保障灵活调节资源充裕性的容量市场机制西安交通大学电气工程学院肖云鹏2023年9月目录标题CONTENTS01容量市场的作用及问题PART保障灵活调节资源充裕性的容量市场出清模型保障灵活调节资源充裕性的容量市场定价与结算机制保障灵活调节资源充裕性的容量市场仿真测算结论与展望2/30Part1作用与问题ü容量市场的建设意义Ø容量市场的主要目的是保障系统充裕度。首要目标是确保电力系统拥有足够的发电能力来满足电力需求，在高峰期或突发情况下保障系统安全运行。电力市场特征容量市场建设意义•新型电力系统不确定性极强可靠性容量保障可再生能源波动性、高峰期电力需求或突发情况威胁系统供电可靠性•火电机组投资成本回收困难火电固定成本回收利用小时数较低的传统机组无法在电能量市场中获得持久稳定的收益•市场多样性创造长期价格信号市场主体增多，电源/负荷结构变化较快，导致多样化的能源需求引导资源投资•竞争性定价电价由市场供需关系决定，系统容量不足时电价高涨，用户用电成本大大提高提供更稳定的定价机制3/30üPJM容量市场的发展Part1作用与问题l容量市场发展历程PJM容量市场建立改革前199920072015容量义务分配模式容量信用市场模式可靠性定价市场模式容量表现市场阶段（CCM）（RPM）•LSE承担容量责任•LSE通过自供给或双•LSE承担容量责任•PJM通过拍卖市场购买后分配对原有容量市场资源做了进一步改善边协商方式实现•LSE通过场内集中、自供给、•LSE通过PJM从拍卖市场分配双边协商方式实现或自供给、双边协商方式实现基本容量容量表现BaseCP4/30Part1作用与问题üPJM容量市场的发展出售容量拍卖市场购买容量PJMlRPM市场架构基础拍卖追加拍卖容量购买费用分摊（BRA）（IA）负荷供应商LSE1供给侧资源在BRA中申报自负荷供应商LSE2发电资源供需求侧资源双边合同双边交易给负荷供应商LSE3能效资源聚合资源双边合同……规划中的资源输电升级项目5/30Part1作用与问题üPJM容量市场的发展三年20个月lRPM市场交易时序10个月3个月持续开展的双边市场PJM市五月九月七月二月六月次年场交易时序六月容量交付年基本拍卖市场第一次追加第二次追加第三次追加拍卖拍卖拍卖条件追加拍卖采购LDA的额外容量，以解决由骨干传输线延迟引起的可靠性问题6/30Part1作用与问题üPJM容量市场的发展对于存在区域输电约束的地区,每个区域（LDA）可以有单独的需求曲线。lRPM模式需求曲线制定——可变容量需求曲线（VariableResourceRequirement,VRR）曲线取决于系统可靠性需求和新建机组的净成本,对市场出清价格有重要影响。1.5NetConeA(0.998IRM,1.5NetCone）需求曲线与价格上限的交叉点价格上限:联合循环燃B(1.029IRM,0.75NetCone)气轮机新进入成本净C(1.088IRM,0)额的150%容量需求——根据资源充裕性目标设定,即峰值负荷加上0.75NetCone所需的装机备用裕度(IRM)根据十年一遇失负荷期望(LOLE)要求计算得出。IRM-0.2%IRMIRM+2.9%IRM+8.8%7/30Part1作用与问题üPJM容量市场的发展需求lRPM市场出清流程：基本拍卖市场中各LDA的VRR供给求解出清结果容量资源供优化算法•区域出清容量给容量和报•区域容量价格价•容量输送权（CTR）价格约束8/30区域限制约束出清容量约束Part1作用与问题üPJM容量市场的发展持续时间可靠性定价市场（RPM模式）需求曲线制定l不同市场模式对比：供给侧资源提前3年的前瞻性容量拍卖市场容量信用市场（CCM模式）定价模式采用倾斜的容量需求曲线提前1年的容量拍卖市场允许需求侧资源、输电升级项目、聚合资源、能效资源以及规划中开展日前、月度和多月容量市场的资源参与市场竞争采用垂直的容量需求曲线考虑传输约束的分区定价所有价格下的容量需求都固定在资源9/30充裕性目标上，导致价格剧烈波动仅限在役发电机组资源利用不充分全区域统一定价不考虑区域间传输约束区域内部受约束地区产生可靠性问题Part1作用与问题ü当前容量市场存在的问题问l新型电力系统对充裕性需求多样化。题l新能源、储能等新兴市场主体的有效容量评估困难。10/30PromotionalArticleaddedbytheECE,notincludedintheoriginalslidesEnergyConversionandEconomics26341581,2022,1,Downloadedfromhttps://ietresearch.onlinelibrary.wiley.com/doi/10.1049/enc2.12050byCochraneChina,WileyOnlineLibraryon[13/11/2022].SeetheTermsandConditions(httDOI:10.1049/enc2.12050ORIGINALRESEARCHPAPERDistributedcontrolstrategyfortransactiveenergyprosumersinreal-timemarketsChenYin1RanDing2HaixiangXu2GengyinLi1XiupengChen3MingZhou11StateKeyLaboratoryofAlternateElectricalPowerAbstractSystemwithRenewableEnergySources,SchoolofTheincreasingpenetrationofdistributedenergyresources(DERs)hasledtoincreasingElectricalandElectronicEngineering,NorthChinaresearchinterestinthecooperativecontrolofmulti-prosumersinatransactiveenergy(TE)ElectricPowerUniversity,Beijing,Chinaparadigm.WhiletheexistingliteratureshowsthatTEofferssignificantgridflexibilityand2StateGridJibeiElectricPowerCo.,Ltd.,Beijing,economicbenefits,fewstudieshaveaddressedtheincorporationofsecurityconstraintsinTE.Herein,amarket-basedcontrolmechanisminreal-timemarketsisproposedtoeco-ChinanomicallycoordinatetheTEamongprosumerswhileensuringsecuresystemoperation.3EngineeringandTechnologyInstituteGroningen,Consideringthedynamiccharacteristicsofbatteriesandresponsivedemands,amodelpre-UniversityofGroningen,Groningen,Thedictivecontrol(MPC)methodisusedtohandletheconstraintsbetweendifferenttimeNetherlandsintervalsandincorporatethefollowinggenerationandconsumptionpredictions.Owingtothecomputationalburdenandindividualprivacyissues,anefficientdistributedalgorithmisdevelopedtosolvetheoptimalpowerflowproblem.Thestrongcouplingbetweenpro-sumersthroughpowernetworksisremovedbyintroducingauxiliaryvariablestoacquirelocationalmarginalprices(LMPs)coveringenergy,congestion,andlosscomponents.CasestudiesbasedontheIEEE33-bussystemdemonstratedtheefficiencyandeffectivenessoftheproposedmethodandmodel.目录标题CONTENTS01容量市场的作用及问题PART02保障灵活调节资源充裕性的容量市场出清模型PART保障灵活调节资源充裕性的容量市场定价与结算机制保障灵活调节资源充裕性的容量市场仿真测算结论与展望Part2出清模型ü容量市场出清模型构建传统容量市场只考虑保障负荷峰值时段系统充裕度，未来在高比例新能源接入的新型电力系统场景下，新能源的波动性和不确定性将对电力系统的调峰能力、灵活爬坡调节能力提出了更高的要求。根据各类型资源有效容量评估方法、系统容量充裕度评估容量市场需求曲线方法、关键断面约束辨识技术，构建充分考虑长期有效容量和资源供应曲线煤电深调容量的容量市场出清模型。Ø目前考虑保障负荷峰值时段系统充裕度、灵活爬坡能力价格/(元/(MW·天))出清价格充裕度。下一步计划将类似考虑调峰能力充裕度。l目标函数：社会福利最大化maxSW=dPld(cgPigchwPwcsPscmePe),nihkkml,nl,nihkm负荷火电风电光伏储能容量/MW12/30Part2出清模型ü容量市场出清模型构建根据各类型资源有效容量评估方法、系统容量充裕度评估方法、关键断面约束辨识技术，构建充分考虑长期有效容量和煤电深调容量的容量市场出清模型。l约束条件：满足系统灵活爬坡调节需求的容量供需平衡约束•供需平衡约束•各类型机组中标容量约束、容量需求约束保障负荷峰值时段系统充裕度•火电机组、储能提供灵活爬坡调节容量的容量供需平衡约束•采用嵌入式优化考虑新能源不确定性波动minDnD,PhwD,PksDFgFeFCIOimsninmnsnPgPwPsPeihkm系统灵活爬坡调节容量需求FR:FRup,ninhnknmn考虑负荷、新能源出力的波动量的nnPCIO=PdCapsnl,nn:,n不确定性偏差snlmin(FgFeFCIO(FR))imsnnDnD,PhwD,PksDinmnsn区域s向区域n传输的容量FRdn0:n,n13/30Part2出清模型ü容量市场出清模型构建储能0PeCPe,max:e,min,e,max,mmmmml约束条件：•供需平衡约束0FeRPee,max:fce,min,fce,max,m•各类型机组中标容量约束、容量需求约束mmmmm火电0PeFePe,max:ep,min,ep,max,mmmmmm0PeFePe,max:en,min,en,max,mmmmmm0PgCPg,max:g,min,g,max,i由边际带负荷能力的有效容量iiii评估方法得到的，火电资源参区域间传输容量0FgRPgg,max:fcg,min,fcg,max,i与容量市场可提供的有效容量iiiiiLmsnaxPCIOLmaxCIO,minCIO,maxPgFgPg,maxgp,mingp,maxsnsn:sn,sn0iii:i,i,i火电资源所能提供的最大灵0PgFgPg,max:gn,min,gn,max,i活爬坡调节容量PCIOPCIO0:CIOiiiiisnnssnLmsnaxFCIOLmax:FCIO,min,FCIO,maxsnsnsnsn新能源容量需求FCIOFCIO0:FCIOsnnssn0PwCPw,max:w,min,w,max,h0PdPd,maxLmsnaxPCIOFCIOLmax:L,min,L,maxhhhhsnsnsnsnsnl,nl,n0PsCPs,max:s,min,s,max,k:d,min,d,max,l,n,n,snkkkkl,nl,n14/30目录标题CONTENTS01容量市场的作用及问题PART02保障灵活调节资源充裕性的容量市场出清模型PART03保障灵活调节资源充裕性的容量市场定价与结算机制PART保障灵活调节资源充裕性的容量市场仿真测算结论与展望Part3定价与结算机制ü容量市场机制与规则设计l容量市场定价机制：保障负荷峰值时段系Cap统容量充裕度的容量n价格容量市场灵活爬坡调节预测需求nEFR出清价格价格满足系统灵活爬灵活爬坡调节向UFRIN坡调节需求的容灵活爬坡调节不确定性偏上偏差需求价格n差需求价格量价格灵活爬坡调节向UFRDN下偏差需求价格n16/30Part3定价与结算机制ü容量市场机制与规则设计灵活UFRINLFRup(uFRup)FRdn(uFRdn)爬坡l容量市场定价机制：调节n(PwD,min)nn(h)nn(h)需求p保障系统灵活性的容量价格向上hn偏差①灵活爬坡调节预测需求价格价格LFRup(uFRup)FRdn(uFRdn)②灵活爬坡调节不确定性偏差需求价格(PsD,min)nn(Hk)nn(Hk)灵活爬坡调节不确定性kn偏差需求价格与负荷、风电、光伏出力波动量的不确定性LFRupuFRup(u)FRdn偏差值有关。(DD,max)nnnn()FRdn,n(2(HK)Nn))n(2(HK)Nn))灵活UFRDNL爬坡FRup(uFRup)FRdn(uFRdn)调节nnnn需求nPwD,max(HKNh)(HKNh)向下偏差hn价格LFRup(uFRup)FRdn(unFRdn)PksD,maxnnn(2HKNk)(2HKNk)nLFRup(uFRup)FRdn(uFRdn),n(DD,min)nn(HKn)nn(HKn)n17/30Part3定价与结算机制ü容量市场机制与规则设计火电机组、储能电站l容量市场结算机制：•保障负荷峰值时段系统充裕性的容量收益•给出火电、新能源、储能等不+保障系统灵活性的容量收益同类型资源相应的结算规则。P()F,igCapg•有效区分不同类型资源的对于FRupFRdng保障负荷峰值时段系统充裕度、n:in灵活爬坡调节能力充裕度的有in:inin:ini效容量贡献与引起灵活爬坡调节需求的责任。P()F,meCapeFRupFRdnen:mnmn:mnmn:mnm风电场、光伏电站•提供容量保障负荷峰值时段系统充裕性的收益-分摊由于自身出力波动造成的灵活调节需求成本jwPCapwEFRn(PwD,exp)UFRDNnPwD,maxn:hhn:hh,hn:hnhUFRIN(PwD,min)n:hnhksCapPsEFRn(PsD,exp)UFRDNnPsD,maxn:kkn:kkn:kk,knUFRIN(PsD,minn:knk)18/30Part3定价与结算机制ü容量市场机制与规则设计区域间传输容量l容量市场结算机制：•考虑了区域之间的价格差异，当区域间传输通道发生•给出火电、新能源、储能等不阻塞时会产生阻塞盈余，应分配给对应输电权所有者。同类型资源相应的结算规则。snPCapCIO(nFRupFRdn)FCIO•有效区分不同类型资源的对于nsnnsn保障负荷峰值时段系统充裕度、灵活爬坡调节能力充裕度的有负荷效容量贡献与引起灵活爬坡调节需求的责任。•向容量市场支付保障负荷峰值时段系统充裕性+保障系统灵活性的容量费用dCapdDEFRD,expnnUFRDN(DnD,min)nnPl,nn,nlUFRINDD,maxnn19/30Part3定价与结算机制ü容量市场机制性质验证•良好的市场机制应满足社会效率、收支平衡、个体理性和激励相容等性质，激励市场主体主动参与，促进资源优化配置。社会效率(SocialEfficiency)所提出的容量市场鲁棒优化出清模型的目标函数为最大化社会福利，即出清结果能够在应对负荷、风电、光伏的任何不确定波动情况下实现尽可能大的社会福利，因此可以满足社会效率性质。20/30Part3定价与结算机制ü容量市场机制性质验证收支平衡(BudgetBalance)•市场运营机构应为非盈利机构，市场的流入和流出资金应相等，即收支平衡。•容量市场流入资金：•容量市场流出资金：(nCapPig(nFRupFRdn)Fig)nINCapPdEFRDexp(UFRDN(DD,min)DUFRIND,max)nl,nnnnnnniOTnlnn(nCapPme(nFRupFRdnFen)m)负荷为引起峰值时段需求、引起灵活调节需求所支付的费用mEFR(PwD,exp)(UFRDNPwD,maxUFRIN(PwD,min))nhnhnh支付给火电、储能保障负荷峰值时段hh系统充裕度、满足系统灵活调节需求的费用风电为引起灵活调节需求所支付的费用PCapwPCapsnhnkEFRPsD,exp(PUFRDNsD,maxUFRINPsD,minnknknk()())hkkk支付给风电和光伏保障负荷峰值光伏为引起灵活调节需求所支付的费用时段系统充裕度的费用(PCapCIO(nFRupFRdn)FCIO)nsnnsn根据供需平衡约束和KKT条件，可以推导出INOTsn区域传输容量阻塞盈余21/30Part3定价与结算机制ü容量市场机制性质验证个体理性(IndividualRationality)•个体理性指市场成员愿意主动参与市场，即各市场成员的净利润非负。以火电机组为例P()FcPgcapg火电机组利润为：FRupFRdnggg根据KKT条件，可以推导出n:iniiin:inin:inicapcg)Pg(FRupFRdn)Fgn:iiin:in:ii(nnn(g,maxg,mingp,maxgp,mingn,maxgn,min)Pigiiiiii(gp,maxgp,mingn,maxgn,minifcg,maxifcg,min)FigiiiiPig,max(g,maxgp,maxgn,max)RgPig,maxifcg,maxiiii022/30Part3定价与结算机制ü容量市场机制性质验证激励相容(IncentiveCompatibility)•激励相容是指市场成员追求自身利润最大的结果与市场整体实现社会福利最大化的结果一致，即市场成员根据市场出清价格计算使得自身利润最大化的出力计划与市场根据成员报价出清的出力计划一致。•容量市场出清模型•市场成员根据市场出清价格以自身利润最大化为目标进行优化的模型mincTxrrx,y,zrs.t.ACapxAFRyRmaxAUFRzBn:τn,nrrrrnrrrnrrrnmaxρCapxrρFRyrρUFRzrcrTxrn:rn:rn:rxr,yr,zrnnn(xr,yr,zr)Χr,rs.t.(xr,yr,zr)Χr,r对偶转换Rmax(ρCap,ρFR,ρUFR)(ρCapxrρFRyrρUFRzrcrTxr)由KKT可得，目标函数满足rn:rn:rn:rn:rn:rn:rrnnnrnnn[Rmax(ρCap,ρFR,ρUFR)(ρCapxrρFRyrρUFRzrcrTxr)]rn:rn:rn:rn:rn:rn:rnnnnnnmin(τ)T(ACapxAFRyAUFRzB)rτn0nnrnrrrnrrrnrrn0(xr,yr,zr)Χr,r当xrxr,yryr,zrzr上式等号成立，即市场成员使得自身利润最大化的容量策略与容量市场出清的中标容量一致23/30PromotionalArticleaddedbytheECE,notincludedintheoriginalslidesEnergyConversionandEconomicsReceived:16December2020Revised:11April2021Accepted:17April2021DOI:10.1049/enc2.12036ORIGINALRESEARCHPAPEROption-basedportfolioriskhedgingstrategyforgasgeneratorbasedonmean-varianceutilitymodelShuyingLaiJingQiuYuechuanTaoSchoolofElectricalandInformationEngineering,AbstractTheUniversityofSydney,Sydney,AustraliaNaturalgasgeneratorsarepromisingdevicesforreducinggreenhousegasemissions.How-ever,gasgeneratorsencounterdifficultiesinthebid-to-sellprocessbasedonarelativelyhighlevelisedcostofenergyforpowergeneration.Therefore,anovelriskhedgingstrategyisdevelopedbasedonthemean-varianceportfoliotheorytoreducetheoperationalrisksofgasgeneratorsandenhancetheirprofits.Threetypesofoptionsareutilisedandcom-binedtoformaportfoliooffinancialhedges:theshortputoption,longputoption,andshortcalloption.Twotypesofenergystoragedevicesareusedtofacilitatetheriskhedgingprocess,namelypower-to-gasandbatterydevices.Simulationresultsdemonstratethattheproposedriskhedgingmodelcanensurehigherprofitsforgasgeneratorswithreducedriskcomparedtothetraditionalriskhedgingmodelandamodelusingonlyonetypeofoption.Additionally,thevariedriskpreferencesofgasgeneratorsleadtovariedportfoliocombinations.Themoreriskaverseagasgenerator,themorelikelythelong-putoptionwillbeutilised.Incontrast,thelessriskaverseagasgenerator,themorelikelythatshortcallswillbeutilised.目录标题CONTENTS01容量市场的作用及问题PART02保障灵活调节资源充裕性的容量市场出清模型PART03保障灵活调节资源充裕性的容量市场定价与结算机制04保障灵活调节资源充裕性的容量市场仿真测算PART结论与展望ü算例分析Part4仿真测算Ø考虑保障负荷峰值时段系统充裕度、灵活25/30爬坡能力充裕度。下一步计划将类似考虑调峰能力充裕度。Ø选取修正的IEEE-118节点系统进行算例分析，将该系统划分为3个区域，其中区域1新能源机组较为集中，共有2台火电机组、7座风电场、5座光伏电站和1座储能电站；区域2和3则具有较多爬坡性能优异的灵活性资源，区域2共有12台火电机组、4座风电场、2座光伏电站和2座储能电站；区域3共有11台火电机组、3座风电场、2座光伏电站和3座储能电站。Part4仿真测算各区域出清价格ü算例分析出清价格/(元/(MW·天))区域1区域2区域3210180210•保障负荷峰值时段系统充裕性的容量价格nCap：Cap1108010n1108010区域2为180元/(MW·天)，低于区域1和3。因为区域0001和区域3需要由区域2来提供容量保障各自区域内EFR的负荷峰值时段系统充裕性，区域2和其它区域之n间存在阻塞，区域1、3的保障负荷峰值时段系统充裕度的容量出清价格高于区域2。UFRINnUFRDNn1000区域需求容量120区域需求容量900火电中标容量800906.75储能中标容量火电中标容量700710风电中标容量光伏中标容量100储能中标容量区域需求容量区间95容量/MW80容量/MW•EFR600545n灵活爬坡调节预测需求价格：区域1为110元50060/(MW·天)，高于区域2、3。因为区域1为高比例新400364.444.5上范围45上范围45上范围300200178.851954038.25能源区域，风电场、光伏电站装机容量占比高达下范围31.5下范围下范围80%，具有较大的灵活调节需求，但其火电机组数202323100量少且爬坡系数小，灵活调节性能较差，需要由其0区域2区域31.25区域2区域3区域10区域1他区域提供容量来保障系统灵活性，传输通道发生(a)各区域保障负荷峰值时段充裕(b)各区域满足灵活爬坡调节需求度的中标容量与需求容量的中标容量与需求容量阻塞。26/30Part4仿真测算各区域出清价格ü算例分析出清价格/(元/(MW·天))区域1区域2区域3210180210•灵活爬坡调节需求向上偏差价格nUFRIN：等于灵活Cap1108010爬坡调节预测需求价格nEF。R因为本算例中各区域n1108010000的灵活调节需求大于0，即表示需要向上的满足灵EFR活调节需求的容量。此时算例中的灵活爬坡调节预n测需求价格与灵活爬坡调节不确定性偏差需求价格均由灵活爬坡供需约束的对偶变量决定。UFRINn•灵活爬坡调节需求向下偏差价格nUFRDN：等于0。UFRDN因为算例中灵活爬坡调节需求大于0，当灵活爬坡n调节需求不确定性向下偏差时，即需求减小，原本的出清结果依旧能够满足需求。1000区域需求容量120区域需求容量900火电中标容量800906.75储能中标容量火电中标容量700710风电中标容量光伏中标容量100储能中标容量区域需求容量区间95容量/MW80容量/MW60054550060400364.444.5上范围45上范围45上范围300200178.851954038.25下范围31.5下范围下范围2023231000区域2区域31.25区域2区域3区域10区域1(a)各区域保障负荷峰值时段充裕(b)各区域满足灵活爬坡调节需求度的中标容量与需求容量的中标容量与需求容量27/30Part4仿真测算ü算例分析典型机组收益•对比火电机组G40和G41，可见•所提出的容量市场机制能够有效区分不同类型资源对于保障负荷峰值时段系二者的报价和装机容量均相同，统充裕度和满足灵活爬坡调节需求的贡献，并给予相应的奖励。相同条件下，由于G40爬坡系数大于G41，灵资源的灵活调节能力越好，可用容量系数越大，则所能获得的收益越多。活调节能力更好，能够提供更多的容量来满足系统灵活调节需求，因此G40的收益高于G41。•对比风电场G28和G29、光伏电站G32和G33、储能电站G34和G35，可见相同报价与装机容量下，可用容量系数越大，即资源参与容量市场的可用容量越大，保障负荷峰值时段系统充裕度的容量中标量越大，收益越多。28/30PromotionalArticleaddedbytheECE,notincludedintheoriginalslidesEnergyConversionandEconomics26341581,2022,1,Downloadedfromhttps://ietresearch.onlinelibrary.wiley.com/doi/10.1049/enc2.12037byCochraneChina,WileyOnlineLibraryon[13/11/2022].SeetheTermReceived:9December2020Revised:3May2021Accepted:11May2021DOI:10.1049/enc2.12037ORIGINALRESEARCHPAPERElectricityeconomicsforex-antedouble-sidedauctionmechanisminrestructuredpowermarketArunaKanagarajKumudiniDeviRaguruPanduDepartmentofEEE,CollegeofEngineeringAbstractGuindy,AnnaUniversity,Chennai,TamilNadu,AuctionmechanismanalysisprovidesfavourableeconomicoutcomesforkeystakeholdersIndiainvolvedintherestructuredpowermarket.Realpowerpricingbasedonlocationalmarginalpricinghasbeenimplementedintheelectricitymarketworldwide.Inthisstudy,theopti-malpowerflowisconsideredtominimisetheoperatingcostoftheactivepowergener-ationintheex-anteenergymarketandanaugmentedoptimalpowerflowintheex-antereservemarket.Thedouble-sidedauctionmechanismhasbettercontrolovertheenergyandreservemarkets,enhancingsocialwelfareintherestructuredpowermarkets.Single-anddouble-sidedauctionmechanismsareconsideredtoanalysetheallocationandpricingeconomicsintheex-anteday-aheadenergyandex-anteday-aheadreservemarkets.Loca-tionalmarginalpricingiscalculatedandanalysedforboththeon-andoff-peakdemandperiods.TheproposedauctionmodelwasvalidatedusinganIEEE30-buspowersystem.Thebenefitsofthedouble-sidedauctionareassessedfromtechnicalandeconomicper-spectives.目录标题CONTENTS01容量市场的作用及问题PART02保障灵活调节资源充裕性的容量市场出清模型PART03保障灵活调节资源充裕性的容量市场定价与结算机制04保障灵活调节资源充裕性的容量市场仿真测算PART05结论与展望PART29/30Part5结论与展望l针对新型电力系统发展下灵活调节资源稀缺性逐渐凸显的问题，提出了保障灵活调节资源充裕性的容量市场机制总l采用不确定性定价方法给出了灵活调节容量电价结l所提机制有效保障了系统灵活调节资源的充裕性l进一步应考虑新型电力系统其他维度的充裕性需求，并与现货电能量与辅助服务市场做好有效衔接30/30谢谢！请批评指正！西安交通大学电气工程学院肖云鹏2023年9月EnergyConversionandEconomics26341581,2022,1,Downloadedfromhttps://ietresearch.onlinelibrary.wiley.com/doi/10.1049/enc2.12050byCochraneChina,WileyOnlineLibraryon[13/11/2022].SeetheTermsandConditions(https://onlinelibrary.wiley.com/terms-and-conditions)onWileyOnlineLibraryforrulesofuse;OAarticlesaregovernedbytheapplicableCreativeCommonsLicenseDOI:10.1049/enc2.12050ORIGINALRESEARCHPAPERDistributedcontrolstrategyfortransactiveenergyprosumersinreal-timemarketsChenYin1RanDing2HaixiangXu2GengyinLi1XiupengChen3MingZhou11StateKeyLaboratoryofAlternateElectricalPowerAbstractSystemwithRenewableEnergySources,SchoolofTheincreasingpenetrationofdistributedenergyresources(DERs)hasledtoincreasingElectricalandElectronicEngineering,NorthChinaresearchinterestinthecooperativecontrolofmulti-prosumersinatransactiveenergy(TE)ElectricPowerUniversity,Beijing,Chinaparadigm.WhiletheexistingliteratureshowsthatTEofferssignificantgridflexibilityandeconomicbenefits,fewstudieshaveaddressedtheincorporationofsecurityconstraintsin2StateGridJibeiElectricPowerCo.,Ltd.,Beijing,TE.Herein,amarket-basedcontrolmechanisminreal-timemarketsisproposedtoeco-ChinanomicallycoordinatetheTEamongprosumerswhileensuringsecuresystemoperation.Consideringthedynamiccharacteristicsofbatteriesandresponsivedemands,amodelpre-3EngineeringandTechnologyInstituteGroningen,dictivecontrol(MPC)methodisusedtohandletheconstraintsbetweendifferenttimeUniversityofGroningen,Groningen,Theintervalsandincorporatethefollowinggenerationandconsumptionpredictions.OwingtoNetherlandsthecomputationalburdenandindividualprivacyissues,anefficientdistributedalgorithmisdevelopedtosolvetheoptimalpowerflowproblem.Thestrongcouplingbetweenpro-CorrespondencesumersthroughpowernetworksisremovedbyintroducingauxiliaryvariablestoacquireXiupengChen,EngineeringandTechnologyInstitutelocationalmarginalprices(LMPs)coveringenergy,congestion,andlosscomponents.CaseGroningen,UniversityofGroningen,9742AGstudiesbasedontheIEEE33-bussystemdemonstratedtheefficiencyandeffectivenessofGroningen,TheNetherlands.theproposedmethodandmodel.Email:a1124756041@163.comFundinginformationStateGridCorporationofChina,Grant/AwardNumber:5201202000161INTRODUCTIONcontrolactions.However,thiscentralizednetworkarchitectureisofgreatconcern,becausesendingallthisinformationtoaDrivenbygrowingenvironmentalandclimateconcerns,dis-systemoperatorintroducesscalability,complexityandprivacytributedenergyresourcesareincreasinginthepenetrationrateissues[2].Consequently,moredecentralizednetworkcontrolofdistributionnetworks,anddistributionpowernetworksareandoptimizationtechniquesarerequiredtosupporttheenergyundergoingafundamentaltransition.Intraditionalpowergrids,amonglargenumbersofprosumers[3].usersonlyhaveloadcharacteristics,butwiththerapiddevelop-mentofdistributedpowergenerationtechnologyandInternetItisnecessarytocoordinatethemarketandcontrolandman-technology,userscangraduallymanageinternalpowergenera-agethesystemthrougheconomicvaluetoensurethatpro-tionandstorageresources,anddeliverelectricalenergy,namelysumersparticipateinmarkettransactionsandthesafeandflex-prosumers.Prosumersareend-useconsumerswithlocalgenera-ibleoperationofthesystem,theexistingresearchaboutmech-tionsources,forexample,photovoltaic(PV)panelsand/orbat-anismdesignforprosumerscanbeclassifiedintotwocate-tery,andareabletomanagetheirconsumptionandproductiongories:distributedoptimization-basedmethod[4]andgameofenergyactively.Underthepromotionofthemarket-basedtheorybasedmethod[5].Intheformerapproach,allprosumerstrading,theseprosumersareheldasindependentstakeholdersarewillingtocollaboratetoachieveacertaingoal,forexample,toparticipateinpowermarketoperation[1].Traditionally,distri-maximizingsocialwelfare.Anon-profitagent,forexample,sys-butionpowernetworksarekeptstableandsecurebycentralizedtemoperator(SO),isprogrammedtosetpricesandindividualprosumerschoosetheircorrespondingstrategiesaspricetakes.ThisisanopenaccessarticleunderthetermsoftheCreativeCommonsAttributionLicense,whichpermitsuse,distributionandreproductioninanymedium,providedtheoriginalworkisproperlycited.©2022TheAuthors.EnergyConversionandEconomicspublishedbyJohnWiley&SonsLtdonbehalfofTheInstitutionofEngineeringandTechnologyandtheStateGridEconomic&TechnologicalResearchInstituteCo.,Ltd.EnergyConvers.Econ.2022;3:1–10.wileyonlinelibrary.com/iet-ece12YINETAL.26341581,2022,1,Downloadedfromhttps://ietresearch.onlinelibrary.wiley.com/doi/10.1049/enc2.12050byCochraneChina,WileyOnlineLibraryon[13/11/2022].SeetheTermsandConditions(https://onlinelibrary.wiley.com/terms-and-conditions)onWileyOnlineLibraryforrulesofuse;OAarticlesaregovernedbytheapplicableCreativeCommonsLicenseTheinteractionbetweenprosumerswiththeSOisprivacypre-optimalpowerflow(OPF)techniqueplaysanimportantroleservingasonlyenergypreferencesarecommunicated.Adis-indealingwiththeseissues.Ref.[21]incorporatestheOPFtributedprice-basedoptimizationmechanismforprosumers’techniquetosolvethetransactiveenergytradingproblem,butenergymanagementisproposedin[6]basedonthealternat-itisimpracticalforprosumerstoknowthenetworktopol-ingdirectionmethodofmultipliers(ADMM)method.In[7],ogyandparameterstodetermineenergypreference.Ref.[22]arelaxedconsensusinnovation(RCI)approachisdescribedtousesOPFtostudytheenergysharingamongmulti-microgrids,solvemulti-bilateraleconomicdispatchprobleminfullydecen-butonlyconsidersnonlinearnetworkconstraintswithinindi-tralizedmanner.Adistributedgenerationanddemandcontrolvidualmicrogrids.Adecentralizedcontrolstrategyisproposedschemesforsecondaryfrequencyregulationinpowernetworksin[23]foranetworkofmicrogridsbyintroducingpowerlinkispresentedtoguaranteesystemstabilityandeconomicoptimal-agents,butlinecongestionandvoltageviolationarenotconsid-itysimultaneously[8].Inthelatterapproach,conflictinginter-ered.AnotheradvantageofincorporatingOPFtechnologyintoestsofprosumersarecharacterized.Thekeypointhereistoenergytradingistodiscoverthedistributionlocationalmarginalmodelthedecision-makingprocessesofprosumersandfindtheprices(DLMPs)[24].Nashequilibriumsothateachprosumermaximizestheirprof-itswhileensuringthesystemsupplyanddemandbalance.Ref.Inthispaper,weproposeanovelmarket-basedcontrol[9]systematicallyclarifiesvariousgame-andauction-theoreticmechanismfordistributionnetworkprosumersinreal-timemethodsusedforpeer-to-peer(P2P)energytradingamongpro-markets.Consideringthevalueofcoordinatedcontrolofbat-sumers.anincentive-compatiblemechanismisproposedin[10]teriesandresponsivedemandsindistributionnetworks,weusetoelicittruthfulbidsofgeneratorsandcoordinatetheeconomicamodelpredictivecontrol(MPC)methodtooptimizesystemoperation.Anoptimalbiddingframeworkisproposedin[11]operationcostsovermultipletimestepsconcurrently.Thenweforaregionalenergyinternettoparticipateinday-aheadmarketsdevelopanefficientdistributedalgorithmforsolvingthecentralconsideringcarbontrading.Anauction-theoreticschemeispre-optimizationproblem.Themaincontributionsareasfollows:sentedforprosumermodelsandresourceconstraintsin[12].Anenergysharingmechanismisproposedin[13]toaccommodate∙OPFtechniqueisincorporatedtoenergytradingamongpro-prosumers’strategicdecision-makingontheirself-productionsumerstoensurethereliabilityandsecurityofdistributionanddemandinthepresenceofcapacityconstraints.Inthisnetwork,whichmakesresultmorerealistic.paper,adistributedoptimizationalgorithmisappliedconsid-eringthefactthattherearesufficientprosumerssothatthey∙MPCmethodisusedtomodeloperationcostsminimizationcannotimprovetheirpositionthroughstrategicprice-settingproblem,consideringconstraintsofbatteriesandresponsivebehaviour.duringmultipletimeintervalsandtakingfulladvantageoftheseresourcestoreducelinecostsandcongestion,whichGridWiseArchitectureCouncil(GWAC)putforwardtheshowsbetterconvergence.conceptoftransactiveenergy(TE)tosolveaboveproblems[14].TEisamechanismwithdualcharacteristicsofmarketand∙ThecouplingconstraintsbetweenprosumersandSOarecontrol,whichtakeseconomicvalueasacontrolfactor,man-decoupledbyintroducingauxiliaryvariablestopreservetheagesdynamicbalanceofenergysupplyanddemandofsystem,autonomyandprivacyofprosumers.andensuresparticipationofprosumersinmarkettransactionandsafeandflexibleoperationofthesystematthesametime2SYSTEMMODEL[15].Ref.[16]aggregatestheprosumersintheelectricalinte-gratedenergysystemintheformofvirtualpowerplants,andThisstudyconsiderstransactiveenergyamongprosumersincoordinatesprosumerstoparticipateintheday-aheadmarketdistributionnetworks,eachwithdistributedgenerators,respon-withthegoalofmaximizingexpectedprofits.Ref.[17]proposessiveloadsand/orbatteries.Anelectricitymarketusuallycon-atransactionmechanisminwhichdistributionnetworkopera-sistsofseveraldifferentphases.Forexample,PJMmarketistorsrepresentlocalprosumerstoparticipateintheinteractivemainlycomposedofcapacitymarkets,day-aheadmarkets,real-energymarket.Distributedoptimizationmethodisaneffectivetimemarketsandancillaryservicesmarkets.Inthispaper,wemeanstorealizeTE.Ref.[18]proposesadistributedenergyfocusonanalysingprosumers’behaviourandsystemreliabilitymanagementmethodforcommunityoperatorsandprosumersinreal-timemarkets.Duringthisphase,prosumerssolvelocalbasedonmaster-slavegamemodel,andref.[19]proposesadis-optimizationproblemtoscheduletheirgenerationandcon-tributedday-aheadoptimalschedulingstrategyforprosumerssumptionpreference,andSOisintroducedtoadjustreal-timeofdistributionnetworknodepricebasedoniterativemethod.energypricesuntilallprosumersreachagreementonascheduleRef.[20]proposesadispatchableregionformationmethodofofsocialwelfaremaximizingpowerflows.Thesimplifiedphysi-electricvehiclesaggregation.calandcommunicationnetworksconnectingprosumersandSOisshowninFigure1.Prosumersaregenerallyconnectedbyanalternativecurrent(AC)distributionnetwork,sonetworkpowerlossesandpowerInphysicalnetwork,eachnodeisanindependentprosumer,transmissionlimitationcansignificantlyimpactpowerbalancewhichexchangesenergywitheachotherbypowernetwork,andtransactiveenergyamongprosumers.Therefore,besidesandexcesselectricalenergywillbegeneratedinthedistributioneconomicissuesofenergytrading,thesecurityandreliabilitynetwork.SOprovidesanetworkinteractiveplatform,whichisissuesofsystemoperationarealsofactorsworthconsideringacommunicationplatformforprosumerconsumptionpartici-patinginpowertransaction,andcoordinatestheoptimizationYINETAL.326341581,2022,1,Downloadedfromhttps://ietresearch.onlinelibrary.wiley.com/doi/10.1049/enc2.12050byCochraneChina,WileyOnlineLibraryon[13/11/2022].SeetheTermsandConditions(https://onlinelibrary.wiley.com/terms-and-conditions)onWileyOnlineLibraryforrulesofuse;OAarticlesaregovernedbytheapplicableCreativeCommonsLicenseCommunicationSystemOperatorWeassumethatgraph(N,L)isdirectedwitharbitrarydirec-Networktion,sothatif(i,j)∈L,then(j,i)∉L.Additionally,foreachProsumerj∈N,weusei∶i→jandk∶j→ktodenotethesetsofbusesthatprecedeandsucceedbusj,respectively.Givenaradi-caldistributionnetwork,thebranchflowmodelisgivenas[25],foralli∈Nand(i,j)∈L,()()vi−vj=2r(i,j)P(i,j)+x(i,j)Q(i,j)−l(i,j)r(2i,j)+x(2i,j)(1)P(i,j)=∑P(j,k)+pj+l(i,j)r(i,j)(2)k∶j→kPhysicalNetworkQ(i,j)=∑Q(j,k)+qj+l(i,j)x(i,j)Informationflow(3)powerflowk∶j→k()l(i,j)=P(2i,j)+Q(2i,j)∕viFIGURE1Simplifiedphysicalandcommunicationnetwork(4)vmin≤vi≤vmax(5)ir(i,j)+jx(i,j)k1Pmin≤P(i,j)≤Pmax(6)jP(j,k1)+jQ(j,k1)P(j,kn)+jQ(j,kn)Qmin≤Q(i,j)≤Qmax(7)P(i,j)+jQ(i,j)knFIGURE2Adistributionnetworkmodelwhereviisthesquareofcomplexvoltageonbusi,piandqiarenetrealpowerandnetreactivepoweronbusi,respec-ofdistributionnetworkintheabsenceofdistributionnetworkoperator.Theprosumerhasitsownenergymanagementsystemtively,whichequalgenerationminusload.r(i,j),x(i,j),l(i,j),P(i,j)(EMS),controllinginternalphotovoltaic,energystoragesystem,andQ(i,j)areresistance,inductance,squareofcomplexcurrent,andcontrollableloadresourcesinterdependently,sharinginfor-realpowerandreactivepoweronline(i,j),respectively.vmaxmationintheinteractiveplatform.andvminarethemaximumandminimumvoltageofbusi.Pmax,Qmax,Pmin,Qminaremaximumandminimumactiveandreac-SOforecastswholesalemarketelectricitypriceofmainnet-tivepoweronlineij.Duetothequadraticequalityin(4),theworkandsharesitamongprosumers,whileprosumersforecasttheirownPVoutputandloaddemand,determinepowerpur-feasiblesetofOPFisnon-convex;therefore,werelaxittothechaseandsaleplanwiththemainnetworkandotherprosumersonthebasisofthewholesalemarketday-aheadelectricitypricefollowingsecondorderconeconstraint:andusers’preferenceforsharedpower,takingintoaccountthephysicaltopologyconstraintsofthepowergrid,andshare‖‖‖(2P(i,j),2Q(i,j),vi−l(i,j))‖‖‖2≤vi+l(i,j)(8)theinformationwithotherprosumersontheinteractiveplat-form.Finally,withreferencetoothers’powerpurchaseandsale2.2Responsivedemandmodellingplans,prosumersupdatetheirplansiterativelyuntiltheymeettherequirementsofalltheprosumersinthedistributionnet-Indistributionnetwork,eachprosumerihasapreferredwork.demanddi,tattimet,whichrepresentstheactualdemandonly2.1Networkmodellingwhennoincentivesareprovidedtothem.However,reschedul-Wedescribethedistributionnetworkmodelbyaconnectedingdemandmaygiverisetoagreatcostreduction,whichgraph(N,L),whereNisthesetofbusesandL⊆N×NishigherthanthecompensationofinconveniencecostCi,tdisthesetoftransmissionlines.Weindexthebusesbyi=incurredbytheloaddeviation.Hereweusethesamenotation1,2,3,…,nandtheterm(i,j)denotesthelineconnectingbusiandjasFigure2shows.itorepresentbusesandprosumers,becauseweassumeeachbusonlyhasaprosumeroraprosumeragentwhichaggregatesagroupofprosumers.Weassumeeachdemandisresponsiveandcanbescheduledacrosstimeifitsatisfiesthefollowingconstraints,pi.t≤pdi,t≤pi.t(9)∑TΔtpdi,t≥Eid,t(10)t=14YINETAL.26341581,2022,1,Downloadedfromhttps://ietresearch.onlinelibrary.wiley.com/doi/10.1049/enc2.12050byCochraneChina,WileyOnlineLibraryon[13/11/2022].SeetheTermsandConditions(https://onlinelibrary.wiley.com/terms-and-conditions)onWileyOnlineLibraryforrulesofuse;OAarticlesaregovernedbytheapplicableCreativeCommonsLicensewherepid,tisactualresponsivedemandofprosumeriattimesteppowerofprosumeri.ThetimevaryingSoclevelisboundedt,pandpi,taretheminimumdemandandmaximumdemandin(13).Charginganddischargingpowerlimitsareexpressedi,tin(15)and(16).Constraintin(17)ensuresthatbatteryonlychargesoronlydischargesattimet[26].WeuseCi,tstoexpressofprosumeriattimestept,respectively.Eid,trepresentsthethecostofbatterydepreciationasfollows,minimumdemandconsumedintimehorizonT.Thealloweddemandadjustmentisrangedby(9).Constraintin(10)restrictsCs=as(pch+pdis)(18)i.tii.ti.ttotaldemandintimehorizonTaboveEid,t,whichmeanssomeloadscanbeshiftedamongdifferenttimeintervals.Inthetrans-actionprocessofprosumers,comparedwiththelossofpowerwhereai,stisthecoefficientofdepreciation.Notethatweignoretheconstraintthatforeachtimeintervalt,eitherpcih,t=0orconsumptionsatisfactioncausedbyloadadjustment,byadjust-pdi,its=0.Thisisbecauseforanysolutionwithbothpcih,tandpdi,itsgreaterthanzero,thereisasolutionthatoneiszeroandanotheringtheloadofeachtimeperiodinthedispatchcycle,prosumersatasmallervaluemakingthecostofbatterydepreciationlower.canreduceelectricitypurchasecostsandobtaingreaterbenefits.Becauseitisaloadadjustment,correspondingtothepowergenerationside,wemodelthecostasaquadraticfunction.Toreflecttheinconvenienceexperiencedbyprosumersduetodemandresponse,wemodeltheinconveniencecostbyacon-2.4Centralizedoptimizationproblemvexquadraticfunctionas,()2Implementingmarket-basedcontrolforprosumersinreal-timeCid.t=aiddi,t−pdi,tmarketsrequirescomputationalspeed.Hereweadoptstrictly(11)convexcostfunctionwidelyusedinpowersystemfordis-tributedgenerators.OneexampleforgenerationcostCi,tgiswhereaidiscoefficientofthecostfunction,whichisrelatedtoexpressedasfollows,electricityprice.di,tisprosumeri’spreferreddemandattimeCig.t=aig(pgi.t)2+bgipgi.t(19)intervalt.2.3BatterymodellingwhereCi,tgisthegenerationpowerofprosumeriattimeintervalt.aigandbgiarequadraticandlinearcoefficientsrespectivelyofBatteriesplayanimportantroleindistributionnetworktokeepsupplyanddemandbalance.Forexample,whentherearesur-generationcostfunction.Theprosumeri’sgenerationpoweratplusenergysupplies,prosumerswillchargetheirbatteriestotpig,tgproduceenergywhensuppliesarenotsufficient.Here,weusetimeintervalisboundedwithitsupperboundpiandlowerthelinearSocmodeltorepresentthedynamicsofbatteriesasfollows,boundpgiasshownin(20),pg≤pgi.t≤pgii(20)Soci,t+1=Soci,t+1+Δt(𝜂chpch−𝜂dispdis)∕Eb(12)SothetotaloperationcostCi,tforprosumeriattimeintervaltii.tii.tiisasfollows,whereSoci,tistheSoclevelofprosumeriattimestept.𝜂ichandCi.t=Cig.t+Cis.t+Cid.t(21)𝜂idisarecharginganddischargingefficiencies,respectively.pchandpdisarethecharginganddischargingpower,respectively.EibisThefollowingdecisionvariablevectordefinedforprosumercapacityofbatteries.Additionalconstraintsarealsoneededas,iisxi,t={pgi,t,pdi,t,pcih,t,pdi,its,Soci,t}.Soci≤Soci,t≤Soci(13)Aswetakethedynamicsofbattery,loadshiftingandthepre-dictionsofpowerconsumptionineachprosumerintoaccount,Soci,T=Socid,eT(14)wemodeltheoptimizationprobleminMPCschemewithtimehorizonTanddurationΔtofeachtimeinterval.So,thecentral-≤pcih.t≤chizedformulationofoveralloptimalproblemcanbestatedas,0pi(15)≤pdi.its≤disminC=∑N∑T0pi(16)xi,tCi.t(22)i∈N,t∈Ti=1t=1pdis∕pdis+pch∕ch≤1(17)i.tipi.tist.(1)–(10),(12)–(16),(20)whereSociandSociareminimumandmaximumSoclevelsofNoticethatallconstraintsstatedin(1)–(10),(12)–(16),prosumeri.Socid,eTisthedesiredSoclevelattheendofthetime(20)arecompactandconvex,whereastheobjectivefunc-chdistionisalsostrictlyconvex.Hence,theproblemisacon-horizon.piandpiaremaximumcharginganddischargingvexoptimizationproblemwithuniqueoptimalsolution[27].YINETAL.526341581,2022,1,Downloadedfromhttps://ietresearch.onlinelibrary.wiley.com/doi/10.1049/enc2.12050byCochraneChina,WileyOnlineLibraryon[13/11/2022].SeetheTermsandConditions(https://onlinelibrary.wiley.com/terms-and-conditions)onWileyOnlineLibraryforrulesofuse;OAarticlesaregovernedbytheapplicableCreativeCommonsLicenseMoreover,accordingtothestrongdualitytheory[28],whenst.[]thecentralizedproblemisstrictlyconvex,thesolutionoftheAz1,z2,…,zn=B(27)dualproblemisidenticaltothesolutionoftheprimalproblem,whichallowsustosolvetheaboveproblemindistributedalgo-xi∈Xi(28)rithm.3DISTRIBUTEDALGORITHMzi−xi=0(29)Inthissection,consideringdynamiccharacteristicsandrespon-Webringconstraint(29)tomakesurethereformulatedprob-sivenessrequirementsofenergystorage,MPCisusedtohan-lem(23)isequivalenttoprimaryproblem(22).Thenweuseadleconstraintsbetweendifferenttimeintervalsandincludedualdecompositionapproachtodecoupleconstraint(29).Byfuturegenerationandconsumptionprediction.Thecomputa-relaxingtheconsensusconstraint(29)throughtheLagrangiantionalburdenandpersonalprivacyissuesareprocessedbydis-multipliers𝜆iandaddingrelaxationtermstotheobjectivefunc-tributedalgorithms,andOPFproblemisfurtherresolved,andtion(23),theLagrangefunctionLcanbedefinedas,theauxiliaryvariableisfurtherdecoupledtoobtainLMPstodecouplethepowernetworkforcedcoupling.()∑N(())∑N()2Lxi,zi,𝜆i=fi+𝜆izi−xi+zi−xi(30)i=1i=13.1StepsofthealgorithmOwingtothedecomposabilityofLagrangefunctionLandconstraints(28)and(29),problem(23)isdecomposedintoN+1Inthissubsection,wedevelopdistributedalgorithmforsolvingindependentoptimizationsub-problems,Atthelocallevel,eachproblem(22).Towardsthisend,thisproblemisfirstexpressedprosumersolvesindependentlyitsoperationcostminimizationinauniformcompactmatrixformformathematicalconcise-problemasfollows,ness,asshownbelow,()minfi+𝜆izi−xi(31)∑Nminf=fixi(23)st.(28)i∈NTheOSsolvesthefollowingsub-problemas,i=1st.∑N([minzi−xi)2(32)Ax1,x2,…,xn]=B(24)i=1xi∈Xi(25)st.(27)Tosolveproblem(31)and(32),weusethegradientmethodwherefiisaconvexfunction,AisaconstantmatrixandBforupdating𝜆i,whichisalsotheprosumeri’sDLMP.Theisaconstantvector.Equation(24)representsagroupoflin-Lagrangianmultipliersareinitiallysetatnon-negativevaluesandearconstraintscouplingalllocalvariablesxi.Xiisaconvexsetareupdatedby(33)ateachinteractionk.and(25)representslocalconstraintsofprosumeri.Therefore,inproblem(23),eachprosumer’sdecisionvariablesarestrongly𝜆ik+1=𝜆ik+𝛼i(zi−xi)(33)coupledwithothers’viatheconstraint(24).Becauseofcom-plexityofnetworkmodelling,itisimpracticaltodecouplethiswhere𝛼iisstepsizeforeachinteraction.TheLagrangianmul-constraintdirectly,wefirstlyreformulateproblem(23)byintro-tipliersadjustmentscanbeinterpretedastheOSfluctuatestheducingauxiliaryvariablesziforeachprosumer,whichrepresentLMPtomakesupplyanddemandbalance,wherethepricesaretheduplicateofpartvariablesinxionthesideofSO.Notethatincreasedinthecaseofexcessdemandanddecreasedintheinproblem(22),ziincludesthenetrealpowerandnetreactivecaseofexcesssupply.Differentwiththecaseallprosumershavepowerofprosumeri,therefore,detailedenergyproductionandthesameLMPwhennetworkconstraintsarenotconsidered,consumptioninformationinprosumersarenotshared,whichinthispaper,eachprosumerhavedifferentDLMP𝜆iwhichensurestheprivacyandautonomyofindividualprosumers.Theincludesnotonlyenergycomponentbutalsocongestionandreformulatedproblem(30)isshownbelow,losscomponent.Forexample,ifthereisalinecongestionhap-peningbetweenprosumeriandj,prosumericannotbuyenergy∑N∑N()2withlowerpricefromprosumerj,makingtheDLMPofpro-minf=fi+zi−xi(26)sumerihigherthanotherprosumers,whichwillbetestedincasexi,zistudy.Overall,withsettingterminationcriterionforinteraction,i∈Ni=1i=16YINETAL.26341581,2022,1,Downloadedfromhttps://ietresearch.onlinelibrary.wiley.com/doi/10.1049/enc2.12050byCochraneChina,WileyOnlineLibraryon[13/11/2022].SeetheTermsandConditions(https://onlinelibrary.wiley.com/terms-and-conditions)onWileyOnlineLibraryforrulesofuse;OAarticlesaregovernedbytheapplicableCreativeCommonsLicenseFIGURE4ModifiedIEEE30-busdistributionnetworkFIGURE3ImproveddistributedalgorithmAdditionally,inourmodel,SOneedstodolocaloptimizationproblemateachiterationstepbeforeupdating𝜆ik,andcompu-distributedcontrolofdistributionnetworkprosumersissum-tationaltimeforthislocaloptimizationproblemismuchlongermarizedinAlgorithm1.thanthatforupdating𝜆ik.Inordertoreducecomputationtime,weimproveourdistributedalgorithmbyallowingprosumerstoAlgorithm1DistributedcontrolforprosumerscommunicatedirectlytogetuniformlyLMPforallprosumers,whereenergysupplyanddemandarebalancedwithoutconsid-FindSoci,0,di,tateachtimetofMPCschemeeringnetworkconstraints.ThenthisuniformlyLMPischosenInitialize𝜆i0,k=0as𝜆i0forourdistributedalgorithm.Thisprocesscanbeinter-WhileterminationcriterionnotmetdopretedasSOadjustDLMPsinrealtimemarketstoensuretheGiventheupdate𝜆ik,eachprosumeri∈Ndoestheirlocalfeasibilityofenergytradingresults.optimizationandupdatexik,taccordingto(31).Prosumerspublishtheirenergypreferencexik,ttotheassociatedSO.3.2.2ImplementationextensionGiventheupdatedenergypreferencexik,t,SOfirstlydoesthelocaloptimizationandupdatezik,taccordingto(32),thenupdates𝜆ik+1Ourmodelconsiderstransactiveenergyamongprosumersinaccordingto(33)andfinallyshares𝜆ik+1toallprosumers.k=k+1distributionnetwork,butdoesnottakeprosumerstradingEndenergywithupperwholesalemarketintoaccount.Forexam-ple,ifLMPindistributionnetworkisveryhighduetolarge3.2Modelimprovementsenergydemand,prosumersaremorewillingtopurchaseenergyfromoutside.Inanotherscenariowheretherearenotsuffi-Basedontheimprovementsabove,distributedcontrolofdistri-cientenergysuppliesunderemergencycondition,prosumersbutionnetworkprosumersissummarizedinFigure3.alsoneedthesupportofwholesalemarket.However,thisprob-lemcanberesolvedbyintroducingwholesalemarketasanagent3.2.1ComputationalefficiencywithcostfunctionCiw,t=aiw,tpwi,t,whereaiw,tisthepredictionofpricesinwholesalemarketandpwi,tisrealpowerinjectedfromThechoiceofinitialLagrangemultipliersplaysanimportantwholesalemarket.roleininfluencingiterativeconvergenceandcomputationaleffi-ciency.Inmostcases,𝜆i0isinitializedaccordingtohistorydata.4CASESTUDYTheprosumeriscomposedofdistributedgenerators,localloads,andenergystoragesystems.Basedonthephysicalrela-tionshipandinformationexchangeamongthecomponentsofTE,wecomparethesignificanceofnetworkconstraintsandanalysistheconvergence.BasedontheIEEE33-bussystem,theresultsshowthatthecostwillincreasewhenconsideringoperationproblem.4.1SystemparametersandsimulationsettingsWeperformnumericaltestingofourdistributedcontrolmethodonthemodifiedIEEE33-busdistributionnetwork.Thedistri-butionnetworkisshowninFigure4anddetailedinformationofthisnetworkcanbefoundin[29].Weconsidereachbusiscon-nectedtoaprosumer,whichisequippedwithneitherdistributedYINETAL.726341581,2022,1,Downloadedfromhttps://ietresearch.onlinelibrary.wiley.com/doi/10.1049/enc2.12050byCochraneChina,WileyOnlineLibraryon[13/11/2022].SeetheTermsandConditions(https://onlinelibrary.wiley.com/terms-and-conditions)onWileyOnlineLibraryforrulesofuse;OAarticlesaregovernedbytheapplicableCreativeCommonsLicensegenerator,batterysystemresponsivedemand(redbuses)oronlycase1case2case3case4responsivedemand(blackbuses).1.1Weusetwohours’electricityloadsofonetypicaldayfrom[30].ThetimehorizonisdividedintothedurationΔt=5minVoltage(p.u.)1.06samples,resulting24samples.Weimplementapredictionhori-zonofT=6,whichmeanseachprosumercantakethe1.02estimatesofloadpatternsofnext30minintoaccount.Theinconveniencecostcoefficientis0.2$/kWh2andresponsive0.98demandisboundedbetween90%and110%ofthepredictions0.94ofloads.Theparametersforbatteriesaresetasfollows:ais=135791113151719212325272931330.5$∕kWh2andbatterieshaveSoclimitsof20–100%,withBusnumbermaximumdischargingandchargingpowerof0.5kW.Theparametersforgenerationcostfunctionareag=0.01$∕kWh2(a)bgiandi=0.5$∕kWh2.Theterminationisseteithercriterionthatiterationsis100ortolerancelevel‖z−x‖2islessthancase1case2case3case410−4.Thesub-problemsaresolvedusingIBM’sCPLEXsolver8[31]inMATLABonanIntelCorei7-6500UCPUwith8GBofTransmissionpower(kW)7RAM.654.2Significanceofnetworkconstraints44.2.1Comparisonofsignificanceofnetwork3constraints2Inthissection,weassume4cases:1Case1:Notransmissionlossesforalllinesandvoltageandlinecapacitylimits.0135791113151719212325272931Case2:Novoltageandlinecapacitylimits.LinenumberCase3:Nolinecapacitylimits.Case4:Thecapacityofline(6,26)islimitedto5kW.(b)Figure5ashowsreferencevalueofbusvoltagesandFIGURE5Comparisonofvoltageandtransmissionpower:(a)referenceFigure5bshowsthevalueoftransmissionpowers.Comparedvalueofbusvoltages;(b)valueoftransmissionpowerswithcase1,becausetransmissionlossesareconsidered,thevalueofvoltagesincase2arelowerthancase1,thetransmissioncase1case2case3case4powersareopposite.Incase3,becausevoltagelimitsarecon-sideredwhilelinecapacitylimitsarenotconsidered,thepeak2.5oftransmissionpowerishigher.Incase4,thecapacityofline25,(6,26)islimited.Therefore,transmissionpowersarecon-Output(kW)2.4trolled,butsomegeneratorsneedtogeneratemore,whichleadstohighervoltage.2.3Therearesevenprosumersequippedwithadistributed2.2generator.Figure6showstheoutputsofthesedistributedgeneratorsinfourcasesbeforeandafterconsideringthenet-2.1131620242731workconstraints.Incase1,weassumethereisnotransmis-7sionlossforalllinesandthevoltageandlinecapacitylim-itsarealsonotconsidered.Additionally,thesegeneratorshaveBusnumberthesamecostfunction,therefore,totaldemandwillbeaver-agelyallocatedamongthemtogetthesameLMPs.ThiscaseFIGURE6Outputsofthedistributedgeneratorsinfourcasesisequaltothecaseinwhichonlyeconomicissuesareconsid-ered.Incase2,althoughthereisnovoltageandlinecapacitycapacityofline(6,26)is5MW,combiningwithFigure5b,welimit,totalpowersupplyisabithigherthanthetotaldemandcanfindthislimitstransactiveenergybetweenthetwodis-duetotransmissionlosses.Incase3,weaddvoltagelimitstrictsconnectedbythisline,makingprosumer27and31can-butlinecapacitiesareunlimited,andthisalsocausesdiffer-notprovideenergywithlowerpricesforprosumersintheentgenerationsamongprosumers.Inlastcase,weassumetheotherdistrict.Thisalsoillustratesifweonlyconsidereconomicissues,theclearingresultsmaynotbefeasible.Thetotaloper-ationcostsoftwohoursinthesefourcasesare1798791.72,1829975.86,1830597.00and1830702.52,respectively,whichshowsthatiftheoperationissuesareincluded,thecostswillbeincreased.8YINETAL.26341581,2022,1,Downloadedfromhttps://ietresearch.onlinelibrary.wiley.com/doi/10.1049/enc2.12050byCochraneChina,WileyOnlineLibraryon[13/11/2022].SeetheTermsandConditions(https://onlinelibrary.wiley.com/terms-and-conditions)onWileyOnlineLibraryforrulesofuse;OAarticlesaregovernedbytheapplicableCreativeCommonsLicense52Lagrangemultiplie50LagrangemultiplieFIGURE8Powerofatypicaldistributedgenerator484644421234567891011121314151617181920Numberofiterations(a)56545250484644421234567891011121314151617181920Numberofiterations(b)FIGURE7Convergencecomparison:(a)Convergenceofthedistributedalgorithmincase1;(b)convergenceofthedistributedalgorithmincase44.2.2ConvergenceanalysisFIGURE9ReferencevalueofatypicalbusmaxvoltageFigure7showstheconvergenceofdistributedalgorithminchargepower,thepowerthatcanbeallocatedbysysteminunitcase1andcase4.Inthefirstcase,becauseonlythebalancingtimealsoincreases.Therefore,generatorpowerisbetterutilized,betweensupplyanddemandisconsidered,Lagrangemultipliesandgeneratoroutputisreduced.Thedistributedgeneratorout-aresupposedtobeconvergenttothesamevalue,butthereisputwithoutdemandresponseis2.935567562.Comparedwithanoscillationphenomenonhappeningduetotheintroductionsystemwithoutdemandresponse,generatoroutputofsystemofenergystorage.Wecanresolvethisproblembylimitingtheequippedwithdemandresponseissignificantlylower.Althoughiterations.Incase4,prosumershavedifferentconvergenceval-outputincreaseswiththeincreaseofcoefficient,itstillshowsues,whichexactlyareDLMPs,becauseoftheoperationcon-obviousadvantagesoverthesystemwithoutdemandresponse.straintsmentionedin3.2andconvergenceisachievedafterThroughoutwholefigure,energystorageperformanceisbetter12iterations.thandemandresponseinregulatingthegeneratoroutput.4.3SignificanceofenergystorageandInFigure9,weselectatypicalbustoanalysisitsmaximumdemandresponsevoltage.Thevoltageofthisbuswithoutdemandresponseis1.018409214.Withtheincreaseofdemandresponsecoeffi-Inthissection,wecomparetheimpactsofdemandresponsecient,nodevoltagealsoincreases,butcomparedwithsystemandenergystorageonpowersystem.Undersufficientenergywithoutdemandresponse,thevoltageisclosertostandardstoragecapacity,wecomparetheimpactsofdifferentchargevalue.Withtheincreaseofenergystoragechargeanddischargeanddischargepowers.Atthesametime,wecomparethepower,powerflowregulationcapacityofsystemalsoincreases,impactsofdifferentcoefficientofthecostfunctionindemandandnodevoltagecanbeeffectivelycontrolled.Throughoutresponse.Inthefollowingfigures,thedarkerthecolour,thewholefigure,energystorageperformanceisbetterthandemandlargerthevalue.responseinregulatingnodevoltage.Figure8showsthepowerofatypicaldistributedgenera-torinfourcasesbeforeandafterconsideringnetworkcon-straints.Withtheincreaseofenergystoragechargeanddis-YINETAL.926341581,2022,1,Downloadedfromhttps://ietresearch.onlinelibrary.wiley.com/doi/10.1049/enc2.12050byCochraneChina,WileyOnlineLibraryon[13/11/2022].SeetheTermsandConditions(https://onlinelibrary.wiley.com/terms-and-conditions)onWileyOnlineLibraryforrulesofuse;OAarticlesaregovernedbytheapplicableCreativeCommonsLicenseFIGURE10TotaloperationcostindifferentcasesORCIDChenYinhttps://orcid.org/0000-0002-6694-0316Figure10showstotaloperationscostindifferentcases.Thecostwithoutdemandresponseis2,058,223.254.ItisobviousREFERENCESthatwhenequippedwithdemandresponse,thecostofsys-temissignificantlyreduced.Withtheincreaseofcoefficient,the1.Parag,Y.,Sovacool,B.K.:Electricitymarketdesignfortheprosumerera.costofsystemalsoin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