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2013 IEEE. Personal use of hs maeral s permed. Permsson from IEEE mus be obaned for all oher users ncludng reprnng/ republshng hs maeral for adversng or promoonal purposes creang new collecve works for
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2013 IEEE. Personal use of hs maeral s permed. Permsson from IEEE mus be obaned for all oher users ncludng reprnng/ republshng hs maeral for adversng or promoonal purposes creang new collecve works for resale or redsrbuon o servers or lss or reuse of any copyrghed componens of hs work n oher works. Dgal Obec Idenfer: /TPWRS Mulple Tme Resoluon Un Commmen for Shor-erm Operaons Schedulng under Hgh Renewable Peneraon Emmanoul A. Bakrzs Suden Member IEEE Pandels N. Bskas Member IEEE Dmrs P. Labrds Senor Member IEEE and Anasasos G. Bakrzs Senor Member IEEE Absrac-- Ths paper nroduces he dea of unfed un commmen and economc dspach modelng whn a unque ool ha performs economc dspach wh o 24-hour look-ahead capably. The ool prov fnancally bndng dspach and exane locaonal margnal prces (LMPs) for he nex 5-mn nerval and advsory commmen dspach schedule and prces for he remanng schedulng horzon. Varable me resoluon and varable modelng complexy are used n order o reduce compuaonal requremens. A fner me resoluon and dealed modelng are used durng he frs hours of he schedulng horzon whle coarser me resoluon and smplfed modelng durng he las ones. The vably of he mehod for medum-szed sysems s demonsraed hrough s applcaon o he Greek power sysem. Index Terms Economc dspach un commmen mxed neger lnear programmng renewable generaon A. Indces and Ses I. NOMENCLATURE c b B overloaded branches durng conngency c c C q branch conngences n model of complexy q f F seps of he margnal cos funcon of un I generang uns I hermal generang uns I I I HY HY hydroelecrc generang uns I I I LS LS long-sar generang uns I I J un sar- ypes J= h w c (= ho warm cold) L loads mm reserves ypes M S3NS where m=1+: prmary- m=1-: prmary-down m=2+: secondary- m=2-: secondary-down m=3s: erary spnnng m=3ns: erary non-spnnng q Q model complexy levels Q low med hgh T hours T me nervals (of varable duraon) Ths work was spored by he Greek Secreara of Research and Technology under Gran 1522-ARISTEIA. The auhors are wh he Deparmen of Elecrcal & Compuer Engneerng Arsole Unversy of Thessalonk Thessalonk GREECE (e-mals: T q T subse of me nervals for whch model complexy level q apples T me nervals exended o he pas T + me nervals exended o he fuure ww wnd farms Φ syn soak dsp : φφ un operang phases B. Parameers bc syn: synchronzaon soak: soak dsp: dspachable : ynchronzaon A shf facor of un on branch b durng conngency c n p.u. bc A shf facor of load on branch b n conngency c. A bc w B f C f h NLC shf facor of wnd farm w on branch b n conngency c. sze of sep f of un margnal cos funcon durng me nerval n MW margnal cos of sep f of un margnal cos funcon durng me nerval n /MWh duraon of me nerval n h no-load cos of un n /h maxc P b branch b rang (c=0: normal c 0: conngency) n MW max(mn) P maxmum (mnmum) power ou of un n MW maxagc P maxmum power ou of un whle operang under AGC n MW mnagc P mnmum power ou of un whle operang under AGC n MW soak P power ou of un a soak phase durng me nerval afer a ype sar- ha naes a me nerval n MW P power ou of un a ynchronzaon phase durng me nerval before he respecve shudown ha occurs a me nerval n MW P Effecve load (= sysem load - mpors + expors + pumpng) durng me nerval n MW. P w avalable wnd power n wnd farm w durng me nerval n MW maxm R maxmum conrbuon (ramp lmed) of un n reserve ype m n MW RD ramp-down rae of un n MW/mn R sys m sysem requremen n reserve ype m durng me nerval n MW ramp- rae of un n MW/mn RU SDC shu-down cos of un n SUC T ( dn) sar- cos of un from sar- ype unl load wh synchronzaon n number of me nervals of he plannng horzon T mnmum (down) me of un a me nerval hw( wc) n me nervals backward (BW) lookng T off-load me before gong from ho (warm) sandby o warm (cold) sandby condon of un a me nerval n me nervals BW lookng syn T synchronzaon me of un under sar- ype a me nerval n me nervals - BW lookng. soak T soak me of un under ype sar- a me nerval n me nervals BW lookng T ynchronzaon me of un a me nerval n C. Varables me nervals BW lookng β f poron of sep f of he -h un s margnal cos funcon loaded n me nerval n p.u. p power ou of un durng me nerval n MW ( soak ) p power ou of un durng he ynchronzaon (soak) phase a me nerval n MW p w power ou of wnd farm w a me nerval n MW m r conrbuon of un n reserve ype m durng me nerval n MW u bnary varable whch s equal o 1 f un s on φ u bnary varable whch s equal o 1 f un s n AGC operang phase φ durng me nerval u bnary varable whch s equal o 1 f un prov secondary reserve durng me nerval 3NS u bnary varable whch s equal o 1 f un prov erary non-spnnng reserve durng me nerval y bnary varable whch s equal o 1 f un s sared durng me nerval y bnary varable whch s equal o 1 f a ype- sar- of un s naed durng me nerval z bnary varable whch s equal o 1 f un s shu- down durng me nerval D. General Remarks on Noaon (a) Tlded me consans are expressed n hours (b) Tme consans expressed n me nervals under a forward-lookng logc (see Secon III-B) are marked wh a sar e.g.: * T mnmum me of un n h T ynchronzaon me of un a me nerval n E. Acronyms me nervals forward (FW) lookng AGC Auomac Generaon Conrol CCGT Combned Cycle Gas Turbne COP Curren Operang Plan DAM Day-Ahead Marke ED Economc Dspach LAED Look-Ahead Economc Dspach LMP Locaonal Margnal Prce LP Lnear Programmng MILP Mxed Ineger Lnear Programmng OCGT Open Cycle Gas Turbne RAC Relably Assessmen Commmen RTM Real Tme Marke SMP Sysem Margnal Prce ST Seam Turbne UC Un Commmen VG Varable Generaon T II. INTRODUCTION HE shor-erm operaons schedulng of power sysems has been radonally based on a wo level un commmen/ economc dspach herarchy paradgm [1]: day-ahead un commmen (UC) schedulng s frs performed a around 12:00 noon of he day precedng he dspach day n order o deermne he commmen saus of all dspachable uns durng all he dspach perods of he dspach day wh an hourly me resoluon. Real-me economc dspach (ED) s performed every 5 mnues and deermnes he acve power ou of all commed dspachable uns (un base-pons) for he nex 5-mn nerval 1. Curren UC pracce assumes deermnsc knowledge (perfec forecas) of sysem condons for he nex day ypcally load demand and componen avalably. Reserve requremens and N-1 conngency analyss ensure a ceran degree of robusness agans forecas errors. Unl recenly he perfec forecas was a reasonable assumpon snce boh he load demand and he avalably of he convenonal dspachable uns could be farly accuraely forecased wh componen falures whn he nex day consdered a raher rare even. When sysem condons devae subsanally from forecass forward (day-ahead) or nra-day revsed UC schedules are compued. The wo level herarchy paradgm of he radonal power sysem shor-erm operaon has been ransferred o he gn of many cenrally organzed wholesale elecrcy markes such 1 A hrd level Auomac Generaon Conrol (AGC) ha correcs he power ou of he uns every few seconds o accoun for demand flucuaons whn he 5-mn dspach perod s ousde he scope of hs paper and wll no be furher dscussed. as he ISO/RTO markes n he Uned Saes n he form of he wo-selemen sysem [2] comprsng a day-ahead forward marke (DAM) wh hourly dspach perod and a real-me marke (RTM) wh 5-mn dspach perod complemened wh a forward or nraday relably assessmen commmen (RAC). RAC comms resources based on load forecass and no solely on parcpan offers bds and schedules used by DAM. Forward or nraday RACs adap resource commmen o sysem condon changes. The growh of varable (nermen) renewable energy n he generaon mx of many power sysems has challenged he radonal paradgm of he shor-erm sysem operaon [3]-[9]. Varable generaon (VG) echnologes delver energy on an asavalable bass and ncrease he level of varably and uncerany n power sysem operaons. As he VG peneraon furher ncreases curren marke and shor-erm operang pracces wll be nadequae and need o be revsed. Advanced forecasng ools especally for VG are requred and sochasc / robus cenralzed schedulng ools wll replace he radonal deermnsc schedulng ools of oday [10]-[18]. In addon more frequenly revsed forward and nraday UC schedules and dspach schedulng wh sub-hourly dspach nervals and look-ahead feaures are requred. Cenrally organzed wholesale elecrcy markes of Norh Amerca are mplemenng such changes n her operang pracces [17]- [20]. In [17] followng a day-ahead RAC an hour-ahead RAC s solved for every hour of he operang day wh hourly granulary and schedulng horzon endpon equal o he one of he las execued day-ahead RAC. The basc dea behnd [18]- [20] s o mplemen a shor-erm (nex 3-6 h) MILP-based fas-sar un commmen adusmen wh sub-hourly (15- mn 30-mn) dspach perods and an LP-based look-ahead dspach schedulng for he nex hour wh 5-mn dspach perod wh approprae ye complex nerface beween hem. Whle respondng o recenly ssued FERC Order 764 [21] some US markes plan o conver hs shor-erm fas-sar un commmen o a fnancally bndng marke ha brdges he gap beween DAM and RTM [22]. The economc benefs of exendng he horzon of he look-ahead dspach n ancpaon of seep varaons of renewable generaon as well as he compuaonal mplcaons are analyzed n [23]. As poned ou n [18]-[20] nconssences n he modelng complexy and he me resoluon of he varous shor-erm schedulng models may creae operaonal problems durng hghly dynamc envronmens. Ths paper nroduces he dea of unfed UC-ED modelng whn a unque ool ha performs ED wh o 24-h lookahead capably. Varable me resoluon and varable modelng complexy are used n order o reduce he compuaonal requremens of he model. A fner me resoluon and dealed modelng are used durng he frs hours of he schedulng horzon whle coarser me resoluon and smplfed modelng durng he las ones. The proposed model combnes he curren look-ahead commmen and real-me dspach funcons provdng bndng dspach nsrucons (Base Pons) for he nex 5-mn nerval and ancpaed power sysem operang condons (un commmen and dspach) for he remanng schedulng horzon. I s an exenson of he look-ahead commmen/dspach model proposed n [18]-[19]. The advanages of he proposed model are he smplcy of mananng a sngle shor-erm model he avodance of he nerface beween dfferen models for dfferen shor-erm me-scales and he smooh ranson beween UC and ED conrolled only by he nal condons. The basc dsadvanage when appled o long look-ahead horzons s s compuaonal requremens. Currenly s applcable o medum-szed sysems as demonsraed by he es resuls. Advances n opmzaon algorhms and compuer hardware are expeced o make our model applcable o large power sysems n he near fuure. III. UNIFIED COMMITMENT DISPATCH MODEL A. Varable Tme Resoluon and Complexy Modelng To faclae he presenaon we begn wh he crpon of a parcular mplemenaon of he varable me resoluon and complexy unfed UC-ED model by specfyng he schedulng horzon he varable me resoluon he varable modelng complexy and he npu requremens. The mplemenaon (melnes me seps look-ahead horzon ec) s ndcave and should be adaped o he parcular power sysem. 1) Schedulng Horzon Assumng ha he DAM gae closure s 12:00 noon he unfed UC-ED schedulng horzon vares from a maxmum of 36 h o a mnmum of 12 h as shown n Fg. 1 where he numbers n parenhess ndcae he begnnng (hh:mm) of he schedulng horzon n fve dfferen cases A-E. A (12:05) C (24:00) B (20:15) E (12:00) D (09:35) 12:00 00:00 24:00 12:00 24:00 Fg. 1. Schedulng horzon defnon. D-1 D 2) Varable Tme Resoluon The basc dea of varable me resoluon s o use a 5-mn me sep for he 1 s schedulng hour a 15-mn me sep for he 2 nd hour a 30-mn me sep for he 3 rd hour and hourly me sep for he remanng schedulng horzon. Ths suaon s shown n he second row of Table I where he schedulng begns a an exac clock hour. In order o algn he varable me nervals wh clock hours n case he schedulng does no begn a an exac clock hour he followng rules apply: (a) use a 5-mn me sep for a leas one hour followed by a 15- mn me sep for a leas one hour followed by a 30-mn me sep for a leas one hour and hourly me sep hereafer; (b) algn nervals of a specfc duraon wh nervals of he mmedaely longer duraon; (c) span he schedulng horzon wh he mnmum number of nervals. All possble cases are presened n Table I where he column header denoes clock hour and he row header denoes he 5-mn nerval whn he hour n whch he schedulng begns. TABLE I DEFINITION OF E VARIABLE TIME INTERVALS Combnng he nformaon of Fg. 2 and Table I s evden ha he sze of he plannng horzon ranges from a mnmum of 29 me nervals o a maxmum 54 me nervals. 3) Varable Model Complexy Table II presens he hree dfferen levels of modelng complexy used n our mplemenaon. The modelng complexy s algned wh he me-sep duraon so ha a dealed UC model s used for he near fuure perods and a smplfed model s used for he far fuure perods. The model complexy levels proposed n Table II are ndcave and sysem specfc. A lnear DC nework model s used n all complexy levels n our mplemenaon. An envsaged real-lfe applcaon n advanced elecrcy markes would use a full AC nework model wh a full se of conngences n he frs hour of schedulng (5-mn me sep) a full DC nework model wh a reduced monored conngency se for he nex 2 hours (15-mn and 30-mn me sep) and a reduced DC nework model wh an even more reduced monored conngency se for he remanng horzon (60-mn me sep). However ncreasng modelng complexy ncreases compuaonal requremens. TABLE II VARIABLE MODEL COMPLEXITY Tme Sep Level Modelng Complexy 5-mn hgh Un echncal consrans Power Balance & Reserve Requremens Full Nework Represenaon: Base Case and full se of Conngences 15-mn & 30-mn 60-mn med low Un echncal consrans Power Balance & Reserve Requremens Full Nework Represenaon: Base Case and reduced se of Conngences Un echncal consrans Power Balance & Reserve Requremens Full Nework Represenaon: Base Case only 4) Inpu Requremens The unfed UC-ED s execued on a rollng bass every fve mnues and prov bndng dspach nsrucons (Base- Pons) and prces (LMPs) for he nex 5-mn me nerval and ancpaed power sysem operang condons (commmen and dspach) for he remanng schedulng horzon. The applcaon of he model requres he followng key npus: (a) real-me nal condons and nework daa from he Sae Esmaor (b) un offer parameers (ncludng echncal daa such as ramp-raes mnmum /down mes ec.) and (c) forecass of he load demand and VG. B. Consran Converson o Varable Tme Sep Before presenng he mahemacal formulaon of he varable me sep UC problem we frs crbe how he consrans of a consan (hourly) me sep UC model whch closely follows [24] are convered o consrans of a varable me sep UC model. As saed n he Nomenclaure Secon denoes me n hours whereas denoes me nervals of varable duraon. Smlarly UC me consans expressed n hours are lded e.g. T. Consrans (1) and (2) below express he mnmum-me consran of a un n consan (hourly) and varable me sep model respecvely: T (1) T 1 u y T 1 T (2) u y Boh consrans ensure ha un s commed durng hour f was sared whn he pror T hours. I s observed ha boh consrans are dencal excep from he fac ha he mnmum me expressed n nervals n (2) s ndexed on me nerval T. Ths s explaned wh he help of Fg. 2 represenng par of a varable me sep schedulng horzon of a un wh T 4h. The 2 nd row of Fg. 2 represens he me nervals consecuvely numbered and he 3 rd row her duraon n mnues. As shown n he fgure he arhmec value of he mnmum me T expressed n me nervals depends on he me nerval a whch ermnaes (for backward-lookng modelng [24]) or a whch sars (for forward-lookng modelng [24]). Thus he mnmum me of 4 hours corresponds o 12 7 or 5 me nervals dependng on wheher he ermnang nerval (n fac he one mmedaely followng n our modelng) s or 26 respecvely. Tha s n (2) whch follows backward-lookng modelng T T and T Snce ceran consrans such as he ynchronzaon consrans follow forward-lookng modelng [24] forward-lookng me consans are also * requred and are denoed by an aserx such as T. In he example of Fg. 2 ha n general T * T * T. * 18 7 T and * 21 5 T. Noe Tme Inervals of Schedulng Horzon Number Duraon Fg. 2. Example ha shows how mnmum- me of T 4h s convered o be used n a varable me resoluon modelng Anoher pon ha requres clarfcaon s he modelng of he un power ou durng he soak and he ynchronzaon phases [24]. Assumng lnear ncrease (decrease) of he un power ou from zero o echncal mnmum (vce versa) durng he soak (ynchronzaon) phase he power ou durng hese wo phases s defned by (3) and (4) respecvely. Fg. 3 and Fg. 4 explan he dervaon of (3) and (4) wh he analyss of he wo smlar rangles (lne and cross-shaded respecvely). For example n Fg. 3 whch explans (3) one can denfy four dsnc me nervals: he sar- (begnnng of he synchronzaon phase) nerval syn* he begnnng of he soak phase nerval T he curren me nerval and he end of he soak phase nerval syn* soak* T T syn* 1. The numeraor of (3) s equal o he T me elapsed from he begnnng of he soak phase ll he end of nerval (30+30=60 mn); he denomnaor equals he oal soak phase me ( =150 mn). Noe ha me consans n Fg. 3 are forward lookng (denoed by a sar) whle me consans n Fg. 4 are backward lookng. mn P 0 y = 1 syn T = 1h30mn soak T = 2h30mn soak P syn* + T Tme nervals duraon (mn) syn* soak* syn* +T + T + T - 1 Fg. 3. Un power ou durng soak (I s assumed ha he un s sared durng nerval ). Power Ou (MW) mn P 0 T = 2h30mn P z = T Tme nervals duraon (mn) Fg. 4. Un power ou durng ynchronzaon (I s assumed ha he un s shu down durng nerval ). soak mn P P soak P P I syn* syn* soak* T syn* T T 1 syn* T syn* syn* soak* T T T T 1 0 oherwse T T h 1 1 mn P P h h h T I syn* T 1 0 oherwse T C. Mahemacal Formulaon of he Varable Tme-Sep UC The varable me-sep UC s formulaed as an MILP opmzaon problem as follows: Mnmze Cos (5) Subec o he followng se of consrans: 1) Cos defnon equaons C f B f β f f F h syn Cos NLC u u T I SUC y SDC z J B β p f F f f f (3) (4) (6) I T (7) 0 β 1 I f F T (8) Equaly (6) defnes he Cos as a funcon of he uns sepwse margnal cos funcon no-load-cos sar- and shudown cos. Consrans (7) and (8) defne he power ou of he un as a funcon of he varables β whch express he poron of he sep f of he un s margnal cos funcon loaded durng nerval. 2) Logcal sae of commmen syn soak dsp u u u u u I T (9) y z u u 1 I T (10) y z 1 I T (11) Consrans (9) ensure ha f un s onlne only one of he commmen saes s allowed. Consrans (10) relae he sar and shu-down saus of un wh s commmen saus. Consrans (11) ensure ha sar- and shu-down do no concde. 3) Sar- ype consrans J y y h T 1 y z hw hw T w T 1 wc I T (12) I T (13) y z I T (14) wc T c 1 y z I T (15) Consrans (12) ensure ha only one sar- ype s allowed. Consrans (13) prohb ho sar- of un a me nerval f dd no shu down n he pror T nervals. Smlarly consrans (14) and (15) prohb warm or cold sar- of un a me nerval f dd no shu down n he approprae me nervals pror o. 4) Synchronzaon phase consran syn u y I T (16) J syn T 1 Consran (16) ensures ha un s n synchronzaon phase durng me nerval f ncurred any ype sar- durng he pror T syn nervals. 5) Soak phase consrans syn T soak u y I T (17) J soak syn T T soak 1 T syn T soak soak p y P J soak syn T T soak 1 (18) T I T Consran (17) ensures ha un s n soak phase durng nerval f ncurred any ype sar- durng he perod soak syn rangng from T T soak 1 nervals before o T syn T nervals before. Consran (18) deermnes he power ou of un durng he soak phase n erms of soak P defned n (3). Noe ha he summaon lms of (17) and (18) represen hourly values soak hw soak syn T T 1 and T respecvely [24] convered o me nervals usng backward lookng logc. A smlar converson usng forward lookng logc was explaned wh he help of Fg. 3 6) Desynchronzaon phase consrans * 1 T 1 u z * 1 T 1 p z P I T (19) I T (20) Consran (19) ensures ha un s n ynchronzaon phase durng nerval f shus down n he nex * T 1 nervals. Consran (20) deermnes he power ou of un durng he ynchronzaon phase n erms of P defned n (4). 7) Mnmum /down consrans u y T 1 1 u z T 1 dn I T (21) I T` (22) Consran (21) ensures ha un remans onlne durng nerval f sared- whn he prevous T nervals. Consran (22) ensures ha un remans offlne f was shu dn down whn he prevous T 8) Ramp /down consrans nervals. max syn soak 1 1 p p RU h P y u u max p p RD h P u z I T I T (23) (24) Consrans (23) and (24) enforce he un ramp-rae lms. The las erms of boh consrans relax he ramp-rae lms durng sy
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