Distribution system state estimation using semidefinite programming

Growing penetration of distributed energy resources connected to power distribution networks requires accurate, robust, and dependable real-time system monitoring tools. This paper considers the state estimation (SE) problem in distribution systems and proposes a new convex relaxation based approach to solve it as a semidefinite programming problem. Even with a simple 4-bus case, we have identified that existing approaches such as the iterative Newton´s method are more prone to convergence issues when measurement quality varies more significantly across different sources. By relaxing the SE problem to a convex SDP, the proposed method has the potential to closely attain the globally optimum solution without suffering from numerical issues caused by the inclusion of e.g., ‘virtual measurements’ at zero-injection nodes. Numerical tests have been performed on the IEEE 4-bus and 13-bus test feeder cases to demonstrate the feasibility and effectiveness of the proposed approach.