A Framework for Analytical Power Flow Solution Using Gaussian Process Learning

Abstract

This paper proposes a novel analytical solution framework for power flow (PF) solutions in active distribution networks under uncertainty. We use the Gaussian process (GP) regression to learn node voltage as a function of effective bus load or negative net-injection vector. The proposed approximation is valid over a subspace of load and provides an understanding of system behavior under uncertainty via GP interpretability. We interpret the relative variation extent of different node voltages using the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">quality ratio</i> (QR) defined based on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">hyper-parameters</i> of GP. Further, the application of the proposed framework in calculation of voltage limit violation probability and dominant voltage influencer ranking has also been presented. Through test simulations for 33-bus and 56-bus systems, the proposed method achieves low mean absolute error (MAE) of order E-05 (pu) in voltage magnitude and E-04 (rad) in angle. The discussions on salient features of the proposed method and comparative analysis with large-scale Monte-Carlo simulations, and state-of-art methods is also presented for the proposed applications.