Bayesian Deep Unfolding for State Estimation in Power Distribution Grids

There has been a significant increase in integration of renewable energy resources into the power distribution grid. This trend demands enhanced situational awareness for reliable control and operation of the power distribution network. Fast and accurate distribution system state estimation (DSSE) is a key step in achieving situational awareness. This study proposes a novel approach termed "deep unfolding," which combines data-driven principles with a model-based neural network architecture to estimate system states in low-observable distribution networks accurately. Our proposed method does not require the distribution system model information. Instead, it relies solely on measurements obtained from sensing devices like mu PMUs and SCADA sensors. Conversely, the "model-based" aspect involves a departure from traditional model-agnostic neural networks. Instead, our approach constructs a neural network by unfolding the iterations of the alternating direction method of multipliers (ADMM) solver into the layers of a neural network. In this paper, for the first time, the deep unfolding approach is augmented with Bayesian neural networks to estimate both the mean and covariance of the system states. Extensive simulation on the IEEE 123 bus network validates the efficacy of our approach in estimating system states while providing associated confidence intervals.