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Implementing state estimation in low and medium voltage power distribution isstill challenging given the scale of many networks and the reliance oftraditional methods on a large number of measurements. This paper proposes amethod to improve voltage predictions in real-time by leveraging a limited setof real-time measurements. The method relies on Bayesian estimation formulatedas a linear least squares estimation problem, which resembles the classicalweighted least-squares (WLS) approach for scenarios where full networkobservability is not available. We build on recently developed linearapproximations for unbalanced three-phase power flow to construct voltagepredictions as a linear mapping of load predictions constructed with Gaussianprocesses. The estimation step to update the voltage forecasts in real-time isa linear computation allowing fast high-resolution state estimate updates. Theuncertainty in forecasts can be determined a priori and smoothed a posteriori,making the method useful for both planning, operation and post-hoc analysis.The method outperforms conventional WLS and is applied to different testfeeders and validated on a real test feeder with the utility Alliander in TheNetherlands.

Linear Single- and Three-Phase Voltage Forecasting and Bayesian State Estimation with Limited Sensing