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

arXiv:2308.07867v4 Announce Type: replace-cross 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.

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.

Systems and Control (eess.SY); Machine Learning (cs.LG)

arXiv:2308.07867 [eess.SY]

(or arXiv:2308.07867v4 [eess.SY] for this version)

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

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