Outlier Reconstruction Based Distribution System State Estimation Using Equivalent Model of Long Short-term Memory and Metropolis-Hastings Sampling

The accuracy of distribution system state estimation (DDSE) is reduced when phasor measurement unit (PMU) measurements contain outliers because of cyber attacks or global positioning system spoofing attacks. Therefore, to enhance the robustness of DDSE to measurement outliers, approximate the target distribution of Metropolis-Hastings (MH) sampling, and judge the prediction of the long short-term memory (LSTM) network, this paper proposes an outlier reconstruction based state estimation method using the equivalent model of the LSTM network and MH sampling (E-LM model), motivated by the characteristics of the chronological correlations of PMU measurements. First, the target distribution of outlier reconstruction is derived using a kernel density estimation function. Subsequently, the reasons and advantages of the E-LM model are explained and analyzed from a mathematical point of view. The proposed LSTM-based MH sampling can approximate the target distribution of MH sampling to decrease the number of the futile iterations. Moreover, the proposed MH-based forecasting of the LSTM can judge each LSTM prediction, which is independent of its true value. Finally, simulations are conducted to evaluate the performance of the E-LM model by integrating the LSTM network and the MH sampling into the outlier reconstruction based DDSE.