Distribution System State Estimation: A Semidefinite Programming Approach

Distribution system state estimation (DSSE) is one of the vital components in the next-generation distribution management system (DMS), which allows the operators to monitor the entire system’s operating conditions. Due to the lack of real-time measurements, DSSE has to process measurements whose quality varies significantly across different sources, which causes convergence issue to the Gauss-Newton solver. In this paper, a semidefinite programming (SDP) framework is developed to reformulate the DSSE problem into a rank-constrained SDP problem. One challenge of this technique is the nonconvex rank-one constraint, which is generally relaxed. However, the relaxed SDP-DSSE problem cannot guarantee a rank-one solution and hence lose optimality. Therefore, we propose two solution approaches, namely the rank reduction approach and the convex iteration approach, to obtain rank-one solutions for the SDP-DSSE problem. The proposed model and the effectiveness of the proposed solution approaches are numerically demonstrated on the IEEE 13-, 34-bus, and 123-bus distribution systems.