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1 Appled Energy 25 (217) Conens lss avalable a ScenceDrec Appled Energy journal homepage: Opmal bddng sraegy for mcrogrds n jon energy and ancllary servce markes consderng flexble rampng producs q Janxao Wang a, Hawang Zhong a, Wenyuan Tang b, Ram Rajagopal b, Qng Xa a,, Chongqng Kang a, Y Wang c a Sae Key Lab. of Power Sysem, Dep. of Elecrcal Engneerng, Tsnghua Unversy, Bejng 184, Chna b Cvl and Envronmenal Deparmen, Sanford Unversy, Sanford, CA 9435, USA c Guangdong Power Grd Corporaon, Guangzhou, Guangdong 51, Chna hghlghs Flexble rampng producs are modelled n he framework of a mcrogrd. Mcrogrds opmal bddng model s proposed n energy and ancllary servce markes. A hybrd sochasc and robus opmzaon approach s adoped. The effecveness of he proposed bddng model s verfed based on real-world daa. arcle nfo absrac Arcle hsory: Receved 4 May 217 Receved n revsed form 3 July 217 Acceped 15 July 217 Keywords: Ancllary servce Flexble rampng produc Mcrogrd Opmal bddng sraegy Robus opmzaon Due o he volale naure of wnd and phoovolac power, wnd farms and solar saons are generally hough of as he consumers of rampng servces. However, a mcrogrd (MG) s able o sraegcally negrae varous dsrbued energy resources (DERs) o provde boh energy and ancllary servces (ASs) for he bulk power sysem. To evaluae he rampng capables of an MG n he jon energy and AS markes, an opmal bddng sraegy s developed n hs paper consderng flexble rampng producs (FRPs). By aggregang and coordnang varous DERs, ncludng wnd urbnes (WTs), phoovolac sysems (PVs), mcro-urbnes (MTs) and energy sorage sysems (ESSs), he MG s able o opmally allocae he capaces for energy, spnnng reserve and rampng. Takng advanage of he synergy among DERs, he MG can maxmze s revenues from dfferen markes. Moreover, he flexbly of he MG for he bulk power sysem can be fully explored. To address he unceranes nroduced by renewable generaon and marke prces, a hybrd sochasc/robus opmzaon (RO) approach s adoped. Case sudes based on a realworld MG wh varous DERs demonsrae he marke behavor of he MG usng he proposed bddng model. Ó 217 Publshed by Elsever Ld. 1. Inroducon 1.1. Movaon The developmen of renewable energy has been drawng aenon across he world n he pas decade. Calforna, for example, announced s ambous goal of achevng a 5% renewable porfolo sandard by 23 [1]. Whle he use of renewable energy q Ths work was suppored by he Naonal Naural Scence Foundaon of Chna (No ), Naonal Key Research and Developmen Program of Chna (No. 216YFB91), and Sae Grd Corporaon of Chna. Correspondng auhor. E-mal address: qngxa@snghua.edu.cn (Q. Xa). conrbues o a more susanable fuure, he varables and unceranes of he renewable sources pose grea challenges o he economc and relable operaons of he power sysem [2]. Wh he ncreasng peneraon of renewable energy, rapd rampng of generaon resources may be nsuffcen o smooh ou he huge flucuaons n renewable energy producon. Thus, s crcal o faclae he accommodaon of renewable generaon whle economcally and relably operang he power sysem. The concep of he mcrogrd (MG) assumes a cluser of loads and dsrbued energy resources (DERs) operang as a sngle conrollable sysem [3]. Takng advanage of he synergy among varous DERs, he renewable generaors can cooperae wh conrollable energy resources o provde boh energy and ancllary servces (ASs) for he bulk power sysem [4]. For example, n a hp://dx.do.org/1.116/j.apenergy /Ó 217 Publshed by Elsever Ld.

2 J. Wang e al. / Appled Energy 25 (217) Nomenclaure Indces and ses me ndex s prce scenaro ndex U B se of decson varables U U se of random varables E superscrp for energy RES superscrp for spnnng reserve servce RAMPU superscrp for upward FRP servce RAMPD superscrp for downward FRP servce WT superscrp for wnd urbnes PV superscrp for phoovolac sysems MT superscrp for mcro-urbnes ESS superscrp for energy sorage sysems Parameers and consans ^P WT pon forecas of hsorcal wnd power (Un: MW) n he MG a me slo ^P PV pon forecas of hsorcal solar power (Un: MW) n he MG a me slo C WT robusness parameer of wnd power C PV robusness parameer of solar power P WT max oal wnd power capacy (Un: MW) n he MG P PV max oal solar power capacy (Un: MW) n he MG N MT number of MTs n he MG N ESS number of ESSs n he MG c s wegh of prce scenaro s N S number of prce scenaros k ðþ ;s day-ahead marke prce (Un: $/MW h) a me slo n scenaro s h me nerval b ðþ expecaon of real-me deploymen rao of ancllary servces c MT operaon cos per un energy producon (Un: $/ MW h) of MT maxmal power (Un: MW) of MT P MT P MT;RAMPU P MT;RAMPD P ESS ;a;max P ESS ;b;max ;a ;b ;mn C ESS Maxmal rampng-up capacy (Un: MW/h) of MT maxmal rampng-down capacy (Un: MW/h) of MT maxmal chargng power (Un: MW) of ESS maxmal dschargng power (Un: MW) of ESS chargng effcency of ESS dschargng effcency of ESS mnmal sae of charge of ESS maxmal sae of charge of ESS capacy (Un: MW h) of ESS E ESS ; nal sored energy (Un: MW h) of ESS n scenaro s load demand (Un: MW) of he MG a me slo P D Varable P AWT P APV e WT e PV R ðþ s C OP P ðþ a ESS ; b ESS ; E ESS ; random varable of avalable wnd power (Un: MW) a me slo random varable of avalable solar power (Un: MW) a me slo normalzed error beween acual and pon forecas wnd power normalzed error beween acual and pon forecas solar power revenue (Un: $) n scenaro s from he day-ahead markes operaon coss (Un: $) of he MG bddng capacy (Un: MW) of he MG or DER for energy or ASs a me slo bnary varable of ESS a me slo represenng he saus of chargng bnary varable of ESS a me slo represenng he saus of dschargng sored energy (Un: MW h) of ESS a me slo sand-alone mode, a wnd farm mus devae from s maxmum power oupu saus and leave a margn o provde rampng servces for he sysem. However, n an MG, he wnd farm s able o leave he rampng margn by chargng a Na/S baery whou devang from s maxmum power. Hence, an MG can sably provde boh energy and ASs by negrang varous DERs [5]. From he sysem pon of vew, MGs show he advanages of low nvesmen coss, low polluan emsson and hgh operaonal flexbly. The flexbly of he MGs provded by he DERs can be aggregaed for power sysem operaons, hereby replacng hgh-cos cenralzed uns and deferrng he generaon expanson. In addon, he MGs are locaed a he demand sde, effcenly offerng capaces o mee he local requremens [6]. Compared wh cenralzed hermal uns, MGs can acheve localzed energy balance whou he loss accompaned wh long-dsance power ransmsson and dffcules caused by ransmsson congesons. Therefore, he concep of he MG provdes new nsghs for explorng he grdfrendly manner of DERs [7]. In mos elecrcy markes across he world, ASs play a crcal role n he relable operaon of power sysems. In Calforna, for example, he reserve and regulaon servces are co-opmzed wh he energy n he day-ahead marke. Wh he ncreasng peneraon of solar energy, he varably and unceranes n ne load demands wll become more severe n he real-me operaon. As llusraed n Fg. 1, he seep rse of he sysem ne loads from 17: o 18: as he sun ses requres over 55 MW of generang capacy o come onlne, whch poses grea challenges o he secure operaon of he power sysem. To cope wh he nadequacy of he sysem s rampng capaces, he flexble rampng produc (FRP) has been nroduced no he Calforna marke recenly o mprove he dspach flexbly and address he operaonal challenges [8,9]. FRPs are flexble generaon capaces dspached by he ndependen sysem operaor (ISO) o deal wh energy mbalances and sasfy he load followng requremens n he real-me operaon. The energy mbalances Megawas Hour Oher renewable energy Sysem load Solar phoovolacs Ne load Fg. 1. Hourly renewable energy and elecrc load demands on March 1, 217 n Calforna.

3 296 J. Wang e al. / Appled Energy 25 (217) can arse due o load and supply varably. The FRPs conss of separae producs n he upward and downward drecons as he energy mbalances may be posve or negave [8]. Currenly, fas-ramp generaors are generally dspached o provde FRPs. Wh he negraon of rapd rampng resources, e.g., mcrourbnes (MTs) and energy sorage sysems (ESSs), he MGs are promsng energy resources o provde fas rampng capaces for he power sysem. In exsng sudes, he bddng sraeges of an MG wh varous DERs parcpang n he energy and reserve markes have been nvesgaed [1 12]. These sudes examned he ables of an MG o provde energy and spnnng reserve. However, few sudes have focused on an MG s parcpaon n dfferen ypes of ASs, especally he FRPs. Therefore, s mperave o evaluae he rampng capables of MGs n he marke envronmen. Ths paper s he poneerng work on he opmal bddng sraegy for MGs parcpang n jon energy, spnnng reserve and FRP markes Leraure revew and conrbuon The opmal bddng sraeges for MGs n he energy marke have been wdely nvesgaed n he las decade. In [1], an opmal day-ahead prce-based power schedulng problem s suded for a communy-scale MG. The model ams a maxmzng he expeced benefs of he MG n he energy marke whle sasfyng users hermal comfor requremens. In [13], he day-ahead bddng sraegy of a commercal vrual power plan (VPP) s addressed consderng varous DERs. To address he unceranes n load consumpons and real-me prces, a hree-sage sochasc opmzaon model s formulaed for opmal energy schedulng. In [14], he opmal bddng sraegy n he day-ahead energy marke of an MG s proposed. The MG coordnaes he energy consumpon and producon of s componens and rades elecrcy n dayahead and real-me markes. A hybrd sochasc/robus opmzaon mehod s adoped o address he unceranes n renewable energy oupus and fuure prces. In [15], he concep of MG aggregaors s nroduced o nvolve small-scale MGs n he real-me balancng marke bddng va a herarchcal marke framework. A he upper level, he bddng sraegy of he aggregaor s opmzed whle he marke s cleared a he lower level. In [16], he bddng problems of VPPs are nvesgaed consderng renewable dsrbued generaors and nelasc demands. A sochasc blevel opmzaon model s formulaed o mnmze he cos of he VPP n day-ahead and balancng markes. An MG, as a conrollable sysem, s able o provde boh energy and ASs for he power sysem by sraegcally coordnang varous DERs [17]. There have been exensve sudes focused on he bddng sraeges for MGs n jon energy and reserve markes [18]. In [19], an arbrage sraegy for VPPs by parcpang n energy, spnnng reserve and reacve power markes s presened. The secury-consraned un commmen (SCUC) model s esablshed o maxmze VPP s profs. In [2], he bddng problem by a VPP n a jon marke of energy and spnnng reserve servce s addressed. The proposed bddng sraegy s a non-equlbrum model based on he deermnsc prce-based un commmen. In [21], a rsk-averse opmal offerng model for a VPP s proposed n he jon energy and reserve markes. Unceranes n renewable generaon and prces from day-ahead and balancng markes are consdered. Reference [21] assesses how oal and surplus profs of a VPP are affeced by rsk-averson. In [12], a mul-objecve jon energy and reserve marke clearng model s presened n whch he paymen cos mnmzaon and volage sably maxmzaon are consdered. In [22], a bddng behavor modelng and an aucon archecure of he MG are proposed. The bddng behavoral saes of he MG are formalzed as Markov processes. In [23], an opmal bddng model of a resdenal MG s formulaed for day-ahead markes, consderng he unceranes n renewable power producon. The renewable unceranes are modeled based on an Analog Ensemble mehod, whch can esmae he probably of solar power by samplng. In [24], a day-ahead opmal energy managemen sraegy of ndusral MGs s presened wh hghpeneraon renewables. Besdes sasfyng s local demands, he MG parcpaes n energy radng wh he power sysem. To he bes of our knowledge, few exsng sudes have focused on he combnaon of dfferen ypes of ASs, especally he rampng servces of an MG. By means of he synergy among varous DERs, MGs can be hough of as promsng energy resources o cope wh he nadequacy of he sysem s rampng capaces. Therefore, s mperave o nvesgae he rampng capables of MGs n he marke envronmen. In hs paper, an opmal bddng model s esablshed o evaluae he rampng capables of an MG n he jon energy and AS markes. By coordnang varous DERs, ncludng WTs, PVs, MTs and ESSs, an MG s able o maxmze s revenues from he day-ahead markes. A hybrd sochasc/robus opmzaon mehod s adoped o address he unceranes n renewable energy generaon and marke prces. The major conrbuons of hs paper are as follows: (1) FRPs are ncorporaed no he bddng model of an MG for he frs me. The rampng capables of he MG can hen be evaluaed by opmzng he bddng model. By negrang varous DERs, he rampng capables of he MG can be grealy mproved. (2) The flexbly of an MG for he bulk power sysem s examned consderng s parcpaon n he jon energy, spnnng reserve and FRP markes. (3) A hybrd sochasc/robus opmzaon approach s adoped o address he unceranes n renewable energy and marke prces. The bddng problem wh unceran coeffcens can be ransformed no a mxed-neger lnear programmng (MILP) model ha can be readly solved. 2. Problem descrpon 2.1. Co-opmzaon of energy and ancllary servce markes Whou loss of generaly, he co-opmzaon of energy and AS markes s mplemened n hs paper [25]. In he pool-based dayahead markes, s assumed ha an MG can smulaneously bd n jon energy and AS markes. Consderng s relavely small capacy, an MG s reasonably assumed o be a prce-aker. As a conrollable eny, he MG wll sraegcally allocae avalable capaces n day-ahead markes o maxmze he revenues. The MG bds energy and ASs, ncludng spnnng reserve servce and FRPs [8]. The FRP provded by an MG s referred o he poenal power oupu change from me slo o + 1, whch reflecs he avalable capacy of he MG reserved for he power sysem o sasfy load followng. FRPs are specfcally desgned o releve he sysemwde rampng consrans, whch are frs nroduced n Calforna and MISO markes n he Uned Saes. The models and applcaons of FRPs have been nvesgaed recenly. In [26], he mahemacal model of FRPs s formulaed accordng o he Calforna marke. In [27], he secury-consraned economc dspach (SCED) model s presened o ncorporae he rampng consrans. Numercal resuls demonsrae he effecveness of he rampng consrans for reducng he nsances of shor-erm scarcy condons. In [28], a rsk-consraned SCED scheme s proposed o opmze he dspach and provson of FRPs. Wh he ncreasng demand for he rampng resources n he power sysem, he FRP marke s expeced o be fully operaonal n he near fuure. The framework of an MG s parcpaon n day-ahead energy and AS markes are shown n Fg. 2. In hs framework, negraed

4 J. Wang e al. / Appled Energy 25 (217) Wnd urbne Energy marke Solar saon Energy sorage Mcro urbne Mcrogrd Inegraon Marke bddng Ancllary servce marke Upward FRP Spnnng reserve Downward FRP Marke clearng Resuls released DERs 1 2 Fg. 2. Framework of an MG s parcpaon n day-ahead energy and AS markes. wh varous DERs, an MG bds n he jon energy, reserve and FRP markes a me, when he ISO opens he day-ahead marke. Then he day-ahead marke bd perod closes a me 1. The ISO begns o run he marke clearng sofware o deermne he hourly dspach schedules and he locaonal margnal prces for he dayahead marke. Fnally, he marke clearng resuls wll be released a me 2. The co-opmzaon of he energy and AS markes s mplemened n mos elecrcy markes operaed by he ISO [29]. The bds of he MG mus be deermned before he closure of he day-ahead markes for he nex day [14]. By nroducng FRP markes, on one hand, he MG s able o ncrease he revenues from marke bddng; on he oher hand, he power sysem wll benef from he mprovemen of he dspach flexbly and he adequacy of he rampng resources Uncerany modelng In hs paper, a hybrd sochasc/robus opmzaon approach s adoped o address he unceranes n renewable generaon and day-ahead marke prces [14,25]. The prces n he energy and AS markes are modeled va scenaro-based sochasc programmng. The unceranes n wnd and phoovolac power are addressed usng RO. For marke prces, an MG s concerned wh he profles of marke prces o opmally allocae s avalable capaces n each marke. The prces n dfferen markes have srong correlaons, whch canno be modeled wh ndependen confdence nervals. For example, boh prces of energy and spnnng reserve are relavely hgh durng peak hours because of hgh load demands. In addon, o allocae he capaces n dfferen markes, he relave dfferences of prces are he major concern nsead of he absolue values of marke prces. Therefore, sochasc programmng wh mulple prce scenaros s more approprae han RO o model he uncerany of marke prces [14]. For renewable generaons, he absolue capaces of wnd and phoovolac power have large mpacs on he bddng sraegy of an MG as well as he operaon of he DERs n he MG. Moreover, because he nervals of wnd and phoovolac power can be obaned accordng o hsorcal daa, RO s an effecve ool o address he unceranes n renewable generaon. Therefore, he robus mxed-neger lnear programmng (RMILP) n [3] s appled n hs paper. The avalable power of he WT and PV n he MG a me slo, denoed by P AWT and P APV, are modeled as ndependen and akes bounded random varables. Under a confdence level r, P AWT values from he mnmum power P AWT P AWT, whle P APV akes values from P APV and P APV o P APV. To oban he conf-, he forecas errors are analyzed dence nervals of P AWT based on hsorcal daases. ^P WT o he maxmum power For example, and P WT are he pon forecas and acual wnd power a me slo. Based on he hsorcal daa from he Wnd Inegraon Daases of he NREL [31], he probably dsrbuon f WT ð^p WT =P WT maxþ of wnd power forecas errors ewt can be acqured,.e., e WT ¼ ^P WT P WT P WT max ; e WT f WT ð^p WT =P WT max Þ: Then he upper and lower bounds of wnd power forecas errors under he confdence level r, e WT ;mn and ewt ;max, can be calculaed as follows: Z w e WT ;mn ¼ Inf w 2½; 1Š f WT ðxþdx P 1 r ; ð2þ 2 e WT ;max ¼ Inf Z w w 2½; 1Š f WT ðxþdx P 1 þ r 2 ð1þ : ð3þ Fg. 3 shows he nervals of forecas errors wh 95% confdence level under dfferen levels of forecased wnd power [32]. Accordng o he forecased wnd power, he mnmum power and he maxmum power can be calculaed as follows: Forecas error (%) Posve error Negave error Forecased wnd power (% nsalled capacy) Fg. 3. The nervals of forecas errors wh 95% confdence level under dfferen levels of forecased wnd power.

5 298 J. Wang e al. / Appled Energy 25 (217) P AWT AWT ¼ ^P P WT max ewt ;max ; ewt ;max > ; ð4þ P PV;E þ P PV;RES þ P PV;RAMPU 6 P APV ; 8; ð13þ P AWT ¼ ^P AWT P WT max ewt ;mn ; ewt ;mn < : Then he random varable for he avalable wnd power a me slo s bounded as follows: P AWT 2½P AWT ; P AWT Š: ð6þ The nervals for he avalable PV power can be obaned n a smlar manner wh wnd power. 3. Opmal bddng model for mcrogrds By coordnang varous DERs, an MG s able o provde flexbly for he bulk power sysem. In hs paper, FRPs are modeled n he bddng sraegy of he MG n he day-ahead markes. As a prce-aker, he MG sraegcally allocaes he hourly capaces n energy, spnnng reserve and FRPs Objecve The objecve of he opmal bddng sraegy for an MG s o maxmze he oal revenue from he energy, spnnng reserve and FRP markes, shown as follows: ½SPS D FTerm 3 6Š½SPS D FTerm 2 Š½SPS D FTerm 4 Š max U B where X N S mn U U s¼1 ð5þ c s ðr E s þ RRES s þ R FRP s C OP Þ; ð7þ ½SPS D FTerm 4 4Š½SPS D FTerm 3 8Š½SPS D FTerm 3 7Š½SPS D FTerm 2 8Š ½SPS D FTerm 2 2Š½SPS D FTerm 2 1Š½SPS D FTerm 1 2Š½SPS D FTerm 6 Š ½SPS D FTerm 5 ŠR E s ¼ XT h k E ;s PE þbres P RES þb RAMP ðp RAMPU P RAMPD Þ h; ð8þ R RES s R FRP s ¼1 ¼ XT ¼1 ¼ XT ¼1 k RES ;s PRES h; ð9þ ðk RAMPU ;s P RAMPU ½SPS D FTerm 4 1Š½SPS D FTerm 2 5Š½SPS D FTerm 9 ŠC OP ¼ XT X NMT c MT ¼1 ¼1 h P MT;E ; þb MT;RES þ k RAMPD ;s P RAMPD Þh; ð1þ P MT;RES ; þb MT;RAMP ðp MT;RAMPU ; P MT;RAMPD ; Þ h: ð11þ The revenues from he energy and reserve markes are shown n (8) and (9). The revenues from he FRPs are shown n (1), composed of he upward and downward FRPs. (11) shows ha he operaonal coss of he MG come from he fuel coss of he MTs. Noe ha n (8) and (11), o consder he nfluences of he real-me deploymen of ASs, he raos b ðþ are used o esmae he poenal energy requremen n provdng AS [25] Consrans The consrans of renewable generaors P WT;E þ P WT;RES þ P WT;RAMPU 6 P AWT ; 8; ð12þ P WT;E P WT;RAMPD P ; 8; ð14þ P PV;E P PV;RAMPD P ; 8: ð15þ In (12) and (13), he energy, reserve and upward FRP of he WT are resrced by he avalable wnd and phoovolac power. In (14) and (15), he dfference beween he energy and he downward FRP should be no less han The consrans of mcro urbnes P MT;E ; þ P MT;RES ; þ P MT;RAMPU ; 6 P MT ; 8; ; ð16þ P MT;E ; P MT;RAMPD ; P ; 8; ; ð17þ ðp MT;E þ ;þ1 PMT;RES ;þ1 ðp MT;E ; þ P MT;RES ; þ P MT;RAMPU ;þ1 þ P MT;RAMPU ; Þ ðp MT;E ; Þ ðp MT;E ;þ1 P MT;RAMPD ; Þ 6 P MT;RAMPU ; 8; ; ð18þ PMT;RAMPD ;þ1 Þ 6 P MT;RAMPD ; 8; : ð19þ In (16) and (17), he bddng capaces of he MTs should be lmed by he maxmum and mnmum power. In (18) and (19), he rampng up/down consrans are modeled The consrans of energy sorage sysems ½SPS D FTerm 4 2Š½SPS D FTerm 2 6Š½SPS D FTerm 1 Š 6 a ESS ; þ b ESS ; 6 1; a ESS ; ; b ESS ; 2f; 1g; 8; ; ð2þ 6 P ESS ;;a 6 aess ; PESS ;a;max ; 8; ; ð21þ 6 P ESS ;;b 6 bess ; PESS ;b;max ; 8; ; ð22þ P ESS;E ; P ESS;E ; ¼ P ESS ;b; PESS ;a; ; 8; ; ð23þ þ P ESS;RES ; þ P ESS;RAMPU ; 6 P ESS ;b;max ; 8; ; ð24þ P ESS;E ; P ESS;RAMPD ; P P ESS ;a;max ; 8; ; ð25þ P ESS;E ; E ESS ; E ESS ; h E þ P ESS;RES h RES þ P ESS;RAMPU P ESS;E ; ; ; h RAMP 6 E ESS ; ; 8; ; ð26þ h E þ P ESS;RAMPD ; h RAMP 6 CESS ; 8; ; ð27þ ¼ E ESS ; 1 þðpess ;a; ;a PESS ;b; =gess ;b ;mn 6 EESS ; =C ESS 6 ; 8; ; ð29þ E ESS ; ¼ EESS ;T ; 8; where a ESS ; and b ESS ; Þh; 8; ; ð28þ condon of he ESS a me slo. a ESS ; ESS s chargng; a ESS ; a ESS ; ¼ ; b ESS ; ð3þ are bnary varables represenng he workng ¼ ; b ESS ; ¼ 1; b ESS ; ¼ ndcaes he ¼ 1 ndcaes he ESS s dschargng; ¼ ndcaes he ESS s sandng by. The power lms of ESSs are shown n (21) and (22). In(23), he energy capaces provded by he ESSs are he dfference beween he dschargng and chargng power. In (24) and (25), he power lms of he ESSs are shown. Consrans (26) and (27) ndcae ha an ESS mus be

6 J. Wang e al. / Appled Energy 25 (217) able o manan he fully deployed oupu level for h E (ypcally 1 h) energy, h RES (ypcally 1 h) spnnng reserve, and h RAMP (ypcally 15 mn) rampng up/down [29]. Consran (28) represens he relaonshp beween sored energy and chargng/dschargng power. In (29), he ESS s bounded by he mnmum and maxmum of he sae of charge (SOC). In (3), he nal and fnal sored energy should be equal The consrans of he mcrogrd P E ¼ P WT;E P m ¼ P WT;m þ P PV;E þ P PV;m þ XN MT ¼1 þ XN MT ¼1 P MT;E ; P MT;m ; 2fRES; RAMPU; RAMPDg; þ XN ESS ¼1 þ XN ESS P ESS;E ; P D ; 8; ð31þ ¼1 P ESS;m ; ; 8; m ð32þ The MG s capacy for energy and AS s suppored by he DERs operaed by he MG aggregaor, as shown n (31) and (32). Therefore, he objecve (7) and he consrans (8) (32) form he proposed bddng model. The soluon algorhm s elaboraed n Secon Reformulaon va robus opmzaon approach Because of s flexbly, conrollably and moderae compuaonal cos, he RO approach provdes applcable soluons o he general sochasc opmzaon problems. In he opmal bddng model, he se of random varables ncludes he avalable wnd and phoovolac power. As elaboraed n he Appendx A, hs problem can be formulaed as an RMILP by nroducng dual and auxlary varables as follows: X N S max U B [ U D s¼1 c s ðr E s þ RRES s þ R FRP s C OP Þ ð33þ subjec oconsrans (14)-(32), P WT;E P PV;E z WT z PV þ P WT;RES þ P WT;RAMPU þ P PV;RES þ P PV;RAMPU þ q WT þ q PV P 1 2 ð P AWT P 1 2 ð P APV þ C WT z WT þ q WT ðpawt þ P AWT Þ; 8; þ C PV z PV þ q PV ðpapv þ P APV Þ; 8; ð34þ ð35þ P AWT Þy WT ; 8; ð36þ P APV Þy PV ; 8; ð37þ y WT ; y PV P 1; 8; ð38þ z WT ; z PV ; q WT ; q PV P ; 8; ð39þ where z WT problems and y WT ; z PV ; q WT ; q PV are he dual varables of he orgnal ; y PV are he auxlary varables ha help ln- and C PV are he robusness parameers, j] and [, jj PV j], where are ses ncludng all random varables n consrans earze he problem. C WT whch ake on values n he nerval [, jj WT J WT and J PV (12) and (13) a me slo. Noe ha here s jus one random varable n each consran, so jj WT ha by varyng C WT 2½; jj WT j¼jj PV j¼1. I s worh menonng jš and C PV 2½; jj PV jš, he flexbly of adjusng he robusness s acqured agans he level of conservasm of he soluon [33]. In pracce, he robusness parameers can be se accordng o he rsk preference of he MG operaor. The deals of he RO approach can be found n [3]. The RMILP seeks o maxmze he MG s revenues from each marke under he wors case caused by he unceranes n renewable generaons. The hourly parameers C WT and C PV adjus he robusness degree of consrans (12) and (13) agans he unceranes n he wnd and phoovolac power. The larger he robusness parameers are, he more conservave he RMILP problem becomes. The nfluences of selecng dfferen robusness parameers are nvesgaed n Secon Case sudes The es envronmen s a ThnkPad T44p operang a 2.4 GHz wh 8 cores. The program s developed usng MATLAB R215a. The opmzaon solver s CPLEX 12.4 [34] Basc daa Hsorcal daa of he Elecrc Relably Councl of Texas (ERCOT) day-ahead marke prces [35] from July 1, 216, o Sepember 3, 216, are used o generae 2 ypcal scenaros o address he unceranes n day-ahead marke prces. These prce scenaros are generaed by K-means cluserng. The average hourly prces n he energy and AS markes are shown n Fg. 4. The wnd and solar power are he real-world daa from a wnd farm and a phoovolac saon n a provnce n Chna. Accordng o he uncerany modelng n Secon 3, under 95% confdence level, he forecased wnd and phoovolac power and he confdence nervals are shown n Fg. 5. The parameers of he oher DERs n he MG are shown n Table 1. To evaluae he rampng capables and he benefs of he MG n jon energy and AS markes, hree cases are consdered: Case 1: () S1, where he MG bds n he jon energy, reserve and FRP markes wh C WT ¼ 1 ; ) S2, where he MG bds n he jon energy and reserve markes wh C WT ¼ 1 ; ) S3, where he MG only bds n he energy marke wh C WT ¼ 1. Case 2: () S1; () S4, where he MG bds n he jon energy, reserve and FRP markes wh C WT ¼ :6; () S5, where he MG bds n he jon energy, reserve and FRP markes wh C WT ¼ :2. Case 3: ) S1; ) S6, where he MG bds n he jon energy, reserve and FRP markes wh C WT Energy and reserve prce ($/MWh) Energy Reserve Upward FRP Downward FRP ¼ 1, whle he FRP prces Tme (h) Fg. 4. Average day-ahead hourly prces n he energy and AS markes FRP prce ($/MWh)

7 3 J. Wang e al. / Appled Energy 25 (217) Wnd power (MW) Forecased wnd power Tme (h) a Phoovolac power (MW) Forecased phoovolac power Tme (h) b Fg. 5. The forecased renewable power and he confdence nervals. Table 1 Parameers of he DERs n he MG. DER c MT ($/MW h) P MT (MW) PMT;RAMPU (MW/h) P MT;RAMPD (MW/h) MT MT MT ESS-1 ;a ;b ;mn C ESS (MW h) E ESS ; (MW h) PESS ;a;max (MW) PESS ;b;max (MW) ESS-2 ;a ;b ;mn C ESS (MW h) E ESS ; (MW h) PESS ;a;max (MW) PESS ;b;max (MW) are 1.2 mes of hose n S1; ) S7, where he MG bds n he jon energy, reserve and FRP markes wh C WT ¼ 1, whle he FRP prces are.8 mes of hose n S Base case resuls In S1, he MG bds n jon energy, reserve and FRP markes. The opmal bddng sraeges of he MG are shown n Fg. 6. The MG sraegcally allocaes he avalable capacy n each hour o maxmze he revenues from he jon energy and AS markes. The bddng sraegy of he MG depends on he physcal consrans of he DERs and he opporuny coss n each marke. In he energy marke, he MG wll generae elecrcy for he bulk power sysem, whch leads o he operaonal coss of he MG. In he AS markes, he MG wll leave a margn for he AS capaces, whch may no cause he operaonal coss. As shown n Fg. 4, when he prces of spnnng reserve are hgh and he opporuny coss are relavely low, he capacy s provded for reserve nsead of bddng n he energy marke. Smlar conclusons can be drawn from he bddng for he upward FRPs. In addon, by curalng renewable generaon, decreasng he MTs oupu and makng he ESSs charge, he MG s able o provde downward FRPs. The opmal bddng sraeges of he DERs n he energy marke are shown n Fg. 7. Because he operaonal coss of wnd and phoovolac power are zero, he capacy of WT and PV s fully used n he energy marke o maxmze he energy revenues. The operaonal cos of M-2 s relavely low; hus, all he avalable capacy s provded for energy. However, he coss of he oher wo MTs are hgher, hereby drvng MT-1 and MT-3 o bd he avalable capacy for ancllary servces durng some perods. In he process of Capacy (MW) Energy Reserve Upward FRP Downward FRP Tme (h) Fg. 6. Opmal bddng sraeges of he MG n he base case. arbrage, he ESSs wll charge durng he valley hours and dscharge durng he peak hours. In addon, because he ESSs can flexbly adjus he consumpon or producon, he ESSs wll sraegcally bd for energy and ancllary servces. The energy capacy of he MG s equal o he dfference beween he capacy offered by he DERs and he load demands. The expeced revenues of he DERs n dfferen markes are shown n Table 2. By sraegcally allocang he capacy of he

8 J. Wang e al. / Appled Energy 25 (217) Capacy (MW) PV WT MT-1 MT DERs n dfferen markes, he MG can oban he opmal expeced revenues wh 2.35% energy, 67.77% reserve and 11.88% FRP. As one can observe, s benefcal for he MG o parcpae n he jon energy and AS markes, n whch FRPs are also mporan fracons Comparson resuls n Case 1 Table 3 shows he expeced revenues from each marke n Case 1. Comparng he resuls n S1 wh hose n S2, one can observe ha he MG can ncrease s revenues by 8.2% f provdng FRPs. Comparng he resuls n S1 and hose n S3, one can observe ha he MG can ncrease s revenues by 24.75% f parcpang n jon energy and AS markes. Therefore, by parcpang n jon energy, reserve and FRP markes, he MG can furher ncrease s revenues from he day-ahead markes. Meanwhle, he MG s able o provde rampng capaces for he bulk power sysem, whch fully ulzes he grd-frendly poenals of he MG Comparson resuls n Case 2 MT-3 Load Tme (h) ESS-1 ESS-2 ESS-1 energy ESS-2 energy 16 Fg. 7. Opmal bddng sraeges of he DERs n he energy marke. Table 2 The expeced revenues of he DERs n dfferen markes. Revenue Energy ($) Reserve ($) FRP ($) Toal revenue ($) WT PV MT MT MT ESS ESS MG The oal FRPs provded by he MG n Case 2 are compared n Table 4. Table 3 The expeced revenues from each marke n Case Sored energy (MWh) Table 4 The oal FRPs provded by The MG n Case 2. S1 S4 S5 Upward FRP (MW) Downward FRP (MW) Table 5 The expeced revenues from each marke n Case 2. Revenue Energy ($) Reserve ($) FRP ($) Toal revenue ($) S S S From he comparson resuls, he oal FRPs provded by he MG ncrease wh he decrease of he conservasm degree. A smaller conservasm degree ndcaes a larger amoun of avalable renewable generaon s expeced, hereby leadng o an ncrease n he rampng capaces of he MG. The expeced revenues from each marke n Case 2 are shown n Table 5. Wh he decrease of he conservasm degree, he revenues from each marke wll ncrease. As he smulaon resuls show, wh he synergy of he DERs n he MG, he renewable generaon can cooperae wh he MTs and ESSs and be fully accommodaed whou curalmen Comparson resuls n Case 3 The FRPs provded by he MG n Case 3 are compared n Fg. 8. From he comparson resuls, when he rampng capaces of he bulk power sysem are nsuffcen, leadng o hgher FRP prces, he MG s able o provde more rampng capaces o suppor he bulk power sysem whle maxmzng s ndvdual revenues. The expeced revenues from each marke n Case 3 are shown n Table 6. From he resuls n S1 and S6, by ncreasng he FRP prces by 2%, he oal revenues of he MG from he day-ahead marke wll ncrease by 2.4%, and he FRP revenues ncrease by 21.77%. Wh more avalable capaces provded for FRPs, he revenues from energy and reserve are reduced n S6. From he resuls n S1 and S7, by reducng he FRP prces by 2%, he oal revenues wll decrease by 2.27%, he FRP revenues decrease by 26.3% whle more capaces can be provded for energy and reserve n S7. Rampng capacy (MW) S1-upward FRP S6-upward FRP S7-upward FRP S1-downward FRP S6-downward FRP S7-downward FRP Revenue Energy ($) Reserve ($) FRP ($) Toal revenue ($) S S S Tme (h) Fg. 8. The FRPs provded by he MG n Case 3.

9 32 J. Wang e al. / Appled Energy 25 (217) Table 6 The expeced revenues from each marke n Case 3. Revenue Energy ($) Reserve ($) FRP ($) Toal revenue ($) S S S Sensvy analyss The RO approach adoped n hs paper offers full conrol on he degree of conservasm for he consrans wh unceran coeffcens. To demonsrae he nfluences of he degree of conservasm on he bddng sraeges, he approach n hs paper wh dfferen robusness parameers s compared wh he mehod proposed n [36], n whch he wors-case and mos conservave scenaro s consdered. The revenues of he MG wh dfferen robusness parameers are shown n Fg. 9(a), and he growh raes of he revenues are shown n Fg. 9(b) compared wh he mehod n [36]. As shown n Fg. 9 (a), wh he ncrease of he conservasm degree, he revenues from each marke are gradually reduced because of he decreasng expecaons of he renewable generaon. As shown n Fg. 9 (b), because he operaonal coss of he WT and PV are zero, mos renewable energy wll be allocaed o he energy marke, leadng o he grea change of he energy revenues wh dfferen robusness. Compared wh he mehod n [36], he conservasm of he bddng problem can be flexbly adjused by usng he approach n hs paper. Noe ha when he robusness parameers are equal o 1., wo mehods acheve he same revenues because he wors-case scenaro s modeled and consdered n he mehod n [36]. Then he base case S1 s smulaed wh dfferen rampng prces o nvesgae he rampng capables of he MG under dfferen levels of prces. Wh he prces of energy and reserve unchanged, he bddng curves of upward and downward FRPs provded by he MG a 1: are shown n Fg. 1. From he bddng curves of FRPs, when he prces go up, he FRPs provded by he MG wll ncrease. The maxmal rampng capaces of he MG a 1: wh dfferen robusness parameers are shown n Table 7. Under dfferen degrees of conservasm, he bddng curves of he MG for FRPs have smlar shapes. However, wh he decrease of he degree of conservasm, he maxmal rampng capaces of he MG wll ncrease because more renewable generaon s expeced. Prce of upward FRP ($/MW) Capacy (MW) 6. Conclusons Upward FRP-Γ=1 Upward FRP-Γ=.6 Upward FRP-Γ=.2 Downward FRP-Γ=1 Downward FRP-Γ=.6 Downward FRP-Γ=.2 Fg. 1. The bddng curves of upward and downward FRPs provded by he MG a 1:. Table 7 The maxmal rampng capaces of he MG a 1:. C ¼ 1 C ¼ :6 C ¼ :2 Upward FRP (MW) Downward FRP (MW) Inegraed wh rapd rampng DERs, an MG s a promsng energy resources o provde flexble rampng producs for he power sysem. In hs paper, flexble rampng producs are ncorporaed n an opmal bddng framework for MGs for he frs me. The bddng model ams a maxmzng he expeced revenues from he day-ahead energy, reserve and FRP markes. To address he unceranes n renewable energy and day-ahead marke prces, a hybrd sochasc/robus opmzaon approach s adoped. The bddng problem wh unceran coeffcens can be ransformed no a mxed-neger lnear programmng model. Case sudes based on an MG wh varous DERs demonsrae he marke behavor of he MG usng he proposed bddng model. Accordng o he smulaon resuls, 1) Compared wh he cases where he MG only bds n he energy marke and bds n energy and reserve markes, he MG s able o ncrease he revenues when Prce of downwward FRP ($/MW) Revenue ($) FRP Energy Reserve Toal revenue Growh rae Energy Reserve FRP Toal revenue Robusness parameer a Robusness parameer b Fg. 9. The revenues and he growh raes of he MG wh dfferen robusness parameers.

10 J. Wang e al. / Appled Energy 25 (217) parcpang n jon energy, reserve and FRP markes by 24.75% and 8.2%, respecvely. 2) A smaller conservasm degree ndcaes ha a larger amoun of avalable renewable generaon s expeced, hereby leadng o an ncrease n he rampng capaces of he MG. 3) By ncreasng he FRP prces by 2%, he oal revenues of he MG wll ncrease by 2.4%, and more avalable capaces wll be provded for FRPs; By reducng he FRP prces by 2%, he oal revenues of he MG wll decrease by 2.27%, whle more capaces wll be provded for energy and reserve nsead. By ncorporang FRPs n he bddng framework of he MG, on one hand, he MG s able o ncrease he revenues from marke bddng; on he oher hand, he power sysem wll benef from he mprovemen of he dspach flexbly and he adequacy of he rampng resources. The proposed model wll provde new nsghs n he developmen of MGs. Appendx A A general robus opmzaon problem nvolvng unceran rgh-hand-sde coeffcens b s expressed as follows: X c j x j ð4þ max x j ;8j mn b ;8 subjec o X a j x j 6 b ; 8 j x j 6 x j 6 x j ; 8j j ð41þ ð42þ where x j ; 8j represens he decson varable. x j and x j are he lower and upper bounds of x j. c j ; 8j and a j ; 8; j are consan. Unceranes only affec rgh-hand-sde coeffcens b of he nequaly consrans. b s a random varable akng values n he nerval ½b ; b Š, where b and b are he lower and upper bounds of b. Then he problem can be ransformed as follows: X c j x j ð43þ max x j ;8j subjec o j X a j x j þ z C þ q 1 2 ðb þ b Þ 6 ; 8 j z þ q þ 1 2 ðb b Þy P ; 8 z ; q P ; 8 y P 1; 8 x j 6 x j 6 x j ; 8j ð44þ ð45þ ð46þ ð47þ ð48þ where z and q are he dual varables of he orgnal problem whle y s an auxlary varable. C 2½; 1Š s he robusness parameer whch s used o adjus he degree of conservasm. The larger he robusness parameer C s, he hgher degree of conservasm s. More deals can be found n [3]. 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