Contextual Robust State Estimation in Distribution Systems with Real-Time Unobservability and Scarce Data

Abstract

Distribution system state estimation faces a double information shortage: real-time measurements are often too sparse to guarantee observability, while historical data, despite being abundant, rapidly loses representativeness as operating conditions evolve. This paper proposes a data-driven methodology that addresses both challenges simultaneously. We first introduce a $K$-nearest neighbor estimator that approximates the conditional distribution of delayed measurements given the available real-time context, casting state estimation as a weighted least squares problem over plausible pseudo-measurement scenarios. Building on this, we develop a Contextual Robust State Estimator (CR-SE) that explicitly accounts for the statistical uncertainty arising from the estimation of pseudo-measurements. Rather than protecting against gross errors or bad data, CR-SE hedges against potential misspecification of the conditional distribution by optimizing over an adversarial reweighting of the nearest neighbors subject to contextual proximity and monotonicity constraints. The resulting min-max problem admits an equivalent single-level reformulation with essentially the same computational tractability as the baseline estimator. Furthermore, the robustness parameter is selected online through a fully data-driven validation procedure based on the most recent training instance. Numerical experiments on the IEEE 38-bus and modified IEEE 123-bus radial networks, as well as the meshed IEEE 30-bus active distribution network, show that CR-SE consistently outperforms the baseline across a wide range of measurement availability, training sizes, and loading conditions, achieving tail-error reductions of up to 18%, with the largest gains occurring precisely in the most challenging scenarios.