%0 Journal Article %A Roel Dobbe %A Werner van Westering %A Stephan Liu %A Daniel Arnold %A Duncan S Callaway %A Claire Tomlin %B IEEE Transactions on Power Systems %D 2020 %G eng %N 3 %P 1674 - 1683 %R 10.1109/TPWRS.2019.2955893 %T Linear Single- and Three-Phase Voltage Forecasting and Bayesian State Estimation With Limited Sensing %V 35 %8 11/2019 %! IEEE Trans. Power Syst. %X

Implementing state estimation in low and mediumvoltage power distribution is still challenging given the scale of many networks and the reliance of traditional methods on a large number of measurements. This paper proposes a method to improve voltage predictions in real-time by leveraging a limited set of real-time measurements. The method relies on Bayesian estimation formulated as a linear least squares estimation problem, which resembles the classical weighted least-squares (WLS) approach for scenarios where full network observability is not available. We build on recently developed linear approximations for unbalanced three-phase power flow to construct voltage predictions as a linear mapping of load predictions constructed with Gaussian processes. The estimation step to update the voltage forecasts in real-time is a linear computation allowing fast high-resolution state estimate updates. The uncertainty 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 test feeders and validated on a real test feeder with the utility Alliander in The Netherlands.