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This paper presents a graph-structured Gaussian process (GP) model fordata-driven risk assessment of critical voltage constraints. The proposed GP isbased on a novel kernel, named the vertex-degree kernel (VDK), that decomposesthe voltage-load relationship based on the network graph. To estimate the GPefficiently, we propose a novel active learning scheme that leverages theadditive structure of VDK. Further, we prove a probabilistic bound on the errorin risk estimation using VDK-GP model that demonstrates that it isstatistically comparable to using standard AC power flow (AC-PF), but does notrequire computing a large number of ACPF solutions. Simulations demonstratethat the proposed VDK-GP achieves more than two fold sample complexityreduction, compared to a generic GP on medium scale 500-Bus and large scale1354-Bus power systems. Moreover, active learning achieves an impressivereduction of over 15 times in comparison to the time complexity of Monte-Carlosimulations (MCS), and have risk estimation error of order 1E-4 for both500-Bus and 1354-Bus system, demonstrating its superior efficiency in riskestimation.

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