A Bayesian Method to Infer Parameters in Power Flow Models Using Linear Sensitivities

This paper presents a Bayesian method to infer parameters in distribution system power flow models from noisy measurements of voltage magnitudes and phase angles along with active- and reactive-power injections collected from a subset of buses with synchronized phasor measurement capability. The proposed method bypasses the large number of repeated nonlinear power flow solutions that would typically be required in sampling-based Bayesian inference. Instead, the proposed method iteratively and analytically linearizes the nonlinear power flow model, converging to the linearized model with the maximum probability of being (closest to) the actual nonlinear model that gave rise to the measurement data. The combination of the linear system, Gaussian parameter prior, and Gaussian measurement noise enables closed-form evaluation of the parameter posterior, model evidence, and their gradients. This can help to improve computational scalability for large-scale networks with potentially many unknown parameters to be inferred. We illustrate the effectiveness and key features of the proposed method with numerical case studies involving the IEEE 33-bus test system.