Optimum Reserve Capacity Assessment and Energy and Spinning Reserve Allocation Based on Deterministic and Stochastic Security Approach

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1 Ausralan Journal of Basc and Appled Scences, 4(9): , 2010 ISS Opmum Reserve Capacy Assessmen and Enery and Spnnn Reserve Allocaon Based on Deermnsc and Sochasc Secury Approach Farzad Parov, Babak Mozafar Deparmen of elecrcal enneern, Islamc Azad Unversy Scence and Research Branch, Tehran, Iran Absrac: In hs paper a new alorhm for deermnaon of opmal acve power reserve capacy requremens and enery and spnnn reserve allocaon n power sysem durn he 24 hours s presened. In he proposed mehod, he opmum amoun of reserve capacy per hour s deermned proporonal o nework secury level requred by he sysem operaor. In hs way, s essenal o defne a proper ndex for measurn sysem secury. Thus, we have used Expeced Load o Served (ELS) o evaluae sysem secury n each hour. The proposed mehod has been mplemened over he IEEE 24-bus es sysem and he resuls are compared wh a deermnsc secury approach, whch consders ceran and fxed amoun of reserve capacy n each hour. Ths comparson s done from economc and relably pons of vew. The promsn resuls show he effecveness of he proposed model whch s solved usn mxed neer lnear prorammn (MILP) and GAMS sofware s used. Key words: ELS, Opmal Reserve Capacy, Spnnn Reserve Allocaon, Sysem Secury, VOLL. omenclaure Parameers umber of eneran uns. l umber of blocks of he pece-wse lnearzaon of he cos funcon. b umber of buses. c umber of connences. mn p Lower bound on p n meawas. P Upper bound on p n meawas. L Demand a bus. F l Maxmum Power flow on lne l. on T Mnmum up me o h un. off T Mnmum down me of h un. RR Power ramp rae n meawa per mnue. q Rae n dollars per meawa-hour offered by h un o provde spnnn reserve. VOLL Value of loss load n bus. ELS Maxmum expeced load no served deermned by sysem operaor. FOR Forced ouae rae of nework elemens. r (k) probably of connency k. Funcons C (p ) Cos funcon n dollars per meawa-hour offered by he h eneran un o produce p. Varables p power oupu n meawas of he h un. R Spnnn reserve n meawas provded by h un u(i) Bnary varable, whch s 1 f he h un s commed and 0 oherwse. X on (-1) Duraon ha h un was onlne ll -1 X off (-1) Duraon ha h un was onlne ll -1 F l Power flow on lne l. D k, () Amoun of nvolunary load sheddn n bus as connency k. Correspondn Auhor: Farzad Parov, Deparmen of elecrcal enneern, Islamc Azad Unversy Scence and Research Branch, Tehran, Iran E-mal: parov_farzad@yahoo.com 4400

2 ELS ework expeced load no served. Indces I Index of eneraors runnn from 1 o Index of buses runnn from 1 o b l Index of ransmsson lnes runnn from 1 o l k Index of connences runnn from 1 o c Index of mes runnn from 1 o 24 ITRODUCTIO In recen years, exensve srucural chanes have occurred n he power sysem operaon and plannn; known as power sysem resrucurn or dereulaon. These chanes nroduced new chalenes n operaon of dereulaed power sysems; snce secury and relably are wo mporan facors n operaon of power sysem, so hey need more aenon and should be revewed wh consdern he new srucure of power neworks and crean compeve markes for purchasn and selln he elecrcy enery. In eneral, power sysem secury s provded by ancllary servces. Amon hem, spnnn reserve has snfcan role n provdn sysem secury afer falure of power plan uns or ransmsson lnes (Krschen, D. and G. Srbac, 2004). One of he common mehods o deermne oal or paral nework power reserve capacy s deermnsc mehod. In hs mehod, he reserve capacy s ofen assumed o be equal o he lares power plan capacy n he nework or consdered area (Bauhman, M.L., 1997); Bauhman, M.L.,1997. For he sake of smplcy and compun speed of hs mehod, many sysem operaors such as REE n Span and IESO n Onaro use o deermne her requred power reserve capacy (hp:// Alhouh hs mehod s much faser and easer, has some dsadvanaes lke non-opmaly of consdered reserve capacy whch may be less or more han nework requremen. If s less han nework requremens, when sysem faces wh s power plans or ransmsson lnes falure, due o lack of reserve capacy, he operaor has o shed nvolunary load; hs caused he sysem secury reduced. Vce versa, consdered reserve capacy may be more han he nework requremens, hs cause an unnecessary ncrease n nework operaon cos, so nework socal welfare decreases. More over, alhouh secury of he sysem ncreases by ncreasn he amoun of reserve capacy or spnnn reserve consdered n he sysem, provdn spnnn reserve mposes coss o he sysem. In oher words, by purchasn a spnnn reserve, safey and secury of he sysem wll ncrease, bu smulaneously he sysem cos would ncrease. Thus, s essenal o equlbrae hese wo mporan quanes o reach an opmal pon. Accordnly, Krschen (2002) suesed ha power sysem secury analyss mehods should evaluae he credbly of falures and her expeced consequences by means of probablsc mehods. Snce he ouaes are random unpredcable evens, her probablsc naure should be ncluded n he opmzaon process. To acheve hs purpose, he sochasc secury approach s used. Unlke he deermnsc secury approach, he amoun of acve power reserve capacy s no defne and predeermned, bu assessed accordn o level of nework secury se by sysem operaor. In (Arroyo, J.M. and D. Galana, 2005), prcn of enery and reserve and her allocaon amon nework eneraon uns s done wh full secury consran. Ths means ha he amoun of acve power reserve capacy s deermned n a way ha f any snle connency (such as eneraon uns or ransmsson lnes ouae) happens n he sysem, no load sheddn wll be occurred. In (Bouffard, F., 2005; Bouffard, F., 2005), prcn of enery and reserve and her allocaon n each bus s done based on sochasc secury approach. In hese papers, he frs sep o deermne opmum amoun of secury s o calculae sysem expeced load no served (ELS) n each perod. Probably of each connency s calculaed based on nework elemens forced ouae rae (FOR). In he second sep, sysem value of loss load (VOLL) s allocaed o he ELS ndex as a load sheddn cos. Ther obecve funcon s sum of cos of power producon, reserve provdn and load sheddn. In hs way, he opmum amoun of he sysem secury (ELS value) s deermned. The model proposed n (Arroyo, J.M. and D. Galana, 2005), may become nfeasble due o lack of enouh eneraon capacy. In oher words, afer occurrence of a connency, here may be suaon n whch no all of nework loads are suppled even when all eneran uns are commed for producn enery. Moreover, probably of dfferen connences has no been consdered; hs could resul n unnecessary ncrease n sysem operaon cos. In he alorhm presened n (Bouffard, F., 2005; Bouffard, F., 2005), value of secury ndex (ELS) s one of he oals of models and s opmal amoun s acheved from solvn he opmzaon problem. However, n operaon of power nework, secury and relably of he sysem have an ousandn 4401

3 mporance ha even f resul o mpose an exra cos, he accepable secury level should be provded. In hs paper, a model for deermnn he opmum acve power reserve capacy and allocan he enery and spnnn reserve amon he uns n boh deermnsc and sochasc secury approach s presened and he resuls are compared from economc and relably pons of vew. In he frs case, sysem reserve capacy s deermned accordn o he deermnsc secury approach crera n whch a fxed amoun of reserve capacy s consdered n each hour. In he second case, sysem reserve capacy s deermned accordn o he sochasc secury approach crera n whch he predefned amoun of ELS s appled as one of he opmzaon problem consran. In oher words, n he second case, he amoun of nework ELS s se by he sysem operaor and hen he opmum amoun of spnnn reserve ha should be provded by each power plan s deermned based on. In comparson wh (Arroyo, J.M. and D. Galana, 2005; Bouffard, F., 2005; Bouffard, F., 2005), he proposed alorhm n hs paper has more flexbly and s able o solve he problem wh dfferen amoun of ELS se by operaor. Furhermore, wh keep hs n mnd ha sysem secury and relably has prory o sysem operaon cos, n he proposed alorhm he cos of sysem operaon s calculaed as a funcon of sysem secury and s ELS value. Moreover, he alorhm proposed n hs paper has he ably o revew he role of VOLL n he sysem secury and he allocaon of load sheddn n dfferen buses. For hs purpose, afer deermnn he opmum amoun of sysem acve power reserve capacy, he amoun of sysem ELS and acvaed spnnn reserve s calculaed and compared n wo dfferen manners: The VOLL amoun s less han spnnn reserve cos The VOLL amoun s more han spnnn reserve cos Also he allocaon of load sheddn n sysem buses s carred ou n wo dfferen manners: The amouns of VOLL n sysem buses are equal The amouns of VOLL n sysem buses are dfferen The frs case llusraes he allocaon of load sheddn based on echncal ssues whle n he second case, n addon o echncal ssues, economc facors are also consdered. In secon 2, he proposed alorhm formulaon for boh deermnsc and sochasc approaches s presened and more llusraed by relevan flowchars n secon 3. Secon 4, presened daa and resuls from IEEE 24-bus relably es sysem over 24-hours horzon. In secon 5, he man conclusons are summarzed. The Proposed Alorhm: Assumpons consdered n he proposed alorhm are: 1. Amoun of load n each bus s consan and no affeced by he enery prce chanes. 2. Enery and reserve are raded n power pool srucure and blaeral conracs are no ncluded. 3. Spnnn reserve comes no operaon n 10 mnues. 4. Power losses n ransmsson lnes are neleced. In he proposed alorhm, frs he un commmen (UC) wh he am of mnmzn oal cos and sasfyn all nework consrans s solve n order o deermne he on/off saus of eneraors and her power producon. Snce only he spnnn reserve s consdered n hs alorhm and because no new uns can be sared and commed o he nework n 10 mnues, so he on/off saus of eneraors and her power producon n each hour s supposed o be fxed. Hence, any chanes n he amoun of power produced by each eneraor are consdered as spnnn reserve provded by ha eneraor. In he second sep, n each hour, all he snle probable connences are appled; for each connency he DC-OPF proram s run n order o deermne he amoun of reserve provded by each eneraor and load sheddn n each bus. The formulaon of he alorhm descrbes as follown. The obecve funcon of UC n each hour s o mnmzed oal eneraon cos. Mn C( p ) u 1 (1) The elecrcy power cos funcon for he eneran un n each hour s usually defned by quadrac funcon as follow: 4402

4 C a p b p c u p 2 () () () () (2) The cos funcon n (2) can be accuraely approxmaed by a se of anen lnes as shown n F.1. The analyc represenaon of hs lnear approxmaon s as follow: F. 1: Pece-wse lnear approxmaon of cos funcon L p m m m1 C () Au () F. (,) L p () (,) P u () m mn m1 (, ) T P 1 1 mn (, ) T T m m m1 L (, ) P T LJ 1 (3) (4) (5) (6) (7) Where F m denoes he slope of he cos curve n block m and A =a.p mn +b.p 2 mn+c 0 s he cos a he pon p mn. The UC problem s subeced o: P b 1 1 L 0 (8) F F F l l l P P P Mn Max RR 60 P ( ) P ( 1) RR 60 (9) (10) (11) 4403

5 on on T X ( 1) u( ) 1 0 off off T X ( 1) 1 u( ) 0 (12) (13) Un commmen consrans wll be compleed by consdern he reserve capacy crera no he model. As menoned, n deermnsc approach, amoun of reserve capacy s ofen consdered equal o he lares eneran un capacy. Thus he reserve capacy consran n deermnsc approach s as follow: 1 b P L (14) However n he sochasc approach, he amoun of reserve capacy s deermned proporonal o desre nework ELS. Thus he reserve capacy consran s modeled by he follown equaons: P 1 1 b L cap( ) (15) cap( ) Maxk 1 k, ( ) Mnk 2 b b d 1 d k, ( ) (16) In (15) and (16), cap() reflecs he amoun of consdered reserve capacy n each hour. In order o calculae he amoun of load sheddn n each hour, afer fxn he on/off saus of eneran uns and her power producon, a DC-OPF problem s solved for all snle connences. Because of fxn he u () and p (), decson varables are R () and d (); where R and d represen he spnnn reserve and load sheddn respecvely. The assocaed obecve funcon and s consrans are presened by equaons Mn C ( P ) R q u b 1 1 b b P R d d L L d VOLL (17) (18) (19) P mn P P R (20) F F F l l l (21) 4404

6 By deermnaon of load sheddn value, n order o calculae ELS, we need o have he probably of each connency, whch s esmaed based on nework elemens' FOR. FOR s probably of elemens falure and calculaed based on he sascal daa of ha elemen; by means of follown equaon: MTTR FOR MTTR MTTF Where MTTR s mean me o repar and MTTF s mean me o falure. The probably of each connency s hen deermned as follow: (22) FORk r( k ) 1 FOR k c 1 FORk 1 (23) Fnally ELS n each hour s deermned as follow: ELS r( k ) k c b 1 1 d( k, ) ; T (24) The obaned ELS s compared wh are value (ELS ) whch s defned pror by he operaor. If s reaer han ELS, he amoun of sysem reserve capacy wll be ncreased based on equaon (16) and hen un commmen and DC-OPF problems are resolved wh modfed cap() value. Ths process s repeaed ll he ELS value becomes less han ELS. Mehodoloy of Implemenon: ELS calculaon as one of he opmzaon consran s shown by flowchar daram n F.2. Mehodoloy of mplemenaon he proposed Alorhm for deermnsc secury approach and sochasc secury approach are shown n F.3 and F.4 respecvely. F.4 llusraes ha n sochasc approach, he amoun of nework ELS s compared wh ELS ; f nework ELS s more han ELS, reserve capacy wll ncrease based on equaon (16) and hen aan nework ELS wll be calculaed ll s amoun became less han ELS. IEEE-RTS Case Sudy: Here he proposed alorhm s esed over he IEEE 24-bus es sysem (The IEEE Relably Tes Sysem, 1996) for boh deermnsc and sochasc secury approach. Ths nework s chosen due o s smlary o a real nework. I conans 32 eneraors and 34 ransmsson lnes ha all her parameers and load nformaon are ven n (The IEEE Relably Tes Sysem, 1996). Value of parameers a, b, c 0 n equaon (2) and parameer q n equaon (17) are adoped from (Wan, J., 2003). In hs secon he resul of mplemenaon he proposed alorhm n boh deermnsc and sochasc approach for 3 amouns of ELS s presened. The resuls are compared from economc and relably pons of vew n order o deermne he opmal approach. Afer deermnn he opmal approach, he effec of VOLL n sysem performance s revewed. Economc Pon of Vew: The amoun of consdered reserve capacy n deermnsc approach and requred reserve capacy n sochasc approach per hour and for 3 dfferen amouns of ELS are ven n able (1). In presened ables n hs secon, column named by 1 refers o deermnsc approach and column named by 2 refers o sochasc approach 4405

7 F. 2: ELS calculaon flowchar F. 3: Alorhm flowchar n deermnsc approach 4406

8 F. 4: Alorhm flowchar n sochasc approach Table 1: Capacy requremen n 24 hours [MW] ELS=0.5 ELS=1.5 ELS= oal Table (1) shown ha as expeced, n sochasc approach he amoun of requred reserve capacy s fully mae he sysem ELS value; wh ncreasn ELS (or decreasn sysem secury), he amoun of requre reserve capacy wll decrease, bu n deermnsc approach he amoun of consdered reserve capacy s consan and does no follow he ELS values. So n deermnsc approach n some cases sysem may face wh surplus of reserve capacy; hs lead o unnecessary commmen of some eneran uns n order o provde he exra capacy, n whch no only ncrease he sysem operaon cos, bu also wear ou he nework 4407

9 equpmen and could made some problems n sysem manenance schedule. In order o revew hs problem, number of eneraors comme o nework n boh approaches durn 24-hour are presen n able (2). umbers ven n he able (2) are calculaed as follow: 1 u(, ) (25) Table 2: number of commed eneraors ELS=0.5 ELS=1.5 ELS= oal Table 2 clearly llusraes ha n frs approach number of commed eneraors s ndependen of nework ELS value. However n second approach affeced by ELS value. Moreover, n able (3), daly sysem operaon cos are shown and compared for boh approaches. To calculae he operaon cos, equaon (26) s used: Cos T 1 1 C ( P ) u(, ) (26) Table 3: Sysem operaon COST ($) ELS=0.5 ELS=1.5 ELS= cos Tables (1-3) clearly prove ha from economc pon of vew, he sochasc secury approach s much beer han deermnsc approach. Relably Pon of Vew: In power sysem plannn, no only an economc creron s menoned bu also sysem secury and relably s consdered. In deermnsc approach, as menoned, he amoun of reserve capacy s deermned reardless he requred secury (defned by ELS), hs may lead o some lms n provdn spnnn reserve and secury. In oher words, ELS value could reduce o a ceran amoun ha n he esed sysem s equal o ow f sysem operaor asks for more secury (ELS less han 0.123), due o lack of reserve capacy, s no possble o mee he operaor reques. However, f operaor asks for less secury (ELS 4408

10 more han 0.123), an nelasc naure of hs approach leads o surplus of reserve capacy whch cause an exra cos. Bu n sochasc secury approach, reserve capacy s deermned proporonal o amoun of ELS se by operaor. Thus, boh wo problems menoned n former approach are solved. In order o examne hs, he amoun of used reserve capacy and nework secury (ELS values) are depced n F.5 and F.6 for 10 eraons based on mehodoloy presened n F.4. These wo fures clearly llusrae he relaon beween spnnn reserve and sysem ELS values. F. 5: Spnnn reserve curve F. 6: ELS curve From wha dscused n hs secon, s concluded ha from relably pon of vew, he sochasc secury approach s beer han deermnsc one, oo. Hence s suesed ha s beer o use he sochasc approach han he deermnsc approach. Accordnly n he nex secons, hs approach s appled. Enery and Spnnn Reserve Allocaon: The allocaon resuls for enery and spnnn reserve n peak hour s repored n able (4). The spnnn reserve values are obaned for falure of 23 rd eneran un. I s supposed ha ELS s se equal o 0.5. The Role of VOLL: Anoher mporan facor whch s consdered n he proposed alorhm and has a deermnn role n a rae of spnnn reserve acvaon and allocaon of load sheddn s value of loss load (VOLL). In order o examne effecs of he VOLL, dfferen senaroes are appled over he proposed alorhm. In he frs senaro, s supposed ha he VOLL values n esed sysem buses are less han spnnn reserve cos. In hs case, n order o mnmze he cos of sysem, proposed alorhm prefer o shed he load nsead of acvae spnnn reserve, hus ELS value wll reach o s mum allowed amoun. Vce versa, n he second senaro he VOLL values consdered o be more han spnnn reserve cos. In hs case, for he sake of mnmzn he cos of sysem, proposed alorhm prefers o acvae spnnn reserve nsead of sheddnd he load, so ELS value wll be much lower han s amoun n frs senaro. In hs way, he low amouns of VOLL are consdered as hey presened n able (5) and he hh amouns of VOLL supposed o be 1000 mes reaer han amouns n able (5). Also s supposed ha he mum amoun of ELS se by operaor s

11 Table 4: Enery and reserve allocaon Generaor ID P R Table 5: VOLL value n each bus Bus number VOLL($/MWh) In F.7 he amouns of ELS durn 24-hour operaon for boh senaros are shown 4410

12 F. 7: ELS curve for low and hh value of VOLL The amoun of acvaed reserve n boh senaros s represened n F.8. F. 8: Reserve curve for low and hh value of VOLL Moreover, he amoun of load sheddn n each bus can be affeced by he VOLL n ha bus. The proposed alorhm has hs ably o consder he value of VOLL n each bus n order o mpose mnmum cos o sysem f s necessary o shed loads. In hs way, load wll be shed n buses wh lower VOLL value. For examne hs maer, wo more senaros defned. In he frs senaro, s supposed ha he amouns of VOLL n all buses are he same and equal o 1[$/MWh] and n he second senaro he VOLL values supposed o be equal o amouns presened n able (5). Resuls are shown n F.9. In hs fure column char shows he amoun of load sheddn n each bus n peak hour as a resul of all snle connency occurrence for wo dfferen defned senaros. In oher words F.9 expresses ha when us echncal ssues s concerned, load sheddn wll be done lke blue column; bu when economc ssue s appled smulaneously, he load sheddn wll be done lke red column. F.9- load sheddn n each bus for dfferen VOLL values Concluson: In hs paper an alorhm for deermnaon of opmum amoun of acve power reserve capacy and 4411

13 allocaon of enery and spnnn reserve wh consdern he sysem secury consran s presened. In he proposed alorhm, all he sysem consrans such as demand and producon equlbrum, eneraors producon lms, Ramp-raes, mnmum up/down mes, ransmsson lnes capacy, sysem secury and reserve capacy are consdered. In order o deermne eneraor power producon, we use UC and for deermnaon of spnnn reserve provded by each eneraor and amoun of load sheddn n each bus, DC-OPF s used. In order o assess sysem secury, a probablsc model s developed. Probably of each connency s calculaed based on equpmen FOR values. In hs paper, acve power reserve capacy s assessed based on deermnsc and sochasc secury approaches and ELS as a secury ndex s used o assess sysem secury and relably. By comparn hese wo approaches from economc and relably pons of vew, s deermned ha he sochasc approach s beer han he deermnsc one. Fnally he effecs of VOLL are suded n he proposed model. In he proposed alorhm, opmum sysem condon wh am of mnmzn sysem cos and load sheddn s acheved. Thus can be used as a udelne for sysem operaor n order o harness he sysem when probable connences occures. REFERECES Arroyo, J.M. and D. Galana, Enery and Reserve Prcn n Secury and ework Consraned Elecrcy Markes, IEEE Transacons on Power Sysems, 20(2): Bouffard, F., F.D. Galana and A.J. Coneo, Marke Clearn wh Sochasc Secury- Par I: Formulaon, IEEE Transacons on Power Sysems, 20(4): Bouffard, F., F.D. Galana and A.J. Coneo, Marke Clearn wh Sochasc Secury- Par II: Case Sudes, IEEE Transacons on Power Sysems, 20(4): Bllnon, R. and R. Allan, Relably Evaluaon of Power Sysems, Plenum Press, ew York, Y. Bauhman, M.L., S.. Sddq and J.W. Zarnkau, Advanced Prcn n Elecrcal Sysems, Par I: Theory, IEEE Transacons on Power Sysems, 12(1): Bauhman, M.L., S.. Sddq and J.W. Zarnkau, Advanced Prcn n Elecrcal Sysems, Par II: Implcaons, IEEE Transacons on Power Sysems, 12(1): Independen Elecrcy Sysem Operaor, avalable from World Wde Web: hp:// Krschen, D., Power Sysem Secury, Power Enneern J., 16: Krschen, D. and G. Srbac, Fundamenals of Power Sysem Economcs, John Wley & Sons. The IEEE Relably Tes Sysem, IEEE Transacons on Power Sysems, 14(3): Wan, J.,.E. Redondo and F.D. Galana, Demand-Sde Reserve Offers n Jon Enery/Reserve Elecrcy Markes, IEEE Transacons on Power Sysems, 18(4):