A Circuit-Theoretic Approach to State Estimation

2019 
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.
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