Title: Establishing Confidence in Power Flow Learning: A Framework for Probabilistic Voltage Risk Assurance

Abstract:

The limited integration of machine learning (ML) into safety-critical power system applications stems largely from the lack of formal performance guarantees. In these contexts, interpretability and confidence are just as crucial as predictive accuracy. This study introduces a probabilistic guarantee for voltage risk estimation and power flow learning, grounded in Gaussian Process (GP) regression. By deriving a bound on the expected estimation error, we link the GP’s predictive variance to the reliability of voltage risk estimates, ensuring that our approach maintains statistical equivalence with Monte Carlo-based Alternating Current Power Flow (ACPF) risk quantification.

To improve model learnability when data is scarce, we propose the Vertex-Degree Kernel (VDK), a topology-aware additive kernel. VDK decomposes voltage-load interactions into local neighborhoods, facilitating efficient large-scale learning. Leveraging this kernel, we develop a network-swipe active learning (AL) algorithm that adaptively selects informative operating points and offers a rigorous stopping criterion, eliminating the need for out-of-sample validation. These innovations address the primary limitation of ML-based power flow—unproven reliability—by merging data efficiency with analytical assurance.

Empirical tests on IEEE 118-, 500-, and 1354-bus systems demonstrate that the proposed VDK-GP model achieves mean absolute voltage errors under 1E-03 p.u. It replicates voltage risk estimates with the same precision as Monte Carlo methods but requires 15 times fewer ACPF computations. Furthermore, the framework reduces evaluation time by more than 120x while providing conservative bounds on violation probabilities.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC