Multi-objective Dynamic Optimal Power Flow of Wind Integrated Power Systems Considering Demand Response

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1 1 Mult-obectve Dynamc Optmal Power Flow of Wnd Integrated Power Systems Consderng Demand Response Ru Ma, Member, IEEE, Xuan, Yang uo, Xa Wu, and Fe Jang, Member, IEEE Abstract Ths paper studes the economc envronmental energy-savng day-ahead schedulng problem of power systems consderng wnd generaton (W) and demand response (DR) by means of mult-obectve dynamc optmal power flow (MDOPF). Wthn the model, fuel cost, carbon emsson and actve power losses are taken as obectves, and an ntegrated dspatch mode of conventonal coal-fred generaton, W and DR s utlzed. The correspondng soluton process to the MDOPF s based on a hybrd of a non-doated sortng genetc algorthm-ii (NSA-II) and fuzzy satsfacton-mzng method, where NSA-II obtans the Pareto fronter and the fuzzy satsfacton-mzng method s the chosen strategy. Illustratve cases of dfferent scenaros are performed based on the IEEE 6-unts\30-nodes system, to verfy the proposed model and the soluton process, as well as the benefts obtaned by the DR nto power system. Index Terms Demand response, low-carbon electrcty, mult-obectve dynamc optmal power flow, NSA-II, wnd generaton. A. W and DR t, T P fore W ndr PDR I. NOMENCATURE Tme perod, tme horzon., P, WC P Forecastng W power, W W curtalment, actual W output. The number of DRs. Power acty of DR. Expense related to DR power acty. P, P DR CDR Maxmum load of the power system. oad percentages to decde DR status. Actve power output of DR. The total expense on schedulng a DR. Manuscrpt receved March17, 017; revsed May 6, 017 ; accepted June 15, 017. Ths work was supported n part by the Natonal Natural Scence Foundaton of Chna under rant and the Educaton Department Innovaton Platform Open Foundaton of Hunan Provnce under rant R. Ma (correspondng author, e-mal: maru818@16.com), X., X. Wu, Y. uo and F. Jang are wth the School of Electrcal and Informaton Engneerng, Changsha Unversty of Scence & Technology, Changsha, Hunan , Chna. DOI: /CSEEJPES ,, The electrcty prce for DR. The swtch varable denotng the dspatch status of DR. B. DOPF u f M n P, U nsc B a, b, c C,, nbus The vector of control varables. Obectve functon. The number of obectves. The number of coal-fred generatons. Actve power necton and voltage of generaton. The number of shunt actors. The shunt susceptance value of shunt actor. Cost coeffcents of generaton. The expense on coal-fred generaton. Emsson coeffcents of generaton. The number of system buses. The phase dfference between bus and., B Conductance and susceptance of the lne between bus and. U, U, U Voltage, voltage lmts. P, P, Q, Q Actve and reactve power lmts of generaton. B, B Shunt susceptance lmts. P, Q down P n up, P Actve and reactve load. Spnnng reserve percentage. Ramp and descendng rate lmts of generaton. The number of system lnes. S, S ne power flow, power lmts. C. Algorthm npq The number of system lnes. H Penalty functon. Out-of-lmt value. cf Syntheszed obectve functon

2 g h consderng penalty functon. Current teraton tmes n NSA-II. Dynamc adustment factor. Obectve satsfacton. II. INTRODUCTION OW-carbon electrcty has long been a core ssue n power systems to cope wth clmate change, fossl energy shortage and envronmental polluton [1]. So power schedulng should be planned consderng both economc and envronmental goals [], [3]. ven the fact that power wastage s ubqutous durng transmsson and sometmes can be pretty consderable n large grd, mzng power loss s also necessary to be taken nto account [4]. Optmal power flow (OPF) [5], [6] s a method proposed to detere the generaton schedule of the commtted unts so as to meet the load demand, wth control varables adusted to optmze specfc obectves and smultaneously wth respect to constrants on the network such as nodal power balance, bus voltage, etc. So a mult-obectve OPF model s an approprate way to mathematcally descrbe optmal power schedulng. Many of the exstng researches on mult-obectve OPF wth at least three or more obectves prmarly rely on the approach of a statc framework [7], whch s used to optmze for a partcular pont n tme. However, the day-ahead power schedulng plan should be made under the tme horzon of a whole day, where the nter-temporal correlatons such as generator ramp rate and load fluctuaton need to be carefully consdered. Therefore, researchers have proposed nter-temporal or dynamc optmal power flow (DOPF) whch s an extended method to solve OPF across a tme-horzon [8] by ncorporatng the nter-temporal constrants. Economc envronmental energy-savng day-ahead power schedulng based on mult-obectve dynamc optmal power flow (MDOPF) s of research value but s seldom reported. Wnd power generaton (W) as an applcaton of the envronmentally-frendly renewable wnd energy, brngs greater challenges to power system operatons wth ts hgh penetraton nto the system [9]-[11], and ts ant-peakng feature whch may deterorate the peak-valley dfferences of the daly net load curve [1]. Ths phenomenon threatens the stablty of the power system and calls for more spnnng reserve n case of emergences. In addton, low-carbon efforts also gve rse to new resources on the user sde such as dstrbuted renewable energy wth large-acty energy storage devces whch can sometmes generate energy for the network f under the management and regulaton of the power system. Development of the smart grd and electrcty market brngs about a demand response (DR) strategy [13], [14]. An ntegrated dspatch scheme nvolvng the two sdes can be much more effectve [15], [16], and DR s proved to be effectve n cost savngs, emsson reducton, and load shftng [1]. Wth the partcpaton of W and DR, the varaton and flexblty of the power system s ncreased, necesstatng dynamc optmal schedulng research under such crcumstances. S. ll, I. Kockar, and. W. Ault [8] studed the DOPF problem of actve dstrbuton networks contanng renewable energy, flexble demand and energy storage under an actve network management context. Be et al. [17] and Ma et al. [18] establshed a day-ahead unt commtment model consderng W and DR. MDOPF s a large-scale, nonlnear, non-convex optmzaton problem wth both statc and nter-temporal constrants, and the obectves n a mult-obectve optmzaton problem are essentally restrcted and conflctng. Researchers have studed and appled many mathematcal optmzaton technques especally heurstc optmzaton algorthms, such as dfferental evoluton [19] and non-doated sortng genetc algorthm-ii (NSA-II) [0]. In [18], the proposed dynamc mult-obectve unt commtment problem s solved by NSA-II to obtan Pareto optmal solutons, and the fuzzy satsfacton-mzng method s adopted n decson-makng. In ths paper, we studed an economc envronmental energy-savng day-ahead schedulng model of a wnd ntegrated power system consderng DR as part of a MDOPF problem, and proposed a soluton process based on NSA-II and the fuzzy satsfacton-mzng method. Frst, a power system wth W and ncentve-based DR s modeled. Next, a MDOPF framework consderng W and DR s bult, wth mum generaton cost, carbon emsson and net loss as obectves. Then, the model s solvng method s developed. Fnally, a case study on MATAB s conducted to prove the effectveness and practcablty of the model and proposed solvng method. III. MODE FOR POWER SYSTEM WITH W AND DR Day-ahead power schedulng for a wnd ntegrated power system frst requres load demand curve and W output curve forecastng. Consderng havng excessve wnd power curtaled, the W output P ( ) W t s decded by: fore W W WC P P P (1) Equpped wth an energy storage system and renewable energy system, the ncentve-based DR s a typcal type of nteractve resource based on a program gvng ncentve payments to nduce hgher electrcty usage n the valley load perod and create generaton to power systems n the peak [13]. An agreement between dspatchers department and consumers s sgned declarng the power acty PDR and the nvolved tme perods. A related fee ( 1,,, n ) s prepad by the DR dspatch department. Durng the whole schedulng tme horzon, DR behavor s needed when the power demand exceeds or drops below a certan percentage of. Consderng DR as a P generaton, ts power output should be: P 0, P P P 0, P P DR DR Thus the peak load can be reduced and the valley load s ncreased. Ths phenomenon s the so-called load shftng. Note that the DR wth such a knd of qualty s effectve n accommodatng wnd power, especally faced wth an ()

3 3 ant-peakng W output curve. The ant-peakng future means that the W generates abundantly durng the valley load perod whle poorly at the peak load tme, whch contradcts wth load shftng. Based on the forecastng load curve, the dspatch department deteres the day-ahead schedulng of the power system and nforms consumers of the plan at length. Consumers can provde feedback to make some adustments. Another part of the payment for consumers s calculated accordng to the power dspatched n ths partcular perod. Thus the total expense on schedulng a DR resource at tth perod s: C P (3) DR DR where, PDR 0, PDR 0 and 1, PDR 0 0, else IV. MDOPF MODE CONSIDERIN WIND ENERATION AND DEMAND RESPONSE A MDOPF framework of a wnd ntegrated power system wth DR s desgned as follows. The optmzaton horzon s for a whole day splt up nto T (T=4) tme perods. The control varable vector s u P1,, P n 1, PDR1,, PDR n, P DR WC, U1,, U n, B1,, B ( ) n t SC (4) (5), where n 1 denotes that the actve power of generaton on the reference bus whch s excluded. A. Obectves 1) Mnmze eneraton Cost T n ndr f1 u C CDR (6) t1 1 1 where C a P b P c (7) The W regulaton s deemed costless, so the optmzaton sums the generaton cost of every coal-fred generaton and dspatchable DR throughout the whole tme horzon. ) Mnmze CO Emsson T n f u P P (8) t1 1 We consder the wnd power generaton process and DR resource as polluton-free, so the obectve sums only the carbon emsson of the coal-fred generaton unts together, as shown n (8). 3) Mnmze Actve Power oss T nbus f3 u U U cos B sn (9) t1 1 where U s the voltage of the bus ( 1,,, n ) at tth bus perod; s the cluster of all buses connected wth bus. B. Constrants 1) Statc Constrants For t 1,, T, t s requred to ensure the followng statc constrants. (1) Power balance lmts 1,, n bus P P U U cos B sn 0 Q Q U U sn B cos 0 () eneraton lmts (10) P P P, 1,, n (11) Q Q Q, 1,, n (1) (3) Bus voltage lmts U U U, 1,, n (13) (4) W curtalment lmts P P (14) WC fore W (5) DR acty lmts P P, 1,,, n (15) DR DR DR (6) Shunt susceptance lmts B B B, k 1,,, n (16) k k k (7) Branch power flow lmts S S, 1,,, n (17) bus (8) Spnnng reserve of power system SC

4 4 n P 1 ndr P (t ) PDR PDR ( t ) P (18) 1 ) Dynamc Constrants The actve power ramp rate constrant of the coal-fred generatons s: Pdown P (t 1) P (t ) Pup,, t n Q (t ) H Q u(t ) m Q 1 npq U (t ) HU u(t ) m 1 U (1) () (19) Consderng the ramp rate lmts, generaton lmts can be decded by: down P (t ) {P, P (t 1) P } up P (t ) {P, P (t 1) P } (0) V. SOUTION PROCESS The proposed MDOPF model, as an extenson of a tradtonal OPF, has ncreased the number of control varable manfolds, and the nter-temporal constrants need to be dealt wth. In addton, the three obectves are conflctng, whch means the mpossblty to have them all optmzed n the same tme frame. In ths paper, the optmzaton s splt nto sub-problems wth ther nter-temporal constrants and s solved by a correspondng soluton process shown n Fg. 1. The mans steps are as follows: 1) Obtan day-ahead load and W forecastng curve, and set t=1. ) Status of coal-fred generatons effected by the prevous dspatch schedule s estmated, and the power output lmts n the current tme perod are decded. By comparng the current power demand wth P and P, the dspatch state of the DR resources, whether as generaton or load, s detered. 3) Apply NSA-II to obtan Pareto optmal solutons, and decde the compromse optmal soluton va the fuzzy satsfacton-mzng method. 4) t+1, and udge f t has exceeded the schedule tme horzon. If so, full day-ahead optmal schedulng s obtaned; f not, return to step ). A. Penalty Functon Method for State Varable Constrant n MDOPF To ensure the constrants on the state varables such as bus voltage and reactve power generaton lmt, we appled the dynamc penalty functon method based on the work n [1]. Note that the actve power output of coal-fred generaton on the reference bus s not the decson varable. Its power necton s acqured after the power flow calculaton, so we consder t as one of the state varables. It s necessary to detere f the PV bus reactve power, PQ bus voltage, reference bus power and generaton ramp-rate are wthn ther lmts. If so, the correspondng penalty functon of ths secton s set to 0. Otherwse, the penalty functon s calculated as: Fg. 1. Flowchart to solve MDOPF. Pp (t ) Pp (t ) Pp (t 1) H p u(t ), u(t 1) m Ppm Pp (3) where the denoator represents the lmt. If the upper bound s overstepped, the denoator s set as the upper bound. Conversely, t s set as the lower one. The numerator denotes the out-of-lmt value.

5 5 The total penalty functon s calculated by: H u(t ) =HQ u(t ) HU u(t ) Hp u(t ), u(t 1) (4) Durng NSA-II optmzng, the non-doated sort and crowdng dstant assgnment proceed based on the calculaton of the syntheszed obectve cf m u(t ). cf m u(t ) f m u(t ) h( g ) H u(t ) f m u( t ) where (5) denotes the value of the obectve m ( m 1,, M ); g s the current teraton tmes n NSA-II; two scenaros: 1) Power systems wth tradtonal coal-fred generatons and a wnd farm at bus 8. ) As for scenaro 1, three DR resources are added at bus, 8 and, respectvely. The system outlne s as shown n Fg.. Both the wnd farm and DRs are located at the buses wth relatvely larger power demand. The day-ahead forecastng system load [] and W power output profle are shown n Fg. 3. Power demand at each bus typcally drops before dawn, and clmbs n the mornng. The W output s a representatve ant-peakng profle from a wnd farm n Chna, to smulate the worst crcumstances. Parameters for the coal-fred generatons are lsted n Table I. h( g )=g g s the dynamc adustment factor whch ncreases wth the teraton accumulaton. Thus the syntheszed obectve of the scheme wth out-of-lmt varables s enlarged dramatcally, and the scheme s to be elated durng the optmzaton. B. Three-dmensonal Pareto Optmal Fronter and Synthetcally Optmal Soluton Based on genetc thought, NSA-II s an advanced algorthm whch can reach Pareto optmalty va non-doated sortng technques and the crowdng dstance operator. Pareto optmal sets of a trple-obectve optmzaton problem form a Pareto fronter n three-dmensonal space, wth each non-doated soluton referrng to a schedule n ths perod. The three-dmensonal Pareto fronter can ndcate the macroscopc relatonshp among the three obectves. The Pareto fronter contans rch nformaton, provdng decson makers wth whatever they prefer to choose. Among all the feasble solutons n the Pareto front, a synthetcally optmal one s chosen through the fuzzy satsfacton-mzng method. For a sngle non-doated soluton numbered by n, the satsfacton mn of each obectve value s calculated by a fallng sem-trapezodal fuzzy set functon [18]: f m f m 1, ( f m f m ) / ( f m f m ), f m f m f m 0, f m f m n m (6) where f m, f m are the mum and the mum value of obectve m n the Pareto soluton set, respectvely. Then the total fuzzy satsfacton n of the nth non-doated soluton n the Pareto fronter s calculated by (7) and the one wth the mum value s selected. M N M n ( m ) / ( m ) m 1 Fg.. Schematc dagram based on 6-unts\30-nodes system. (7) n 1 m 1 VI. CASE STUDY We carry out a case study based on the IEEE 6-unts\30-nodes system on MATAB, wth a 4-h optmzaton horzon splt up nto 1-hour tme-steps and wth Fg. 3. Forecastng system load and W output profles. In scenaro 1, coal-fred generatons and W regulaton are avalable wth the means to be dspatched. Wthout W regulaton,.e. W output and the daly load form the power demand from coal-fred generatons, the ant-peakng W output would deterorate the peak-valley dfferences by dggng the demand curve s valley whle barely ameloratng the peak load condton. If the demand drops to a level n whch all coal-fred generatons need to break ther lower lmts on power output, grd relablty s eopardzed. And the sudden rse of

6 6 power demand n the mornng may requre unrealstc ramp rates for coal-fred generatons. Therefore, only by curtalng wnd power can the grd mantan supply-demand balance and relablty, as n scenaro 1. Snce wnd curtalment causes en Bus P P Q MVar Q MVar TABE I PARAMETERS OF COA-FIRED ENERATIONS up P down P a $/( h) energy waste and frequent operatons, one purpose to ntroduce DR s to help handle the problems. Related parameters for DR resources n scenaro are lsted n Table II. b $/( h) c $/h t/( h) t/( h) t/h DR Bus TABE II PARAMETERS OF DR RESOURCES P DR $/( h) $/( h) $ Wthn NSA-II, we set the populaton sze as 100, Pareto fracton as 0.35 and generatons as 500. Examples of Pareto fronters n scenaro 1 and scenaro durng smulaton are shown n Fg. 4 and Fg. 5. Each dot refers to a feasble dspatch scheme whch satsfes constrants on the generaton and network. Sngle dots form a lne ndcatng that reducng CO emsson wll ncrease generaton cost, along wth reducng power loss. In scenaro, when pursung economc goals, the generaton cost can be lowered to 10.40$, wth t CO emsson and h power loss. kewse, the envronmental am wll be best acheved wth hgh monetary expense. Comparng the soluton of mum generaton cost wth the one of mum CO emsson, we fnd that CO emsson can be cut by t wth a 9.37$ ncrease n generaton cost, meanwhle net loss can be reduced by h, whch s benefcal to the electrc lne mantenance. sted n Table III are day-ahead solutons of the two gven scenaros. Comparson of the solutons mples that CO emsson and net loss n scenaro are t and h lower than that n scenaro 1, whle generaton cost ncreases by $ The calculatons pont out that, wth DRs partcpatng, the optmzng result can acheve 8.79% reducton n CO emsson and 4.55% reducton n net loss, by ncreasng.19% of the power generaton cost. Fg. 4. Three-dmensonal Pareto fronter, Scenaro 1, 15th perod. Fg. 5. Three-dmensonal Pareto fronter, Scenaro, 15t h perod. TABE III OBJECTIVE VAUES OF OPTIMA SOUTIONS Obectve value Scenaro 1 Scenaro eneraton cost ($) 0, , CO emsson (t) Net loss ( h) Detaled day-ahead schedulng solutons for scenaro 1 and scenaro are shown n Fg. 6 and Fg. 7. Power output curves for generatons n scenaro 1 are more fluctuant than n scenaro, especally generaton wth an obvous declne durng 11 to 13 perods and three tmes that of the large ramp or decent close to the lmt. Through data analyss, t s found that the total ramp power of all generatons throughout the whole day s

7 n scenaro 1; whle t s n scenaro. So the DR s behavor can mtgate the power fluctuaton of coal-fred generatons. In scenaro, negatve values of DRs n the valley perod denote that they need to absorb power from the system. Furthermore, durng the valley perod, consderng the fact that wnd power output brngs about a sudden fall n power demand of the W connected bus, whch would defntely cause voltage and stablty problems on ths very bus f no measure s taken, a DR resource s ntroduced here to better accommodate the wnd power. The smulaton result turns out to show that, each DR, whether n the W connected bus or not, has smlar schedules. Thus, by means of MDOPF, the burden on one partcular bus can be shared by other partcpants throughout the whole system. W power necton nto the grd would not cause that much mpact on the optmal schedulng of the local DR resources, as we may have consdered. Fg. 7. Optmal day-ahead schedulng for scenaro. W schedules of the two solutons are compared, and are shown n Fg. 8 and Table IV. Obvously, curtalment of wnd power s remarkably reduced when DR partcpates. Data analyss proves that, wnd power curtalment n scenaro s 1.5% less than that n scenaro 1. And utlzaton of wnd power has been ncreased from 76.78% to 98.3%. Wth a better utlzaton of renewable energy acheved, the DR s ablty to accommodate wnd power s manfested. It s noteworthy that the W output curve n ths case study represents a worst-case scenaro among all actual possbltes. Stll, wnd power can be well accommodated, showng the effectveness of the proposed model and soluton process. Fg. 6. Optmal day-ahead schedulng for scenaro 1. Fg. 8. W schedule curves comparson. TABE IV W CURTAIMENT AND PEAK-VAEY DIFFERENCE OF OAD W curtalment Peak-valley dfference of net load ( h) (%) () Scenaro Scenaro

8 8 Fg. 9. Net load comparson. Fg. 9 compares system net load under two scenaros. In scenaro, net load s obtaned by addng DR to the fxed load demand. DR s schedule can allevate peak-valley dfferences of the net load curve, by reducng t by almost 30% of scenaro 1. VII. CONCUSION Ths paper presents a MDOPF model for day-ahead schedulng of wnd ntegrated power systems wth DR, and proposes a soluton method based on a hybrd of NSA-II and fuzzy satsfacton-mzng theory. Through the case study and analyss, t s shown that: 1) The ntegrated dspatch mode of a conventonal coal-fred power generaton, W and DR are effectve to accommodate wnd power, allevate peak-valley dfferences of the load curve as well as carbon emsson reducton. ) DR s partcpatng can help coordnate the conflctng obectves by promotng low-carbon and low-loss benefts. 3) By nvestgatng an extreme stuaton of the W output curve, smulaton results of the case study hghlght DR s ablty n accommodatng wnd power and the shftng load. 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(n Chnese) Ru MA (M 11) receved a B.Sc. degree n electrcal engneerng from Changsha Unversty of Electrc Power n 1994, a M.Sc. degree n control theory and control engneerng from Hunan Unversty n 1999, and a Ph.D. degree n electrcal engneerng from North Chna Electrc Power Unversty n 006. He was a vstng scholar at Texas A&M Unversty, TX, USA from September 009 to July 011. Presently, he s a Professor of the School of Electrcal and Informaton Engneerng n Changsha Unversty of Scence and Technology. Hs research nterests are power system securty analyss, renewable energy accessng, electrcty market, and low-carbon electrcty. Xuan I receved a B.Sc. degree n electrcal engneerng from Changsha Unversty of Scence and Technology n 014. She s now pursung a M.Sc. degree n electrcal engneerng at Changsha Unversty of Scence and Technology. Her research nterests nclude optmal power flow and low-carbon electrcty.

9 9 Yang uo receved a B.Sc. degree n cvl engneerng from Central South Unversty of Forestry and Technology n 011, and a M.Sc. degree n electrcal engneerng at Changsha Unversty of Scence and Technology n 015. Hs research nterests nclude power system demand response and low-carbon electrcty. Xa Wu receved a B.Sc. degree n electrcal engneerng from Changsha Unversty of Scence and Technology n 014. She s now pursung a M.Sc. degree n electrcal engneerng at Changsha Unversty of Scence and Technology. Her research nterest s power system modelng and hgh penetrated wnd power generaton. Fe JIAN (S 15-M 16) receved B.S and M.S. degrees n electrcal and nformaton engneerng from Changsha Unversty of Scence and Technology n 007 and 01 respectvely, and a Ph.D. degree n electrcal engneerng from Hunan Unversty n 016. From 007 to 009, he was an Assstant Electrcal Engneer at Northwest Chna rd Co. td., X'an, Chna. He s currently a lecturer of the School of Electrcal and Informaton Engneerng n Changsha Unversty of Scence and Technology. Hs research nterests nclude power qualty control, power electroncs, and power system securty analyss.