🤖 AI Summary
To address the lack of formal performance guarantees for machine learning in safety-critical power system applications, this paper proposes a graph-structured Gaussian process (GP) method for voltage-constraint risk assessment. We introduce a novel vertex-degree kernel (VDK) that explicitly encodes topological dependencies between voltages and loads on the power grid, and design an active learning strategy aligned with the additive structure of VDK. Theoretically, we prove that the risk estimation error of the VDK-GP matches that of the AC power flow model and establish, for the first time, a statistically grounded probabilistic error bound for graph-based stochastic modeling. Evaluations on 500- and 1354-bus systems demonstrate over a twofold reduction in sample complexity, more than 15× speedup in computation versus Monte Carlo simulation, and risk estimation errors at the 10⁻⁴ level.
📝 Abstract
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.
