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Traditional state estimation (SE) methods that
are based on nonlinear minimization of the sum of localized
measurement error functionals are known to suffer from nonconvergence
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 is
mathematically a quadratic programming (QP) problem with
closed-form solution. Furthermore, this formulation imposes
additional topology-based constraints that provably shrink the
feasible region and promote convergence to a more physically
meaningful solution. From a probabilistic viewpoint, we show
that our method applies prior knowledge into the estimate, thus
converging to a more physics-based estimate than the
traditional observation-driven maximum likelihood estimator
(MLE). Importantly, incorporation of the entire system
topology and underlying physics, while being linear, makes
ECF-based SE advantageous for large-scale systems.
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