Fast Risk Assessment in Power Grids through Novel Gaussian Process and Active Learning

This paper presents a graph-structured Gaussian process (GP) model for data-driven risk assessment of critical voltage constraints. The proposed GP is based on a novel kernel, named the vertex-degree kernel (VDK), that decomposes the voltage-load relationship based on the network graph. To estimate the GP efficiently, we propose a novel active learning scheme that leverages the additive structure of VDK. Further, we prove a probabilistic bound on the error in risk estimation using VDK-GP model that demonstrates that it is statistically comparable to using standard AC power flow (AC-PF), but does not require computing a large number of ACPF solutions. Simulations demonstrate that the proposed VDK-GP achieves more than two fold sample complexity reduction, compared to a generic GP on medium scale 500-Bus and large scale 1354-Bus power systems. Moreover, active learning achieves an impressive reduction of over 15 times in comparison to the time complexity of Monte-Carlo simulations (MCS), and have risk estimation error of order 1E-4 for both 500-Bus and 1354-Bus system, demonstrating its superior efficiency in risk estimation.