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{"title":"Constrained State Estimation with Probabilistic Error Model for Underdetermined Systems Such as Distribution Network","authors":"Masatoshi Kumagai, Masahiro Watanabe","doi":"10.1002/tee.70054","DOIUrl":null,"url":null,"abstract":"<p>Constrained state estimation (CSE) clarifies the interval of the feeder voltage profile of an unobservable distribution network containing fewer telemetric sensors than state variables to be estimated. By using the given information about the power flow equations and network operating ranges such as maximum load and photovoltaic generator ratings, CSE provides the estimation interval that minimizes the square error against the partial telemetric measurements while satisfying the network operating ranges. We also developed a probabilistic model of the estimation error outside the estimation interval characteristic of the CSE algorithm. The probabilistic error model is derived by superposition of the error distribution around the arbitrary estimation within the estimation interval. The validity of the probabilistic error model was confirmed by a case study simulation on a benchmark network, in which the model-based probabilistic error distribution well explained the simulation-based estimation errors. This result is necessary to understand the estimation accuracy of CSE for the voltage control application of the distribution network. © 2025 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.</p>","PeriodicalId":13435,"journal":{"name":"IEEJ Transactions on Electrical and Electronic Engineering","volume":"20 8","pages":"1186-1194"},"PeriodicalIF":1.1000,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEJ Transactions on Electrical and Electronic Engineering","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/tee.70054","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
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Abstract
Constrained state estimation (CSE) clarifies the interval of the feeder voltage profile of an unobservable distribution network containing fewer telemetric sensors than state variables to be estimated. By using the given information about the power flow equations and network operating ranges such as maximum load and photovoltaic generator ratings, CSE provides the estimation interval that minimizes the square error against the partial telemetric measurements while satisfying the network operating ranges. We also developed a probabilistic model of the estimation error outside the estimation interval characteristic of the CSE algorithm. The probabilistic error model is derived by superposition of the error distribution around the arbitrary estimation within the estimation interval. The validity of the probabilistic error model was confirmed by a case study simulation on a benchmark network, in which the model-based probabilistic error distribution well explained the simulation-based estimation errors. This result is necessary to understand the estimation accuracy of CSE for the voltage control application of the distribution network. © 2025 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.
基于概率误差模型的配电网络等欠定系统约束状态估计
约束状态估计(CSE)明确了不可观测配电网馈线电压分布的区间,其中遥测传感器数量少于待估计的状态变量。CSE利用给定的潮流方程和网络运行范围信息,如最大负荷和光伏发电机额定值,给出了在满足网络运行范围的情况下,对部分遥测测量的平方误差最小的估计区间。我们还建立了CSE算法估计区间外估计误差的概率模型。通过对估计区间内任意估计周围的误差分布进行叠加,得到概率误差模型。通过对一个基准网络的实例研究仿真,验证了概率误差模型的有效性,基于模型的概率误差分布很好地解释了基于仿真的估计误差。这一结果对于了解CSE在配电网电压控制应用中的估计精度是必要的。©2025日本电气工程师协会和Wiley期刊有限责任公司。
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