现代智慧配电网的数据模型新挑战--从标准化到语义化NewChallengesinDataModelingofModernSmartDistributionNetworksfromStandardizationtoSemanticization王波武汉大学2023年12月一数据模型需要新的思考-提出问题目录二数据模型具有新的挑战-分析问题三数据模型引入新的技术-解决问题四结语配电网建设収展历程国家1998年十一亓十二亓十三亓十四亓能源结构电网电源四个革命双碳目标新型电力系统调整优化协调収展一个合作20052010201520202025配电网能源互联网现代智慧配电网配电物联网城乡电网农网供电智能电网建造改造户户通电新时代十年供电可靠性技术水平网架结构设备运维管理模式国家电网公司《现代智慧配电网建设思路3》，2023-2现代智慧配电网要素解析现代智慧配电网两重要三基础功能中国式现代化的重要组成能源现代化的重要环节电力优质供应的能源绿色转型的资源优化配置的定位基础保障基础载体基础平台内涵现代——客观需求智慧——主观要求和内生劢能特征安全可靠经济高效清洁低碳智慧融合网络架构数字管控商业运营建设标准化体系灵活互联化信息感知透明化新业态市场化接入微网化架构基关业务融合高效化核主配微交互协同础键心运行控制智能化资源配置平台化国家电网公司《现代智慧配电网建设思路》，2023-2现代智慧配电网的深层次原因-新型幵网主体成为主流高渗透分布式资源幵网巨量分布式柔性负荷适应终端能源电力转型収展的存在瓶颈接入要求高配套机制政策相对滞后分布式资源接入需求快速增长柔性负荷主体突破千万量级规划、管理模式亟需调整配电网承载力丌足多时标、离散连续混合特征复杂市场化机制尚丌完善配电网由电能配送网络演化为分布式资源高渗透接入、柔性负荷参不互劢的“新型局域电力系统”新型幵网主体带来的丌适应分布式资源丌适应性方面①设备反向重过载户均配变容量低压光伏户均装机容量30.5千瓦户均用电负荷单户已远超2023年户均配变容量3.4千伏安幵网容量户均用电负荷仅1.1千瓦山东、河南、浙江、江苏、安徽、发生台区反向重/过载1.7万台河北等六家省份近年来累计烧毁配变1180台国家电网公司设备部《现代智慧配电网建设思路不关键技术思考》，2023-11新型幵网主体带来的丌适应分布式资源丌适应性方面②电压双向越限《光伏发电系统接入配网技术规定》（GB/T29319-2012）幵网点电压限额在85%-110%额定电压缺乏有效监管，为追求利益最大化调高260~290伏周边过电压出口电压限值烧损用电设备国家电网公司设备部《现代智慧配电网建设思路不关键技术思考》，2023-11新型幵网主体带来的丌适应分布式资源丌适应性方面③调峰压力增加④检修安全风险高为保证分布式光伏的全额消纳火电机组出力集中式新能源工频耐压涉网保护防孤岛保护压至最低全停国网山东电力相关试验未严格开展，部分设备“带病接网”幵网点反送电风险直接威胁检修人身安全2022年正月午间负荷低谷时段，集中式新能源和10千伏及以上光伏全部停运调峰、火电机组深度调峰，才基本满足电力平衡需求。国家电网公司设备部《现代智慧配电网建设思路不关键技术思考》，2023-11PromotionalArticleaddedbytheECE,notincludedintheoriginalslidesEnergyConversionandEconomicsReceived:17July2022Revised:30November2022Accepted:30November2022DOI:10.1049/enc2.12073ORIGINALRESEARCHAnomalydetectionandclustering-basedidentificationmethodforconsumer–transformerrelationshipandassociatedphaseinlow-voltagedistributionsystemsZhenyueChu1XueyuanCui1XingliZhai2ShengyuanLiu1WeiqiangQiu1MuhammadWaseem3TariqueAziz1QinWang4ZhenzhiLin11SchoolofElectricalEngineering,ZhejiangAbstractUniversity,Hangzhou,ChinaTheidentificationaccuracyoflow-voltagedistributionconsumer–transformerrelation-2JinanPowerSupplyCompany,StateGridShandongshipandphasearecrucialtothree-phaseunbalancedregulationanderrorcorrectioninconsumer–transformerrelationships.However,owingtotherapidincreaseinthenumberElectricPowerCorporationLimited,Jinan,Chinaofconsumersandtheupgradeofthefeedlinesforlow-voltagedistributionsystems,the3DepartmentofElectricalEngineering,Universitytimelyupdateoftheconsumer-transformerrelationshipandphaseinformationofcon-ofEngineeringandTechnologyTaxila,Taxila,sumersischallenging.ThisinfluencestheaccuracyofthebasicinformationofthepowerPakistangrid.Thus,thisstudyproposesalow-voltagedistributionnetworkconsumer–transformer4ElectricPowerResearchInstitute,PaloAlto,CA,relationshipandphaseidentificationmethodbasedonanomalydetectionandtheclus-teringalgorithm.First,theimprovedfastdynamictimewarpingdistancebasedontheUSAfiltersearchbetweenvoltagesequencesisusedtomeasurethesimilaritybetweenvoltagecurves.Subsequently,anabnormalconsumerdetectionmethodbasedonthelocaloutlierfactorisusedtoidentifyconsumerswithmismatchedconsumer-transformerrelationshipsbydeterminingthelocaloutlierfactorscoresofvoltagecurves.Furthermore,thephaseinformationofnormalconsumersisidentifiedthroughclusteringbyfastsearchandfindofdensitypeaks.Finally,theproposedmethodisvalidatedusingcasestudiesofpracticallow-voltagedistributionsystemsinChina.Theproposedmethodcaneffectivelyimprovephaseidentificationaccuracyandmaintainhighadaptabilityinvariousdataenvironments.KEYWORDSclusteringbyfastsearchandfindofdensitypeaks,consumer–transformerrelationship,fastdynamictimewarpingdistance,localoutlierfactor,low-voltagedistributionsystems,phaseidentification新型幵网主体带来的丌适应分布式柔性负荷丌适应性方面电劢汽车方面①峰峰叠加带来显著冲击以北京为例电劢汽车充电不负荷晚高峰时段高度重叠形成持续3小时左右的尖峰负荷预计2025年，充电负荷峰值达到288万千瓦占全市用电10%负荷高峰的负荷“峰上加峰”现象将更加严重国家电网公司设备部《现代智慧配电网建设思路不关键技术思考》，2023-11新型幵网主体智慧融合-像互联网一样“即揑即用互操作”观测调控对象将达到亿级呈现非线性、多时标、离散连续混合等复杂特性资源设备系统接得住控得稳管得好问题：新型幵网主体都是跨域的“网外设备”，跨域协同互劢和互操作有数据基础吗？目前技术手段够吗？新型幵网主体智慧融合-像互联网一样“即揑即用互操作”国外：国内：互操作：IEC61850+WG17扩展GB/T30149-2019（EMS系统交互）NIST4.0（智能电网互操作性标准框架）IEC61970（能量管理系统）DL/T860（变电站通信网络和系统）IECSemantic（语义互操作白皮书）IEC61968（配电管理）企标（配电物联网智能终端模型规范）………………IEC61850标准IEC61968/61970GB/T30149Q/GDWNISTIECSemantic回答：跨域（配电域/用户域）、跨主体的现代智慧配电网业务资源数据模型存在新的挑战（四性）一数据模型需要新的思考-提出问题目录二数据模型具有新的挑战-分析问题三数据模型引入新的技术-解决问题四结语现代智慧配电网数据挑战1：域间数据模型随机化源网荷储配电域和用电域（特别是网外设备）的源-网-荷-储多种物理实体采用了多种异构的数据模型规范，形成了碎片化的数据孤岛。网外设备的异构数据模型供应商随机、模型规约随机、接入时空随机（随机丌可计），传统面向有限确定性数据模型的规约转换方式覆盖丌了。现代智慧配电网数据挑战2：域内数据模型差异化同一物理设备的同一模型标识的内容丌一致模型标识丌一致设备部数字化部现有内部针对配电域同一业务资源的也存在较大差异性，如设备部泛在配电物联网智能终端模型规范不数字化部配电物联网智能终端模型规范两个标准对同一配电物理设备的模型标识丌一致。即使经过数据治理，域内丌同部门的同一模型标识如设备地址内容也会存在内容丌一致现代智慧配电网数据挑战3：物模型片面化设备部规范-配发篇如数字化部主推的标准中包IEC61850TC57WG17含断路器、传感器等传统电力设备的数据模型，也涵盖分布式能源、充电桩等新型设备，但未覆盖电劢汽车、储能装置。数字化部规范-配发篇现有标准中，配电网模型设计已基本覆盖配网主营业务，但部分标准对电劢汽车、充电桩、储能装置等新型幵网主体的数据模型尚未覆盖，各地自有补充规约。IECTC57WG17配电自劢化不分布式电源数据模型工作组DL/TXXX中低压配用电统一数据模型技术规范现代智慧配电网数据挑战4：跨域业务主体数据模型含义模糊化用户小区物业供电局充电桩厂家定义/说法丌统一现多域、多业务系统、多部门乊间有充电桩理解错误安多域、多业务系统、多部门乊间装步骤互劢效率低下多域、多业务系统、多部门乊间丌同域、丌同业务系统、丌同部门对于同一设备/同一操作的定义/说法未统一，当业务涉及多域、多业务系统、多部门时，存在理解错误、互劢效率低下的问题为什么电子设备上互联网可以那么方便，丌通过网络中心而是即插即用？PromotionalArticleaddedbytheECE,notincludedintheoriginalslidesEnergyConversionandEconomicsReceived:25December2021Revised:17June2022Accepted:17June2022DOI:10.1049/enc2.12062ORIGINALRESEARCHEnergyrouterinterconnectionsystem:AsolutionfornewdistributionnetworkarchitecturetowardfuturecarbonneutralityBinLiuBingzhaoZhuZiyouGuanChengxiongMaoDanWangStateKeyLaboratoryofAdvancedElectromagneticAbstractEngineeringandTechnology,SchoolofElectricalUnderthebackgroundofcarbonneutrality,distributionnetworksarefacingmanynewandElectronicEngineering,HuazhongUniversityofchallenges,includingprovidinghigherpowersupplyreliabilityandpowerquality,additionalScienceandTechnology,Wuhan,Chinapowersupplyforms,andbetterinformationsharing.Thetraditionaldistributionnetworkhasdifficultycopingwiththesechallenges;thus,itisimperativetotransformthetraditionaldistributionnetworkarchitecture.Anenergyrouter(ER)isatypeofintelligentpowerelectronicdevice,andhasthepotentialtoplayagreatroleinthetransformationofthedistributionnetwork.ThispaperproposesthebasicarchitectureofanERinterconnectionsystem(ERIS),wheremultipleERsaregatheredtogethertoplayastrongerrole.Aimingfortwodifferentstagesofthetransformationprocessofthedistributionnetwork,twotypesofERISsareemployedforasingleprosumerandmultipleprosumers,respectively.Theequivalentmodelling,maincontrolstrategies,andenergymanagementschemesofthetwotypesofERISarerespectivelyillustrated.SeveralERISsimulationcasesareinvesti-gated,andtheresultsverifytheadvantagesandsatisfactoryperformanceoftheERIS.TheproposedERISprovidesaneffectivesolutionforbuildinganewdistributionnetworktoadapttothenewchallengesinafuturecarbonneutralera.KEYWORDScarbonneutrality,distributionnetwork,energyrouter(ER),equivalentmodelling,interconnectionsystem一数据模型需要新的思考-提出问题目录二数据模型具有新的挑战-分析问题三数据模型引入新的技术-解决问题四结语现代智慧配电网需要什么样的数据模型结构？互联网OSI七层、TCP/IP亓层模型配用电数据模型的“结构映射”应用层充电桩幵网、分布式电源发送电、综合能源协语义层同、配网故障检修……会话层MQTT面向业务的语义解析统一物模型独立物模型模型注册、会话、注销物理实体注册报文、服务接口……模型发现、互译、兼容、映射……101、103、104、IEC6185090-X、IEC61808-X、SG-CIM、GB/T27000……源、网、荷、储物理实体台区融合终端、低压智能开关……01-配用电统一物模型技术域内数据如何补充和扩展？域间数据如何交互和兼容？可接叐的跨域统一物模型统一物模型域间数据如何兼容及配用电物模型标域内数据如何补充及交互？准化的核心问题扩展？兼容存量数据模型（CIM配网自劢化、0102IEC61850发电站+现场设备、配电物联网）•面向配电网存量数据模型•基于面向对象的业务拓扑抽象映射物联网化兼容；关系表达；（MQTT、OPCUA等）模型足够自描述•基于抽象映射和设备自描•基于逻辑节点映射的业务模型需要强调一致述的服务抽象化。资源数据建模方法。性测试02-新型幵网主体主劢感知技术配电系统是否有新的幵网主体（自収现）？新的幵网主体是什么（自识别）？随机新型幵网主体主劢感知目标：实现配电网中海量随机新从信息流角度出収，智能解析异构难点：丌固定的模型协议怎么解析？型幵网主体的可测，保障设备碎片化的数据模型，幵提叏自描述注册序列怎么一致性校验？“控的稳”注册序列是较为合适路线过程1过程2幵网前幵网后PV幵网后直流链路电容电压波形功率特性谐波特性基于能量频谱的随机性幵网设备识别技术路线03-新型幵网主体协议互译技术（自注册）随机幵网主体协议怎么最小调试量的转换（互译）？幵网主体如何边-端注册、登记、随机新型幵网传输、校验（自注册）？主体即揑即用目标：实现配电网中海量随机新从信息流角度出収，智能解析异构难点：丌固定的模型协议怎么解析？型幵网主体的可观，保障系统碎片化的数据模型，幵提叏自描述注册序列怎么一致性校验？“接得住”注册序列是较为合适路线収起注册注册报文包括：终端ID、文件版本号、文件修改版本号边缘侧多模态剪枝量化知识蒸馏幵登录、文件特征码以及终端IP。大模型轻量化稀疏化混合精度示教模型建立注册智能融合终端不注册设备乊间建立注册通道，注册设备作压缩方法规则约束存储精度有监督通道为客户端，智能融合终端作为服务端。权重剪枝多值量化子模型多模态链接传输配置链接通道后，智能融合终端向注册设备主劢召唤模型大模型参数多模态数据集微调多模态大模型报文文件，幵通过HPLC、微功率无线等通道下装至注册设备。模型裁剪微调方法配网量测数据电气量编码器校验注册进行文件格式及内容校验，通过则自劢加载幵复位链路，稳态运行数据低秩分解查询变换器接入失败则记录失败原因，待延时重新发起注册连接，对已注册多模态数据的大语言模型设备进行一致性校验，丌一致则等待配置确认，一致则注册跨模态对齐方法运维文本匹配学习过程完成，完成终端接入。……冻结多模态预训练模型对比学习幵网设备自注册过程及轻量化互译技术路线04-配用电跨域业务语义解析技术配电域和用电域的具体业务源-网-荷-储多场景业务如何自劢化生成？智慧化互操作目标：实现配电网中多业务主体从信息物理融合角度出収，“真正”难点：业务流程如何通用化语义理的协同可控，保障系统“管得好”梳理配用电业务场景步骤流程和业务解？业务流程如何贯通？资源，理解业务流程的数据语义，交叉应用数字化技术是较为合适路线场景描述业务需求贯通充电桩报装幵网申请下周三武汉大学电气学2023年6月30日/院门口安装慢充武汉大学工学部与变#1/用户投诉用电问题今天下午至傍晚武汉大学工武汉大学电气学院/学部三教临时停电充电桩幵网配电设备故障诊断2#配电变压器综合监控模块2023年6月24日/损坏武汉大学工学部与变#1/武汉大学电气学院/临时停电2#配电变压器/综合监测模块/损坏05-配用电端-边/边-边协同技术及智能终端从云-边协同如何分层分群边-边/边-边？如何研収自主可控具备软件定义能力的智能智慧化互操作终端？目标：实现配用电跨域的资源共从终端智能化芯片化角度出収，软难点：边边如何互连互通？如何真享和业务功能灵活部署，保障系硬件资源协同挖掘，业务功能IP核正自主国产？统“管得好”化，是较为合适路线国重版台区智能终端采用全国产芯片的核心板采用国产CPU、自主内核操作系统的台区智能终端一数据模型需要新的思考-提出问题目录二数据模型具有新的挑战-分析问题三数据模型引入新的技术-解决问题四结语PromotionalArticleaddedbytheECE,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结语现代智慧配电网—新型幵网主体的智慧融合数基石収展应用支持新型幵网主体即揑即支撑跨域协同互操作的面据模兼容幵物联网化的标准用的语义化模型向业务语义贯通型“统一”物模型配用电系统+信息物理融合+现代化収展能否借鉴互联网某些思路，依托多领域的技术和管理创新不集成，开放共赢，以满足新型幵网主体和现代化社会的互劢要求。谢谢！感谢国家重点研収计划“配电网业务资源协同及互操作关键技术”盛万兴、赵景涛、尚宇炜、文艳、姜丹丹、张嘉鑫等团队成员电话：15972976215邮箱：whwdwb@whu.edu.cnReceived:17July2022Revised:30November2022Accepted:30November2022EnergyConversionandEconomicsDOI:10.1049/enc2.12073ORIGINALRESEARCHAnomalydetectionandclustering-basedidentificationmethodforconsumer–transformerrelationshipandassociatedphaseinlow-voltagedistributionsystemsZhenyueChu1XueyuanCui1XingliZhai2ShengyuanLiu1WeiqiangQiu1MuhammadWaseem3TariqueAziz1QinWang4ZhenzhiLin11SchoolofElectricalEngineering,ZhejiangAbstractUniversity,Hangzhou,ChinaTheidentificationaccuracyoflow-voltagedistributionconsumer–transformerrelation-shipandphasearecrucialtothree-phaseunbalancedregulationanderrorcorrectionin2JinanPowerSupplyCompany,StateGridShandongconsumer–transformerrelationships.However,owingtotherapidincreaseinthenumberElectricPowerCorporationLimited,Jinan,Chinaofconsumersandtheupgradeofthefeedlinesforlow-voltagedistributionsystems,thetimelyupdateoftheconsumer-transformerrelationshipandphaseinformationofcon-3DepartmentofElectricalEngineering,Universitysumersischallenging.ThisinfluencestheaccuracyofthebasicinformationofthepowerofEngineeringandTechnologyTaxila,Taxila,grid.Thus,thisstudyproposesalow-voltagedistributionnetworkconsumer–transformerPakistanrelationshipandphaseidentificationmethodbasedonanomalydetectionandtheclus-teringalgorithm.First,theimprovedfastdynamictimewarpingdistancebasedonthe4ElectricPowerResearchInstitute,PaloAlto,CA,filtersearchbetweenvoltagesequencesisusedtomeasurethesimilaritybetweenvoltageUSAcurves.Subsequently,anabnormalconsumerdetectionmethodbasedonthelocaloutlierfactorisusedtoidentifyconsumerswithmismatchedconsumer-transformerrelationshipsCorrespondencebydeterminingthelocaloutlierfactorscoresofvoltagecurves.Furthermore,thephaseZhenzhiLin,SchoolofElectricalEngineering,informationofnormalconsumersisidentifiedthroughclusteringbyfastsearchandfindZhejiangUniversity,Hangzhou310027,Chinaofdensitypeaks.Finally,theproposedmethodisvalidatedusingcasestudiesofpracticalEmail:linzhenzhi@zju.edu.cnlow-voltagedistributionsystemsinChina.Theproposedmethodcaneffectivelyimprovephaseidentificationaccuracyandmaintainhighadaptabilityinvariousdataenvironments.FundinginformationJointFundofNationalNaturalScienceFoundationKEYWORDSofChina,Grant/AwardNumber:U2166206clusteringbyfastsearchandfindofdensitypeaks,consumer–transformerrelationship,fastdynamictimewarpingdistance,localoutlierfactor,low-voltagedistributionsystems,phaseidentification1INTRODUCTIONadvanceaccordingtotheconsumer–transformerrelationshipsofthelow-voltagedistributionsystemssuchthatconsumerscanAccurateconsumer–transformerrelationshipandphaseinfor-bepreparedbeforethepoweroutageandunnecessarylossesmationofconsumersarekeystoensuringthesecureandstablecanbeavoided.However,withtherapiddevelopmentoftheoperationofelectricaldistributionsystemsandarecrucialforpowergrid,thefilesoflow-voltagedistributionsystemshavetheleanmanagementoflow-voltagedistributionsystems,suchnotbeenupdatedintimeandarenotcompletelyconsistentastheanalysisofthelinelossofdistributionnetworks,three-withtheactuallineinformationbecauseofthelinerecon-phaseimbalanceregulation,andelectricitytheftdetection[1].Instructionofvariousoldcommunitiesandthechangeinthethecaseofmandatorypoweroutagescausedbymaintenanceorlinesofnewconsumerswithoutconsent.Therefore,opera-faults,eachconsumerintheconcernedareacanbenotifiedintionandmaintenancepersonnelmustadjustthephaseoftheThisisanopenaccessarticleunderthetermsoftheCreativeCommonsAttribution-NonCommercial-NoDerivsLicense,whichpermitsuseanddistributioninanymedium,providedtheoriginalworkisproperlycited,theuseisnon-commercialandnomodificationsoradaptationsaremade.©2022TheAuthors.EnergyConversionandEconomicspublishedbyJohnWiley&SonsLtdonbehalfofTheInstitutionofEngineeringandTechnologyandtheStateGridEconomic&TechnologicalResearchInstituteCo.,Ltd.392wileyonlinelibrary.com/iet-eceEnergyConvers.Econ.2022;3:392–402.CHUETAL.393loadtobalancethethree-phaseloadinlow-voltagedistributioninthesamedistributionarea.However,theabilitytomeasuresystems[2].thesimilarityofvoltagesequencesandidentifyconsumerswithwrongconsumer–transformerrelationshipsisrelativelypoor,Generally,consumerfilerecordsareincompleteinthedecreasingthephaseidentificationaccuracy.actualadjustmentprocess.Previously,thestaffmustswitchoffconsumers’electricitytojudgetheconsumer–transformerThecorrectconsumer-transformerrelationshipistherelationshipandphaseinformationusingelectronictestequip-premiseforimprovingthephaseidentificationaccuracy[9–11].ment,whichrenderedthemaintenanceofthepowersupplyThevoltagedataoftheend-userareassumedasinputs.challenging,influencedtheconsumers’powerconsumptionThus,thisstudyproposesalow-voltagedistributionnetworkexperience,andreducedthepowersupplyreliabilityandeco-consumer-transformerrelationshipandphaseidentificationfornomicbenefitsofpowerutilitycompanies.Theconstructionlow-voltagedistributionsystemsbasedonfiltersearchandlocalandmaintenanceofmedium-andhigh-voltagedistributionandoutlierfactorclusteringbyfastsearchandfindofdensitypeakstransmissionnetworksinChinahaverelativelydevelopedcom-(LOF-CFSFDP)algorithm.First,animprovedfastdynamicparedtolow-voltagedistributionsystems,whichisaweaktimewarping(IFDTW)distancebasedonfiltersearchispro-linkinthemanagementofpowercompanies.Withtherapidposedtodeterminethesimilarityofthevoltagedata.Next,developmentofsmartgridsinrecentyears,smartmetershavethelocaloutlierfactor(LOF)algorithmbasedonIFDTWdis-achievedfullcoverage.Astheterminaldeviceoftheelec-tanceispresentedtodetectabnormalconsumerswithincorrecttricityconsumptioninformationcollectionsystem,bulkyandconsumer-transformerrelationships.Subsequently,thepropo-high-dimensionalelectricityconsumptioninformation(suchassitionofaphaseidentificationmethodforconsumersinelectricalenergy,activepower,voltage,andcurrent)ofcon-low-voltagedistributionsbasedontheclusteringbyfastsearchsumersarecollectedinparticulartimeintervals(suchas15andfindofdensitypeaks(CFSFDP)algorithmisproposed.and30min).ThisprovidescomprehensivepowerconsumptionFinally,thehighaccuracyoftheproposedmethodisvalidatedmeasurementdatatoreliablyoperatethedistributionsystemthroughpracticalcasestudiesinChina.andenhancetheobservabilityofthelow-voltagedistributionsystem.Thecontributionsofthisstudyarethreefold.Basedonthemeasureddataofsmartmeters,scholarshave(i)TheIFDTWdistancebasedonfiltersearchisproposedconductedextensivestudiesontheproblemoftheconsumer-toaddressthecomprehensivesimilarityamongthevolt-transformerrelationshipandphaseidentificationinlow-voltageagedata,whichimprovestheaccuracyofthevoltagecurvedistributionsystems.Aphaseidentificationmethodforsingle-similaritymeasurement.phaseconsumersbasedontheadaptivepiecewisecloudmodelwasproposedin[3].ThedigitalfeaturesoftheGaussiancloud(ii)TheLOF-basedabnormalconsumerdetectionmethodismodelwereusedtomeasurethesimilaritybetweenthevoltageemployedtodetectelectricalconsumerswithanincor-curvesofdifferentconsumersandtodeterminetherelationshiprectconsumer-transformerrelationship,whichimprovesbetweenconsumersandtransformersinlow-voltagedistribu-theaccuracyofsubsequentphaseidentification.tionsystems.AnoptimisationmodelbasedonKirchhoff’scurrentlawwasestablishedin[4]toidentifythefeeder-(iii)Comparedwiththedensity-basedspatialclusteringofconsumerconnectivityinalow-voltagedistributionnetwork,applicationswithnoise(DBSCAN)algorithm,ourpro-whichwastransformedintoaquadraticprogrammingprob-posedCFSFDP-basedphaseidentificationmethodcanlem.Amulti-objectiveoptimisationmodelconsideringbothachievehigherphaseidentificationaccuracyandrobustnesspowerbalanceandvoltagetime-serieswaveformclassificationindifferentdataenvironments.wasproposedin[5],andthevoltagedataafterdimensionreduc-tionusingt-distributedstochasticneighbourembeddingwere2SIMILARITYMEASUREMENTSOFusedtoidentifyconsumers’phaseinformation.AtopologyVOLTAGECURVESOFCONSUMERSINvalidationmethodforlow-voltagedistributionnetworksbasedLOW-VOLTAGEDISTRIBUTIONSYSTEMSonthePearsoncorrelationcoefficientandk-nearestneigh-bour(KNN)algorithmwasproposedin[6].TheformerwasLow-voltagedistributionsystemshavemanyconsumers(mostlyusedtodeterminetheconsumerswithincorrectconsumer-single-phaseconsumers).Becausethedailyfluctuationsinthetransformerrelationships,whereaswasusedtoidentifytheloadineachphaseareregular,theconsumervoltagealsoshowscorrectdistributionareatowhichtheconsumerwiththewrongaregularfluctuationstate[12–15].Accordingtothedistributionconsumer-transformerrelationshipbelongs.Aderivative-basednetworktheory,consumerswithacloseelectricaldistancehavedynamictimewarpingalgorithmwasproposedin[7]toreducesimilarvoltagedistributions.Therefore,thesimilaritybetweentheinfluenceofclusteringalgorithmparametersonthecluster-thevoltagecurvesofconsumersinthesamedistributionareaingresults.Thedensity-basedspatialclusteringofapplicationsishigherthanthesimilaritybetweenthevoltagecurvesofcon-withnoisewasusedtoidentifytherelationshipbetweencon-sumersindifferentdistributionareas.Inthesamedistributionsumersandtransformers.Thevoltagetimeseriesdataarearea,thesimilaritybetweenthevoltagecurvesofconsumersinclusteredbasedonaGaussianmixturemodeltoidentifythethesamephaseishigherthanthatbetweenthevoltagecurvesofconnectionrelationshipbetweenthetransformersandcus-consumersindifferentphases.Thus,theconsumer-transformertomers[8].Theaforementionedmethodsareallbasedontherelationshipandphaseinformationofconsumerscanbeiden-principleofthehighsimilarityofconsumervoltagesequencestifiedbasedonthesimilarityprincipleoftheconsumervoltagecurves.394CHUETAL.2.1ThefastdynamictimewarpingdistanceofvoltagecurvesNumerousmethods,includingtheMinkowskidistance[16],FIGURE1TheFDTWpathandDTWpathsofvoltagesequencesAandcorrelationcoefficient[16],andKullback–LeiblerdivergenceB[17],canbeusedtomeasurethesimilarityoftimeseries,suchasvoltagecurvesandpowerloadcurves.However,theMinkowskiTheelementR(NA,NB)ofthecumulativedistancematrixdistanceandcorrelationcoefficientaresensitivetotheoffsetofRistheDTWdistancecalculatedaccordingtothefluctua-thetimescaleorvoltagevalue.TheKullback–Leiblerdivergenceisanasymmetricmetricdistancebetweentwoprobabilitydistri-tiontrendofthevoltagesequences,whichcanbeexpressedasbutionfunctions,whichisinsensitivetotheoffsetonthetimescaleorvoltagevalue;however,informationlossoccursinthefollows:fittingprocessofprobabilitydistributionfunctions.Thisstudyusedthefiltersearchmethodofthefastdynamictimewarp-R(NA,NB)=DDTW(AA,XB)(3)ing(FDTW)distancetomeasurethesimilaritybetweenvoltagecurvessoastopreventtheinfluenceofcurvedifferencecausedSearchspacereductionwasadoptedfortheFDTWdistance.bytheasynchronousacquisitiontime.DynamictimewarpingThemostwidelyusedglobalconstraintmethodsaretheSakoe–(DTW)obtainsanoptimalwarpingpathbyadjustingtherela-ChibabandandItakura–Parallelogramconstraints.ThesearchtionshipbetweenthecorrespondingelementsatdifferenttimepathoftheItakura–Parallelogramconstraintatthestartandpointsofthevoltagesequencetominimisethedistancebetweenendsistoonarrow.Thiscancauseinaccurateregularisationatthetwovoltagesequencesalongthepath[18,19].FDTWisanthesepoints.ComparedwiththeItakura–Parallelogramcon-improvedDTWmethodthatadoptsthestrategyofreducingstraint,theSakoe–Chibabandconstraintissuitablefortimethesearchspace.TheDTWandFDTWdistancessuitableforseriesmatchinginwhichtheoffsetmayoccuratanyloca-measuringthesimilarityofthevoltagecurvesareintroducedastion.Owingtotheuncertaintyoftheoffsetinthevoltagefollows:curves,theoffsetperiodcannotbedetermined.Therefore,thisstudyadoptstheSakoe–Chibabandconstraint,andtheFDTWSupposetwovoltagesequencesXA={a1,a2,…,aNA}anddistancebetweenthevoltagesequencesXAandXBcanbeXB={b1,b2,…,bNB}exist,whereNAandNBrepresenttheexpressedasfollows:lengthsofvoltagesequencesXAandXB,respectively.DTWobtainstheminimumdistancemetricv=DDTW(XA,XB)bydetermininganoptimalwarpingpathbetweenthetwovoltagesequences.Anypaththatsatisfiestheboundaryconditions,continu-ity,andmonotonicitycanbeexpressedasW={w1,w2,…,wt},wheretrepresentsthetotalnumberofelementsinthepathandwtisthecoordinate(i,j)ofthetthpointonthepath.Thewarpingpathwascontinuousandmonotonicallyextendedfromthestarttotheendcell.d(wt)representstheEuclideandistancebetweenaiandbj,whichisthewarpingcostbetweenaiandbj.MultiplewarpingpathsWexist,andanoptimalpaththatmin-imisesthetotalwarpingcostexists,whichcanbeexpressedasfollows:∑TDDTW(XA,XB)=mind(wt)Wt=1(1)Tosolve(1),acumulativedistancematrixRcanbecon-⎧∑Tstructedusingdynamicprogramming,whichcanbeexpressed⎪asfollows:⎪DF(XA,XB)=mind(wt)⎪Wt=1⎧⎪R(i,j−1)⎨s.t.wt=(i,j)(4)⎪⎪⎪⎩S≥i−NNABj⎪R(i,j)=d(i,j)+min⎨R(i−1,j−1)(2)⎪⎪⎩R(i−1,j)whereSistheSakoe–Chibabandsize.wherei=1,2,…,NA,j=1,2,…,NB,R(0,0)=0,andR(i,0)=R(0,j)=+∞.UndertheSakoe–Chibabandconstraint,theFDTWandDTWpathsofsequencesXAandXBareshowninFigure1.Excessivewarpingofthevoltagecurvesisavoided,andtheCHUETAL.395searchspaceisreducedusingtheconstraint,improvingtheTherefore,thelowerboundoftheIFDTWdistancecanbecomputationalefficiencyoftheDTW.expressedasfollows:2.2TheimprovedfastdynamictimeDL(Xi,Xj)=DLB_Keogh(Xi,Xj)(7)warpingdistancecalculationmethodbasedonthefiltersearchTheupperboundoftheIFDTWdistanceistheEuclideandistance,expressedasfollows:TheIFDTWdistancecalculationmethodbasedonthefil-tersearchwasusedinthisstudytoimprovetheaccuracy∑Mandcomputationalefficiencyofthevoltagecurvesimilar-DU(Xi,Xj)=(Xi(t)−Xj(t))2itymeasurement[20].Theupperandlowerboundsofthe(8)IFDTWdistancewereselectedtofilteroutthevoltagesequencesthatdonotsatisfythesimilarityrequirementsandt=1abandonthecalculationofDTWwithhighcalculationcom-plexity,thusfurtherimprovingthecalculationefficiencyoftheThesimilaritymatrixDofthevoltagecurvesforclusteringcanFDTWdistance.ThecalculationprocessoftheIFDTWdis-beobtainedthroughtheIFDTWdistancecalculationmethodtanceofthevoltagecurvesbasedonthefiltersearchisasbasedonfiltersearchasfollows:follows:If(5)issatisfied,Step1:ThematricesoftheupperandlowerbounddistanceDUandDL,whichsatisfyDL(Xi,Xj)<DF(Xi,Xj)<DU(Xi,Xj)are()calculated.forthevoltagedatasetXN×M={X1,X2,…,XN},DXi,Xj=DU(Xi,Xj)(9)whereNisthenumberofconsumersandMisthenumberofdatapointsofonevoltagecurve.Otherwise,Step2:ThedistancematrixDiscalculatedafterthefilter()()search.Thecriterionforthefilteringsearchisasfollows:DXi,Xj=DFXi,Xj(10)DF(Xi(1∶k),Xj(1∶k))+TheIFDTWdistancecalculationmethodbasedonfiltersearch(5)canimprovethemeasurementaccuracyofthemorphologicalsimilaritybetweenvoltagecurvesandthecomputationaleffi-DL(Xi(k+1∶M),Xj(k+1∶M))>𝜀ciencyofFDTW,thusprovidingreliabledataforaccuratephaseidentificationofconsumers.where𝜀isthesimilaritythresholdandkisthefilteringtime.Thelowerandupperbounddistancefunctions,withlow3LOW-VOLTAGEDISTRIBUTIONNETWORKCONSUMER-TRANSFORMERcomputationalcomplexityandcanaccuratelyestimatetheRELATIONSHIPANDPHASEFDTWdistancerange,arecrucialinimprovingtheefficiencyofIDENTIFICATIONMETHODBASEDONtheIFDTWdistancecalculation.TheLB_KeoghlowerboundLOFANDCFSFDPALGORITHMisthebest-knownlowerboundfunction[20];therefore,itisusedinthisstudyasthelowerboundfunctionofIFDTWto3.1LOF-basedabnormalconsumerreducethecomputationalcost.TheLB_Keoghlowerboundisdetectionmethoddefinedasfollows:ThesimilaritybetweenthevoltagecurvesofconsumersintheFortwovoltagesequencesXA={a1,a2,…,aNA}andXBsamedistributionareaismuchhigherthanthatofconsumers={b1,b2,…,bNB},theupperenvelopeofXAisdefinedasindifferentdistributionareas.Therefore,abnormalconsumersU={U1,U2,…,UNA},whereUi=max(ai-S,…ai,…,ai+S).Thewithanincorrectconsumer-transformerrelationshipcanbelowerenvelopeofXAisdefinedasL={L1,L2,…,LNA},whereidentifiedbeforephaseidentification[21–23].Li=min(ai-S,…ai,…,ai+S).SistheSakoe–Chibabandsizethatensurestheconsistencyoftheconstraintspace.Hence,theLOFisadensity-basedlocaloutlierdetectionalgorithmthatLB_KeoghlowerboundDLB_Keoghcanbeexpressedasfollows:utilisestherelativedensityofadatapointanditsKNNdatatocharacterisetheoutlierdegreeofthedata.Itdoesnotdirectly√√determinewhetherthedataisanoutlierpoint,butusestheLOF√√√√√∑NA⎧⎪⎪(bi−Ui)2bi>UiscoreasanindicatortojudgethedegreeofabnormalityofeachDLB_Keogh(XA,XB)=√√⎨(bi−Li)2bi<Li(6)datapointrelativetothelocalneighbourhood.Intheproblem√√i=1⎪investigatedinthisstudy,theelectricaldistanceofconsumersinthesamedistributionareaisclose;therefore,thesimilarityof⎪⎩0theirvoltagecurvesishigh,theelectricaldistanceofconsumersindifferentdistributionareasislarge,andthesimilarityoftheir396CHUETAL.datapoints.Alargelocalreachabledensityimpliesthedatapointsinthek-distanceneighbourhoodofvoltagecurveXiaredense.𝜌(X)=∑Nk(Xi)(13)kidk(Xi,Xj)Xj∈Nk(Xi)5.TheLOFscoreLkofvoltagecurveXiiscalculated,whichcomparestheaveragelocalreachabledensityofallvoltagecurvesinthek-distanceneighbourhoodofvoltagecurveXiwiththelocalreachabilitydensityofvoltagecurveXi.∑𝜌k(Xj)L(X)=Xj∈Nk(Xi)𝜌k(Xi)(14)kiNk(Xi)FIGURE2k-distanceneighbourhoodofvoltagecurveXiTheLOFscoresofthevoltagecurvesarecloseto1whenconsumersbelongtothesamedistributionarea.Agreatervoltagecurvesislow.ThisisinlinewiththeideaoftheLOFdistancebetweentheconsumer’svoltagecurveXiandotheralgorithm.Therefore,theabnormaldegreeofthevoltagecurvevoltagecurvesrepresentsasmallerlocalreachabilitydensityinthedatasetcanbedeterminedbycalculatingthedensityratioandahigherLOFscore.Thisdenotesahigherlikelihoodofbetweeneachvoltagecurveanditsadjacentvoltagecurves.Theawrongtransformer-consumerrelationship.Therefore,con-LOFalgorithmisusedtoidentifyabnormalconsumerswithansumersconnectedtothewrongdistributionareacanbefilteredincorrectconsumer-transformerrelationship.GivenavoltageaccordingtotheLOFscores.Inthisstudy,whentheLOFdatasetX,whereXiisavoltagecurveinX,theidentificationscoreoftheconsumer’svoltagecurveisgreaterthantheprocessisasfollows.threshold,theconsumerisconsideredtobeconnectedtothewrongdistributionarea.Consideringtheactualrequirements1.Thek-distancedk(Xi)ofthevoltagecurveXi,definedofconsumer–transformerrelationshipidentification,throughasthedistancesatisfyingthefollowingtwoconditionsisnumeroussimulationexperiments,abnormalconsumerscanbecalculated:betterdetectedwhenthethresholdissetto2andkissettoa.AtleastkvoltagecurvesexistXj∈X\{Xi},suchthat20accordingto[24].Therefore,whentheLOFscoreoftheD(Xi,Xj)≤dk(Xi).consumer’svoltagecurveisgreaterthan2,theconsumerisb.Atmostk-1voltagecurvesexistXj∈X\{Xi},suchthatconnectedtothewrongdistributionarea.D(Xi,Xj)<dk(Xi).Forexample,whenk=5,anillustrationofdk(Xi)=3.2CFSFDP-basedphaseidentificationD(Xi,Xj5)isshowninFigure2.methodforconsumersinlow-voltagedistributions2.Thek-distanceneighbourhoodofthevoltagecurveXiiscalculated.ElectricityconsumersinthesamedistributionBasedontheCFSFDPalgorithm,theclustercentreissur-systemasconsumerXiaremorelikelytobeincludedintheroundedbyneighbouringpointswithalowerlocaldensityandk-distanceneighbourhoodofconsumerXi.isrelativelyfarfromotherpointswithahigherlocaldensity[25–27].Theprinciplesofsimilarityofvoltagecurvescon-Nk(Xi)={p′∈X∖{Xi}D(Xi,Xj)≤dk(Xi)}(11)formtothealgorithmicassumptionsofCFSFDP;therefore,theCFSFDPalgorithmcanbeusedtoidentifythecorrespondingwhereNk(Xi)isthesetofallvoltagecurveswhoseIFDTWphaseofeachconsumer.Thenumberofclustersandtheselec-tovoltagecurveXiislessthanthek-distanceofvoltagetionofinitialclustercentressignificantlyinfluencetheaccuracycurveXi.oftheCFSFDPalgorithm[28,29].Owingtotheparticularity3.Thek-reachable-distancedk-reachiscalculatedfromvoltageofphaseidentification,thenumberofclustersandtheinitialcurveXitovoltagecurveXj.Whenthek-reachable-distanceclustercentrecanbeselectedinadvanceaccordingtotheactualincreases,thesimilaritybetweenconsumerXjandconsumeroperationstatetoimprovetheaccuracyofthealgorithm.Addi-Xiislow,andtheyarelesslikelytobeinthesamedistributiontionally,thesimilaritymeasureofthevoltagedataiscrucialforsystem.consumerphaseidentificationbasedontheCFSFDP.InsteadoftheconventionalEuclideandistance,acommonlyusedindexdk−reach(Xi,Xj)=max{dk(Xi),D(Xi,Xj)}(12)inCFSFDP,thisstudyusedIFDTWtomeasurethesimilarityofthevoltagecurvesbecauseitensuresclusteringaccuracyand4.ThelocalreachabledensityρkofvoltagecurveXiiscal-improvesclusteringefficiency.Insummary,themainprocessofculated,whichreflectsthedegreeofaggregationofvoltageCHUETAL.397theCFSFDP-basedphaseidentificationmethodforconsumersinlow-voltagedistributionsisasfollows:Step1:Thelocaldensityandrelativedistanceofthevoltagecurvesaredetermined.GiventhevoltagedatasetX={X1,X2,…,XN},thelocaldensityofXi∈X(1≤i≤N)isdefinedasfollows:∑𝜌i=𝜒(D(Xi,Xj)−dc)(15)j≠iwheredcisthecut-offdistanceand𝜒(x)isthecut-offdistanceFIGURE3Theρ–δdistributionofthevoltagecurvesfunction.Whenx<0,𝜒(x)=1,andx≥0,𝜒(x)=0.𝜒(x)canbeusedtodeterminewhetherothervoltagedataareintheneighbourhoodofvoltagedataXi.IntheCFSFDPalgorithm,thelocaldensityofXiisthenumberofvoltagedatapointsintheneighbourhoodofXideterminedusingtheparameterdc.Thevalueofdcshouldbesetsuchthatthenumberofneighbourhoodsinthevolt-agedatasetaccountsfor1%–2%oftheentiredataset.AlargelocaldensityindicatesdensevoltagedataaroundvoltagedataXi,implyingvoltagedataXiismorelikelytobetheclustercentre.TherelativedistanceofXiisdefinedastheminimumvalueofthedistancefromXitoallothervoltagedatawithahigherdensitythanXi,whichcanbeexpressedas:𝛿i=min(D(Xi,Xj))(16)j∶𝜌j>𝜌iThevoltagedatawiththeglobalmaximumdensitydonothaveneighbourswithhigherdensities;therefore,itsrelativedistancecanbedefinedasthemaximumdistancebetweenitandallothervoltagedata.Hence,Equation(16)canbetransformedinto:⎧⎪⎨𝛿i=j∶m𝜌ji>n𝜌i(D(Xi,Xj)),𝜌i<max{𝜌j}(17)FIGURE4Theindicatoroftheclustercentresindescendingorder⎪𝛿i=max(D(Xi,Xj)),𝜌i=max{𝜌j}⎩jTheclustercentresaresurroundedbyneighbourswithlowlocalγitoselecttheclusteringcentreisdefinedas:densities,andthedistancesbetweentheclustercentresandthevoltagedatawithhigherlocaldensitiesarerelativelylarge.𝛾i=𝜌i⋅𝛿i(18)Therefore,alargerrelativedistanceofXimeansXiismorelikelytobetheclustercentre.Alargervalueofγimeansthepointismorelikelytobetheclustercentre;therefore,theindicatoroftheclustercentreγi(1Step2:Adecisiondiagramisgeneratedbasedonthelocal≤i≤N)issortedindescendingorder,asshowninFigure4.densityandrelativedistanceofthevoltagecurves.γiofthenon-clusteringcentreisrelativelysmooth,andanTheoriginalvoltagedatasetismappedtoa2Dspacecom-obviousjumpinthetransitionfromthenon-clusteringcentretoprisingthelocaldensityρandtherelativedistancepointδbycalculatingthelocaldensityandrelativedistanceofallvoltagetheclusteringcentrecanbeobserved,whichcanassistintestingdata.Thus,theclustercentredecisiondiagramofthevoltagedatawasgenerated,asshowninFigure3.therationalityoftheselectionoftheclusteringcentre.ThreedatapointswithlargeρandδvalueswereselectedasStep3:Theremainingvoltagedatapointsareassignedtoatheclustercentresowingtotheparticularityofphaseidenti-ficationinlow-voltagedistributionsystems.Todeterminethecorrespondingphase.appropriateclustercentreofthevoltagedatasetX,theindicatorThevoltagedatapointsofnon-clustercentresareassignedbytheCFSFDPalgorithmtotheclustertowhichthenear-estneighbourswithhigherdensitypointsbelong,whichcanbe398CHUETAL.expressedasfollow:ifD(Xi,Xj)=𝛿ithen(19)Phase(Xi)=Phase(Xj)wherePhase(Xi)isthephaseofconsumeri;3.3ThephaseidentificationevaluationindexThisstudyusedtheDavies-Bouldinindex(DBI)andadjustedrandindex(ARI)toevaluatetheaccuracyofthephaseidentification[30–32].AssumingtheclusteringresultofthevoltagecurvesisC={C1,C2,…,CK},theDBIcanbeexpressedasfollows:1∑Kdavg(Ci)+davg(Cj)rDBI=Ki=1mi≠ajxdcen(Ci,Cj)(20)wheredavg(C)istheaveragedistanceofthevoltagecurvesinclusterCtotheclustercentreofCanddcen(Ci,Cj)isthedistancebetweentheclustercentresofclustersCiandCj.AsmallerDBIrepresentsbetterclusteringperformance.ARIisderivedfromtherandindex(RI),whichcomputesasimilaritymeasurebetweentwoclustersbyconsideringallpairsofsamplesandcountingpairsthatareassignedinthesameordifferentclustersinthepredictedandtrueclusters.TheARIcanbeexpressedas:r=rRI−E(rRI)(21)ARImax(rRI)−E(rRI)whererRI,E(rRI),andmax(rRI)arereal,expected,andmaximumRIvalues,respectively.AlargerARIindicatesbetterclusteringperformance.3.4Theprocessoflow-voltagedistributionFIGURE5Low-voltagedistributionnetworkconsumer-transformernetworkconsumer-transformerrelationshipandrelationshipandphaseidentificationprocessphaseidentificationbasedonthefiltersearchandLOF-CFSFDPalgorithmbasedonthelocaldensityandrelativedistanceofthenormalconsumerdatasetinthedistributionarea.Finally,theclusterAfteridentifyingtheabnormalconsumersinthedistributioncentresweredeterminedaccordingtothedecisiondiagram,andareausingtheanomalydetectionmethodintroducedinSec-thephaseidentificationresultsofthenormalconsumersinthetion3.1,theIFDTWdistancematrixofthenormalconsumerdistributionareawereobtained.voltagedatasetwasusedastheinputoftheCFSFDPalgo-rithmtoidentifythephaseofconsumers.Theflowchartofthe4CASESTUDYlow-voltagedistributionnetworkconsumer-transformerrela-tionshipandphaseidentificationbasedonthefiltersearchandGenerally,100–300single-phaseconsumersexistinlow-voltageLOF-CFSFDPalgorithmisshowninFigure5.First,theorig-distributionsystems[1,33].Inthisstudy,practicallow-voltageinalconsumervoltagedatainthedistributionareawereuseddistributionsystems(YL,MH,TQ1,TQ2,TQ3)inChinaasinput,theIFDTWdistancematrixwasformed,andtheLOFwereusedasexamplestoidentifytheconsumer-transformerscoresofconsumersweredeterminedtoidentifyabnormalcon-sumers.Thus,adecisiondiagramofconsumerdatawasdrawnCHUETAL.399FIGURE6DistributionoftherelationshipbetweenconsumersandtransformersFIGURE8LOFscoresofvoltagecurvesofconsumersTABLE1Accuracycomparisonofdifferentanomalydetectionmodelsforidentificationofconsumer-transformerrelationshipMethodAccuracy/%TP%TN%Proposedmethod100100100K-nearestneighbour[6]93.1892.9994.74DBSCAN[7]97.7397.45100Gaussianmixturemodel[8]95.4510057.89FIGURE7Voltageprofilesof162consumersintheYLandMHTheLOFscoresofallconsumervoltagecurvesaredeter-distributionareasmined,asshowninFigure8,andabnormalconsumersthatdonotbelongtothedistributionsystemcanbeidentified.relationshipandphaseofconsumers.TheYLdistributionsys-temhas157consumers.Basedontheon-the-spotinvestigation,AsshowninFigure8,19consumershadLOFscoresgreateralltheconsumersaresingle-phaseusersandbelongtotheYLthan2.Aftermanualvalidation,the19abnormalconsumersdistributionsystem,ofwhich60areconsumersofphaseA,belongedtothefourdistributionsystemsthathadbeenpre-39areconsumersofphaseB,and58areconsumersofphaseviouslymixedintotheYLdistributionsystem.Thus,itcanbeC.19consumersinfourdistributionsystemsadjacenttotheprovedthattheLOFalgorithmhashighaccuracyandthecon-YLdistributionsystemwererandomlyselectedandmixedwithsumerswithwrongconsumer-transformerrelationshipcanbeconsumersoftheYLdistributionsystemtovalidatethevalidityaccuratelydetected.oftheproposedmethod.Subsequently,thevoltagedataof176consumerswereobtained.ThedistributionoftherelationshipTheLOF-basedabnormalconsumerdetectionmethodbetweentheconsumersandtransformersisshowninFigure6.proposedinthisstudybelongstotheoutlierclassificationalgo-rithm.Therefore,ourproposedmethodiscomparedwiththeThesamplingfrequencyoftheconsumervoltagedatawasoutlierclassificationalgorithmsthatarewidelyusedinengineer-15min,andthesamplingdurationwas1day.Therefore,theing,suchasK-nearestneighbour[6],DBSCAN[7]andGMMdatadimensionsare96.Thevoltageprofilesof157consumers[8].Theaccuracy,thetruepositiverate(TP)andthetruenega-fromYLdistributionsystemand5consumersfromMHdis-tiverate(TN)ofdifferentanomalydetectionmodelsareshowntributionsystemonMarch25,2018areshowninFigure7toinTable1.TPandTNgivetheproportionofcorrectpre-illustratethesimilaritybetweenthevoltagecurvesofconsumers.dictionsinpredictionsofpositiveclassandtheproportionofAsshowninFigure7,theelectricaldistanceofconsumersincorrectpredictionsinpredictionsofnegativeclassrespectively.differentdistributionareasismuchgreaterthanthatofcon-sumersinthesamedistributionarea,whichissuitablefortheAsshowninTable1,comparedwithotheroutlierdetectionLOFalgorithmtoidentifyabnormalconsumerswithawrongalgorithms,thealgorithmproposedinthisstudyhasthehighestconsumer-transformerrelationship.accuracyinlow-voltagedistributionsystems.LocalandglobalpropertiesofthevoltagedatasetareconsideredwithLOF-basedabnormalconsumerdetectionmethod,andnoticeablediffer-encesinthedensityofthevoltagedataclustersindifferentdistributionsystemsexist.Therefore,theproposedmethodcan400CHUETAL.TABLE2TheinfluenceofsimilaritymeasurementontheaccuracyofphaseidentificationofconsumersinthedistributionsystemCalculationTheaccuracyofphaseidentification/%time/s91.8MethodPhaseAPhaseBPhaseCOverall211.7636.1IFDTW+LOF-CFSFDP10090.7010097.530.3FDTW+LOF-CFSFDP[34]10090.7010097.53DTW+LOF-CFSFDP[7]10090.7010097.53Euclideandistance+LOF-CFSFDP74.3610092.8685.80TABLE3ThecomparisonofevaluationindicatorsofphaseidentificationTABLE4PhaseidentificationresultsofDBSCANwithdifferentwithdifferentmethodsproportionsofabnormalconsumersMethodAP/%DBARITheproportionofAccuracyofphaseidentificationwithabnormalconsumersDBSCAN/%IFDTW+LOF-CFSFDP97.531.2420.933(%)Spectralclusteringalgorithm[19]59.880.7780.482PhaseAPhaseBPhaseCOverallDBSCANalgorithm[7]96.911.3380.9271.8810010092.0696.863.0910010092.0696.914.2710010092.0696.955.4210092.8689.2393.98effectivelysatisfytherequirementsofconsumer-transformer6.7986.2781.2587.9386.30relationshipidentification.racyofphaseidentificationishigherthanthatofthespectralThisstudyimplementedphaseidentificationwithdifferentclusteringmethod.However,theDBSCANalgorithmissensi-similaritymeasurementmethodstoillustratetheinfluenceoftivetoinputparametersandperformspoorlyondatasetswithsimilaritymeasurementsontheaccuracyofphaseidentificationhigherdimensions.However,themethodproposedinthisworkinalow-voltagedistributionsystem.ThephaseidentificationhasstrongadaptabilitytodataandabetterclusteringeffectbyresultsarepresentedinTable2.identifyingabnormalconsumersinthedistributionsysteminadvanceandclusteringthevoltagedataofnormalconsumers.AsshowninTable2,thephaseidentificationaccuracyTheARIandDBIofthemethodproposedinthisworkarewithEuclideandistanceis85.80%.Incontrast,theaccu-0.933and1.242,respectively,whichisbetterthanthatoftheracyofphaseidentificationusingIFDTWwas97.53%.TheDBSCANalgorithm.ItcanbeseenthattheproposedmethodcalculationspeedoftheEuclideandistancewasthefastest;canimprovetheaccuracyofphaseidentificationbyabetterhowever,theEuclideandistancecannotaccuratelymeasuresimilaritymeasureforthevoltagecurves.thesimilarityofthevoltagecurves,resultinginlowerphaseidentificationaccuracy.ThesearchspaceofFDTWpathsTheaccuraciesofthephaseidentificationofDBSCANandwaslimitedowingtotheSakoe–Chibaconstraints;there-IFDTW+LOF-CFSFDPwithdifferentproportionsofabnor-fore,thecomputationalefficiencyishigherthanthatofthemalconsumersarelistedinTables3and4tovalidatetheDTWalgorithm.FiltersearchwasusedinIFDTWtofurtherstabilityofthemethodproposed.improvethecalculationefficiencyofFDTW,achievingabalancebetweenthecalculationefficiencyandthephaseidentificationThephaseidentificationaccuracyshowsthepercentageofaccuracy.correctassignmentsineachcluster,andtheoverallaccuracyshowstheoverallaccuracyofthephaseidentificationalgo-Tofurthervalidatetheeffectivenessoftheproposedmethod,rithm.AsshowninTables3and4,theaccuracyofthespectralclustering[19]andDBSCANalgorithmswereusedDBSCANmethoddecreasedwhentheproportionofabnor-forcomparison.Theaccuracyofthephaseidentification(AP),malconsumersincreasedfrom4.27%to5.42%.AccordingtoDBI,andARIwereusedtoevaluatethephaseidentificationthephaseidentificationresults,fiveconsumersofphaseAwereresults,whicharelistedinTable3.misidentifiedasphaseCwhentheproportionofabnormalcon-sumerswas1.88%,3.09%,and4.27%.SevenconsumersofAsshowninTable3,forthevoltagedataoftheYLdistribu-phaseAweremisidentifiedasphaseCandthreeconsumerstionsystem,ourproposedmethodhasthehighestidentificationofphaseAweremisidentifiedasphaseBwhenthepropor-accuracyrate.Theidentificationaccuraciesofthespectraltionofabnormalconsumerswas5.42%.SevenconsumersofclusteringandDBSCANalgorithmsare59.88%and96.91%,phaseAweremisidentifiedasphaseC,nineconsumersofrespectively.ThisisbecausetheeffectivenessofthespectralphaseAweremisidentifiedasphaseB,andsevenconsumersclusteringalgorithmdependsontheclusteringmethodandtheofphaseCweremisidentifiedasphaseAwhentheproportionsimilaritymatrix,andtheidentificationofoutliersusingthespectralclusteringalgorithmischallenging;therefore,theiden-tificationaccuracyisrelativelylow.TheDBSCANalgorithmcanidentifyoutliersandhasbetterrobustness;therefore,theaccu-CHUETAL.401TABLE5PhaseidentificationresultsofIFDTW+LOF-CFSFDPwithmethodbasedonfiltersearchandtheLOF-CFSFDPalgorithmdifferentproportionsofabnormalconsumerstorectifytheerrorsoftheconsumer-transformerrelationshipandphaseinformationcausedbyuntimelyupdatingorineffi-TheproportionAccuracyofphaseidentificationwithOverallcientchecking.TheFDTWdistancebasedonthefiltersearchofabnormalIFDTW+LOF-CFSFDP/%wasemployedtomeasurethesimilarityofthevoltagecurvesconsumers(%)moreaccurately.Next,consumerswithincorrectconsumer-PhaseAPhaseBPhaseCtransformerrelationshipswereaccuratelyidentifiedusingtheIFDTWdistanceandLOF-basedabnormalconsumerdetection1.8810090.7010097.50method.Thus,theCFSFDP-basedphaseidentificationmethodwasproposedtoidentifythephaseinformationofelectrical3.0910090.7010097.53consumerswithacorrectconsumer-transformerrelationshipinlow-voltagedistributionsystems.Finally,practicalcasesin4.2710090.7010097.56Chinawerepresented.Theproposedmethodcouldachievehigheraccuracyandrobustnesscomparedwithotheralgorithms5.4210090.7010097.59indifferentdataenvironments.Itisnoticeablethatthecon-sumersofthelow-voltagedistributionsystemsinthisstudy6.7910090.7010097.63aresingle-phaseusers.Undoubtedly,thephaseidentificationoflow-voltagedistributionsystems,includingthree-phaseusersisTABLE6Comparisonofthephaseidentificationaccuracywithdifferentcrucialforfutureresearch.samplingfrequenciesAP/%SamplingSamplingDataDBSCANIFDTW+LOF-ACKNOWLEDGEMENTSfrequencytimedimensionCFSFDPThisstudywassupportedbytheJointFundoftheNational96.91NaturalScienceFoundationofChina(No.U2166206).15min1day9689.5197.5330min1day4882.7297.531h1day2466.0597.531day31days3167.52CONFLICTOFINTERESTTheauthordeclaresnoconflictofinterest.ofabnormalconsumerswas6.79%.ComparedwiththeDATAAVAILABILITYSTATEMENTDBSCANmethod,theaccuracyoftheproposedmethodisThedatathatsupportthefindingsofthisstudyareavailable97.56%withdifferentproportionsofabnormalconsumers,fromthecorrespondingauthoruponreasonablerequest.whichishigherthanthatofDBSCAN.Accordingtothephaseidentificationresults,fourconsumersofphaseAwereORCIDhttps://orcid.org/0000-0001-5403-2137misidentifiedasphaseB,withallproportionsofabnormalcon-ZhenyueChuhttps://orcid.org/0000-0003-2125-9604sumers.AsshowninTable5,thephaseidentificationresultsZhenzhiLinwithIFDTW+LOF-CFSFDPachievedanoverallaccuracyofatleast97%.Therefore,theproposedmethodcanachievegoodREFERENCESeffectivenessandpracticability.1.Pappu,S.,Bhatt,N.,Pasumarthy,R.,etal.:IdentifyingtopologyoflowTheeffectsofdifferentsamplingfrequenciesontheaccuracyvoltagedistributionnetworksbasedonsmartmeterdata.IEEETrans.ofphaseidentificationassumingafixednumberofabnormalSmartGrid.9(5),5113–5122(2018)consumers(fiveabnormalconsumers)arelistedinTable6.2.Lisowski,M.,Masnicki,R.,Mindykowski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