Optimizing the Level of Commitment in Demand Response

Transcription

1 Optmzng the Level of ommtment n Demand Response Joshua omden, Zhenhua Lu, and Yue Zhao Stony rook Unversty {joshua.comden, zhenhua.lu, yue.zhao.}@stonybrook.edu STRT Demand response (DR) s a cost-effectve and envronmentally frendly approach for mtgatng the uncertantes n renewable energy ntegraton by takng advantage of the flexblty of the customers demand. Exstng DR programs, however, suffer from the nflexblty of commtment levels. In partcular, these programs can be splt nto two classes dependng on whether customers are fully commtted or fully voluntary to provde demand response. Full commtment makes customers reluctant to partcpate, whle the servng entty (LSE) cannot rely on voluntary partcpaton for relablty and dspatchablty consderatons. Ths paper proposes a generalzed DR framework called Flexble ommtment Demand Response (FDR) to allow for explct choces of the level of commtment. We perform numercal smulatons to demonstrate that the optmal level of commtment n FDR brngs n sgnfcant (around %) socal cost reductons, consstently under varous settngs. Ths benefts both the LSE and customers smultaneously. Further, lower cost and hgher levels of commtment can be smultaneously acheved wth the optmal level of DR commtment.. INTRODUTION One of the major ssues wth the ntegraton of renewable energy sources nto the power grd s the ncreased varablty that they brng []. ddtonally, the lmted capablty to accurately predct ths varablty makes t challengng for the servng enttes (LSEs) to respond to t [6]. If ths varablty s not suffcently addressed, t wll lmt the further penetraton of renewables nto the grd and even result n blackouts []. Varous approaches have been mplemented or proposed to address ths ssue. These nclude mprovng renewable generaton forecast [8], aggregatng dverse renewable sources [], fast-respondng reserve generators, energy storage [9, ], and demand response (DR) [], among others. In partcular, n, the alforna state legslature enforced a soluton by passng a bll that requres, MW of grd energy storage by [7, ]. In order for ths soluton to be cost-effectve, the prce of storage needs to be wthn the range of $7-7/kWh. However, n when the law was passed, prces were about three tmes that amount [9]. ompared to energy storage, demand response has advantages to provde reserves to the LSEs n a cost-effectve and envronmentally frendly way [, ]. Despte the great potental, the ncrease n the amount of DR s much slower than that of renewable ntegraton [], partally evdenced by the alforna s move towards more grd-level energy stor- opyrght s held by author/owner(s). age. There are multple reasons about ths, but the level of DR commtment s an mportant factor. Roughly speakng, there are two types of DR programs based on how much commtment customers need to make n the electrc reducton. In the frst type, customers are requred to make full commtment n reducton, e.g., regulatons servce [], capacty bddng []. ccordngly, a customer takes all the responsbltes of managng the rsks/uncertantes n meetng ts own commtment. Snce such a full commtment s often costly, a hgher payment s necessary to ncentvze a customer to partcpate n DR programs than what are normally used n practce. In the latter type, customers do not need to make any commtments, and therefore are wllng to partcpate n DR programs. Examples nclude emergency demand response programs [6] and concdent peak prcng []. The drawback, however, s that from LSE s perspectve ths sort of voluntary demand response s not relable or suffcently dspatchable. Ths actually rases the followng fundamental queston: what should be the optmal level of DR commtment? Ths paper serves as a frst step towards answerng ths queston by makng the followng two man contrbutons: () The desgn of the Flexble ommtment Demand Response framework: We propose a generalzed framework for demand response programs called Flexble ommtment Demand Response (FDR). Under FDR, we explctly allow an LSE to specfy her requrement on the level of commtment from the customers by settng the value of a parameter. The two types of DR programs mentoned above are specal cases of the proposed FDR wth = and =, respectvely. We nclude the detals of FDR n Secton.. () Performance evaluatons of FDR: We conduct numercal experments to llustrate the benefts of allowng the possblty of dfferent levels of DR commtment. Our study yelds the followng key nsghts: The optmal level of commtment brngs n a sgnfcant socal cost reducton. For nstance n our case studes, we acheve a consstent decrease of around %. Moreover, ths benefts LSE and customers at the same tme, so that both sdes are ncentvzed to stay n the program. Whle lower prce and hgher levels of DR commtment are usually consdered to be conflctng wth each other, our results hghlght the (somewhat surprsng) opportunty to acheve both wth the optmal level of commtment. We provde some nsghts about who should decde the level of commtment. The result s partcularly exctng as the optmal decson of LSE s near the socal optmum. Ths means that we can rely on the LSE s (selfsh/ratonal) decson to reach the socal optmum.

2 The optmal level of commtment ncreases wth larger DR amount, and vares based on the customers demand characterstcs. The most related work n lterature s probably []. [] studes the program where the LSE generates random numbers to decde whether a partcular customer s requred to provde the peak reducton.. FLEXILE OMMITMENT DEMND RESPONSE FRMEWORK We start by modelng the LSE and customers, and then propose the flexble commtment demand response program.. Modelng the system We consder a system wth one LSE and a set of customers denoted by N. ustomers For customer N, her electrcty demand s wthn a range [l, h ]. We employ a random varable Y to represent her demand at a future tme snce she may not know t exactly beforehand due to uncertantes. The probablty densty functon of Y s denoted by f (y). lthough future demand may depend on other factors (e.g. tme of day, weather), we leave t as general as possble to allow the framework to be talored for varous statstcal models. In the current operaton of the power grd, t s possble that future demand may be correlated wth the LSE s need for DR but our own data analyss shows ths correlaton to be weak at best (cf. Fgure (c)). ddtonally as renewable energy penetraton ncreases, t wll add more uncertanty nto the future supply. Ths wll result n the correlaton beng further weakened, e.g. make DR necessary at non-peak hours []. For smplcty, we model the future demand as an ndependent random varable nstead of condtonng on the LSE s DR demand. However, our model can be adapted to ncorporate ths dependency. For customer, we defne ts demand reducton as x = y y, where y s what her demand would realze wthout DR, and y s her actual demand after performng DR. The nternal cost for customer to reduce ts demand by x s modeled by a functon (x ) wth a nondecreasng nonnegatve margnal cost. Specfcally n our numercal smulatons, we consder the one-sded quadratc customer cost functon: { cx, f x (x ) = (), otherwse where the constant c > represents the customer s ncreasng rate of dsutlty from reducton. We leave t up for future work to study the effects of dfferent customer cost functon structures. The customer s total cost s the dfference between the nternal cost and payment px receved from the LSE (as explaned n the followng subsecton): The servng entty (x ) px () We assume that the LSE has a targeted expected aggregate demand reducton D n total from all the customers. In order to reach ths target, the LSE ncentvzes the customers wth payment. Specfcally, the LSE sets a prce p and f customer provdes x amount of demand response, she gets pad px. Note here x s normally a non-decreasng functon of p. In many cases, the realzed DR amount x s dfferent from D. The LSE ncurs a cost G ( D ) x for managng the dfference. In our numercal smulatons we use a onesded quadratc cost functon: ( G D ) { a(d x = x), f D x (), otherwse where a > s a constant that represents the ncreasng cost rate of copng wth the msmatch. Our model s general enough to ncorporate other cost functons. The LSE s total cost s the summaton of the msmatch cost and the payment gven to all the customers for ther ndvdual reductons: ( G D ) x + p x. () In order to model the total cost to the socety, we smply sum the total cost of the ndvdual customers and the LSE s total cost and thus ( the payments cancel: G D ) x + (x ). (). The FDR framework The Flexble ommtment Demand Response framework conssts of two key components: one parameter (level of commtment), and one structural requrement for customers specfed by a threshold parameter, y l, for customer. The proposed FDR requres customer to reduce her demand to a level no hgher than y l wth probablty no less than. In other words, the LSE allows the customers to volate the commtment of demand reducton to y l wth probablty up to when reductons may be too severe for the customer (see the peak levels n Fgure (b)). Ths explans the reason why s called the level of commtment. Intutvely, as we ncrease, the customer has less leeway to mss her commtment. = mples a full commtment and = mples complete voluntarness. We assume that, after agreeng to some, the customers must meet ths probablstc commtment level. Ths can be enforced wth a very hgh penalty otherwse. Under the FDR framework, the average amount of DR s calculated as the effectve demand reducton. Specfcally, t s the expected dfference between unaffected desred demand (baselne) Y and demand after reducton Y, calculated as follows: E[x ] = E[Y Y ] (6) Note that n practce the LSE can combne the demand responses from multple (heterogenous) customers to mtgate the randomness of each ndvdual s flexble commtment demand response. Our data analyss shows that the demands of ndvdual customers are only weakly correlated (cf. Fgure (c)).. Decson makng of LSE and customers Under the FDR framework, we consder that the LSE determnes the prce p and the level of commtment, and each customer decdes ts y l. Ths way, customer s gven the freedom to not partcpate n DR by choosng ts y l = h. ustomers Each customer makes the level decson Y as well as y l to mnmze her expected total cost () whle fulfllng the Whether the LSE or the customers should decde y l s a future drecton.

3 cdf cdf cdf..... tme (day) (kw) (a) Load (kw) (b) umulatve dstrbuton functons (c) 9 Homes Fgure : For Homes,, and : (a) Load (kw) trace n fve-mnute ntervals from May 6-8,, (b) umulatve dstrbuton of the fve-mnute s (kw) of the days along wth the means (dashed lnes). (c) Heatmap showng the correlaton coeffcent matrx for one day of s from 9 buldngs. level of commtment : mn yl,y EY [ (Y Y ) p(y Pr(Y yl ). s.t. Y )] (7) (8) Under full commtment ( = ), f the customer s realzed desred demand s Y > yl, then the customer must reduce her demand by Y yl. ut what should the customer decde f she s gven the chance to mss the commtted demand response by a probablty? ustomer s optmal choce of y : The customer mnmzes ts cost by avodng events that would acheve the hghest costs. Snce the customer s cost of reducng demand s a functon wth a nondecreasng nonnegatve margnal cost n the amount demand reducton, t would be best to not reduce demand when y yl s large and only reduce demand when y yl s low. Specfcally, we proved that (the detals are omtted due to space lmt) there exsts a threshold yu such that when Y > yu, then the customer would decde not to reduce her demand and otherwse reduce to yl. The customer must also make sure that the chosen threshold yu does not volate her commtment oblgaton; thus, the requrement of (8) smply becomes a lower bound on yu : yu F () (9) F () where s the nverse cumulatve dstrbuton functon of Y. Ths redefnes problem (7), (8) to be based on only choosng ts lower and upper thresholds. Snce the s reduced only when Y (yl, yu ), the customer optmzaton problem becomes: R yu (t yl ) p(t yl ) f (t)dt () mn yl yl,yu such that (9) s satsfed. It wll be shown later that () s not convex, and the customer can use an exhaustve search on decdng yu and yl. lthough ths nave algorthm has a quadratc tme complexty, one thousand ponts n each decson varable for a resdental customer who has a -kw can gve.kw precson. Ths s good enough for control purpose. The servng entty The LSE decdes the prce p and the commtment level to mnmze ts expected total cost (): P P mn EY G(D x (p,, Y )) + p x (p,, Y ) () p, where Y = {Y } N, and x (p,, Y ) are functons that depend on how each customer behaves toward p, and ther desred demand Y, as fully characterzed above. Note that although the uncertanty of Y s not explctly stated n the objectve functon, t s mplctly taken nto account when takng the expectaton of G( ). The LSE can decde the prce p and commtment level by exhaustve search snce prce has lmted granularty and the shape of the cost functon () s qute smooth around the optmal commtment level (see Fg. (b)), whch allows moderate precson to be suffcent.. DT NLYSIS. ustomer Loads We use the Smart Data Set obtaned from the Unversty of Massachusetts Trace Repostory [8]. The specfc data we use s the data from three dfferent homes located n Western Massachusetts gven n one-second ntervals from days between May, through June,.We average them nto fve-mnute ntervals and use these for our trace-based smulatons. concurrent three day sample of the three homes s gven n Fgure (a), whch shows peak s are non-overlappng n many cases. Fgure (b) dsplays the emprcal cumulatve dstrbuton functon of the three homes over the days along wth ther means. The large peak-to-mean ratos ndcate the potental beneft that a reduced commtment level for DR would brng for a customer. ustomers s are only weakly correlated, f at all. The northwest corner of Fgure (c) shows a heatmap of the correlaton matrx between the three homes whch shows vrtually lttle correlaton. In addton to the three homes, the Unversty of Massachusetts Trace Repostory [8] provdes the s of buldngs for one complete day n one-second ntervals whch we averaged nto fve-mnute ntervals. heatmap of the correlaton matrx between 9 of the buldngs s shown n Fgure (c) whch gves evdence that most customers have s whch are only weakly correlated.. Load Servng Entty We use the followng data from the ISO New England for the Western Massachusetts zone [7]. The specfc data s gven n one-hour ntervals of the real-tme, day-ahead market demand, and the real-tme prce for the same days as the prevously descrbed customer data (Homes,, and ). We calculate the real-tme msmatch of supply and demand as the dfference between the real-tme and day-ahead market provsoned. Fgure (a) dsplays a

4 msmatch prce ($/kwh) tme (day) (a) Load msmatch (MW) and prce cdf cdf msmatch (MW) real-tme prce ($/kwh) (b) umulatve dstrbuton functons msmatch real-tme prce real-tme msmatch prce (c) Homes,, and Fgure : (a) The ISO-NE msmatch (MW) between real-tme and day-ahead provsoned for the Western Massachusetts zone, and the real-tme market prce from May -9,. For the same data durng a perod of days: (b) umulatve dstrbuton functons for the msmatch of ISO-NE, and real-tme prce, (c) Heatmap showng the correlaton coeffcent matrx for of s from homes,,, the msmatch of ISO-NE, and real-tme prce. one week sample of the msmatch and ts correspondng real-tme prce. The southeast corner of Fgure (c) shows that they are weakly correlated over the sampled days. The emprcal cumulatve dstrbuton functons of the msmatch and the real-tme prce for the days are shown n Fgure (b). In partcular, the peak-to-mean rato of the real-tme prce s whch ndcates that DR can be extremely valuable for an LSE.. NUMERIL RESULTS. Setup We smulate a system wth one LSE and, homogeneous customers. For each customer, her demand has the same probablty densty functon. The emprcal dstrbuton functons used for three dfferent smulatons are from Homes,, and n the prevous secton (cf. Fgure (b)) [8]. The cost of reducng her demand s modeled as a one-sded quadratc functon () wth c = $/(kwh). The goal of the LSE s to obtan a certan aggregated amount (e.g. kwh) of demand reducton from the customers (resultng n.kwh) for a gven fve-mnute tmeslot. Recall the average demand of a customer s kw [], whch means the reducton s about % gven the fvemnute tme frame. The LSE faces a penalty of not meetng the aggregated DR goal, modeled as another quadratc cost functon n () wth a = $./(kwh). Snce the functons are qute complcated and non-convex as we can see later n the results, both the LSE and customers use exhaustve search to determne ther decson varables.. Economc beneft of FDR The LSE performs an exhaustve search over and p to mnmze ts cost (). For each par of and p, each customer responds wth an amount of FDR that mnmzes ts own cost. To observe the mpact of dfferent commtment levels n reducng costs, we plot n Fgures (a), (b) and (c) the costs to the socety (.e., the LSE plus the customers), the LSE, and an ndvdual customer, as a functon of. These costs are normalzed by the cost wth a fully commtted DR program, namely, =. To understand the nner workng of FDR, we further plot the total expected DR and the optmal prce chosen by the LSE as a functon n Fgures (d) and (e). We make the followng observatons: Wth the optmal level of commtment, the cost to the socety s sgnfcantly reduced from that wth a close to. Indeed, from Fgure (e), when s close to, the cost of performng DR by the customers ncreases sgnfcantly, so that a much hgher prce s needed to ncentvze them to supply the desred amount of DR. In the extreme case wth, the prce to ncentvze the customers can become so hgh that the LSE would nstead resort to other expensve alternatves, characterzed by ts cost functon (). Ths s evdenced n Fgure (d), where wth the extracted DR falls to zero, meanng that the LSE has turned away from usng DR. The optmal level of commtment leads to a lower cost to the socety than a fully voluntary DR (.e., = ). Ths s because the requrement of restrcts the acton space of the customers n a way that benefts the socety. In partcular, a hgher level of commtment decreases the uncertanty of the extracted DR. There s a dscontnuty n Fgures (a), (c), (d) and (e). Ths s caused by the non-convexty of the customer s optmzaton problem, as wll be shown n more detal n the next subsecton. There s a flat secton towards lower n all of these curves. Ths s due to the followng reason: a fully voluntary DR ( = ) can already lead to certan non-zero level of commtment vol, so that settng vol does not change the behavor of the customers at all from that wth a fully voluntary DR program. Interestngly, we further observe that the optmal choce of by the socety s located relatvely near that by the LSE. To nvestgate ths n more detal, we plot the optmal by the socety and that by the LSE wth varyng levels of D n Fgures (a), (b), and (c). We observe that they concde wth each other closely. s a result, the proposed FDR framework n whch LSE optmzes and p n () acheves the socal optmum. In addton, as expected, we observe that the optmal ncreases wth a hgher amount of desred DR. lso note that at hgher levels of D, all three homes approach an optmal commtment level around.9 whch mples that dfferences n customer dstrbutons become less mportant as the amount of desred DR ncreases.. Optmal decsons by LSE and customers We now provde more nsghts nto the decson makng processes of the LSE and the customers n the proposed FDR framework.

5 Normalzed Socal ost Normalzed LSE ost Normalzed ustomer ost (a) Normalzed Socal ost Expected ggregated DR (kwh) (d) Total amount of DR extracted (b) Normalzed LSE ost prce ($/kwh) (c) Normalzed ndvdual customer ost (e) Prce of DR Fgure : Results for emprcal dstrbutons from Homes,, and : (a)-(c) llustrate the cost reducton from the perspectve of the socety, LSE, and a sngle customer under dfferent commtment levels (). Here, all cost numbers are normalzed by the socal cost when =. (d) and (e) show the amounts of demand response extracted, and demand response prces under dfferent s Optmal.6. Optmal.6. Optmal.6.. LSE Socety. LSE Socety. LSE Socety Desred DR (kwh) (a) Home Desred DR (kwh) (b) Home Desred DR (kwh) (c) Home Fgure : Optmal for a gven desred DR whch hghlghts the LSE s optmal choce of approxmates the socal optmum. LSE ost ($).. =.8 =.9 = prce ($/kwh) (a) LSE ost Expected ggregate DR (kwh) =.8 =.9 = prce ($/kwh) (b) Extracted DR y u (kwh)..... =.8 =.9 = prce ($/kwh) (c) y u ustomer ost ($) y l (kwh) p = $.7/kWh p = $./kwh p = $./kwh (d) ustomer ost Fgure : Home when D = kwh: (a) LSE cost versus prce of DR, (b) Extracted DR amount versus prce of DR, (c) y u versus prce of DR, (d) Indvdual customer cost versus y l when D = kwh, =.9. Dfferent lnes correspond to dfferent values of or p.

6 ... LSE s decson on and p. In solvng (), gven any level of commtment, the LSE needs to decde the optmal DR prce p. Fgure (a) llustrates the complcated tradeoff under the emprcal dstrbuton of Home (see our extended verson onlne for Homes and ). In general, when the prce s too low, there s not enough DR extracted from the customers. Ths can be seen from Fgure (b). The LSE therefore suffers from the hgh penalty of not beng able to meet the DR target. On the other hand, f the prce s set too hgh, the LSE pays too much for the extracted DR. s shown n the fgures, the tradeoff s complcated and non-convex. The optmal prce brngs n sgnfcant cost reductons. The observatons are consstent under all three of these emprcal dstrbutons.... customer s decson on y u and y l. Gven the level of commtment and prce of DR p, the customers need to decde the amount of demand response by settng the values of y u and y l. Ths then leads to dfferent amount of DR provded to the LSE. In partcular, Fgure (b) llustrates the amount of DR provded under the emprcal dstrbuton of Home wth dfferent prces of DR. learly, the amount of extracted DR s ncreasng n the prce offered. Under the three dstrbutons, there s a seres of stages: a convex ncreasng stage, jump stage(s), smooth ncreasng stage(s), a flat stage, and a concave ncreasng stage. In order to understand the reason behnd ths phenomenon, we provde the optmal values of y l and y u selected by the customer under dfferent prces of DR n Fgures (c), and (d). Specfcally, In the frst convex stage, y u vares (cf. Fgure (c)), and the probablty of respondng s Pr(Y y u ) s greater than but y l s hgh resultng n lttle effectve DR. s p ncreases, the customer s ncentvzed to provde more effectve DR by adjustng both y l and y u snce the emprcal dstrbuton s not monotonc. The jump stage(s) s caused by the non-convex cost functon when a customer makes ts decson on y l. Specfcally, we plot a customer s cost as a functon of y l n Fgure (d) for dfferent p around the prce at whch the jump happens n Fgure (b). It can be seen that: a) fndng the optmal y l nvolves mnmzng a non-convex cost functon, and b) as p ncreases, the optmal y l can swtch from the mddle part to ether dfferent local mnmum or to the lower bound l n a dscontnuous manner. Ths thus explans the jump behavor n the amount of DR n Fgure (b). The smooth ncreasng stage(s) s caused by the mgraton of the local mnmum from ncreasng the prce as can be seen n Fgure (d). In the sem-fnal flat stage, y u remans unchanged n order to meet the requrement of response probablty, whle y l also stays at the lower bound l. In the fnal concave stage, y l stays at the lower bound l, whle y u ncreases wth p (cf. Fgure (d)) because the customer s now wllng to provde even hgher response probablty than due to the suffcently hgh prce p.. ONLUSION Ths paper proposes a novel framework for demand response called Flexble ommtment Demand Response (FDR), whch enables explct choces of the level of DR commtment. Numercal results hghlght the great benefts of the optmal level of commtment. In partcular, there s roughly a % decrease n socal cost compared to programs requrng full commtment, and up to % of addtonal demand response extracted wth a lower DR prce compared to programs wth no commtment. 6. KNOWLEDGMENTS We would lke to thank Srnvasan Keshav for hs nsghtful comments and suggestons. Ths work was supported by NSF through NS REFERENES [] oncdent peak. Onlne. utltes/busness/rates/electrc/concdent-peak. [] Frequently asked questons. Onlne. [] The smart grd: an ntroducton. Onlne. http: //energy.gov/oe/downs/smart-grd-ntroducton-. [] Quckfacts table. Onlne, -. [] Grd ntegraton. Onlne, prl 6. [6] Varablty of renewable energy sources. Onlne, prl 6. varablty.html. [7] Zonal nformaton. Onlne, May 6. com/soexpress/web/reports/prcng/-/tree/zone-nfo. [8] S. arker,. Mshra, D. Irwn, E. ecchet, P. Shenoy, and J. lbrecht. Smart*: n open data set and tools for enablng research n sustanable homes. SustKDD, ugust, :,. [9] E. tar, R. Rajagopal, P. Khargonekar, and K. Poolla. The role of co-located storage for wnd power producers n conventonal electrcty markets. In mercan ontrol onference (), pages IEEE,. []. K. herry. Electrc schedule E-P. Techncal report, Pacfc Gas and Electrc ompany, February. [] M. howdhury, M. Rao, Y. Zhao, T. Javd, and. Goldsmth. enefts of storage control for wnd power producers n power markets. to appear n IEEE Transactons on Sustanable Energy, 6. [] P. Denholm and M. Hand. Grd flexblty and storage requred to acheve very hgh penetraton of varable renewable electrcty. Energy Polcy, 9():87 8,. [] N. Framework. Roadmap for smart grd nteroperablty standards, release. (jan. )(nst specal publcaton 8). [] P. Harsha, M. Sharma, R. Natarajan, and S. Ghosh. framework for the analyss of probablstc demand response schemes. Smart Grd, IEEE Transactons on, ():7 8,. []. J. Krby. Frequency regulaton bascs and trends. Unted States. Department of Energy,. [6] New York Independent System Operator, Rensselaer, NY. Emergency Demand Response Program Manual, 7. edton, October. [7]. J. Peterman. R. --7 OM/P/jv. alforna Publc Utltes ommsson, October. [8] P. Pnson. Wnd energy: Forecastng challenges for ts operatonal management. Statstcal Scence, 8():6 8,. [9] K. Slversten. alforna s new energy storage mandate under the mcroscope. Energyz, October. calforna-s-new-energy-storage-mandate-under-mcroscope. [] N. Sknner. ssembly bll no.. alforna State ssembly, September. [] J. S. Vardakas, N. Zorba, and. V. Verkouks. survey on demand response programs n smart grds: Prcng methods and optmzaton algorthms. IEEE ommuncaton Suverys Tutorals, 7(): 78,. []. Werman, Z. Lu, I. Lu, and H. Mohsenan-Rad. Opportuntes and challenges for data center demand response. In Green omputng onference (IG), Internatonal, pages. IEEE,. [] Y. Zhao, J. Qn, R. Rajagopal,. Goldsmth, and H. V. Poor. Wnd aggregaton va rsky power markets. Power Systems, IEEE Transactons on, ():7 8,.