  An equivalent circuit formulation for power system analysis was demonstrated
to improve robustness of Power Flow and enable more generalized modeling,
including that for RTUs (Remote Terminal Units) and PMUs (Phasor Measurement
Units). These measurement device models, together with an adjoint circuit based
optimization framework, enable an alternative formulation to Power System State
Estimation (SE) that can be solved within the equivalent circuit formulation.
In this paper, we utilize a linear RTU model to create a fully linear SE
algorithm that includes PMU and RTU measurements to enable a probabilistic
approach to SE. Results demonstrate that this is a practical approach that is
well suited for real-world applications.
