A Study on the Sensitivity Matrix in Power System State Estimation by Using Sparse Principal Component Analysis

This paper analyzes the joint impact of uncertainties in the input data on the power system state estimator. The approach is based on the sensitivity analysis of the estimated telemetry data with respect to the measurement data and the branch parameters with the main goal of locating relevant input components. In order to find relevant inputs, we analyze the normalized sensitivity matrix by sparse principal component analysis (PCA). The non-zero entries of the loading vectors related to the dominant principal components are considered to be the relevant inputs to the state estimator as they mainly contribute to the amplification of the estimated values. It turns out that PCA shows an elementary structure of the sensitivity matrix: All non-zero entries of a loading vector corresponding to a positive singular value belong either to the telemetry data or to the branch data. We show that this property is also valid for PCA with different sparsity-promoting constraints on the loading vector. The proposed analysis method is demonstrated by a numerical study.