Data-Driven Learning-Based Optimization for Distribution System State Estimation

Distribution system state estimation (DSSE) is a core task for monitoring and control of distribution networks. Widely used algorithms such as Gauss–Newton perform poorly with the limited number of measurements typically available for DSSE, often require many iterations to obtain reasonable results, and sometimes fail to converge. DSSE is a non-convex problem, and working with a limited number of measurements further aggravates the situation, as indeterminacy induces multiple global (in addition to local) minima. Gauss–Newton is also known to be sensitive to initialization. Hence, the situation is far from ideal. It is therefore natural to ask if there is a smart way of initializing Gauss–Newton that will avoid these DSSE-specific pitfalls. This paper proposes using historical or simulation-derived data to train a shallow neural network to “learn to initialize,” that is, map the available measurements to a point in the neighborhood of the true latent states (network voltages), which is used to initialize Gauss–Newton. It is shown that this hybrid machine learning/optimization approach yields superior performance in terms of stability, accuracy, and runtime efficiency, compared to conventional optimization-only approaches. It is also shown that judicious design of the neural network training cost function helps to improve the overall DSSE performance.