Method for compensating multi-time measurement data of distribution network based on alternating minimization matrix completion combined with VMD-ARIMA-LSTM

Abstract

Modern distribution networks with high penetration of distributed energy resources (DERs) are undergoing continuous expansion in scale. However, the increasing complexity of network structure and the high installation cost of measurement equipment introduce operational challenges including state variability and measurement data incompleteness. Substantial data loss significantly compromises fault detection accuracy and network performance, creating obstacles for distributed energy management and posing critical challenges to distribution network state estimation. To address these issues, this paper proposes a hybrid state estimation framework (MC-VMD-ARIMA-LSTM) that integrates alternating-minimization matrix completion (MC) with variational mode decomposition (VMD), autoregressive integrated moving average (ARIMA) modeling, and long short-term memory (LSTM) neural networks for enhanced power flow analysis in low-observability distribution networks. The methodology features a dual-timescale approach: (1) At individual time intervals, an alternating-minimization matrix completion model is formulated, incorporating linearized power flow constraints; (2) For multi-timescale analysis, the measurement dataset undergoes VMD-based decomposition, with subsequent specialized processing where ARIMA handles low-frequency components and LSTM manage high-frequency residuals. The results of state estimation are obtained through systematic component reconstruction. Comprehensive evaluations using IEEE 33-bus distribution network and actual distribution system measurement datasets demonstrate the framework's effectiveness in both multi-timescale data assimilation and state estimation accuracy under limited observability conditions.