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

• According to the characteristics of the measured data of distribution network, we develop a physics-informed matrix completion framework that incorporates multiphase power flow equality constraints, with hybrid data-physics fusion strategy enhanced missing-data recovery capability. • The algorithms in this paper also consider the missing of single section data and time series data, improves the data scale that can be completed by the algorithm, and controls the completion error at a low level, ensuring the effectiveness of the algorithm in the analysis of distribution network measurement data. • The proposed methodology employs VMD to decouple the inherent multiscale characteristics of spatiotemporal measurement data, where the low-frequency components are processed through ARIMA modeling for trend extrapolation, while high-frequency residuals are analyzed via LSTM networks to capture temporal dynamics. This hybrid decomposition-reconstruction architecture demonstrates prediction accuracy improvements of 38% RMSE reduction. • Under severe data incompleteness conditions, the proposed algorithm maintains solution stability through adaptive regularization based on real-time observability evaluation and physical constraint, effectively prevents significant estimation bias or even non-operation situations. . 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. This paper proposes an alternating minimization matrix completion method (MC) based on constrained low-rank matrices combined with variational mode decomposition (VMD), autoregressive integrated moving average (ARIMA) model, and long short-term memory (LSTM) neural network. This algorithm first employs MC model to handle single-time-slice data missing problems, and then utilizes VMD to decouple the inherent multiscale characteristics of spatiotemporal measurement data. Specifically, the low-frequency components are processed through ARIMA model, while the high-frequency residuals are analyzed via LSTM network. This study can enhance effectiveness in both multi-timescale data completion and state estimation under low-observability distribution network conditions. .