Learning Power Flow with Confidence: A Probabilistic Guarantee Framework for Voltage Risk

• URL: http://arxiv.org/abs/2308.07867v3
• Date: Wed, 15 Oct 2025 03:20:32 GMT
• Title: Learning Power Flow with Confidence: A Probabilistic Guarantee Framework for Voltage Risk
• Authors: Parikshit Pareek, Sidhant Misra, Deepjyoti Deka,
• Abstract summary: We present a probabilistic guarantee for power flow learning and voltage risk estimation.<n>The proposed VDK-GP achieves mean absolute voltage errors below 1E-03 p.u., reproduces Monte Carlo-level voltage risk estimates with 15x fewer ACPF computations, and achieves over 120x reduction in evaluation time.
• Score: 1.4592479124539988
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The absence of formal performance guarantees in machine learning (ML) has limited its adoption for safety-critical power system applications, where confidence and interpretability are as vital as accuracy. In this work, we present a probabilistic guarantee for power flow learning and voltage risk estimation, derived through the framework of Gaussian Process (GP) regression. Specifically, we establish a bound on the expected estimation error that connects the GP's predictive variance to confidence in voltage risk estimates, ensuring statistical equivalence with Monte Carlo-based ACPF risk quantification. To enhance model learnability in the low-data regime, we first design the Vertex-Degree Kernel (VDK), a topology-aware additive kernel that decomposes voltage-load interactions into local neighborhoods for efficient large-scale learning. Building on this, we introduce a network-swipe active learning (AL) algorithm that adaptively samples informative operating points and provides a principled stopping criterion without requiring out-of-sample validation. Together, these developments mitigate the principal bottleneck of ML-based power flow-its lack of guaranteed reliability-by combining data efficiency with analytical assurance. Empirical evaluations across IEEE 118-, 500-, and 1354-bus systems confirm that the proposed VDK-GP achieves mean absolute voltage errors below 1E-03 p.u., reproduces Monte Carlo-level voltage risk estimates with 15x fewer ACPF computations, and achieves over 120x reduction in evaluation time while conservatively bounding violation probabilities.

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