A Framework for Analytical Power Flow Solution using Gaussian Process Learning

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 quality ratio (QR) defined based on the hyper-parameters 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.