第七届IEEE能源互联网与能源系统集成会议（EI22023）清华大学电机系/清华四川能源互联网研究院/DepartmentofElectricalEngineering,SichuanEnergyInternetResearchInstitute,TsinghuaUniversity鲁宗相/ZongxiangLu2023年12月16日汇报提纲一、“水光充储”接入的配电网低碳规划技术发展现状Currentsituationoflow-carbonplanningofdistributionnetworkwith"hydro-PV-charging-Outlinesstorage"(HPCS)二、面向分布式水、光资源的电力交通网络供需特性与协调运行模拟技术Simulationtechnologyofsupplyanddemandcharacteristicsandcoordinatedoperationofelectrictransportationnetworkfordistributedwaterandlightresources三、考虑充电设施空间布局与适应“水光充储”协同的配电网结构形态Thespatiallayoutofchargingfacilitiesandthestructureofdistributionnetworkthatadaptstothecoordinationof“hydro-PV-charging-storage"areconsidered四、考虑碳流分布的“水光充储”配电网联合规划方法Ajointplanningmethodfordistributionnetworkof“hydropowerphotovoltaicchargingandstorage"consideringcarbonflowdistribution五、面向“电-碳”市场耦合的电力交通网灵活性资源聚合效应挖掘与商业运营模式Flexibleresourceaggregationeffectminingandbusinessoperationmodelofelectrictransportationnetworkfor"electric-carbon"marketcoupling六、结论Conclusion2一、“水光充储”接入的配电网低碳规划技术发展现状Currentsituationoflow-carbonplanningofdistributionnetworkintegratedwith"hydro-PV-charging-storage"(HPCS)3“水光充储”形态背景Morphologicalbackgroundof"hydro-PV-charging-storage“(HPCS)国家“双碳”和新型电力系统建设背景下，国网公司发布“碳达峰、碳中和”行动方案，以分布式光伏、小水电为代表的分布式清洁能源将迎来快速发展。Withthebackgroundofthenational"dualcarbon"andnewpowersystemconstruction,theStateGridCorporationissuedthe"carbonpeak,carbonneutral"actionplan,anddistributedcleanenergyrepresentedbydistributedphotovoltaicandsmallhydropowerwillusherinrapiddevelopment.480008006000.25470006005000.2460004004000.15Distributedphotovoltaicandhydropower45000demonstrationprojects300分2000.1440002000.05100布04300000式2016201720182019202020212022201120122013201420152016201720182019农村水电站保有量当年新投产新能源车销量渗透率光四川梯级水光蓄互补发联合发电项目农村小水电保有量大，保持增长新能车增长迅速，渗透率快速攀升伏SichuancascadewaterandlightstorageandTheamountofsmallhydropowerinruralareasislargeElectricvehiclesaregrowingrapidlyandpenetrationis水complementarypowergenerationproject150andhaskeptgrowingclimbingrapidly100电示50范0项201720182019202020212022“水光充储”配电网形态初步具备！分布式光伏装机容量分布式光伏新增容量目“交通+能源”融合分布式光储项目光照资源丰富，分布式光伏持续增长"Transportation+energy"integratedSolarresourcesareabundant,anddistributedPVcontinuestogrow.高速充电桩分布High-speedchargingpiledistributiondistributedlightstorageproject4HPCSdistributionnetworkformisinitiallyavailable!传统规划存在的问题Challengestotraditionalplanning新型“水光充储”配电网结构下，传统配电网规划方式已经无法适应。ThetraditionaldistributionnetworkplanningmethodhasbeenunabletoadapttheHPCSdistributionnetworkstructure.Problemsexistingintraditionalplanning1、光伏“强随机波动”和充电负荷“短时大容量”特征改变原始源荷特性传Thecharacteristicsofphotovoltaic"strongrandomfluctuation"andchargingload"shorttimelargecapacity"研究分布式清洁能源与电力交通网融changetheoriginalsourcechargecharacteristics合的“水光充储”配电网联合规划技术统2、短时尖峰负荷增大区域电网投资容量，电网利用率及平均负载率极低Short-timepeakloadincreasestheinvestmentcapacityofregionalpowergrid,andtheutilizationrateandThejointplanningtechnologyofHPCSdistributionnetworkbasedontheintegrationofaverageloadrateofpowergridareverylowdistributedcleanenergyandelectric规3、配网容量无法满足电动汽车接入，严重制约电动汽车产业发展transportationnetworkisstudied划Thecapacityofthedistributionnetworkcannotmeettheneedsofelectricvehicleaccess,whichseriouslyrestrictsthedevelopmentoftheelectricvehicleindustry存4、源-荷-储时间不匹配导致配电网局部出现电压越限等安全问题提出电力-交通网络灵活性资源的配Themismatchofsource-charge-storagetimeleadstosafetyproblemssuchasvoltageover-limitinlocal电网规划综合解决方案在distributionnetworkAcomprehensivesolutionofdistributionnetworkplanningforpower-transportation5、规划阶段未考虑“水光充储”协同优化运行以平抑新能源、负荷波动networkflexibilityresourcesisproposed问Theplanningstagedidnotconsiderthecoordinatedoptimizationoperationof"waterandlightchargingandstorage"tosmoothoutnewenergyandloadfluctuations5题6、现有规划无法发挥最大的减碳效益，不能体现灵活调节资源减碳价值Theexistingplanningcannotmaximizethebenefitsofcarbonreduction,andcannotreflecttheflexibleadjustmentofthecarbonreductionvalueofresources国内外研究现状Researchstatusathomeandabroad国内外学者在考虑电力网-交通网融合的配电网规划方面展开了大量研究，但在电力交通网协调运行、配电网结构形态、规划方法、灵活性资源聚合与商业模式等方面仍有一定不足。Domesticandforeignscholarshavecarriedoutalotofresearchondistributionnetworkplanningconsideringtheintegrationofpowernetworkandtransportationnetwork,buttherearestillsomeshortcomingsinthecoordinatedoperationofelectrictransportationnetwork,distributionnetworkstructure,planningmethod,flexibleresourceaggregationandbusinessmodel.理论类型国内外研究现状现有研究不足TheoryResearchstatusathomeandabroadShortage电力交通网络协⚫主要集中在分布式水电参与调度优化、接入⚫缺乏对充电负荷与分布式光伏、分布式水电的时空耦合关系及调运行与消纳、经济性分析方面其关键影响因素研究Coordinated⚫Itmainlyfocusesondistributedhydropower⚫Thereisalackofresearchonthespatio-temporalcouplingoperationofparticipationindispatchingoptimization,relationshipbetweenchargingloadanddistributedphotovoltaicaccessandconsumption,andeconomicanddistributedhydropoweranditskeyinfluencingfactorselectricanalysistransportationnetwork6国内外研究现状Researchstatusathomeandabroad理论类型国内外研究现状现有研究不足TheoryResearchstatusathomeandabroadShortage配电网结构形⚫充电站布局优化侧重于光伏、充/换电站和储能之间⚫车流-路况及充电灵活需求与交通网流量相结合的研究较少；态研究的协同配置规划；配网形态主要针对典型拓扑接线⚫未充分考虑水电、光伏、充电站以及储能共同接入的场景进行Researchon⚫Therearefewstudiesonthecombinationoftrafficflow-roaddistribution⚫Theoptimizationofchargingstationlayoutfocusesonconditionandflexiblechargingdemandwithtrafficnetworkflow.networkthecollaborativeconfigurationplanningamongPV,⚫Scenariosinwhichhydropower,photovoltaic,chargingstationsandstructureformenergystoragearejointlyconnectedarenotfullyconsidered.charging/changingstationandenergystorage.The⚫缺乏对光伏和储能充电站带来的环境效益、节能效益等综合configurationofthedistributionnetworkismainly效益潜力的分析basedonthetypicaltopologyconnection⚫Thereisalackofanalysisonthepotentialofcomprehensivebenefitssuchasenvironmentalbenefitsandenergysavingbenefits联合规划方法⚫对于充电站内电源规划的研究大多从经济性角度出broughtbyphotovoltaicandenergystoragechargingstations研究发⚫较少结合国情研究电碳市场耦合；Researchon⚫Mostoftheresearchonpowerplanningincharging⚫缺乏灵活资源减碳价值及降碳贡献评估的理论；⚫几乎没有源网荷储一体化灵活性资源商业模式研究jointplanningstationsisfromtheeconomicview⚫Lesscombinedwithnationalconditionstostudythecouplingofmethodselectriccarbonmarket;灵活性资源聚⚫针对国外碳市场的研究较多；⚫Lackofflexibleresourcecarbonreductionvalueandcarbon合与商业模式⚫目前对商业模式的研究多集中在储能领域。reductioncontributionassessmenttheory;Flexible⚫Therearemanyresearchesonforeigncarbonmarket.⚫Thereisalmostnoresearchontheflexibleresourcebusinessmod7elresource⚫Mostofthecurrentresearchonbusinessmodelsaggregationandoftheintegrationofsourcenetwork,loadandstoragebusinessmodelsfocusesonthefieldofenergystorage二、面向分布式水、光资源的电力交通网络供需特性与协调运行模拟技术Simulationtechnologyofsupplyanddemandcharacteristicsandcoordinatedoperationofelectrictransportationnetworkfordistributedwaterandlightresources8光伏中长期出力预测技术PVmedium-longtermoutputforecastingtechnology分析影响分布式光伏发电功率的资源、气象、环境因素；引入集成学习中的XGBoost算法利用光照强度、温度、湿度等因素构建了光伏出力的确定性预测模型；基于确定性预测的误差，应用Copula模型构建光伏出力时间相关性上的条件概率分布，进一步提出了光伏出力的概率预测模型，从而实现了长时间尺度下光伏出力的合理全面估计。Analyzetheresource,meteorologicalandenvironmentalfactorsthataffectthepowerofdistributedPVpowergeneration;XGBoostalgorithmbasedonensemblelearningwasintroducedtoconstructadeterministicpredictionmodelofPVoutputbyusinglightintensity,temperature,humidityandotherfactors.Basedontheerrorofdeterministicprediction,theCopulamodelisusedtoconstructtheconditionalprobabilitydistributionofPVoutputtimecorrelation,andtheprobabilisticpredictionmodelofPVoutputisfurtherproposed,soastoachieveareasonableandcomprehensiveestimationofPVoutputoveralongtimescale.光伏发电功率影响因素分析确定性预测模型结果示例AnalysisofinfluencingfactorsofPVDeterministicforecastingmodelResultexamplepowergeneration（xgboostmodel）𝑃𝑃𝑉𝑡=𝑃𝑃𝑉,𝑟×𝑓𝑃𝑉×𝐼𝑇𝑡概率预测模型结果示例𝐼𝑇,𝑆𝑇𝐶ProbabilisticpredictionmodelResultexample×[1+𝜇×(𝑇𝑃𝑉(𝑡)−𝑇𝑃𝑉,𝑆𝑇𝐶)]（copulaprobabilisticmodel）光伏出力概率预测模型算法框架Photovoltaicoutputprobabilitypredictionmodelalgorithmframework9光伏中长期出力预测技术PVmedium-longtermoutputforecastingtechnology应用四川攀枝花华电新能源有限公司2022-2023年的光伏出力数据结合相关地区天气、光照等数据对所提出模型分别在月统计尺度（12个月）和小时统计尺度（8760小时）进行了验证。其中，在小时统计尺度下，确定性预测指标MAPE为15.3%，概率预测指标50%置信区间的PICP和CPDI分别为0.9532和0.9032，相关结果体现了本课题所提出光伏预测模型的有效性和良好的预测性能。ThePVoutputdataofPanzhihuaHuadianNewEnergyCo.,Ltd.from2022to2023combinedwithweatherandlightdataofrelevantregionswereusedtoverifytheproposedmodelinmonthlystatisticalscale(12months)andhourlystatisticalscale(8760hours),respectively.Where,atthehourlystatisticalscale,theMAPEofthedeterministicpredictionindexis15.3%,andthePICPandCPDIofthe50%confidenceintervaloftheprobabilitypredictionindexare0.9532and0.9032,respectively.Therelevantresultsreflecttheeffectivenessandgoodpredictionperformanceofthephotovoltaicpredictionmodelproposedinthistopic.光伏区间预测全年结果（月尺度）光伏预测全年结果（小时尺度）PVRangeForecastAnnualResults(Monthlyscale)PVForecastAnnualResults(Hour-scale)10PromotionalArticleaddedbytheECE,notincludedintheoriginalslidesEnergyConversionandEconomicsReceived:29November2022Revised:24February2023Accepted:28March2023DOI:10.1049/enc2.12088REVIEWAnanalysisofdistributionplanningunderaregulatoryregime:AnintegratedframeworkAprajayVermaKShantiSwarupDepartmentofElectricalEngineering,IndianAbstractInstituteofTechnologyMadras,Chennai,Distributionsystemplanningisamultifacetedtopicinvolvingfinancial,regulatory,andTamilnadu,Indiasystemlevelanalysis.Thewidenatureofthetopicwarrantsaholisticstudyconsideringallaspectsofanalysis.Thedistributionutilityisanaturalmonopolythatissubjectedtoutilityregulation.Theregulatorcanimpactcustomerexperiencebystrategicallyinfluencingtheplanningdecisionsoftheutility.Hence,thispaperreviewstheexistingutilityregulationmethodsinthecontextofthedistributionsystemandtheirefficacyinimprovingcertainreliabilityandefficiencyobjectives.Atwo-bussystemisusedtodemonstratetheimpactofclassicalmodelsinalleviatingreliabilityandefficiencyissuesthroughdemandresponse.Further,areviewisconductedondistributionsystemplanningmodelswithoutaregulatoryregime,andsuitablemodelsforholisticanalysisareidentified.Atwo-personcompleteinformationregulatorandutilitygamewithacomprehensivedistributionsystemmodelatthelowerlevelisproposed.AframeworkbasedontheMixedIntegerBilevelLinearProgram(MIBLP)isdiscussedtofindtheequilibriumpointoftheproposedgame.KEYWORDSenergyeconomics,investmentandplanning,operationandoptimization水电中长期出力预测技术Hydropowermedium-longtermoutputforecastingtechnology分析影响分布式水利发电功率的资源、气象、环境因素；引入深度学习算法LSTM利用降雨量和水电出力时间序列构建了水电出力的上时间尺度预测模型。应用四川省攀枝花市米易县普威金盈电站的数据对模型进行了验证，结果显示本课题提出的基于LSTM的水电出力预测模型预测MAPE为13.4%。Theresource,meteorologicalandenvironmentalfactorsaffectingthepowerofdistributedhydropowergenerationareanalyzed.AdeeplearningalgorithmLSTMisintroducedtoconstructapredictionmodelofhydropoweroutputonuppertimescalebyusingrainfallandhydropoweroutputtimeseries.ThemodelwasverifiedbyusingthedataofPuweiJinyingPowerStationinMiyiCounty,PanzhihuaCity,SichuanProvince.TheresultsshowthatthehydropoweroutputpredictionmodelbasedonLSTMproposedinthisprojectpredictstheMAPEof13.4%.预测模型predictionmodel（LSTMmodel）预测结果Predictingresults（四川省攀枝花市米易县普威金盈电站的数据）径流量对分布式水电出力影响分析(DataofPuweiJinyingpowerStation,MiyiCounty,PanzhihuaCity,SichuanProvince)Analysisoftheinfluenceofrunoffontheoutputofdistributedhydropower分布式水电出力物理模型h(t)=(Zu(t)+Pu(t)+αuVu2)−(Zd(t)+Pd(t)+αdVd2)−ΔhPhysicalmodelofdistributedρg2gρg2g11hydropoweroutput“车-站-网”时空耦合分析技术Spatio-temporalcouplinganalysistechniqueof"vehicle-station-network"基于交通网和配电网拓扑的抽象和构建的基础上，分别研究了电动汽车充电的时间和空间分布特性，研究了从充电需求估计-充电负荷估算-充电负荷与配电网耦合完整的作用机理和建模方法，通过算例仿真分析了不同场景下电动汽车接入配电网对电网负荷时空分布的影响。所提出模型可以在同时考虑交通流和能量流的情况下完成“车-站-网”时空概率分布特性的合理分析。Basedontheabstractionandconstructionoftrafficnetworkanddistributionnetworktopology,thetimeandspacedistributioncharacteristicsofEVchargingarestudiedrespectively,andtheintegratedactionmechanismandmodelingmethodfromchargingdemandestimation-chargingloadestimation-chargingloadcouplingwithdistributionnetworkarestudied.TheeffectsofEVsconnectedtothedistributionnetworkonthetemporalandspatialdistributionofpowergridloadindifferentscenariosareanalyzedbysimulationexamples.Theproposedmodelcanreasonablyanalyzethespatio-temporalprobabilitydistributioncharacteristicsofvehicle-station-networkconsideringbothtrafficandenergyflow.电网与交通网关系拓扑充电行为时间分布特性RelationshiptopologybetweenpowergridTimedistributioncharacteristicsofchargingbehaviorandtransportationnetworkSpatial充电行为空间分布特性behavior充电需求与配电网的耦合方法distributioncharacteristicsofchargingCouplingmethodofchargingdemandanddistributionnetwork不同场景下电动汽车接入配电网对电网负荷时空分布的影响仿真分析Simulationanalysisoftheinfluenceofelectricvehiclesconnected充电需求耦合12tothedistributionnetworkonthetemporalandspatialChargingdemand𝑞𝑟𝑒𝑎𝑙=𝐷𝑤(𝜇𝐸𝑉,𝑤)=𝑞𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙𝑒𝑥𝑝(−𝜃𝜇𝐸𝑉,𝑤)couplingdistributionofpowergridloadunderdifferentscenarios负荷特性耦合𝑑𝑖𝑚,𝑗𝑛,𝑘,𝑛𝑐=𝑑𝑖𝑚,𝑗𝑛+𝑑𝑖𝑚,𝑘𝑛+𝑑𝑘𝑚,𝑗𝑛Loadcharacteristiccoupling“水-光-充“协同运行策略“Hydro-PV-charging"cooperativeoperationstrategy分别提取了分布式水电，分布式光伏和充电站的典型和概率出力/负荷特性。通过对所获取特性进行缩放和组合，获取了不同水-光-充协同运行的出力特性，不但可以体现不同规模三类电源/负荷特性协同运行的趋势特性，同时展示了不确定性（主要为光伏和充电负荷）对协同出力特性的影响。Thetypicalandprobabilisticoutput/loadcharacteristicsofdistributedhydropower,distributedphotovoltaicandchargingstationsareextractedrespectively.Byscalingandcombiningtheobtainedcharacteristics,theoutputcharacteristicsofdifferentwater-light-chargecooperativeoperationareobtained,whichcannotonlyreflectthetrendcharacteristicsofthecollaborativeoperationofthreetypesofpowersupply/loadcharacteristicsofdifferentscales,butalsoshowtheinfluenceofuncertainties(mainlyphotovoltaicandchargingload)onthecollaborativeoutputcharacteristics.光伏出力分布PVpowerdistribution水电出力分布水光协同出力分布不确定性对水-光-充协同出力特性的影响分析HydropoweroutputHydro-PVcooperativedistributionoutputdistributionAnalysisoftheinfluenceofuncertaintyonHydro-PV-chargeco-outputcharacteristics13三、考虑充电设施空间布局与适应“水光充储”协同的配电网结构形态Thestructureofdistributionnetworkconsideringspatiallayoutofchargingfacilitiesandadaptingtothecoordinationof“hydro-PV-charging-storage”14电动汽车充电设施需求分布预测方法Themethodforforecastingthedistributionofelectricvehiclecharginginfrastructuredemands构建了电动汽车充电需求时空分布预测模型，主要包括行程链模拟模块、充电行为决策模块和充电过程仿真模块，各个模块的输入输出互相承接、串联，该模型应用蒙特卡洛方法模拟任意规模充电汽车的充电需求分布。Aspatial-temporaldistributionforecastingmodelforelectricvehiclechargingdemandhasbeenconstructed.Itprimarilyconsistsofatripchainsimulationmodule,achargingbehaviordecisionmodule,andachargingprocesssimulationmodule.Theinputsandoutputsofeachmoduleareinterconnectedandlinked.ThemodelappliesMonteCarlomethodstosimulatethechargingdemanddistributionforelectricvehiclesofanyscale.变电站商场超市办公场所居民小区183322232491011192561781220213425302926151413313228271617基于配电网拓扑的充电需求空间划分充电需求时空分布仿真结果15充电需求预测方法ChargingdemandspatialpartitioningSimulationresultsofspatiotemporalChargingdemandforecastingmethodbasedondistributiongridtopologydistributionofchargingdemand充电设施站址布局方法Chargingfacilitysitelayoutmethod采用动态规划设计充电站选取决策算法，结合充电需求估计，以充电距离成本和充电站建设成本的综合成本最小为目标函数，考虑配网潮流、排队等待等实际约束条件，构建充电设施站址布局优化模型。Utilizingdynamicprogrammingtodesignachargingstationselectiondecisionalgorithm,integratingwithchargingdemandestimation.Theobjectivefunctionminimizesthecomprehensivecost,encompassingchargingdistancecostandchargingstationconstructioncost.Themodeltakesintoaccountpracticalconstraintssuchasdistributionnetworkflowandqueuing,aimingtooptimizethelayoutofchargingfacilitylocations.基于Dijkstra最短ObjectivefunctionConstraint路径ChargingQueuingwaiting构建距离矩阵distancecostconstraintConstructingadistancematrixCharging16constructioncostbasedonDijkstra'sshortest充电设施站址布局模型ChargingFacilitySiteLayoutModelpath33节点电动汽车充电需求ElectricVehicleChargingDemandat33Nodes充电设施站址布局方法Chargingfacilitysitelayoutmethod选取计算用例，分析了是否考虑配网约束及充电负荷与分布式光伏、分布式水电和储能协同运行等六个场景下充电站选址算法的优化结果，并对优化结果进行了对比分析。Selectingcomputationalcases,weanalyzedtheoptimizationresultsofchargingstationsitingalgorithmsinsixscenarios,consideringfactorssuchasdistributionnetworkconstraints,chargingload,andthecoordinatedoperationofdistributedphotovoltaics,distributedhydropower,andenergystorage.Subsequently,acomparativeanalysiswasconductedontheoptimizationoutcomes.方案设置ProgramConfiguration优化结果OptimizationResults不考虑配网约束时（方案1），主要在节点1、2、4、7、13、19、26、28、32节点投建充电站；而考虑水电、光伏、储能运行特性后，为促进水电和光伏的消纳，充电站易在光伏和水电节点投建，如方案EV充电站光伏电站小水电储能算例3、4、5、6考虑光伏运行特性后，光伏节点20均投建充电站；算例5、6考虑水电运行特性后，水电节点24均投建充电站。Withoutconsideringdistributionnetworkconstraints(Scenario1),charging1（EV）×（不考虑配网约束）×××2（EV_G）√（考虑配网约束）×××stationsaremainlydeployedatnodes1,2,4,7,13,19,26,28,and32.However,whenconsideringtheoperationalcharacteristicsofhydropower,photovoltaics,andenergystoragetofacilitatetheintegrationof3（EV_PV）√√××hydropowerandphotovoltaics,chargingstationsareeasilydeployedatnodeswithphotovoltaicandhydropowerresources.Forexample,incases3,4,5,and6,wherethephotovoltaicoperational4（EV_PV_STO）√√×√characteristicsareconsidered,chargingstationsaredeployedatnode20,whichhasphotovoltaicresources.5（EV_PV_H）√√√×6（EV_PV_H_STO）√√√√Incases5and6,consideringtheoperationalcharacteristicsofhydropower,chargingstationsaredeployedatnode24,whichhashydropowerresources.优化结果的经济性分析EconomicAnalysisofOptimizationResults算例2~6规划方案成本对比如下表所示，对比分析可知，方案3、5考虑光伏和分布式小水电后，购方案充电站投资年排队等待充电路途损耗网损成本购电成本弃光成本弃水成本总成本电成本明显减少，但弃光、弃水惩罚成本较高；方案4、6考虑储能运行特性后，弃光、弃水惩罚成本（万元）成本（万元）成本（万元）（万元）（万元）（万元）（万元）（万元）成本明显减少，储能有效提高了可再生能源的消纳能力。Thecostcomparisonofplanningscenarios2（EV_G）5.220.0018.006.60134.00//163.82forcases2to6isshowninthetablebelow.Throughcomparativeanalysis,itisevidentthatscenarios3and5,whichconsiderphotovoltaicsanddistributedsmallhydropower,exhibitasignificantreductionin3（EV_PV）5.310.0011.004.6021.4073.20/115.51purchasedelectricitycosts.However,thecostsassociatedwithcurtailmentofsolarandhydropowerare4（EV_PV_STO）5.220.005.664.600.0051.00/66.48relativelyhigh.Ontheotherhand,scenarios4and6,whichconsidertheoperationalcharacteristicsofenergystorage,showasignificantreductioninthecostsassociatedwithcurtailmentofsolarand5（EV_PV_H）5.220.0015.004.405.6087.4016.40134.00hydropower.Energystorageeffectivelyenhancestherenewableenergyabsorptioncapacity.6（EV_PV_H_STO）5.220.6213.004.000.0067.6015.00105.4417“水光充储”灵活性供需平衡方法“hydro-PV-charging-storage”FlexibilitySupply-DemandBalancingMethod确定“水光充储”系统中的灵活性资源特性，研究“水光充储”协同运行机理及时空耦合特性，构建系统灵活性资源供需平衡仿真计算模型，实现对“水光充储”不同场景下供需平衡的自动匹配和校验。Identifytheflexibilityresourcecharacteristicsinthe"Hydro-OptoChargingandStorage"system,investigatethecooperativeoperationmechanismandspatiotemporalcouplingcharacteristicsofthe"Hydro-OptoChargingandStorage,"constructasimulationmodelforbalancingflexibilityresourcesupplyanddemand,andachieveautomaticmatchingandverificationofsupply-demandbalanceindifferentscenariosof"Hydro-OptoChargingandStorage."充电站Chargingstation空间供需耦合特性SpatialSupply-EnteratypicalsceneDemandCouplingCharacteristics分布式光伏DistributedEntertheobjectivefunctionPhotovoltaicsoftheapplicationscenario分布式风电DistributedPWV(t)+Pess(t)=Pcs(t)+Pl(t)InputapplicationWindPowerscenarioconstraints储能EnergyStorageknc协同运行Coordinated时间供需平衡模型TimeSupply-ComputeOperationDemandBalanceModelHydro-PV-charging-灵活性供需平衡模型FlexibilitySupply-storageflexiblesupplyandDemandBalanceModeldemandbalancestrategy灵活性供需平衡应用流程ApplicationProcessof18FlexibilitySupply-DemandBalancing高渗透率快充电站与分布式光伏、水电、储能协同配置High-PenetrationFastChargingStationsCoordinatedwithDistributedPhotovoltaics,Hydropower,andEnergyStorageConfiguration以最小化配网最大负荷和最大化配网运营经济性为目标，建立“水光充储”配电网优化规划模型，提出高渗透率快充电站与分布式光伏、分布式水电、储能协同的配电网规划方案。并在不同规模充电汽车场景下对所提出模型进行了应用，分别计算得到了最优的匹配方案。Withtheobjectivesofminimizingdistributiongridpeakloadandmaximizingoperationalcost-effectiveness,establishanoptimizationplanningmodelforthe"Hydro-OptoChargingandStorage"distributiongrid.Proposeadistributiongridplanningschemethatinvolveshigh-penetrationfastchargingstationscoordinatedwithdistributedphotovoltaics,distributedhydropower,andenergystorage.Applytheproposedmodeltovariousscalesofelectricvehiclechargingscenarios,calculatingoptimalmatchingsolutionsforeach.minPnlmin(CINV+CO&M−CREV+CNV)pPtV+pt+pt+pntl=pcts+pt,tTHydBdisload0pi,tPi,iIHyd,tTHydHydIHydpt=pi,t,tTHydHydi=1pttSOCt+1=SOCt−Bdisb,tTEb0pi,tPPiV,tT电动汽车规模光伏容量水电容量（MW）储能容量（MW）总经济成本PV（MW）(亿元)01538931.1IHyd13291539231.3103321542033.4pPtV=pi,t,tT203551545435.9PV381i=1“水光充储”配电网优化规划模型"Hydro-OptoChargingandStorage"DistributionGrid传统负荷和高渗透率快充接入下的规划结果Planningresultsunder19OptimizationPlanningModeltraditionalloadandhigh-penetrationfastchargingintegrationPromotionalArticleaddedbytheECE,notincludedintheoriginalslidesEnergyConversionandEconomicsReceived:5May2022Revised:28January2023Accepted:28January2023DOI:10.1049/enc2.12080ORIGINALRESEARCHOptimizedplanningofchargersforelectricvehiclesindistributiongridsincludingPVself-consumptionandcooperativevehicleownersBiswarupMukherjee1FabrizioSossan1,21MINESParis-PSL,CentrePERSEE,SophiaAbstractAntipolis,FranceThispaperpresentsamathematicalmodeltositeandsizethecharginginfrastructurefor2HES-SOValais-Walliselectricvehicles(EVs)inadistributiongridtominimizetherequiredcapitalinvestmentsandmaximizeself-consumptionoflocalPVgenerationjointly.Theformulationaccountsfortheoperationalconstraintsofthedistributiongrid(nodalvoltages,linecurrents,andtransformers’ratings)andtherechargingtimesoftheEVs.ItexplicitlymodelstheEVowners’flexibilityinpluggingandunpluggingtheirvehiclestoandfromachargertoenableoptimalutilizationofthecharginginfrastructureandimproveself-consumption(cooper-ativeEVowners).Theproblemisformulatedasamixed-integerlinearprogram(MILP),wherenonlineargridconstraintsareapproximatedwithlinearizedgridmodels.KEYWORDSchargingstations,electricvehicles,PVself-consumption,siting四、考虑碳流分布的“水光充储”配电网联合规划方法Ajointplanningmethodfordistributionnetworkof“hydropowerphotovoltaicchargingandstorage"consideringcarbonflowdistribution20电动汽车负荷碳排放强度评估模型Carbonemissionintensityassessmentmodelforelectricvehicleload基于电力系统潮流计算理论和碳排放流理论，考虑源荷时空分布特性，建立电动汽车负荷的碳排放强度评估模型，实现配电网潮流分布和碳流分布的协同计算，为碳流分布的分析与优化奠定了基础。Basedonthepowersystempowerflowcalculationtheoryandcarbonemissionflowtheory,thecarbonemissionintensityevaluationmodelofelectricvehicleloadisestablishedconsideringthetime-spacedistributioncharacteristicsofsource-load,andthecollaborativecalculationofpowerflowdistributionandcarbonflowdistributionisrealized,whichlaysafoundationfortheanalysisandoptimizationofcarbonflowdistribution.()()支路潮流分布矩阵Branchpowerflowdistributionmatrix：PB=PBijNNfPi=Pis−UiUjGijcosij+Bijsinij=0ji()()机组注入分布矩阵Unitinjectiondistributionmatrix:PG=PGijKNf=Q−UUGsin−Bcos=0()负荷分布矩阵Loaddistributionmatrix：QiisijijijijijPL=PLjimjMNT()节点有功通量矩阵Nodeactivefluxmatrix：PN=diagN+KPZ，其中PZ=PBPG()发电机组碳排放强度向量Carbonemissionintensityvectorofgeneratorset：E=GEG1k1K()节点碳势矩阵Nodecarbonpotentialmatrix：E=P−PT−1PTENNBfpGGfp−1fp=U支路碳流率分布矩阵DistributionmatrixoffqfqU()branchcarbonflowrate：fqRB=PBdiagENU负荷碳流率向量Loadcarbonflowratevector：RL=PLEN潮流分布与碳排放流分布协同计算原理Powerflowdistributionisbasedonthecooperativecalculationprincipleofcarbonemissionflowdistribution21电动汽车负荷碳排放强度评估模型Carbonemissionintensityassessmentmodelforelectricvehicleload基于所建立的潮流分布于碳排放流分布协同计算模型，应用某实际配电网拓扑及电源负荷分布数据，计算了配电网节点碳势及碳排放量的时空分布。Basedontheestablishedcollaborativecalculationmodelofpowerflowdistributionandcarbonemissionflowdistribution,thespatialandtemporaldistributionofcarbonpotentialandcarbonemissionofdistributionnetworknodesarecalculatedbyapplyingthetopologyandpowerloaddistributiondataofarealdistributionnetwork.算例网络拓扑及节点配置Examplenetwork碳排放强度评估结果Carbonintensityassessmentresults22topologyandnodeconfiguration电力交通网络的“电-碳”时空分布特性Space-timedistributioncharacteristicsof"electric-carbon"inelectrictransportationnetwork考虑电动汽车出行时空分布特征和充电负荷空间分布特性，基于碳排放强度计算模型研究不同场景下电动汽车充电负荷造成的碳排放分布，分析电动汽车充电行为与充电网络碳排放的耦合关系。ConsideringthespatialandtemporaldistributioncharacteristicsofEVtravelandthespatialdistributioncharacteristicsofchargingload,thecarbonemissiondistributioncausedbyEVchargingloadunderdifferentscenariosisstudiedbasedonthecarbonemissionintensitycalculationmodel,andthecouplingrelationshipbetweenEVchargingbehaviorandcarbonemissionofchargingnetworkisanalyzed.输入电动汽车充电负荷时空分布数据Inputthespatial-temporaldistributiondataofelectricvehiclechargingload输入光伏，水电发电功率，储能数据Inputphotovoltaic,hydropowerpower,energystoragedata输入节点负荷数据Enternodeloaddata“电-碳”时空分布特性分析算例拓扑图Topologydiagramof"electric-carbon"space-timedistributioncharacteristicsanalysisexample电力系统碳排放模型Carbonemissionmodelofpowersystem电力交通网络充电负荷“电-碳”时空分布特性分布图时空分布图SpatialandSpatialandtemporaldistributionof“电-碳”时空分布Space-timedistributionof"electric-carbon"temporaldistributionof"electric-carbon"“电-碳”时空分布特性分析方法流程chargingloadinelectric"Electric-carbon"space-timedistributiontransportationnetworkcharacteristicsanalysismethodflow23“水光充储”一体化容量配置"Hydropowerphotovoltaicchargingandstorage"integratedcapacityconfiguration基于电力交通网络的“电-碳”潮流时空分布特性，分析在低碳目标下电力交通网络的“电-碳”潮流时空分布运行策略；考虑系统年收益最大和光伏供给负荷占比等优化目标，建立计及新能源碳排放利用的“水光充储”一体化容量配置模型和碳排放分析模型。Basedonthespatio-temporaldistributioncharacteristicsof"electric-carbon"powerflowinelectrictransportationnetwork,thepaperanalyzesthespatio-temporaldistributionoperationstrategyof"electric-carbon"powerflowinelectrictransportationnetworkunderthelow-carbongoal.Consideringtheoptimizationobjectivessuchasthemaximumannualrevenueofthesystemandtheproportionofphotovoltaicsupplyload,anintegratedcapacityallocationmodelof"Hydropowerphotovoltaicchargingandstorage"andacarbonemissionanalysismodelwereestablishedtakingintoaccountthecarbonemissionutilizationofnewenergy.()fPi=Pis−UiUjGijcosij+Bijsinij=0ji()fQi=Qis−UiUjGijsinij−Bijcosij=0jifpfp−1“水光充储”一体化容量配置"Hydropowerfp=Uphotovoltaicchargingandstorage"integratedfqfqUcapacityconfigurationfqU水电光伏出力分布图Hydropowerphotovoltaicoutputdistributionmap(t)=Fes(t)scEes(t)R(t)=(t)P(t)disscdis()()()TTFchdiscbRtdtt=Rtdt−i=0tch,ichi=0tdis,idis碳排放分析模型Carbonemissionanalysismodel碳排放分析模型算例分析图Carbonemission24analysismodelexampleanalysisdiagram“水光充储”一体化容量配置"Hydropowerphotovoltaicchargingandstorage"integratedcapacityconfiguration考虑系统年收益最大和光伏供给负荷占比等优化目标，选取计算用例，分析了不同规模分布式光伏、分布式水电和储能协同运行等方案下的碳排放结果，并对结果进行了对比分析。ConsideringtheoptimizationobjectivessuchasmaximumannualrevenueofthesystemandtheproportionofPVsupplyload,thecarbonemissionresultsofdifferentscaledistributedPV,distributedhydropowerandenergystoragecollaborativeoperationschemeswereanalyzedbyselectingcalculationcases,andtheresultswerecomparedandanalyzed.1.0200050012001800经济性最优0.81600Economicoptimization10001400目标函数400Objectivefunction800光伏本地消纳最大化300MaximizePVlocalaccomadation600200400光伏容量(MW)0.61200储能容量(MWh)高碳机组发电占比1000碳排放量(t)0.4800水光储充配网联600合优化规划模型0.2400Hydropowerphotovoltaic100200charginganddistribution200networkjointoptimization000.0方案2方案30方案2方案3planningmodel方案1方案1方案1方案光伏容量方案2方案3储能容量方案高碳机组方发案电占比The方案水电容量方案水光储匹配容量Matchingproportionofhigh-carbon方案碳排放量Schemecarbonemissioncapacityofwaterandlightstoragegeneratingunitsinthescheme随着光伏容量的增加，所需配置的储能容量随方案光伏容量Photovoltaic水电容量Hydropower储能容量Energystorage碳排放量Carbon之增加，高碳机组的发电占比和碳排放量随之schemecapacity（MW）capacity（MW）capacity（MWh）emission（t）减少。Withtheincreaseofphotovoltaiccapacity,therequiredconfigurationofenergy1420157961206storagecapacitywillincrease,andthe2329153891611proportionofpowergenerationandcarbonemissionsofhigh-carbonunitswilldecrease.3505151176843模型优化结果Modeloptimizationresult25五、面向“电-碳”市场耦合的电力交通网灵活性资源聚合效应挖掘与商业运营模式Flexibleresourceaggregationeffectminingandbusinessoperationmodelofelectrictransportationnetworkfor"electric-carbon"marketcoupling26电-碳市场的耦合机制Couplingmechanismofelectric-carbonmarket研究电力市场与碳市场耦合关系，分析电力市场电能成本随碳排放价格的变化趋势，分析从电力需求到电力供给的市场主体逻辑关系和相互影响关系机理，获取了碳市场对电力市场影响的科学描述。Thispaperstudiesthecouplingrelationshipbetweenelectricitymarketandcarbonmarket,analyzesthechangetrendofelectricitycostwithcarbonemissionpriceinelectricitymarket,analyzesthelogicalrelationshipandmutualinfluencerelationshipmechanismofmarketplayersfromelectricitydemandtoelectricitysupply,andobtainsascientificdescriptionoftheinfluenceofcarbonmarketonelectricitymarket.电力市场与碳市场耦合关系电力市场电能成本随碳排放价格变化分析碳市场与电力市场的交互影响CouplingrelationshipbetweenAnalysisofchangesofelectricitycostInteractionofcarbonmarketandelectricitymarketelectricityandcarbonmarketwithcarbonemissionpriceinelectricity➢传统化石能源发电量越多，碳配额需求越大，碳价升高；CarbonVolumeofmarketThemoretraditionalfossilenergygeneration,thegreaterthepricetransactiondemandforcarbonallowances,carbonpricesriseCarbon➢发电企业碳成本增加，进而拉低企业总体利润水平，企market业装机投建趋于收缩、发电量减少、碳配额需求减少，Electricitymarket最终达到动态均衡。TheincreaseofcarboncostwilllowertheoverallprofitelectrovalencePowersupplylevelofenterprises,andtheinstalledcapacityinvestmentandstructureconstructionofenterpriseswilltendtoshrink,thepowergenerationwilldecrease,thedemandforcarbonquotaswilldecrease,andfinallyreachadynamicequilibrium.碳市场模式下灵活性资源调节能力评估方法Assessmentmethodofflexibleresourceregulationcapacityundercarbonmarketmodel提出电力交通网内灵活性资源的调节能力评估方法：分析价格型需求响应，得到需求响应后的负荷曲线;引入碳交易机制，并将碳交易机制下的碳交易成本作为目标函数的组成部分;最后在满足约束条件下求解出碳交易机制下的灵活性资源调节能力。Thispaperputsforwardamethodtoevaluatetheadjustmentcapacityofflexibleresourcesinelectrictransportationnetwork:analyzingthepricedemandresponseandobtainingtheloadcurveafterthedemandresponse;Introducethecarbontradingmechanism,andtakethecarbontradingcostunderthecarbontradingmechanismasacomponentoftheobjectivefunction;Finally,theflexibleresourceadjustmentcapacityunderthecarbontradingmechanismissolvedundertheconstraintconditions.PowerpurchasecostFlexibilityof负荷平衡约束Pe−Pe+Pe−PeresourceLoadbalanceb,ts,tWT,tHP,tCarbontradingcostregulationunderconstraintConsidertheloadOperationandcarbonmarket+PCeHP,t+Pe,dis−Pe,chcurveafterthemechanism水光出力约束ES,tES,tPricebasedmaintenancecostWaterandlightdemandresponsedemandresponseObjective碳市场机制下outputconstraints=Pe0+PCeL,t+Lrt,eInitialloadfunction的灵活性资源L,t调节能力PePWeT,F;PPeV,tPPeV,FWT,t()可削减负荷ej−0je024储能充放电约束变化量PCL,t=PCL,tECLt,jConstraintsonchargingandLoadReductionAvailablej=10jdischargingenergystorageConstraint()可转移负荷ee024j−0jconditionPSL,t=PSL,tESLt,jinPEinSoutPout变化量j=10jSES,t+1=SES,t+ES,t,t+ES,tES,tTransferableloadPromotionalArticleaddedbytheECE,notincludedintheoriginalslidesEnergyConversionandEconomicsReceived:1August2022Revised:30November2022Accepted:30November2022DOI:10.1049/enc2.12074REVIEWOverviewofcollaborativeresponsebetweenthepowerdistributionnetworkandurbantransportationnetworkcoupledbyelectricvehicleclusterunderunconventionaleventsYingWangYinXuJinghanHeSeungJaeLeeSchoolofElectricalEngineering,BeijingJiaotongAbstractUniversity,HaidianDistrict,Beijing,ChinaWiththerapiddevelopmentofelectricvehicles,theyhavebecomeanimportantpartofurbandistributionandtransportationnetworks.Thepowerdistributionnetworkandtrans-portationnetworkarecoupledbyelectricvehicleclustersandintegratedthroughstronginteractions,creatingacoupledsystem.Thispaperpresentsthestudyontheircollaborativeresponsesisessentialtoreducelossesandimproveurbanresilienceduringunconven-tionalevents.First,themultidimensionalanddeep-leveltime-varyingclosed-loopcouplingeffectsofthepowerdistributionnetworkandurbantransportationnetworkcoupledbyelectricvehicleclustersareanalysedunderunconventionalevents.Second,basedonthedifferentscalesofunconventionalevents,asummaryofrelevantstudiesismadeonthecollaborativeresponsestrategiesofthecoupledsystemtourbanlocalpoweroutagesandlarge-scaleblackoutsfollowingunconventionalevents.Finally,futureresearchdirectionsarediscussed.KEYWORDSelectricvehicles,extrmeevents,interdependency,powerdistributionnetwork,resilience,urbantransportationnetwork碳市场模式下灵活性资源调节能力评估方法Assessmentmethodofflexibleresourceregulationcapacityundercarbonmarketmodel以供需平衡为目标，建立灵活性资源的调节能力评估模型。应用分时电价算例计算需求响应下灵活性资源对系统负荷调节的贡献，验证了所提出灵活性资源调节能力评估方法的有效性。Aimingatthebalanceofsupplyanddemand,amodelforassessingtheadjustmentcapacityofflexibleresourcesisestablished.AnexampleofTOUisusedtocalculatethecontributionofflexibleresourcestosystemloadregulationunderdemandresponse,andtheeffectivenessoftheproposedmethodisverified.in+out1ES,tES,tPoutoutPoutPoutoutES,tES,tES,minES,tES,max功率容量约束inPin模型输入ModelinputPowercapacityconstraintES,tES,minPininPinES,tES,tES,maxinPEinSPoutoutSES,t+1=SES,t+ES,t−ESES,tSES,minSES,tSES,maxSES,0=SES,1供需平衡约束Pe−Pe+Pe−Pe+Pe+Pe,dis−Pe,chb,ts,tWT,tHP,tCHP,tES,tES,tSupplyandPe0PCeL,tLrt,edemandbalance=L,t++constraint灵活性资源的约束灵活性资源调节能力评估结果ConstraintsonflexibleresourcesResultsoftheassessmentoftheabilitytoadjustflexibleresources碳市场模式下降碳贡献评估Carbonmarketmodeldeclinescarboncontributionassessment提出基于全生命周期评估的降碳分析方法。通过对比不同灵活性资源参与调节的情景和煤电情景间对应碳排放的差额来评估一个典型日内的降碳贡献，提出降碳效益计算方法。Acarbonreductionanalysismethodbasedonthewholelifecycleassessmentisproposed.Thecarbonreductioncontributionofatypicaldaywasevaluatedbycomparingthecarbonemissiondifferencebetweenthescenarioswithdifferentflexibleresourcesandthescenarioswithcoalpower,andthecalculationmethodofcarbonreductionbenefitwasproposed.降碳效益=电网电量边际碳排放因子的平均值-灵活性资源的碳排放总量/总发电量CarbonreductionAveragevalueofmarginalcarbonTotalcarbonemissionsTotalgenerationbenefitemissionfactorofpowergridfromflexibleresources电量边际排放因子250000totalMarginaldischargefactorofelectricity2000001500002019年0.8587tCO2/MWh100000105772.372018年0.8770tCO2/MWhkgCO250000PVhydro37745.8502017年0.9014tCO2/MWh91237.57storage105772.3791237.572016年0.9229tCO2/MWh光伏37745.852015年0.9515储能水电总计tCO2/MWh灵活性资源降碳效益评估结果水光出力曲线2015-2019年四川省电网电量边际排放因子表AssessmentresultsofcarbonreductionbenefitsofflexibleresourcesWaterandlightoutputcurveTableofmarginalemissionfactorsofpowergridinSichuanProvincefrom2015to2019六、结语Conclusion31结语与展望Conclusion➢引入了深度学习算法LSTM利用降雨量和水电出力时间序列构建了水电出力的上时间尺度预测模型，算例表明所提出的基于LSTM的水电出力预测模型预测MAPE为13.4%。ThedeeplearningalgorithmLSTMwasintroducedtoconstructthehydropoweroutputpredictionmodelontheuppertimescalebyusingtherainfallandhydropoweroutputtimeseries.TheresultsshowedthatthehydropoweroutputpredictionmodelbasedonLSTMproposedinthisprojectpredictedtheMAPEof13.4%.➢考虑光伏和分布式小水电后，购电成本明显减少，但弃光、弃水惩罚成本较高；考虑储能运行特性后，弃光、弃水惩罚成本明显减少，储能有效提高了可再生能源的消纳能力。Consideringphotovoltaicanddistributedsmallhydropower,thecostofelectricitypurchaseissignificantlyreduced,butthepenaltycostofabandoninglightandwaterishigher;Afterconsideringtheoperationcharacteristicsofenergystorage,thepenaltycostofabandoninglightandwaterissignificantlyreduced,andenergystorageeffectivelyimprovestheabsorptioncapacityofrenewableenergy.➢在电力系统节点上增加可再生能源有助于降低电力系统的碳排放，使得电力系统的能源结构更为多样化，有助于降低对传统能源的过度依赖，对气候变化产生积极影响。Theadditionofrenewableenergyatthenodesofthepowersystemcanhelpreducethecarbonemissionsofthepowersystem,maketheenergystructureofthepowersystemmorediversified,helpreducetheover-dependenceontraditionalenergysources,andhaveapositiveimpactonclimatechange.➢提出基于全生命周期评估的降碳分析方法。通过对比不同灵活性资源参与调节的情景和煤电情景间对应碳排放的差额来评估一个典型日内的降碳贡献，提出降碳效益计算方法。Acarbonreductionanalysismethodbasedonthewholelifecycleassessmentisproposed.Thecarbonreductioncontributionofatypicaldaywasevaluatedbycomparingthecarbonemissiondifferencebetweenthescenarioswithdifferentflexibleresourcesandthescenarioswithcoalpower,andthecalculationmethodofcarbonreductionbenefitwasproposed.3233Received:29November2022Revised:24February2023Accepted:28March2023EnergyConversionandEconomicsDOI:10.1049/enc2.12088REVIEWAnanalysisofdistributionplanningunderaregulatoryregime:AnintegratedframeworkAprajayVermaKShantiSwarupDepartmentofElectricalEngineering,IndianAbstractInstituteofTechnologyMadras,Chennai,Distributionsystemplanningisamultifacetedtopicinvolvingfinancial,regulatory,andTamilnadu,Indiasystemlevelanalysis.Thewidenatureofthetopicwarrantsaholisticstudyconsideringallaspectsofanalysis.ThedistributionutilityisanaturalmonopolythatissubjectedtoutilityCorrespondenceregulation.TheregulatorcanimpactcustomerexperiencebystrategicallyinfluencingtheAprajayVerma,DepartmentofElectricalplanningdecisionsoftheutility.Hence,thispaperreviewstheexistingutilityregulationEngineering,IndianInstituteofTechnologyMadras,methodsinthecontextofthedistributionsystemandtheirefficacyinimprovingcertainChennai,Tamilnadu,India.reliabilityandefficiencyobjectives.Atwo-bussystemisusedtodemonstratetheimpactEmail:ee16d210@smail.iitm.acinofclassicalmodelsinalleviatingreliabilityandefficiencyissuesthroughdemandresponse.Further,areviewisconductedondistributionsystemplanningmodelswithoutaregulatoryregime,andsuitablemodelsforholisticanalysisareidentified.Atwo-personcompleteinformationregulatorandutilitygamewithacomprehensivedistributionsystemmodelatthelowerlevelisproposed.AframeworkbasedontheMixedIntegerBilevelLinearProgram(MIBLP)isdiscussedtofindtheequilibriumpointoftheproposedgame.KEYWORDSenergyeconomics,investmentandplanning,operationandoptimization1INTRODUCTIONtricity;therefore,theutilityhastoconductnetworkexpansionplanningtocatertofuturedemand.TheutilitycanadoptnewThedistributionsystemistheweakestlinktoapowersystemtechnologywhileservicingtherequireddemandtomaximizeastheyareamajorsourceofcustomerserviceinterruptions;profit.However,theregulatorexercisessomecontrolovertheaccordingto[1],92%ofconsumerinterruptionsintheUSrevenueofDNO.Theamountofrevenuethattheregulatorcancanbetracedbacktoafailureinthedistributionsystem.Theallowtheutilitytocollectdependsontheutility’sinvestmentconsumersconnectedwithMVandLVareusuallysmallscaleplan.Iftheregulator’sbehavioristransparent,theutilitycanconsumerswho,ontheirown,don’thaveanymarketpower.manageitsnetworkinvestmentbasedonthepredictedregu-Sincethefixedcostinvestmentinthedistributionnetworkislator’sreactiontotheinvestment.Beforearatehearingutilityhigh,andtheaveragecostdecreaseswitheachcustomer,theproposesitsinvestmentplan,basedonwhichtheregulatorsetsdistributionnetworkisoperatedasaregulatedmonopoly.DNOtherateforthenextregulatoryhearing.Hence,theregulatorcanmisuseitspositionofmonopolyonsuchconsumers.Henceandutilitymodelsmustinculcateeachother’sreactionswhileappropriateregulationmechanismsarerequiredtoarbitratedecidingrespectiveactions,formingaregulator-utilitygame.onbehalfofconsumerswhilebeingfairtoDNO.IncasestheThistwo-persongameistermedintegrateddistributionplan-retailhasbeenderegulated,thephysicalnetworkisstillownedning.Theframeworkforintegrateddistributionplanningcanbyasingleentity[2].Usually,theregulatorobligatestheDNObeseeninFigure1.Suchastudywouldhelpstrengthenthetoincreaseitsconsumerbasetoensuretheaccessibilityofelec-distributionsystemtoadaptnewtechnologies.ThisisanopenaccessarticleunderthetermsoftheCreativeCommonsAttribution-NonCommercial-NoDerivsLicense,whichpermitsuseanddistributioninanymedium,providedtheoriginalworkisproperlycited,theuseisnon-commercialandnomodificationsoradaptationsaremade.©2023TheAuthors.EnergyConversionandEconomicspublishedbyJohnWiley&SonsLtdonbehalfofTheInstitutionofEngineeringandTechnologyandtheStateGridEconomic&TechnologicalResearchInstituteCo.,Ltd.EnergyConvers.Econ.2023;4:179–201.wileyonlinelibrary.com/iet-ece179180VERMAANDSWARUPDecisionVariablesInformationVariablesThemaincontributionofpaperare:Network/CustomersRegulatorWillingness1.ThepaperreviewstheexistingliteratureonutilityregulationtoPayReliabilityinthecontextofdistributionsystem.MaximizesTotalTechnicalEfficiencySurplusPerformance2.TheroleofeachregulatorymodelisdemonstratingformetricsimprovingreliabilityandenergyefficiencybytakingatwoPriceInvestmentbussystem;timevaryingfailureratesoflineandtransformerDecisionCostwereconsideredtomodeltheimpactofaging.StructureUtility3.Toconductaholisticanalysis,theregulatoranddistribu-PerformancetionutilitymodelsmustbeshuntedtogetherasaMIBLPMaximizesmetricsframeworkwasdiscussedtosolvesuchagame.ProfitPrice4.AbranchandboundmethodisdiscussedtosolvetheMIBLPmodel.FIGURE1Frameworkforintegrateddistributionplanning.1.2UtilityregulationacrosstheworldTABLE1RegulatorymodelsusedbyEuropeancountries.TheregulatoryexperiencevariesacrossdifferentregionsacrossSnoRegulatorymodelsCountrytheworld.Theregimemayvarybasedoneconomicconditions.TheutilityregulationinNorthAmericafollowsahierarchical1CostplusBelgiumstructure[7],acentralauthorityoverseestheinterstateelec-tricitytransferandlargescalegeneration.Inmostcases,the2IncentivebasedCzechRepublic,France,Germany,statehaspreemptiveauthorityoverlocalgovernments.TheUSTheNetherlandselectricitymarketstructuredoesnotfollowaunifiedapproach.Duetothediscretionarypowerofeachsinglestatelegisla-3Revenue/price-/incomecapPoland,Romania,Slovakia,tor,thereisawidespectrumofregulatorymodels.AsimilarhierarchicalstructureisimplementedinIndia,whereaCERCSweden,TurkeyandaSERCareresponsibleforsettingratesandensuringeffi-cientelectricitymarketoperations.Thedistributionsectorin4CombinationofmodelsFinland,Greece,Italy,Spain,Indiahasbeenanachillesheelofthepowersector,consis-Switzerland,TheUKtentlymakingsignificantlosses(estimatedatRs90,000cr.forFY21)[8,9],institutionalsmartnesslikehigh-qualityregu-1.1Motivationlationmayalleviatesomeoftheweaknessinoperationandinfrastructure.Inliterature,hitherto,theregulatorymodelsanddistributionplanningmodelsaredevelopedindependently,therecontin-InLatinAmerica,usually,acentralregulatorcontrolstheuestobedisconnectbetweenregulatorymechanisms,whichrate-settingaspects.Asophisticatedregulatorytoollikeincen-aredesignedbyeconomistsandnetworkengineersfocusedtiveregulationwerefirstimplementedinChile[10].Theutility’sonphysicalcomplexitiesofelectricpowersystem[3].Hence,profitsincreasedtoasmuchas35%duetotheconsumersanintegratedstudyisrequiredtocapturetheimpactsofnotbeingproperlyinformedofthelowercostofelectricityregulatorypoliciesondistributionnetworkstoquantifytheprocurementduetomarketefficiencyinthewholesalemar-impactofpoliciesoncustomerexperience.Thispaperpro-ket.ThecostofpurchasingelectricityfromGENCOSandvidesamathematicalframeworkcombiningexistingregulatorythevalueaddedofdistributionarethetwomainfactorsthatanddistributionplanningmodels.[4]proposesaframeworkmakeupthepriceofelectricity(VAD).TheVADistypicallytoconductsuchananalysisforrevenuecapregulationandestablishedtoattainaspecifiedrateofreturnforadistributionPBR,whereas[5]proposesaframeworktoconductdistribu-companythatisseentobeconceptuallyefficient.Thepricetionplanningconsideringyardstickregulation.However,thecapapproach,sometimescalledRPI-X,limitstariffincreasesliteraturedoesnotconsideranextensivedistributionmodelbyusingacapthatchangesfollowingpriceinflationlessanXatlowerlevel.Theintegrationofmodernopenaccessbasedfactorthatrepresentsanex-anteestimateoffutureefficiencyconceptsliketransactiveenergyrequireupgradationoftheincreases.communicationandphysicallayerofthedistributionnetwork.ThecurrentframeworkcanbeusedtolayablueprintforaInEurope,theCEERcoordinatesbetweeninter-countryutilityandregulatortoaddmorefeaturesandenablemod-transmissionlinesandregulatesvariousindependentregulatorsernpeer-to-peertransactionsinthedistributionnetworktoforeachcountry.Table1depictstheregulatorymodelsusedbysupportthepenetrationofEVandrenewableenergyoveraeachcountry.fixedtimehorizon[6].Hence,thispaperprovidesanextensivemathematicalformulationofalltheregulatormodelsconsider-Regulatorsallacrosstheglobearefocusedoncreatingingextensivedistributionplanningformulationinlowerlevel.avenuesforutilitiestoinnovateandimplementlatesttechnolo-ThepaperalsoprovidesanMIBLPbasedframeworktosolvegies,bymimickingcompetitiontocreateadistributionsmartthebi-levelmodelwithintegervariablesinboththelevels.gridthatcanmeetsustainabilitygoals.Theproposedframeworkcantestthemodernincentivebasedregulatoryfortheirefficacyinmeetingdesiredcommunitygoals.VERMAANDSWARUP181TABLE2Transformercharacteristicsofvariousalternatives.TABLE3Linecharacteristicsofvariousalternatives.SnoParameterAlternative1Alternative2Alternative3SnoParameterAlternative1Alternative2Alternative31Resistance(p.u.)0.000670.000350.000431Resistance(p.u.)0.00220.00160.00180.00060.00070.00160.00182Reactance(p.u.)0.001215122Reactance(p.u.)0.002210109500007000000.450.323Rating(MVA)7.50.050.023Rating(MVA)10203218021029870191404Investmentcost($)500000224Failurerate(Kl0)(occ/year)0.411151510105Failurerate(Kt0r)0.15Repairtime(𝜏rlep)(min)306Repairtime(𝜏rtrep)(min)2406Investmentcost($)150207Gamma(𝛾tr)27Gamma(𝛾l)18Life(years)(𝛽tr)158Life(years)(𝛽l)101.3CriteriaofselectionforliteratureFIGURE2Failureratewithage.GoogleScholarwastheprimarysurveytool;papersfromIEEE,FIGURE3Twobussystem.JSTOR,Elsevier,Springer,Wiley,andTaylorandFranciswereselected.Literatureondistributionsystemregulationwascol-lineandtransformerwereassumedtobedependentonageaslectedandcategorizedintoempiricalandtheoreticalworks;showninFigure2andFigure3.moreover,sometechnicalreportsofwellknownutilitiesandregulatoryauthoritieswerealsoincludedtocoverimplementa-2.1.2Systemcharacteristicstions.Theclassicalpapersdefiningthetheorybehindregulatorymodelsareincluded,andempiricalevidenceisdrawnfromThesystemcharacteristicsareshowninTable4,whereastheworksinthe21stcentury;empiricalanalysesbeforethe21stdemandresponseandcostvariationduringthedayisassumedcenturywererejected.DistributionsystemplanningliteraturetofollowcurvesinFigures4and5,respectively.wassearched,andliteraturepertainingtooptimalplacementsofcomponentsinthenetworkwasalsoincluded.Theclassical2.2Costofserviceregulationpapersregardingdistributionplanningarecited,andrecentcasestudiesbasedonpapersdoneaftertheyear2000areincluded.ThecostofserviceregulationistheoldestformofutilityTherestofthepaperisdividedasfollows:Section2discussesregulation.Theregulationlimitstheutility’sprofittoafixedclassicalregulatorymodels,andabilevelmodelisconstructedpercentageofservicecost(ratebase).Themodelwasanalyzedfortwobussystemforeachmodelusingsampledata.Section3in[11],andthemodelsolvedforthequantityaregulatedfirmdiscussestheliteratureonthedistributionplanningmodelinwouldproduceunderCOSRconstraints.detail.Section4proposestheframeworkofintegrateddistribu-tionplanning,andliteraturepertainingtoalgorithmsforsolvingMIBLPisdiscussed.2REGULATORYMODELSTheregulatorymodelsfallintofollowingcategories:-1.CostofServiceRegulation(COSR)2.PriceCapRegulation(RPI-X)3.RevenueSharingandProfitSharing4.ServiceQualityRegulation2.1Datausedforillustration2.1.1LineandtransformercharacteristicsThelinecharacteristicsareshowninTable3,andtransformercharacteristicsareshowninTable2.Thefailurerateofthe182VERMAANDSWARUPFIGURE6Consumersurpluswithaninversedemandcurve.TABLE4Systemparameters.SnoParametersValue1Cost(Cbase)($/MWh)2662Activeload(MW)3.620003Reactiveload(MVar)74(Valueoflostload)VOLL10($/Mw-min)7Alternative15Ageofline(𝜒l)(years)Alternative36.5-p6Ageoftransformer(𝜒tr)52(years)e7Regulatoryperiod(years)(h)2e8Currentline7000009Currenttransformer1.814e(990.7)∗20000−1.24∗10−4∗I210DemandcurveQ(p)(MW)70000011DSMinvestment($)12DSMpeakshaving(MW)13DSMrecovery($)14VOLLinvestment($)15DSMinvestmentcap($)(e)FIGURE7MinimumInvestmenttomaintainfirmprofitabilityincomparisontoadjustmentfactor.utility’sprofitbys%ofrevenue.∞maximizeU=∫Q(p′)dp′+(pQ(p)−c2Q(p)−I),(1a)FIGURE4Demandusedforillustration.pFIGURE5Costofpurchasingelectricityusedforillustration.p2.2.1Mathematicalmodels.t.pQ(p)−c2Q(p)−I≤spQ(p),(1b)Theregulatormaximizessocialwelfare,whichisthesumofcon-p≥0.(1c)sumersurplusasshowninFigure6andFigure7andutility’sprofitandisrepresentedin(1a).Theconstraint(1b)limitstheTheutilitymaximizesitprofit,whichisevaluatedasdiffer-encebetweentotalutilityrevenueandinvestmentandfollows(2a)–(2c).maximize(pQ(p)−c2Q(p)−I),I(2a)s.t.I≤K,(2b)I≥0.(2c)Asmentionedearlier,themodelingoftheregulatorisknowntotheutility,andthefinancingandinvestmentdecisionsoftheutilityareknowntotheregulator.Hence,bothagentswouldmaximizetheirownutilityfunctiongiventhebehaviorofanotheragent.ThisphenomenoncanberepresentedasaVERMAANDSWARUP183two-personStackelberggame,whichcanbeformulatedasaTABLE5Profitandpricefordifferentinvestmentlevels.bileveloptimization(3a)–(3e).Sno1Investment($)Profit($)Price($)230.7∞500,000952927.7632.30950,000998182.83maximizeQ(p′)dp′+(pQ(p)−c2Q(p)−I),(3a)∫pps.t.pQ(p)−c2Q(p)−I≤spQ(p),(3b)transformersfromyearswithconstantandexponentialfailurerates.maximizepQ(p)−c2Q(p)−I,I(3c)𝜏′=∑h−𝜒lI≤K∶𝜇,(3d)𝜏average=(𝛽l−𝜒l)∗K0l∗𝜏rlep+𝜏′=1K0le𝜏′𝛾l𝜏rlep+I≥0∶𝜇.(3e)(𝛽tr−𝜒tr)∗K0tr∗𝜏rtrep+𝜏′=∑h−𝜒trK0tre𝜏′𝛾tr𝜏rtrep,(5)(∑𝜏=4𝜏′=1)Since,thelowerlevelproblemislinearinI,wecanreplaceitby𝜏average=3∗0.4∗30+0.4e𝜏∗30+5∗0.1∗240+equivalentKKTconditions.𝜏=1∞(∑𝜏=2)maximize∫Q(p′)dp′+(pQ(p)−c2Q(p)−I),(4a)0.1∗e2𝜏∗240(6)p,𝜇,I𝜏=1ps.t.pQ(p)−c2Q(p)−I≤spQ(p),(4b)𝜏average=2660minTheaveragefailuredurationinthesystemwhentheutility(pQ(p)−c2Q(p)−I)=𝜇K,(4c)decidestoreplacethetransformerwithinvestmentalternative1attheendoflifefortheincumbentis(7).𝜇≥0,(4d)(∑𝜏=4)𝜏aKverage=3∗0.4∗30+0.4∗e𝜏∗30+7∗0.1∗240p≥0,(4e)𝜏=1(7)I≤K,(4f)𝜏akv1erage=1200min𝜇≥0.(4g)Theaveragedurationoffailureinthesystemwhentheutilitydecidestoreplacethetransformerwithinvestmentalternative2attheendoflifeis(8).Byusingcomplementaryconditionsatlowerlevel0≤𝜇⟂∑𝜏=4(I−K)≥0,itcanbeprovedthroughenumerationthatI=K𝜏akv1erage=4∗0.4∗30+0.4∗30∗e𝜏+5∗0.1∗240attheoptimumpoint.Hence,theutilitywillinvestthemaximumamount,irrespectiveofcustomerrequirements.Thisregulation𝜏=1wasmostpopularduringthe1980s,asitincentivizedutilitytoincreaseitscustomerbase,introducingelectricalsupplytomore+2∗0.05∗180(8)areas.However,thisregulationalsopromoteswastefulexpendi-turesandinflatesthepriceofelectricity,asdemonstratedinthe𝜏akv2erage=1181mintwobusexamplesforanincreaseinreliability.However,whenthemodel(4a)–(4g)issolvedforK=500,000$2.2.2Increaseinreliabilityand950,000$asshowninTable5,thepriceofelectricityforcustomersishigherforrelativelymarginalimprovementinqual-Theaveragedurationoffailureinthesystemisgivenby(5)asityofsupplyduetoutility’sproclivitytowardscostlyfixedcostshownin[12].Thefirstsummandof(6)representsthecontri-investmentcorroboratingwiththeclaimthatCOSRpromotesbutionoffailuresofthelinefromyearswherethefailureratewastefulexpendituresfromtheutility.wasconstantasinFigure2.Thesecondsummandrepresentsthecontributionoffailuresofthelinefromyearswherethefail-2.2.3Demandresponseurerateincreasedexponentiallywithtime.Similarly,thethirdandfourthsummandsrepresentthecontributionoffailuresofIftheutilitywantstoreducethecostofpurchasingelectric-ityfromthegridbyreducingthepeakload,thenthedemandresponsecanbeimplementedbyinvestinginsmartmeters.The184VERMAANDSWARUPinvestmentinsmartmetersiscappedate.ThebilevelmodelOnlysolutionthatispossibleis𝜇=0.854.Fromthecomple-(9a)–(9f)modelsratepricesetting,asshownbyTable4,theinvestmentindemandresponseereducedthecostofsupplymentaryconditione=0.□by0.854e.Hence,irrespectiveofpricep,e=0.Theratebaseofthe⎛∞⎞utilityisdecreasedbyimplementingenergyefficiencyschemes.⎜Q(p′)dp′⎟Sinceprofitisproportionaltotheratebase,theutilitywillnotmaximize⎜∫⎟+pQ(p)−c2Q(p)+0.854e(9a)investindemandresponse.Thecritiqueofcostofservicereg-ulationhasbeenwelldocumentedintheliterature[13].Incasesp⎝p⎠theutilityraisescapitalthroughdebt,thecostofservicereg-ulationisindirectlyimplementedifthecosttothecustomers.t.forutilitybankruptcyishigh.Theregulator,inthiscase,wouldhavetoensurethatutilityprofitsremainhigherthantheface(1−s)pQ(p)−c2Q(p)+0.854e≤0,(9b)valueofdebts.Hencecapitalcostisreflectedasdebt[14].More-over,theratesettingprocesscanberepresentedasaNashp≤p,(9c)equilibriumproblembetweencustomersandclaimholders.ThepricemarkupfrommarginalcostinCOSRisinverselypropor-maximizepQ(p)−c2Q(p)+0.854e,e(9d)tionaltodemandelasticity.Thisisalsocalledthesecondbestprice,orRameseypricing[15].Iftheregulatorisnothavinge≤e∶𝜇,(9e)completeinformationonthecostofthepowerprocurementfromtheutility,thenthestackelberggametransformsintoae≥0∶𝜇.(9f)Bayesiangameasin[16].TheBayesianincentivesareimprac-ticaltowardsdirectimplementation;however,theinsightsfromReplacinglowerlevelproblemwithKKTconditions,primaltheirpropertiescanbecombinedwithapracticalnon-Bayesianfeasibilityanddualfeasibilityconstraints.mechanismfortransmissionpricing[17].Therecanbeanincen-tivefortheutilitytodistortforecastedrevenuetomaximize⎛∞⎞theprofit.Toalleviatethisissue,IQIwasusedintroducedby⎜Q(p′)dp′⎟OFGEM.InformationQualityIncentivesisamechanismformaximize⎜∫⎟+pQ(p)−c2Q(p)+0.854e,(10a)settingpricecontrolallowancesusedbyOFGEMthatpro-videsex-anteincentivesforDNOstosubmitaccurateforecastsp⎝p⎠oftheirexpectedexpenditureandprovidesincentivesforeffi-ciencyimprovementsoncethepricecontrolhasbeenset.Thiss.t.(1−s)pQ(p)−c2Q(p)+0.854e≤0,(10b)encouragesutilitiestoproducehighqualityandwelljustifiedbusinessplans[18].p≤p,(10c)pQ(p)−c2Q(p)+0.854e=𝜇∗e,(10d)𝜇−𝜇+0.854=0,(10e)e≤e,(10f)2.3Pricecapregulatione≥0,(10g)AsopposedtotheCOSR,thepricecapregulationcontrolstheupperlimitofthepriceutilitycanchargetocustomers.Athe-𝜇≥0,(10h)oreticalmodelofpricecapregulationwasproposedin[19].Theregulatorsetsanupperlimitonthepricethattheutility𝜇≥0.(10i)canchargethecustomer.Thereforeutilitycanappropriatecostsavingsuntilthenextratecase.2.3.1MathematicalmodelLemma1.Inmodel(9a)–(9f),e=0∀pinfeasibilitysetProof.Duetocomplementaryconditiononlyoneofthe𝜇,𝜇LetautilitywithmarginalcostC(0)reduceitsmarginalcostcanbenonzero.Fromequation10d,10hand10i.byinvestingeandwithmarginalcostC(e).AssumingΔisthe𝜇−𝜇+0.854=0,(11)lagbetweentheinvestmenttimeandwhenthecostreduction𝜇≥0,(12)occurs.TheregulatorsetsaninitialpricecapP0,andanadjust-mentxtakesplaceattimeΔ,withthepricecapatΔbeingP0−x.Iftheutilityprofitisnegative,theutilitymaydemandaratecase,andtheregulatorwillhavetosetaratesuchthattheutilitymakeszeroprofit.Thepricesetbytheregulatoris(14).𝜇≥0.(13)B(P0−x,C)=max{C,P0−x}.(14)VERMAANDSWARUP185Theratesettingprocesscanbedescribedas(15a)–(15g),thex≥x,(16c)(15a)–(15b)isregulator’smodeland(15d)–(15g)utility’sprofit.(16d)The(15a)includesVOLLaswell,whichisafunctionofI.max𝜋(e)=−[P∗]∗(6.5−P∗)∗61320+P∗maxixmize∫Q(p′)dp′+VOLL(I)+P∗∗Q(P∗)e52−∞(P∗)−C(e)∗Q(P∗)−e(15a)1594320∗6.5−52+I−0.815e,e≤e∶𝜇e,(16e)s.t.(15b)−e≤0∶𝜇,(16f)x≥x,(16g)emax𝜋(P∗,e)=[B(P∗,C(e))]Q(B(P∗,C(e)))−e,(15c)(15d)I≤I∶𝜇I,P∗,eI≥0∶𝜇,(16h)P∗≤P0−x,e≤e,(15e)P∗≤P0−x∶𝛽,(16i)−e≤0,(15f)P∗≥0∶𝛽.(16j)P∗≥0.(15g)ThelowerlevelproblemcanbereplacedbyitsequivalentKKTconditions;thelowerlevelformulationisquadratic,andstrongTakingtwobusexamples,assumingP0−xisbinding.dualitywillresultinnon-convexequality.Hence,thelowerlevelisreplacedbycomplementarityconditions,whichcanbesolvedeitherbybranchandboundmethod[20],orbyFortunyMccarlmethod[21].2.3.2InvestmentinreliabilityanddemandP∗(p′)responseConsideringthevalueoflostloadreliabilityinthecon-maxixmize∫6.5−∗61320dp′−(990.7∗20000sumersurplus,thebilevelmodelconsideringreliabilityand52demandresponseinvestmentis(16a)–(16j).Themodelrepre-sentstheRPI-Xforatwo-bussystemwithdatasubstitutedfrom−∞Tables2–4.Theregulatordecidestheadjustmentfactorx,thatallowsthesavingsmadeduetoinvestmenttobepassedonto−1.24∗10−4∗I2)+(P∗)∗(6.5−P∗)∗61320−customeraswell.52(P∗)1594320∗6.5−52−I+0.815e,(17a)P∗(p′)maxixmize∫6.5−∗61320dp′−(990.7∗20000−s.t.52[P∗]∗(6.5−P∗)∗61320−1594320∗(6.5−P∗)−I+−∞1.24∗10−4∗I2)+(P∗)∗(6.5−P∗)∗613205252520.815e≥0,(17b)(P∗)−1594320∗6.5−52−I+0.815e,(16a)x≥x,(17c)s.t.2P∗∗61320−1594320+𝛽−𝛽−6.5∗61320=0,(17d)(P∗)∗(6.5−P∗)∗61320−1594320∗(6.5−P∗)−I52525252+0.815e≥0,(16b)1+𝜇I−𝜇I=0,(17e)186VERMAANDSWARUP−0.815+𝜇e−𝜇e=0,(17f)TABLE6ClassificationofmethodsforbenchmarkingofXfactor.0≤𝜇I⟂(I−I)≤0,(17g)0≤𝛽⟂(P∗−P0+x)≤0,(17h)SnoBenchmarkingMethodLiterature1Dataenvelopmentanalysis(DEA)[38–47]2Stochasticfrontieranalysis(SFA)[28,31,35,41,43,47–50]3Conditionalordinarylinearsquares(COLS)[43,51]0≤𝜇⟂(−I)≤0,(17i)2.4RevenuesharingI0≤𝛽⟂(−P∗)≤0,(17j)Revenuesharingisanotherformofyardstickregulation;theutilityhastoshareaportionofrevenueasaconsumerdivi-0≤𝜇e⟂(e−e)≤0,(17k)dendbeyondaparticularbenchmarkrevenue.Asutilityisstillallowedtokeepsomepartofexcessrevenue,ithasanincentive0≤𝜇⟂(−e)≤0.(17l)toreducethecostofsupplybyinvestinginthenetwork.More-eover,theutilitiesmightbelessinterestedinlobbyingforhigherpricesasshownthroughmodel(18a)–(18g)whichisbasedonIfthemodelissolvedforP0suchthatutilityprofitissetat[25].The𝜋andRisbenchmarkprofitandrevenue,the(18e)10%ofitstotalrevenue,theoptimalinvestmentinreliabilityincludestermsminimizingtheexcessrevenuetheutilityhastois0,evenwithxas0.Itexposesthedrawbackofthisregu-sharewithcustomer.latorymethodasreliabilityimprovementsforcustomersmightnottranslatetohigherreturnsforutility.∞(p′)Ifthetransformedmodel(17a)–(17l)solved.Itisdemon-Maximize∫6.5−∗61320dp′−stratedthatthehighertheadjustmentfactor,themore52investmenttheutilityisforcedtomaketheirventureprofitable.pHowever,iftheadjustmentfactoristoohigh,theutilitywillnotmakeanyinvestment.Thiseffectissimilartotheproofin[19].pThepricecapregulationiscalledRPI-Xregulation,where(990.7∗20000−1.24∗10−4I2)+Xistheefficiency/adjustmentparameter.Theefficiencyfactorusuallyimpliesthatautility’saveragepriceforabasketofits(p)(p)outputsisassumedtodependonthecostofitsownactivity[22].TheanalysesfortheUKgovernmentdivulgedthatRPI-X[6.5−52∗p∗61320−1594320∗6.5−52−islessvulnerablethancostplusregulationinacontextofinef-ficiencyandover-capitalization[22].AconsequentstudywasI+0.854∗IDSM−𝜋],(18a)doneonItalyaswell[23].ATornquistindexasameasureofhistoricalproductivitygrowthofthesectororentireeconomy(p)(p)insettingtheefficiencyfactorXwasreportedin[24].Thedraw-backofpricecapregulationwasfoundin[25].Itwasproved6.5−52∗p∗61320−1594320∗6.5−52thatthepricecapregulationwithdownwardpriceflexibilitypro-videsweakincentivestoacquireinformationaboutcosts.The−I≥𝜋,(18b)regulationstyleincorporatingbenchmarkingcomesundertheumbrellaofyardstickregulation.Underyardstickregulationit(p)isalwaysoptimalforlowperformingutilitiestoinvestincostreductiontechnologiesuntiltheoperationalcostbecomesequal61320∗p∗6.5−≥R,(18c)toanaveragecostofsimilarutilities[26].Unlike,(16a)–(16e),52theX-factorisevaluatedthroughbenchmarking.Sincetheutil-(p)(p)itieshavealotofheterogeneityamongstthemselves,evaluatingafairbenchmarkisachallengingproblem[27,28].Maximize6.5−∗p∗61320−1594320∗6.5−,I5252ThebenchmarkingtechniquescanbecategorizedintoDEA,SFAandCOLSasshownintheTable6.Usually,forcost(18d)efficiencyTFPisquantifiedasMalmquistIndex[29,30]and−I+0.854∗IDSM−(1−𝛼𝜋)∗(p∗(6.5−p)∗61320−TornqvuistIndex[30,31].Apartfromtheliteraturementionedhitherto,theimplementationofRPI-Xregulationwasalsostud-52iedforBrazil[32],Ukraine[33],Sweden[34],Japan[35,36],andIndia[37].(p)1594320∗6.5−52−I−𝜋)−(1−𝛼R)∗((6.5−p)∗p∗61320−R),(18e)52I≤K∶𝜇,(18f)IDSM≤KDSM∶𝜇DSM.(18g)ThemodelcanbesolvedbyreplacinglowerlevelproblembyKKTconditionssimilarto(17a)–(17l).Theresultoftherevenuesharingisshownforπ=10000$andR=1594320$inFigure8fordifferent𝛼𝜋and𝛼R.Thelower𝛼Rpushestheregulatedpriceupasutilityisnotallowedtoappropriateexcessrevenue.Thisalsodemonstratesthatforappropriatevaluesof𝛼R,theVERMAANDSWARUP187TABLE7ProfitandInvestmentdecisionforpenaltyfactorinSQRdemonstration.SnoPenaltyfactor($/min)InvestmentDecisionProfit($)10None1.24∗106Linealternative11.20∗1062100Linealternative20.9∗106Transformeralternative11.1∗10631000Transformeralternative32.2∗1064200059900FIGURE8Regulatedpricefordifferent𝛼𝜋and𝛼R.dependingupontheutility’sperformanceintheregulatoryperiod.utilitywon’tbeincentivizedtolobbyforhigherpricesandcanalsotakesomeportionofcostsavings.Theinvestmentinrelia-(p)(p)bilityisI=0,andthedemandresponseisIDSM=KDSM.Therevenuecapregulation,likepricecapregulation,doesnotincen-maximizep6.5−∗52560−1366560∗6.5−tivizeimprovingqualityandsecurityofsupplybecauseallthexd5252extracostreducesprofit.ThiseffectwasobservedforFinnishutilitiesin[52].−I+RP,(19a)Modelingtherevenuesharingregulationforthetelecommu-RP=a∗(SAIDI−SAIDI),(19b)nicationindustrywasdone,anditwasclaimedthatearningsharingplansareemployedin(Colorado,Connecticut,Florida,I∑(19c)Georgia,Kentucky,Tennessee,andTexas)[53].ModelingtheSAIDI=Idxd,(19d)profitsharingschemeasthedynamicgamebetweenafran-(19e)chiseholderandowner,thedrawbackofrevenueregulationwasd∈Ωdstatedasprofitsharingprescriptionswouldrequireauditedcostinformationtocalculateallowableprofitlevels,whichareusu-∑allydifficultforaregulatortocollect[54].ADEAmodelwas=SAIDIdxd,usedtoevaluatetheRevenuecapfor123distributionfirmsinNorway[55].Thestudyofqualityregulationofelectricitydis-d∈ΩdtributionintheNetherlandsinferredthatarevenuecaphastheadvantageofallowingnetworkoperatorstosetindividualtariffs∑[56].xd≤1,2.5ServicequalityregulationdSincetheclassicalmethodsdiscussedhithertocannotencour-xd∈{0,1}∀d∈Ωd.(19f)ageutilitiestoimprovereliabilityeffectively,powerqualityfactorssuchasreliabilityaredirectlycoupledwiththeutil-Assumingthepricewassetapriorias30$/MWh,andSAIDIisityprofitsalongwithclassicalmodelsmorphingtheclassicalmodelintoSQR.ThePBRisthemostcommonimplementa-usedasanindex,thebenchmarkvalue,SAIDI,waskeptat1400tionofSQR[57].InPBR,theutilityispenalizedorrewardedmin.Theimpactofpenaltyfactor,a,intheutilitydecisionwasbasedonameasurableperformancemetric.TheservicequalityshowninTables7and8.Thehighvalueofthepenaltyfactorregulationalsocomesundertheumbrellaofyardstickregula-mayleadtohigherinvestmentand,consequently,betterreliabil-tion[58]sincetheservicequalityisbenchmarkedastechnicality.However,afinanciallystressedutilitywithlittlepurchasingefficiency.Hence,thepricecapregulationcanbedirectlycapacitycangetstressedevenfurther,leadingtofinancialinsol-extendedintoSQRasRPI+X+Z,whereZisthequal-vency.Ifthepenaltiesarerelaxed,therewardhastobepaidityfactordeterminedbytechnicalefficiency,andXisacostasalumpsumppaymentassubsidiesareexogenousofthefactordeterminedbycostefficiency.(19a)–(19f)modelsutilitycustomer-utilityinteraction.Hence,theregulatormustrestrictprofitmaximizationunderPBR,theRPisthereward/penaltyitspenaltyfactorthatishighenoughtonudgeutilitytoimprovewhichisdependentonSAIDI(19b).Itwasassumedthatreliabilitybutnottoohightocausemajorfinancialdistress.thepaymentcorrespondingtoZwouldbemadeex-ante,InUSPBRmaymakeuseofaslidingscalemethodwherethereisadead-bandaroundatargetrateofreturn.There-fore,theslidingscalemethodcanbeviewedasaformofaveragebenchmarking[59].[22]evaluatesthetechnicaleffi-ciencyoftheUKpowernetwork.Ex-antepaymentforqualityregulationisusedinGermany[46].Distributionplanningcon-sideringreliabilityevaluationandPBRisconductedin[60–62].Thequalityofnetworkandqualityoftheconsumedservicesaretypicallyimportantforconsumers,butnotnecessarilytothesameextent.ItwasconcludedthatregulatorsshouldsethigherincentiveratesforhigherreliabilitylevelsinsteadofafixedincentiveforastudydoneforChina[63].AfrontierbasedmethodforevaluatingNPAMforSwedishutilitieswasstudied188VERMAANDSWARUPTABLE8Comparisonofdifferentregulatorymodels.SnoAttributesCOSRPriceCapRegulationRevenueSharingServiceQualityRegulation1MainpremiseTheregulationentailslimitingTheregulatorsetsanupperTheutilityisstillallowedtoPowerqualityfactorssuchasprofitoftheutilitytoafixedlimitofpricethatutilitycankeepsomepartofexcessreliabilityaredirectlycoupledpercentageofcostofchargecustomer,thereforerevenue,ithastheincentivewithutilityprofitsandclassicalprovidingservice(rateutilitycanappropriatecosttoreducethecostofsupplymodels.base).savingsuntilthenextratebyinvestinginthenetwork.case.2AdvantagesEasiesttoimplementPromotesinvestmentinenergyAsutilityisstillallowedtoPBRhaveaddedadvantage,astheefficiencykeepsomepartofexcessperformancemetriccanberevenue,ithastheincentivechosenaprioribytheregulatortoreducethecostofsupplytonudgeutilitiesinthedirectioninvestinginthenetwork.ofsocialissues.3DrawbacksPromoteswastefulPricecapregulationwithTherevenuecapregulationRelativelyhardtoimplement.expendituresandinflatesdownwardpriceflexibilitylikepricecapregulationdothepriceofelectricity.providesweakincentivestonotincentivizeforacquireinformationaboutimprovingqualityandcosts.securityofsupplybecauseallextracostreducedprofit.4ImplementationsEarliestformofregulation,TheRPI-XwasimplementedRevenuesharingisTechnicalefficiencyoftheUKbuthavebeenphasedout.inBrazil[32],Ukraine[33],implementedin(Colorado,powernetwork,ex-anteSweden[34],Japan[35,36],Connecticut,Florida,paymentforqualityregulationisandIndia[37].Georgia,Kentucky,usedinGermany[46],afixedTennesseeandTexas)[53],incentivestudywasdoneforinNorway[55]andtheChina.AfrontierbasedmodelNetherlands[56].forevaluatingNetworkPerformanceAssessmentModel(NPAM)forSwedishutilitieswasstudiedin[64].in[64],andareferencenetworkwascreatedinthecontextofthemodel.Therearesomeotherexogenousfactorswhichcanincentiveregulation.beincorporatedintwo-persongame:-Theutilitieshaveaddedresponsibilityformaintainingenergy1.BiasedRegulator:-Theregulator’sbiastowardsthecon-efficiencyandincludingrenewableenergy.PBRhasaddedsumer’swelfareandutilitywelfarecanbemodeledbyaddingadvantage,astheperformancemetriccanbechosenaprioribyaweightingfactor.theregulatortonudgeutilitiesinthedirectionofsocialissues.However,modelingthePBRtoselectappropriateparameters𝛾∗ConsumerSurplus+(1−𝛾)∗UtilityProfit,(20)ischallengingsinceitrequiresextensivemodelingdistributionsystemplanningandreliabilityevaluation.Hence,thefollowing0≤𝛾≤1.(21)sectiondiscussestheliteraturefordistributionsystemplanning,andlateraframeworktointegratePBRregulatorymodelwithHowever,therearenoempiricalmethodsquantifying𝛾thatplanningmodelsisproposed.Theinformationabouttherev-reflectsthebias.enueforecastoftheutilitycanchangethepricethataregulator2.BayesianGame:-Incasesthetransparencybetweenutil-allowsautilitytochargethecustomer.Therate-settingprocessityandregulatorisnotthere,theycanmodeleachotherhasbeenmodeledinliteratureasatwo-persongameextensivelybyinformationsetsandaprobabilitydistributionover[65].SincethemodernregulationincludesPBRinthesurplusthosesets.However[17]mentionedBayesianincentivesareformulationofaregulator,theutilityhastoincludethedis-impracticalfordirectimplementation,theinsightsfromtheirtributionplanningandoperationmodelinitsformulationtopropertiescanbecombinedwithpracticalnon-bayesianevaluatethevalueofrelevantperformancemetrics.Compari-mechanisms.sonofdifferentregulatorymodelsisprovidedinTable8.Theauthorsagreethereareotherstakeholdersengagedinthisdis-3DISTRIBUTIONSYSTEMPLANNINGtributionplanningprocess.Theequilibriumpointsobtainedbythetwo-playergamecanbeusedtotestvariousregulatorypol-Theclassificationofliteraturefordistributionplanningisshownicyhypotheses;eventhoughtheactualquantitiesmaychangeinFigure9.fromtheoneusedinthemodel,thequalitativeresultregardingtheregulatorypolicywillstillremaintrue.Forexample,COSRmodel(3a)–(3e)willdemonstratethepropensityofpolicytopromotewastefulexpenditureirrespectiveofquantitiesusedinVERMAANDSWARUP189[98][130][141][185][147,134][72][98][141][121][178][233][232][141][178][78][104][234][131][158][93][231][81][174][177][139][202][160][131]73[104][78][230][91][235][132][181][87][105][171][97][168][101][169][141][142]FIGURE9Classificationofliteratureindistributionsystemplanning.3.1Classificationaccordingtouncertaintymentcostcanbemanagedbychance-constrainedoptimization,handlingallowingtheconstraintstobeviolatedwithsometoleranceprobability.Sincethevariablessuchasloadgrowth,solarirradiationandwind-speedcanbeperceivedasrandomvariablesandhenceare3.2Classificationaccordingtoformulationtoberepresentedbyvariousuncertaintymodelingtechniques,structurethesetechniquesaredividedintotwoparts:1)UncertaintySet2)Scenarioformation.Theuncertaintysetmodelsrandomvari-Thestructureofanoptimizationproblemoftendecidestheablesastherangeofvalues,andtheoptimizationproblemsolverandguaranteesoptimality.Intheliterature,thesolutionisusuallysolvedfortheworstpossibleresult.Thistechniquemethodologyisclassifiedandorderedaccordingtotheeaseofgettingtheworstpossibleresultisalsoknownasrobustofsolvingasfollows:i)LP,ii)MILP,iii)MISOCP,andiv)optimization.Thismethoddoesnotrequiretheprobabilitydis-MINLP.LPisthemostsoughtafterformulationasithasthetributionfunctionofaninputvariable.Thescenariosrepresentmostreliablesolvers.However,thedistributionsystemplanningthespecificpointsoftherandomvariable,witheachpointhav-problemusuallyhasACOPF,whichisanon-linearproblem.ingaprobabilityassignedtoit.ThismethodalsoincorporatesHence,anapproximationorrelaxationisrequiredtoconvertIPF[66]thatusesaffinearithmetictosolvepowerflowequa-theproblemintoLP.First,suchapproximationwasproposedtions.Thescenarioscanbecreatedbythefollowingmethods:1)in[71]tosolvetheoptimalplacementofthecapacitor.How-HMM[67];2)2mPEM[68];3)FuzzyC-Means[69];4)k-meansever,sinceequipmentplacementisitselfanintegervariable,[70];and5)PDFDiscretization.TheHeuristicMomentMatch-linearprogrammingcansolveonlythesizingpartoftheprob-ing,orHMM,generatesscenariosbydecomposingthejointlem.TheMILPcanmodeltheplacementofequipmentbydistributionintomultivariateproblemsintounivariateones.anintegerproblem.TheMILPdoesnotguaranteeoptimal-The2mPEMgenerates2mpointsandtheirweightstogen-ity;however,commerciallyavailablesolverslikeCPLEXcaneratethemomentsoftheoutputvariable.The2mPEMcangivereliablesolutions.Thenon-convexpartofACOPFcanalsobeusedtogenerateacompleteprobabilitydistributionbelinearizedbyasimilarmethodin[72]andcansufferfromoftherandomvariable.FuzzyC-meansandk-meansareboththesameflawsofapproximation.However,adifferentdis-clusteringtechniquesusedtofindthemosttypicalpointdenot-cretizationbasedapproximationwithintegervariablescanbeingascenariowiththeirprobability.ThePDFdiscretizationconstructedasin[73],whichistighterthanlinearprogramming.involvescalculatingtheareaunderacontinuousprobabilitydis-TheMISOCPusestherelaxationproposedin[74,75],thenon-tributioncurvetoevaluatetheprobabilityofvariousintervalsconvexpartofACOPFisrelaxedbyasecondorderconebyofarandomvariable.Inextremescenarios,thehighinvest-190VERMAANDSWARUPrelaxingpowerflowinbranchconstraint,theplacementisstillrequiredtosupplyfutureloads.Inthecaseofmulti-stageopti-modeledasanintegervariable.Insomecases,duetoadditionalmization,theinvestmentsaremadeacrossdifferentstages,timeconstraints,noneoftherelaxations/approximationsmentionedstepsinplanninghorizonstocompareamongvariousinvest-hithertosuffices.Inthosecases,metaheuristicalgorithmslikementoptionsandtoweighthefutureoperationcosts;reliabilityGA[76–86],PSO[87–94],orothernon-linearsolverslikecosts;andoperationandmaintenancecosts,theNPVisusedinIPOPTcanbeusedtosolvetheproblem.Thelevelofdetail[5,76,78–80,91,95,102–112].TheNPVtakesthedifferenceandtightnessofthemodelusuallyfollowsanoppositepatternbetweenthepresentvalueofcashflows,andthepresentvalueofeaseofsolving.ofcashoutflowsin(23).3.3Inclusionbasedonreliabilityconstraints∑Cti∑CtoNPV=(1+r)t−(1+r)t.(23)Sinceindistributionplanning,theDISCOMShavetomain-tainacertainreliabilitystandard.Theproblemofreplacingttobsoletefeedersandtransformerswithnewequipmentcanalsoberationalizedasadecisioninpursuitofobtainingbet-TheNetPresentvaluewasfurtherclassifiedintothefollow-terreliabilityforthesystem.Thereliabilityevaluationisdoneingcategoriesi)TheNetpresentvalueofexpansion(TPV)ii)bysolvingtheunderlyingfinitestateMarkovchain.Anempir-Netpresentvalueofmaintenance(MPV)iii)NetpresentvalueicalformulaforSAIDIisproposedin[95].However,Supposeofoperation(OPV)iv)LoadSheddingPresentValue(LSPV).thedistributionsystemisbeingoperatedradiallywithasin-glesupplypoint.Inthatcase,theaveragefailureprobabilityIRRwasmaximizedin[104].IRRistherateofreturnwhenoffeederscanbeevaluatedbyjustsummingtheaveragefail-NPVbecomeszero.TheIRRisusediftheinvestorshavetoureprobabilityofallupstreamcomponents[96,97],thereforeestablishiftherateofreturnismorethantheMARR.Hence,representingreliabilitymetricsasalinearequation.However,theutilitycandiscardanexpansionplanifIRR<MARR.aMILPbasedformulationtoevaluateEENSandSAIFI’sreliabilityindicesinbi-directionalpowerflowisproposedAnothermetric,BCRwasusedin[96,113].Thebenefitcostin[98,99].ratiogivestheratioofpresentvaluesofcashoutflowsandinvestmentdecisions.3.4Inclusionbasedonradialityconstraints3.6ClassificationbasedondevicesThedistributionsystemusuallyoperatesinradialmode;sinceinThedistributionsystemplanningcansolveinvestmentdecisionsdistributionsystemplanning,thenetworktopologyisconstantlyofanycomponentthatcanalleviatetheincreasingdemand.Pre-evolving,andnewfeedersareaddedtotheplanninghorizon,itdominantly,thedevicesarecategorizedintothefollowingparts:becomesimperativetoimposetheradialityconstraintsinthe(i)FeederAddition/Replacement,(ii)SubstationPlanning,(iii)optimizationproblem.TheradialtopologycorrespondstotheDistributedGeneration,(iv)EnergyStorage(v)ElectricVehi-tree.NecessaryandsufficientconditionforagraphGwithnbcles.TheliteraturediscussinganyoneofthecategoriesisgivenverticesandneedgesisinTable10.TheincreaseininterestinplanningdistributedGeneration,energystorage,andelectricvehiclescanbeseenne=nb−1,(22)overtime.Aplanningproblemcantakeintoaccountmul-tipledevices.ThecorrelationisgiveninTable9.SincetheandgraphGisconnected.Inthecontextofdistributionsystemfeederaddition/upgradationisrequiredtokeepthelinelim-planning,the(22)canbetestedbyintroducingbinaryvariablesitsincheck,thesubstationplanningisrequiredtoaddnewcorrespondingtoeachbranch,whereastheconnectedconditiontransformerstomanagethesystemcapacity.TheDistributedforasinglesubstationcanbetestedbyimplementingKCLasGeneration(DG),ifcoupledwithfeederplanning,candeferin[98].Inordertotestformultiplesubstationsanddistributedtheinvestmentinnetworkinfrastructure.Thistypeofplanninggeneration,[100]proposedconditionsforradialitybyusingdualisknownas“planningwithNon-WiresAlternative(NWA)”graphs,the[101]solvestheproblembyexploitingtheproperty[211].Theco-planningofenergystoragewithdistributedGen-thatatreecanbeobtainedbytakinganyoneofthesubstationerationisusuallystudiedtoreducethedependenciesofthenodesastherootnode.distributionsystemfromimportingpowerfromthewholesalemarketbymanagingtheintermittenciesofdistributedGener-3.5Classificationbasedonfinancialmetricsation.[212]proposedaGISbasedenergystorageplanning.ItwasestablishedthatenergystorageistheeconomicallyandThefundamentalmotivationforinvestmentbyaDISCOMortechnicallymostprudentoptiontomitigatethevariablepowerDGENCOistomaximizetheanticipatedprofitthatcanbedemandcausedbyplug-inelectricvehicles.Hencerelativelymadeasaresultoftheinvestment;thiscanminimizethecosthighercorrelationcanbeseenbetweenEVswithenergystor-age.ApartfromthedevicesgiveninTable10,reactivepowermanagementdevicessuchasdistributioncapacitor[82,86,140,150,213–217],voltageregulator[81,130,185,218,219],andVERMAANDSWARUP191TABLE9Correlationininclusionofsimultaneousplacementofdevicesforplanning.EV7.5%FeederAddi-SubstationDistrib-utedEner-gy5.5%tion/ReplacementPlanningGenerationStorage2.7%15.38%FeederAddition/Replacement100%39.6%30.3%9.4%100%SubstationPlanning58.3%100%27.7%5.5%DistributedGeneration27.5%17.2%100%5.7%EnergyStorage29.4%15.38%23.07%100%ElectricVehicles66.6%33%33%33%TABLE10Theclassificationofliteratureaccordingtodevices.<20002000-20102010-presentFeederaddition/replacement/upgradation[114–118][119–123][73,76,78,79,81,82,91,95,103–105,124–149,150–155]Substationplanning[117,118,156][84,119,120,123][78,79,82,89,91,98,104,107,110,125–128,130–132,135,139,140,Distributedgeneration[117][164]144,146,157–163][72,77,79,83,87,89,90,92,96–99,102,103,107,110,112,124,126,EnergystorageElectricvehicles129,132,133,138,141,142,145,147,148,150,159,160,162,165–196][80,88,93,97,101,127,131,134,170,180,181,189,193,197–205][76,82,131,154,181,206–210]StaticVarCompensators(SVC)[82,86,90,174,202,219]arethistransformationdoesnotaddanyadditionalcomplexityalsostudied.intheformulationstructure.Iftheupperlevelproblemhasnon-linearities,itcanbediscretized.Thistransformationis4INTEGRATEDDISTRIBUTIONrelevantforintegrateddistributionplanningduetotheavail-PLANNINGabilityofmultiplealgorithmstosolvebilevelmixedintegerproblems.Intheillustrationforimplementingregulatorypolicies,a2bussystemwaschosenbecausetheplacementofequipmenttobe4.1Mixedintegerbilevellinearproblemreplacedorinstalledisnotadecisionvariableina2busnetwork.(MIBLP)This,ingeneral,isnottrue.Inaregulatoryperiod,iftheutilityoperatingunderaservicequalityregulationwantstoinstallatieMIBLPproblemsarewidelyencounteredinmultipledomainslineorreplaceanexistingline,withanyoneofthealternatives,[220].Thegeneralstructureofthebilevelproblemisgivenasinthenetwork,withanobjectivetoachievemaximumreduc-(24)-(26).TheMIBLPisacomputationallychallengingprob-tioninSAIDI,theutilitywouldhavetoincorporatedistributionlemsincethecomputationalcomplexityisintheclassofΣ2pplanningmodelwithreliabilityasexplainedinSection3.3inthehard.ThealgorithmstosolveMIBLPwheretheupperlevellowerlevel,iftheregulatoristestingthepolicyparameterstoproblemisanintegerislimited.Thefoundationforprovid-observeanimpactoncustomers,ithastocreateabilevelmodelingalgorithmsforsuchproblemwaslaidbyBM[221].Thewithdistributionplanninginlowerlevel.Thebilevelmodelisalgorithmwasbasedonenumerationandheuristics.TheBMtermedintegrateddistributionplanning.algorithmcan’tsolvetheproblemswheretheupperlevelprob-lem’sfeasibilitysetdependsonthelowerlevelvariables.ThisThedistributionsystemplanningcontainsanoperationprob-limitationisnotconducivetointegrateddistributionplanninglemembeddedinit.Theoperationproblemusuallycomprisesastheregulatorusuallymodelsthepositiveprofitconstraintoptimalpowerflowequations,whicharenon-convex.More-asshownin(16j).TheBMalgorithmwasimprovedandover,theplanningvariablesareintegers.Hence,thelowerlevelgeneralizedby[222][223]proposesanexactalgorithmthatcannotbereplacedbyitsKKTconditions.AsmentionedinalleviatessomeissuesofBMalgorithmandprovestotermi-Section3.2,thenon-convexpartcanberelaxedintocon-natecorrectlyinfiniteiterations.The[224]proposedabendersvexform.However,solvingintegerconvexatlowerlevelisdecompositionbasedalgorithmthatrepresentsthelowerlevelstillachallengingproblem.Thenon-linearityinlowerlevelprobleminfunctionalform.Thebendersdecompositionbasedcanbetransformedbystate-spacediscretizationintoMILP.methodalsohasaddedadvantageofdecomposabilityandparal-Sincetheplanningproblemalreadyhasanintegerproblem,192VERMAANDSWARUPandH𝛼besettherespectivebounds.Theadditionofcutstoimproveboundsdivulgesanewmethodproposedinliterature.Since,themodels(4a)–(4g)havebilinearterms,theyhavecanbelinearizedbyintroducingauxiliaryvariables,whichcanbecontinuousordiscretetobesolvedinMIBLPframework.FIGURE10BranchandBoundapproachforBilevelMixedInteger4.1.1ConvergenceLinearProgram.Toprovideconvergenceconditions,followingsetshavetobelelprocessing.Thebilevelproblemingeneralcanbedescribeddefined:-as1.Feasibleset,𝛾zIBLP=max{c1x+d1y∣x∈PU(y);y∈𝛾={(x,y)∶x∈PU(y)≤b1,y∈argmin{dTy∶y∈PL(x)}}.argmax{d2y∣y∈PL(x)}},(24)(27)PU(y)={x∈ℝn1−r1xℤr1∣A1x≤b1−G1y},(25)2.Highpointfeasibilityset,ΩPL(x)={y∈ℝn2−r2xℤr2∣G2y≤b2−A2x}.(26)Ω={(x,y)∶A1x+G1y≤b1;A2x+G2y≤b2}.(28)ThePL(x)isthelowerlevelfeasibilityconstraintsforafixedx,andPU(y)istheupperlevelfeasibilityconstraintsforafixed3.TheupperlevelvariablesforwhichA2≠0arecalledxL.y.Theconstraintofproblem(24)containsanoptimizationproblemembeddedinit.TheconvergenceoftheMIBLPmodeltoanoptimalpointisgivenby[225]:-Branchandboundstrategyisusuallyusedtosolvesuchaproblem.Anupperboundcanbeachievedbydropping1.xL∈ℤL.thelowerleveloptimizationconstrainty∈argmax{d2y∣y∈2.𝛾isbounded.PL(x)}.ThisrelaxedproblemiscalledtheHPP.Relevantcuts3.Ω≠𝜙areaddeduntilintegralityconditionsaresatisfied,theintegerupper-levelvariablesareusedasinputtolower-levelproblemsThefirstconditionisgenerallynottrueinthemodelstogetafeasiblesolutiontothebilevelproblem.Thefeasibledescribedabove.Hence,someupperlevelvariableshavetobesolutionoflowerlevelproblemgivesthelowerboundofthediscretized.Thenonlinearmodelscanbediscretizedintolinearproblem.Thefeasiblespaceispruned,andprocessisrepeatedmodelsusingthefollowingtechniques.untilconvergenceisachieved.ThebranchandboundmethodisshowninFigure10,wherevariable𝛼andH𝛼canbeincluded4.1.2LinearizationmethodassetofvariableswhicharerestrictedbybranchandboundThelinearizationofbilineartermscanbeclassifiedintothefollowingmethods[226]1.PiecewiseLinear:-Thepiecewiselinearapproximationofnonlineartermscanbedonebyseparableprogramming[227].Thenonlineartermisdecomposedbyfinitedif-ferencemethods.However,ifthefunctionis,non-convexseparabilityconditionsmustbeimposed.Theseparabilityconditionrequiresmodificationofthesimplexalgorithm.Inthecontextofdistributionplanning,therearenonconvextermsinbothbranchflowandbusinjectionformula-tion[228].Hence,thismethodologycannotbeappliedtointegrateddistributionplanning.However,piecewiselinearapproximationusingintegervariablesremovesthesepara-bilityconditionbyuniquenessequation.Thisallowstheprogramtobesolvedbyoff-theshelfsolversbutincreasescomputationalcomplexity.McCormickrelaxationsalsousesbinaryvariablestoconvexnonlineartermsintoconvexhullbypolyhedralsets.VERMAANDSWARUP193ThepQ(p)andothernon-lineartermsappearinginthemod-elscanbeapproximatedtopiecewiselinearfunctionsbyaddingbinaryvariables.FIGURE11Discretizationoffunction.5FUTUREWORK2.Approximationbasedmethod:-TheapproximationbasedIncludingPBRinutilityregulationtunedtomeetlargerclimatemethodinvolveslinearizingthenonlineartermaboutasin-andsocietalgoalsisachallengingproblem.Apotentialtopictoglepointbytaylorseries.Theaccuracyoflinearizationisconsideristofindquantifiableperformancemetricsthatincludeaffectedforvaluesthatdeviatefromthereferencepoint.Thebroadercommunitygoals.Themodernregulationsystemmusterrorvariesbyafactorofsquareofdistanceandmaynotpromotetheupgradationofadistributionsysteminawaythatprovideanyboundonanon-convexfunctions.couldsupportdecentralizedsystems,promotingtheintegra-tionofrenewableenergysources,electricvehicles,andflexible4.2LinearizationofnonlineartermswithloadsinLVnetworks.Whiletheeconomiesofdevelopingcoun-singlevariabletriesgrowtocreateasubstantialcustomerbaseparticipatingindecentralizedmarketsliketransactiveenergy.Moderndistribu-ThenonlineartermswithsinglevariablelikepQ(p)canbetiongridsandsustainableenergyadvancementscanberealizedinfutureregulatoryregimestomeetimmediateclimategoals.linearizedbyintroducingbinaryvalues,andpartitioningtheTheincreaseinautomationofsubstationshasmadepowergridsdomainintoNbinswithsizeΔxasshowninFigure11.Assum-morepronetocyberattacks.Hence,regulatoryauthoritiesmustincentivizeutilitiestogalvanizethesystemfromsuchattacks.ingxLandxHbethelowerandupperlimitofthedomain.TheHowever,differentiatingifanoutageiscausedbyacyberattackΔxcanbegivenasorafaultisachallengingproblem.Regulationtoimprovetheresiliencyofthesystemisalsoanupcomingtopic.ResiliencyΔx=xL−xH.(29)isdifferentfromreliabilityasresiliencyexclusivelyinvolvestheNperformanceofutilitiesinextremeweatherevents.ChoosingaresiliencymetricreflectingoverallconsumerwelfareisalsoanThenforkthbinupcomingproblem.xL(k)=xL+(k−1)∗Δx,∀k={1,…,n−1},,(30)Duetothehighproliferationofrenewableenergysources,distributionplanningmustincorporatemoresophisticatedxH(k)=xL+(k)∗Δx,∀k={1,…,n}(31)uncertaintyhandlingtechniques.Theclassicalsampleaverageapproximationdoesnothaveagoodfinitesampleguaran-LetfkLbetheevaluationoff(x)atxL(k),andfkHbetheevalua-teeandarepronetounderestimaterisk[229],whereasthetionoff(x)atxH(k).Thenpiecewiselinearapproximation̂f(x)isrobustoptimizationistooconservative;alternativetechniques,givenbysuchasdatadrivenDROcanbridgethegapbetweenstochas-ticoptimizationandrobustoptimization.Aconvextractablêf(x)=∑k=n∗f(k)+fH(k)−fL(k)∗(x−u(k)x(k))(32)DROformulationforanoptimizationproblemwithSOCPu(k)constraintsondecisionvariablesisafutureresearchdirectionk=1LxH(k)−xL(k)Lthatcanincludestate-of-the-artuncertaintytechniquesindistri-butionplanningmodels.Moreover,theadditionofupcomingu(k)∗xL(k)≤x≤u(k)∗xH(k)∀k∈{1,…n}(33)energysourceslikehydrogencombustionbasedsystemsandcouplingsuchsystemswithconventionalelectricpowerrequires∑k=nu(k)=1extensivemodelingoftheconversionprocesses.Decomposi-tionbasedstrategiessuchasADMMcanassistinmodeling(34)interconnectedbutseparatelyownedenergysystems.Consid-eringasignificantportionofenergytransactionsbetweenutilityk=1andwholesalemarketsarestilldonethroughlongtermbilat-eralcontracts,thisarrangementdiscouragesopenaccessatu(k)∈{0,1}∀k∈{1,…n}(35)thedistributionlevelsincetheutilitycan’thandleuncertaintyduetointermittentpenetration.Hence,regulatoryauthoritiesmustconstructmechanismstoincentivizeutilitiestopro-curepowerfromshorttermandspotmarket.Theregulationpoliciesandratesettingprocessaresusceptibletochangesinthepoliticalclimateofthejurisdiction.Henceprudenceofanymodelforthewelfarefunctionoftheregulatorisephemeral.194VERMAANDSWARUPTheillustrationsdemonstratethattheregulatorymodelsdoeMaximuminvestmentinDSM($)notconsiderelectricityprocurementbydistributedgeneration.xMinimumadjustmentinPriceCapRegulationModelingsuchanarrangementintroducesanotherlevelthatΩdSetofdevicesmodelstheinteractionofDISCOMwithDGENCO,model-SAIDIdSystemAverageInterruptionDurationIndexwheningtheprocurementofpowerthroughPPAs.ImplementingdevicedisusedMIBLPischallengingproblem,andfurtherworkisrequiredtoDSMDemandSideManagementbuildlibrariestosolvesuchmodels.DNODistributionNetworkOperatorMediumVoltage6CONCLUSIONMVLowVoltageLVKarushKuhnTuckerThedistributionsystemisusuallyoperatedasamonopoly,KKTPowerPurchaseAgreementrestrictedbyaregulatoryregime.ThebehavioroftheregulatorPPAValueofLostLoadcanimpactthedistributionsystem’splanningdecisions;hence,aVOLLHighPointProblemcomprehensivesurveyofbothregulatorypoliciesanddistribu-HPPElectricVehiclestionplanningalgorithmswasdoneinthispaper.A2bussystemEVCentralElectricityRegulatoryCommissionwasusedtodemonstratethecharacteristicsofeachregulatoryCERCStateElectricityRegulatoryCommissionpolicyandcomplementedtheneedforbilevelformulation.SERCCentralEuropeanEnergyRegulatorCEERCostofServiceRegulationThepaucityofalgorithmsinsolvingIntegerBilevelproblemsCOSRPerformanceBasedRatesposesachallengeinconductingintegrateddistributionplanning.PBRServiceQualityRegulationTheformulationstructureoflowerleveldistributionplanningSQRSystemAverageInterruptionDurationIndexmodelhastoberestrictedtoMILP.SAIDIDataEnvelopmentAnalysisDEAStochasticFrontierAnalysisThemodelingforthecostofserviceregulationrevealeditsSFACorrectedOrdinatyLeastSquaresdrawbackofpromotingwastefulexpendituresanditsinabilitytoCOLSTotalFactorProductivitypromoteefficiency.Ontheotherhand,pricecapregulationandTFPOfficeofGasandElectricityMarketsrevenue-sharingmechanismsareabletopromotecostreduc-OFGEMInformationQualityIncentivetionbutareunabletoincentivizeutilitytoimprovereliability.IQIMaximumrateofreturnServiceQualityregulationincorporatestheimprovementofreli-IntervalPowerFlowabilityandefficiencybutishardertomodelandimplement.AllsHeuristicMomentMatchingthemodelsassumedutilityprovidescorrectinformationaboutIPFPointEstimateMethodcostandprojectedrevenue.Inpractice,thismaynotbetrue.HMMProbabiltyDistributionFunctionHence,theIQImechanismmaybeincludedinmodeldesignPEMLinearProgramfuturework.PDFSecondOrderConeProgramLPAlternatingDirectionMethodofMultiplierTheliteratureondistributionplanningwasclassifiedbasedSOCPMixedIntegerLinearProgramonoptimization,uncertainty,andasinglestageormulti-stageADMMMixedIntegerSecondOrderConeProgrammodelwasused.Theinclusionofreliabilityandradialitycon-MILPGeneticAlgorithmstraintswasalsodiscussed.AcorrelationinliteratureforMISOCPParticleSwarmOptimizationmodelingofdifferentdeviceswasreported.GAMixedIntegerNonLinearProgramPSOExpectedEnergyNotSuppliedAMIBLPbasedframeworkwasestablishedtosolvetheMINLPDistributionallyRobustOptimizationgenericregulatoryanddistributionplanninggame.Implement-EENSBard&MooreingtheMIBLPframeworkischallengingduetothelackofaDRONetPresentValuestandardofftheshelfsolverandisenvisionedasfuturework.BM:NetPresentvalueofexpansionState-of-the-artalgorithmstosolveproblemsofsuchstructureNPVInternalRateofReturnwerediscussed.ThepaperlaysthefoundationofamoreholisticTPVMinimumacceptableRateofReturnframeworktododistributionplanning,withutilityoperatingasIRRBenefitCostRatioaregulatedmonopoly.MARRGeographicalInformationSurveyBCRKirchoff’sCurrentLawNOMENCLATUREGISMaximumallowedrevenue($)KCLBinaryInvestmentDecisionValueforInvestmentpPricechargedtocustomer($/MW)Penalty/Rewardforinterruptionduration($/hr)Q(p)Demandcurveofcustomer(MW)pxdBudgetconstraintofutility($)c2Operationalcostofpower($/MW)ProfitutilityisallowedtokeepentirelyIFixedcostinvestmentinreliability($)a:-RevenueutilityisallowedtokeepentirelyeFixedcostinvestmentinDSM($)P0Pricecapsetbyregulator($)I𝜋RVERMAANDSWARUP195𝛼𝜋PercentageofexcessprofitthatisrequiredtobeRegulationandItsReform:WhatHaveWeLearned?pp.291–344.sharedtocustomersUniversityofChicagoPress,Chicago(2014)𝛼RPercentageofexcessrevenuethatisrequiredtobe4.Ajodhia,V.,Hakvoort,R.:Economicregulationofqualityinelectricitysharedtocustomersdistributionnetworks.UtilitiesPolicy13(3),211–221(2005)c1Coefficientofxinupperlevelobjectiveforbilevel5.Huang,Y.,Söder,L.:Evaluationofeconomicregulationindistributionproblemsystemswithdistributedgeneration.Energy126,192–201(2017)d1Coefficientofyinupperlevelobjectiveforbilevel6.TheroleofintegrateddistributionsystemplanninginmaximizingproblemresiliencyintheAPECregion.Tech.Rep.(2022)d2Coefficientofyinlowerlevelobjectiveforbilevel7.FloresEspino,F.,Tian,T.,Chernyakhovskiy,I.,Mercer,M.,Miller,M.:problemCompetitiveelectricitymarketregulationintheunitedstates:Aprimer.PU(y)UpperlevelfeasibilitysetsTech.Rep.,NationalRenewableEnergyLab.(NREL),Golden,COPL(x)Lowerlevelfeasibilitysets(2016)Coefficientofxinupperlevelinequality8.Regy,P.V.,Sarwal,R.,Stranger,C.,Fitzgerald,G.,Ningthoujam,J.,Gupta,A1CoefficientofyinupperlevelinequalityA.,etal.:Turningaroundthepowerdistributionsector:LearningsandG1Coefficientofxinlowerlevelinequalitybestpracticesfromreforms(2021)A2Coefficientofyinlowerlevelinequality9.OrganizationforEconomicCooperation&Development(OECD):G2UpperlevelconstantRegulatorypolicy:Towardsanewagenda.Tech.Rep.,OECD,Parisb1Lowerlevelconstant(2010)b2Failurerateoftransformertr10.Fischer,R.,Serra,P.,Joskow,P.L.,Hogan,W.W.:Regulatingtheelec-K0trAverageRepairtimeoftransformertricitysectorinlatinamerica[withcomments].Economia1(1),155–218𝜏rtrep(2000)𝛾trExponentialgrowthrateoffailureforendoflifeof11.Averch,H.,Johnson,L.L.:Behaviorofthefirmunderregulatorytransformertrconstraint.TheAmericanEconomicReview52(5),1052–1069(1962)𝛽trLifeoftransformertr12.Billinton,R.,Pan,Z.:Historicperformance-baseddistributionsystemriskK0lFailurerateoflinelassessment.IEEETrans.PowerDelivery19(4),1759–1765(2004)𝜏rlep13.Kuosmanen,T.,Nguyen,T.:CapitalbiasintheNordicrevenuecapreg-𝛾lRepairtimeoflinelulation:Averch-Johnsoncritiquerevisited.EnergyPolicy139,111355(2020)𝛽lExponentialgrowthrateoffailureforendoflifeof14.Spiegel,Y.:Thecapitalstructureandinvestmentofregulatedfirmsunder𝜒llinelalternativeregulatoryregimes.J.Reg.Econ.6(3),297–319(1994)𝜒trLifeoflinel15.Ramesey,F.P.:AContributiontotheTheoryofTaxation.Econ.J.hAgeoflinel37(145),47–61(1927)Ageoftransformertr16.Baron,D.P.,Myerson,R.B.:Regulatingamonopolistwithunknowncosts.xRegulatoryperiod(Years)Econometrica50(4),911(1982)xAdjustmenttakesplaceattimeΔ17.Cambini,C.,Rondi,L.:Incentiveregulationandinvestment:EvidenceIDSMLowerlimitofadjustmentfactorfromEuropeanenergyutilities.J.Regul.Econ.38(1),1–26(2010)NPAMInvesmentCostforDSM18.OFGEM:Financialmodelmanual–Distributionpricecontrolreview5NetworkPerformanceAssessmentModel(DPCR5).Tech.Rep.,OFGEM(2009)19.Cabral,L.M.B.,Riordan,M.H.:IncentivesforcostreductionCONFLICTOFINTERESTSTATEMENTunderpricecapregulation.In:PriceCapsandIncentiveRegu-Theauthorshavedeclarednoconflictofinterest.lationinTelecommunications,pp.155–165.Springer,NewYork(1991)DATAAVAILABILITYSTATEMENT20.Bard,J.F.,Moore,J.T.:AbranchandboundalgorithmforthebilevelDatasharingnotapplicable-nonewdatagenerated,ortheprogrammingproblem.SIAMJ.Sci.Stat.Comput.11(2),281–292(1990)articledescribesentirelytheoreticalresearch.21.Fortuny-Amat,J.,McCarl,B.:Arepresentationandeconomicinterpre-tationofatwo-levelprogrammingproblem.J.Oper.Res.Soc.32(9),ORCID783–792(1981)AprajayVermahttps://orcid.org/0000-0002-2299-431222.Weyman-Jones,T.G.:RPI—Xpricecapregulation:ThepricecontrolsusedinUKelectricity.UtilitiesPolicy1(1),65–77(1990)REFERENCES23.Ajodhia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