Matrix Completion Using Alternating Minimization for Distribution System State Estimation

TL;DR

This paper introduces an efficient alternating minimization algorithm for matrix completion in power distribution system state estimation, improving scalability and accuracy with time-series data under low-observability conditions.

Contribution

It reformulates the constrained matrix completion problem as a bilinear optimization and proves its convergence, enabling scalable state estimation with historical data.

Findings

Algorithm converges reliably and efficiently.

Scalability demonstrated on IEEE 123-bus system.

Adding historical data improves accuracy and reduces computation time.

Abstract

This paper examines the problem of state estimation in power distribution systems under low-observability conditions. The recently proposed constrained matrix completion method which combines the standard matrix completion method and power flow constraints has been shown to be effective in estimating voltage phasors under low-observability conditions using single-snapshot information. However, the method requires solving a semidefinite programming (SDP) problem, which becomes computationally infeasible for large systems and if multiple-snapshot (time-series) information is used. This paper proposes an efficient algorithm to solve the constrained matrix completion problem with time-series data. This algorithm is based on reformulating the matrix completion problem as a bilinear (non-convex) optimization problem, and applying the alternating minimization algorithm to solve this problem. This paper proves the summable convergence of the proposed algorithm, and demonstrates its efficacy and scalability via IEEE 123-bus system and a real utility feeder system. This paper also explores the value of adding more data from the history in terms of computation time and estimation accuracy.