基于张量分解的智能电表电压数据缺失填补算法

A Missing Voltage Data Imputation Algorithm for Smart Meters Based onTensor Decomposition

为了降低配电台区智能电表采集的电压监测数据缺失给电力监测、供电质量分析精确度所带来的负面影响,针对传统算法利用二维数据分布特征填补数据缺失的不足,提出了一种基于张量分解的填补算法来估计智能电表电压数据的部分缺失。首先随机抽取一条线路相邻台区智能电表连续7天的电压数据样本,构建三阶张量模型,分析张量数据各维度间的相关性;然后基于电压数据各维度间的相关性,通过CANDECOMP-PARAFAC分解(CP分解)过程,将张量分解成3个一维的因子矩阵,利用交替最小二乘法进行因子矩阵的迭代更新,达到预设的最大迭代次数时,即可得到缺失电压的估计值。实验结果表明,基于张量分解的电压缺失数据填补算法能够充分利用电压数据在各维度间的相关性,填补衡量电力系统电能质量时有价值的缺失参数。在65%至80%缺失率下,缺失值填补误差显著低于传统的K近邻(K-nearest neighbor,KNN)缺失值填补算法,有效解决了高缺失率下的电压数据缺失问题。三阶张量建模为处理智能电表电压数据缺失问题提供了新的角度。

The missing voltage data sampled by smart power meters tends to have negative impacts on statistical inference accuracy of the power grid parameter surveillance and power supply quality analysis.To address this issue,this paper proposes a tensordecomposition-based imputation algorithm to estimate the voltage data that is partially missing on smart voltage meters.First,voltage data of seven consecutive days,on smart voltage meters of neighboring transformer districts,is randomly sampled,and a thirdorder tensor model is built,before the correlation between the dimensions of the tensor data is analyzed.Second,based on the correlation between the dimensions of the voltage data,the tensor is decomposed into three one-dimensional factor matrices through the CP(CANDECOMP-PARAFAC)decomposition process,and the missing voltage data can be estimated when a preset number of iterations is reached after the factor matrix is iteratively updated using alternating least squares method.It turns out that via this approach,the correlation among the voltage data across dimensions can be fully utilized to make up the missing picture of valuable parameters for power grid performance measurement.In cases where as large as 65%-80%voltage data is missing,the deviation level via the proposed approach in this paper,is significantly lower than the that via the approach based on traditional K-nearest neighbor(KNN)missing value imputation algorithm.The third-order tensor modeling based approach proposed in this paper provides a new perspective for dealing with missing voltage data on smart meters in power grids.