A Circuit-Theoretic Approach to State Estimation

Traditional state estimation (SE) methods that are based on nonlinear minimization of the sum of localized measurement error functionals are known to suffer from non-convergence and large residual errors. In this paper we propose an equivalent circuit formulation (ECF)-based SE approach that inherently considers the complete network topology and associated physical constraints. We analyze the mathematical differences between the two approaches and show that our approach produces a linear state-estimator that imposes additional topology-based constraints to shrink the feasible region of the estimator and promote convergence to a more physically meaningful solution. From a probabilistic viewpoint, we show that under independent Gaussian noise assumption, our method applies prior knowledge into the estimate, thus converging to a more physics-based estimate than traditional purely observation-driven methods such as the maximum likelihood estimator (MLE). Importantly, this incorporation of entire system topology and physics while being linear makes ECF-based SE advantageous for large-scale systems.