Double-Layers Stacking Estimation Model for Feeder Statistical Line Loss Rate Based on Tree-Based Ensemble Learning and MoE
Wang Shouxiang1,2, Zhang Bingjie1,2, Zhao Qianyu1,2, Guo Luyang1,2, Zhang Sheng1,2
1. Key Laboratory of Smart Grid of Ministry of Education Tianjin University Tianjin 300072 China; 2. Tianjin Key Laboratory of Power System Simulation and Control Tianjin University Tianjin 300072 China
Abstract Reducing line loss is important for power grids to save energy and achieve carbon neutrality. Statistical line loss rate is an important indicator for the refined management of line loss in the power grid. However, abnormal data collection of power consumption, interruption of data transmission and other factors lead to the abnormality or missing of statistical line loss rate. At present, the ensemble learning framework is applied to the field of line loss estimation, but models used for estimation are all machine learning models, so the estimation accuracy needs to be improved. In order to improve the accuracy of statistical line loss rate estimation, a double-layers estimation model for feeder statistical line loss rate based on tree-based ensemble learning and mixture of experts (MoE) is proposed. Firstly, the maximum information coefficient (MIC) is used to effectively analyze the nonlinear relationship between the statistical line loss rate and its correlated features, so as to build a feature set of statistical line loss rate. Secondly, the feature vector of each feeder is input to the robust K-Medoids clustering algorithm to realize the fine division of feeders. Thirdly, using the Stacking integrated learning framework, the feeder statistical line loss rate is estimated in two stages based on the base estimation and meta estimation double-layer models. The decision tree, gradient boosting decision tree (GBDT), adaptive Boosting (AdaBoost), extreme gradient Boosting (XGBoost), random forest and extremely randomized tree (ExtraTree) are selected as base estimation models for preliminary estimation of the statistical line loss rate, and the output results of each base estimation model are input into the meta estimation model MoE for final estimation. A comprehensive set of experiments has been conducted on a real-world feeder statistical line loss rate dataset (1) The MIC values of statistical line loss rate and theoretical line loss rate, total length of line, line power supply, line operation time, rated capacity of distribution transformer, operation time of distribution transformer are respectively 0.948, 0.81, 0.701, 0.672, 0.768 and 0.683, which demonstrates the high correlation between each feature and the statistical line loss rate. (2) Feature vectors are fed into the K-medoids algorithm, feeders are divided into three parts. Through clustering, the total RMSE and MAE of statistical line loss rate estimated by the proposed model are decreased by 5% and 7% respectively. (3) Compared with other models, the error distribution of proposed model is concentrated in the low error area, and the between the median value and the mean value is closer, which means the proposed model has better accuracy and stability. The comparison between the proposed model and other ensemble model which has the best performance shows that, the RMSE of each type of feeders estimated by the proposed model are reduced by 4%, 2%, 5% respectively, and the MAE of each type of feeders estimated by the proposed model are reduced by 10%, 3%, 9% respectively. The following conclusions can be drawn from the simulation analysis: (1) The maximum information coefficient is used to verify the rationality of using the theoretical line loss rate and its related features for feeder clustering and statistical line loss rate estimation. (2) Compared with direct estimation, the estimation accuracy of statistical line loss rate can be improved by clustering feeders using K-medoids algorithm. (3) Compared with the existing ensemble estimation model, the estimation model proposed in this paper has lower RMSE and MAE, which means the statistical line loss rate estimated by the proposed model is more reasonable.
Wang Shouxiang,Zhang Bingjie,Zhao Qianyu等. Double-Layers Stacking Estimation Model for Feeder Statistical Line Loss Rate Based on Tree-Based Ensemble Learning and MoE[J]. Transactions of China Electrotechnical Society, 2024, 39(3): 774-784.
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2024, Vol. 39 
