  AC State Estimation (ACSE) is widely recognized as a practical approach for
determining the grid states in steady-state conditions. It serves as a
fundamental analysis to ensure grid security and is a reference for market
dispatch. As grid complexity increases with rapid electrification and
decarbonization, there is a growing need for more accurate knowledge of the
grid operating state. However, existing ACSE algorithms have technical gaps.
Critically, current ACSE algorithms are susceptible to erroneous system
parameters, which are assumed to be fixed in traditional approaches. In this
paper, we build a novel circuit-theoretic joint parameter-state estimation
algorithm to address this limitation. The innovative algorithm builds an
analogous equivalent circuit of the grid with states and certain parameters
unknown. It solves a circuit-constrained optimization to estimate the most
likely grid states and parameters given a set of measurements. Further, it
quantifies the goodness of the estimated output by formulating tight convex
envelopes around the original non-convex problem to quantify the quality of
estimates. We compare the various proposed approaches on systems with up to
2869 nodes while demonstrating a tradeoff between solution optimality and model
fidelity.
