang Ya Gao Je Lu Facuy o Engneerng & Inormaon echnoogy Unversy o echnoogy Sydney O Box 3 SW 007 Ausraa {zhanggyagaoeu}@.us.edu.au Absrac Sraegc bddng probems are becomng key ssues n compeve eecrcy markes. hs paper appes beve opmzaon heory o dea wh hs ssue. We rs anayze generang company sraegc bddng behavors and bud a beve opmzaon mode or a day-ahead eecrcy marke. In hs beve opmzaon mode each generang company w choose her bds n order o maxmze her ndvdua pros. A marke operaor w deermne he oupu power or each un and unorm margna prce based on he mnmzaon purchase eecrcy are. For sovng hs compeve sraegc bddng probem descrbed by he beve opmzaon mode a parce swarm opmzaon (SO)-based agorhm s. Expermen resus have demonsraed he vady o he SO-based agorhm n sovng he compeve sraegc bddng probems or a day-ahead eecrcy marke. Keywords beve programmng eecrcy marke opmzaon parce swarm agorhm sraegc bddng I. IRODUCIO Many decson probems have herarchca srucures or whch beve programmng echnques have been deveoped. In a beve decson probem a decson maker a he upper eve s known as he eader and a he ower eve he oower []. remendous research has been done on beve probems and a o o achevemens have been obaned []-[4]. he nvesgaon o beve probems s srongy movaed by rea word appcaons and beve programmng echnques have been apped wh remarkabe success n deren domans such as decenrazed resource pannng [5] eecrc power marke [6] ogscs [7] cv engneerng [8] and road nework managemen [9][0]. hroughou he word eecrc power ndusres are undergong enormous resrucurng processes rom naonazed monopoes o compeve marke. Because o he sgncance and parcuary o eecrcy energy o naona economcs and he socey eecrcy marke mus be operaed under he condons o absoue secury and sabzaon. he research o eecrcy marke has concerned a o o researchers owners and managers rom eecrcy enes and auhores. he compeve mechansm o day-ahead markes s one o very mporan ssues n he eecrcy marke sudy whch can be descrbed as oows. Each generang company (GC) subms a se o houry (or ha-houry) generaon prces and he avaabe capaces or he oowng day. Accordng o hese daa and an houry (or ha-houry) oad orecas a marke operaor (MO) aocaes generaon oupu or each un. Many researches have been done on how o sraegcay bd prces or hose GCs and how o dspach generaon oupu or MOs o each o her uns. Davd and Wen [] gave a eraure survey on sraegc bddng probems n compeve eecrcy markes. Reerences []-[4] used suppy uncon equbrum modes o descrbe a day-ahead eecrcy marke o maxmze GCs pros and ge ash equbrum[7]. Reerences [5]- [7] used game heory o bud a sraegc bddng mode or generang companes and reach a ash equbrum souon. However hese modes dd no ncude ramp rae consrans whch are very cruca o guaranee a rea opma souon ha consders acors rom he rea word. In addon because sraegc bddng probems nvove wo herarchca opmzaons and are deren rom a convenona game mode a new ash equbrum s needed as a souon. From eraure ony ang and Fukushma [7] gave a genera ash equbrum concep. Reerence [8] used a beve opmzaon mehod o bud a generaon oupu aocaon mode bu dd no consder compeve bddng probem rom GCs. Reerence [9] bu a compeve sraegc bddng mode usng beve opmzaon by means o he Courno and Berrand mode bu dd no ncude ramp rae consrans n her mode. hereore hs paper addresses he compeve sraegc bddng probem n eecrcy markes usng beve opmzaon echnques. I w propose a se o heores ncudng a new ash equbrum concep and reaed beve opmzaon mode and aso provde a way he SO agorhm o ge souons. he res o hs paper s organzed as oows: Secon II presens a compeve sraegc bddng mode or GCs and a generaon oupu dspach mode or a MO n a day-ahead eecrcy marke. Based on he anayss o sraegc bddng behavors n Secon II Secon III proposes a beve opmzaon mode whch ncudes ramp rae consrans or descrbng sraegc bddng probems n compeve eecrcy markes. o sove he probems descrbed by a beve opmzaon mode Secon IV deveops a parce swarm opmzaon (SO) echnque-based souon agorhm. A se o expermens have been organzed o es he vady o he proposed beve opmzaon mode and he SO-based agorhm. Secon V shows hese expermen resus whch can eecvey suppor obanng a souon or he compeve /09/$ IEEE 67

2 sraegc bddng probems n an eecrcy marke. Fnay concusons and urher sudy are hghghed n Secon VI. II. BIDDIG SRAEGY AALYSIS I COMEIIVE ELECRICIY MARKES In an aucon-based day-ahead eecrcy marke each GC w ry o maxmze s own pro by sraegc bddng. Generay speakng each GC subms a se o houry generaon prces and avaabe capaces or he oowng day. Based on hese daa and an houry-oad orecas a MO w aocae generaon oupu. hs s a ypca beve decson probem. GCs are eaders and a MO s a oower. In hs secon under he anayss o bddng sraegy opmzaon probems we bud a compeve sraegc bddng mode or GCs and a generaon oupu dspach mode or a MO n a day-ahead eecrcy marke. A. Generang Companes Sraegc rcng Mode In he upper eve each GC (eader) concerns how o choose a bddng sraegy whch ncudes generaon prce and avaabe capacy. Many bddng uncons have been proposed. For a power sysem he generaon cos uncon generay adops a quadrac uncon o he generaon oupu.e. he generaon cos uncon can be represened as C ( ) = a b c () where s he generaon oupu o generaor and a b c are coecens o generaon cos uncon o generaor. he margna cos o generaor s cacuaed by λ = a b () I s a near uncon o s generaon oupu. he rue n a goods marke may expec each GC o bd accordng o s own generaon cos. hereore we adop hs near bd uncon. Suppose he bddng or -h un a me s R = α β (3) where s he me nerva s me nerva number represens he un number s he generaon oupu o un a me and α and β are he bddng coecens o un a me. Accordng o he Jusce rncpe o he same quay he same nework and he same prce we adop a unorm margna prce (UM) as he marke cearng prce. Once he energy marke s ceared each un w be pad accordng o s generaon oupu and UM. he payo o GC s = ( ( )) = G G (4) F UM a b c where G s he sux se o he uns beonged o GC. Each GC wshes o maxmze s own pro F. In ac F s he uncon o and uns bddng UM and β and oupu power UM s he uncon o a whch w α mpose mpac o each oher. hereore we can esabsh a sraegc prcng mode o hese GCs as oows max F = F( α β α β ) α β G ( UM ( a b c )) = G = where L s GC number G = L = =. he pro cacuang or each GC w consder boh and UM whch can be compued by a MO accordng o he marke cearng mode. B. A Marke Operaor s Generaon Oupu Dspach Mode A MO acuay represens he consumer eecrcy purchase rom GCs under he condons o secury and sabzaon. he obecve o a MO s o mnmze he oa purchase are whe encouragng GCs o bd prce as ow as possbe. I s reasonabe ha he ower he prce he more he oupu. hus he uncon vaue o a MO s obecve w be cacuaed accordng o he bddng prce. Mos prevous bddng sraegc modes do no ncude ramp rae consrans whou whch he souon or generang dspach may no be a ruy opma one. We shoud consder he ramp rae consrans n he rea word when modeng a generang dspach. However a mode ncudes ramp rae as consrans he number o decson varabes nvoved n he probem w ncrease dramacay whch mposes sronger reques or a more poweru souon agorhm. Based on he anayss above we bud a MO s generaon oupu dspach mode as oows: mn = ( α β α β ) = R = D = mn max D U = = = where s he me nerva s me nerva number represens he un number s he generaon oupu o un a me and α and β are he bddng coecens o un a me D s he oad demand a me mn s he mnmum oupu power o he -h un max s he maxmum oupu power o he -h un D s he maxmum downwards ramp rae o he -h un and U s he maxmum upwards ramp rae o he -h un. Aer recevng a GCs bd daa MO deermnes he oupu power o each un and UM or a me so. UM can be cacuaed accordng o he oowng seps: (5) (6) 68

3 Sep: cacuae oupu power o each un or a me so usng ormua (6) Sep: compue bddng generaon oupu Sep3: accounum = max R. III. = R correspondng o he A BILEVEL OIMIZAIO MODEL FOR COMEIIVE ELECRICIY MARKES From he anayss n Secon II we know ha n an auconbased day-ahead eecrcy marke each GC res o maxmze s own pro by sraegc bddng and each MO res o mnmze s oa eecrcy purchase are. he decson rom eher o hem w nuence he oher. hs s a ypca beve decson probem whch has mu-eaders and ony one oower wh generang companes as eaders and a marke operaor as a oower. By combnng he sraegc prcng mode dened n (5) wh he generaon oupu dspach mode dened n (6) we esabsh a beve opmzaon mode or compeve sraegc bddng-generaon oupu dspach n an aucon-based dayahead eecrcy marke as oows: where max F = F ( α β α β ) α β G = ( UM ( a b c )) = G αmn α αmax βmn β βmax = = = L mn = ( α β α β ) = R = = = D = mn max - D U = α and β are he bddng coecens o un a me L s he number o generang companes (7) = G mn s he mnmum oupu power o he -h un max s he maxmum oupu power o he -h un D s he maxmum downwards ramp rae o he -h un and U s he maxmum upwards ramp rae o he -h un. IV. A ARICLE SWARM OIMIZAIO-BASED ALGORIHM In hs secon we use he sraegy adoped n SO mehod [0] o deveop a SO-based agorhm o reach souons or probems dened n (7). Fgure ounes he srucure and process o hs agorhm. We rs sampe he eaders-conroed varabes o ge some canddae choces or eaders. hen we use he SO mehod ogeher wh Srechng echnoogy [0] o ge he oower's response or every eader's choce. hus a poo o canddae souons or boh he eaders and he oower s ormed. By pushng every souon par movng owards curren bes ones he whoe souon poo s updaed. Once a souon s reached or he eaders we use Srechng echnoogy [0] o escape oca opmzaon. We repea hs procedure by a pre-dened coun and reach a na souon. Fgure. he oune o he SO based agorhm he deaed SO-based agorhm has wo pars Agorhm whch s o generae he response rom a oower and Agorhm whch s o generae opma sraeges or a eaders. hese wo agorhms are speced as beow. Agorhm : Generae he response rom a oower Sep : Inpu he vaues o x rom L eaders Sep : Sampe canddaes y and he correspondng veoces v y = Sep 3: Inae he oower's oop couner k =0 Sep 4: Record he bes parces p y and Sep 5: Updae veoces and posons usng k K K K K K K v = w v c r ( p y ) c r ( y y ) y y y K K k = y y y v y rom p y = Sep 6: k = k Sep 7: I k MaxK or he souon changes or severa consecuve generaons are sma enough hen we use Srechng echnoogy o oban he goba souon and go o Sep 8. Oherwse go o Sep 5 Sep 8: Oupu y as he response rom he oower. Agorhm : Generae opma sraeges or eaders Sep : Sampe parces o x and he correspondng veoces v x Sep : Inae he eaders' oop couner k = 0 Sep 3: For he k-h parce k = cacuae he opma response or each eader 69

4 Sep 3.: Sampe parces x whn he consrans o x Sep 3.: By cang Agorhm we cacuae he raona response rom he oower Sep 3.3: Usng SO echnque we oban he opma response or each eader Sep 4: Cacuae he uncon vaue o every parce by Formua (7) Sep 5: Record p x x = Sep 6: Updae veoces and posons usng k K K K K K K v = wv cr ( p x ) cr ( x x ) x x x K K k = x x x v or each x = Sep 7: k = k Sep 8: I he sum o he derences beween sampes and opma responses s smaer han ε or k MaxK hen we use Srechng echnoogy o curren eaders' souons o oban he goba souon. oaons used n he agorhms are deaed n ABLE I. ABLE I. x px x vx k y py y vy k MaxK MaxK w w c c r r r r EXLAAIO OF SOME OAIOS USED I HE SO-BASED ALGORIHM he number o canddae souons (parces) or eaders he number o canddae souons (parces) or he oower he -h canddae souons or he conrong varabes rom -h eader he bes prevousy vsed poson o x curren bes one or parce x he veocy o x curren eraon number or he upper-eve probem he -h canddae souon or he conrong varabes rom he oower he bes prevousy vsed poson o y curren bes one or parce y he veocy o y curren eraon number or he ower-eve probem he predened max eraon number or k he predened max eraon number or k nera weghs or eaders and oower respecvey (coecens or SO) acceeraon consans or eaders and oower respecvey (coecens or SO) random numbers unormy dsrbued n [0 ] or eaders and oower respecvey (coecens or SO) V. EXERIMES AD CASE SUDIES In hs secon we empoy a rea word sraegc bddng probem n an eecrcy marke o es he beve opmzaon mode and he SO-based agorhm deveoped n hs sudy. A. es Daa In order o es he eecveness o he proposed beve opmzaon mode and he agorhm n sovng he mode dened by (7) a ypca compeve sraegc bddng case conssng o 3 companes wh 6 uns and 4 me nervas s chosen. he generaon cos uncon can be cacuaed by usng ormua () where he cos coecens a b c o un and oher echnques daa are gven n ABLE II he oad demands or each me nerva are gven n ABLE III. Un o. ABLE II. a ECHICAL DAA OF UIS mn (MW) max Un o. b c D (MW/h) (MW) U (MW/h) In ABLE II Un and Un beong o GCUn 3 and Un 4 beong o GC Un 5 and Un 6 beong o GC3. ABLE III. LOAD DEMADS I DIFFERE IME IERVALS D D D D

5 o smpy compuaon he m o sraegc bddng coecens does no vary by deren me so we suppose: α = 7 α = 9 β = β = mn max mn max = = B. Expermen Resus hs exampe s run by he SO-based agorhm proposed n hs paper whch was mpemened by Vsua Basc 6.0 and esed on a deskop compuer wh CU enum 4.8GHz RAM G Wndows X. runnng resus or varabes vaues are sed rom ABLE IV o ABLE VIII. ABLE IV. RUIG RESULS FOR α FROM HE EXAMLE ABLE V. RUIG RESULS FOR β FROM HE EXAMLE ABLE VI. RUIG RESULS FOR UM FROM HE EXAMLE = = = 3 = 4 = 5 = = 7 = 8 = 9 = 0 = = = 3 = 4 = 5 = 6 = 7 = = 9 = 0 = = = 3 = ABLE VII. RUIG RESULS FOR FROM HE EXAMLE Under hese souons he obecve vaues or boh he eaders and he oower are sed n ABLE VIII ABLE VIII. OBJECIVE VALUES FOR HE DECISIO MAKERS he s GC he nd GC he 3rd GC MO

6 VI. COCLUSIOS Based on he anayss on he compeve sraegc mode or day-ahead eecrcy marke hs paper presens a beve opmzaon mode or bddng probems n eecrcy markes. he proposed SO-based agorhm can oban souons or he compeve sraegc bddng probems by provdng GCs a compeve sraegc bddng whn nework secury consrans. he agorhm has been mpemened n a beve decson suppor sysem soware. Consderng he cos wh uncerany budng uzzy opma sraegc bddng mode or day-ahead eecrcy marke w be our nex research ssue. We w aso deveop more appcaons o es and mproved he deveoped beve decson suppor sysem soware. ACKOWLEDGME he work presened n hs paper was suppored by Ausraan Research Counc (ARC) under he dscovery proec D REFERECES [] G. Zhang J. Lu Y. Gao A Fuzzy Mu-obecve Mu-oower ara Cooperave Beve rogrammng Agorhm Inernaona Journa o Inegen & Fuzzy Sysems vo. 9 pp [] G. Zhang J. Lu Y. Gao Fuzzy beve programmng: Mu-obecve and mu-oower wh shared varabes Inernaona Journa o Uncerany Fuzzness and Knowedge-Based Sysems vo. 6 pp [3] M Sakawa and I. shzak Ineracve uzzy programmng or woeve nonconvex programmng probems wh uzzy parameers hrough genec agorhms Fuzzy Ses and Sysems vo. 7 pp [4] J. Lu C. Sh and G. Zhang An exended branch-and-bound agorhm or beve mu-oower decson makng n a reerena-uncooperave suaon Inernaona Journa o Inormaon echnoogy and Decson Makng vo. 6 pp [5] H. Yu C. Dang and S. Wang Game heoreca anayss o buy--now prce aucons Inernaona Journa o Inormaon echnoogy and Decson Makng vo. 5 pp [6] B. F. Hobbs B. Mezer and J. S. ang Sraegc gamng anayss or eecrc power sysem: an mpec approach IEEE ransacons on ower Sysem vo. 5 pp [7] G. Zhang and J. Lu Mode and approach o uzzy beve decson makng or ogscs pannng probem Journa o Enerprse Inormaon Managemen vo. 0 pp [8] J. Ama and B. McCar A represenaon and economc nerpreaon o a wo-eve programmng probem Journa o he Operaona Research Socey vo. 3 pp [9] C. Feng and C. Wen B-eve and mu-obecve mode o conro rac ow no he dsaser area pos earhquake Journa o he Easern Asa Socey or ransporaon Sudes vo. 6 pp [0] Y. Gao G. Zhang J. Lu and S. Gao A beve mode or raway ran se organzng opmzaon n 007 Inernaona Conerence on Inegen Sysems and Knowedge Engneerng (ISKE007). Aans ress pp [] A.K. Davd and F. Wen Sraegc bddng n compeve eecrcy markes: a eraure survey ower Engneerng Socey Summer Meeng IEEE vo. 4 pp [] A. Rudkevch Suppy Funcon Equbrum: heory and Appcaons Sysem Scences roceedngs o he 36h Annua Hawa Inernaona Conerence 003. [3]. L and M. Shahdehpour Sraegc bddng o ransmssonconsraned GECOs wh ncompee normaon IEEE ransacons on ower Sysems Vo. 0 pp Februray 005. [4] H. Haghgha Hossen Se and R. Kan Ashkan Gamng Anayss n Jon Energy and Spnnng Reserve Markes IEEE ransacons on ower Sysems Vo. pp ovember 007. [5] F. Wen and A. D. Kumar Opma bddng sraeges and modeng o mperec normaon among compeve generaors IEEE ransacons on ower Sysems Vo. 6 pp. 5 Februry 00. [6] J. D. Weber. J. Overbye J. D. Weber and. J. Overbye An Indvdua Weare Maxmzaon Agorhm or Eecrcy Markes IEEE ransacons on ower Sysems Vo. 7 pp Augus 00. [7] J. ang and M. Fukushma Quas-varaona nequaes generazed ash equbra and mu-eader-oower games Compuaona Managemen Scence Vo. pp. -56 January 005. [8] M. BJØDAL and K. JØRSE he Dereguaed Eecrcy Marke Vewed as a Beve rogrammng robem Journa o Goba Opmzaon vo. 33 pp [9] M. Fampa L.A. Barroso D. Canda and L. Smone Beve opmzaon apped o sraegc prcng n compeve eecrcy markes Compu Opm App [0] K. E. arsopouos and M.. Vrahas Recen approaches o goba opmzaon probems hrough parce swarm opmzaon aura Compung vo. pp