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Beyond the Neural Fog: Interpretable Learning for AC Optimal Power Flow

Salvador Pineda, Juan Pérez-Ruiz, Juan Miguel Morales

TL;DR

The paper addresses the non-convexity of the $AC$-OPF problem and limitations of the $DC$-OPF approximation by proposing a hybrid, interpretable learning-based approach. It combines $K$-nearest-neighbor regression to infer a nearby operating point from historical data with a first-order Taylor expansion to create convex surrogates, resulting in two variants: $KT$-AC (active and reactive power with voltage magnitudes) and $KT$-DC (active power and angles). Empirical results across 14-, 30-, 57-, and 118-bus networks show that $KT$-AC generally achieves the best accuracy and low infeasibility, while $KT$-DC significantly improves upon $DC$-OPF and offers strong data efficiency; both outperform simple neural networks, especially when training data are scarce. The approach provides a practical, transparent alternative that retains convex optimization guarantees while closely approximating the true $AC$-OPF solution, facilitating trust and adoption in real power-system operations.

Abstract

The AC optimal power flow (AC-OPF) problem is essential for power system operations, but its non-convex nature makes it challenging to solve. A widely used simplification is the linearized DC optimal power flow (DC-OPF) problem, which can be solved to global optimality, but whose optimal solution is always infeasible in the original AC-OPF problem. Recently, neural networks (NN) have been introduced for solving the AC-OPF problem at significantly faster computation times. However, these methods necessitate extensive datasets, are difficult to train, and are often viewed as black boxes, leading to resistance from operators who prefer more transparent and interpretable solutions. In this paper, we introduce a novel learning-based approach that merges simplicity and interpretability, providing a bridge between traditional approximation methods and black-box learning techniques. Our approach not only provides transparency for operators but also achieves competitive accuracy. Numerical results across various power networks demonstrate that our method provides accuracy comparable to, and often surpassing, that of neural networks, particularly when training datasets are limited.

Beyond the Neural Fog: Interpretable Learning for AC Optimal Power Flow

TL;DR

The paper addresses the non-convexity of the -OPF problem and limitations of the -OPF approximation by proposing a hybrid, interpretable learning-based approach. It combines -nearest-neighbor regression to infer a nearby operating point from historical data with a first-order Taylor expansion to create convex surrogates, resulting in two variants: -AC (active and reactive power with voltage magnitudes) and -DC (active power and angles). Empirical results across 14-, 30-, 57-, and 118-bus networks show that -AC generally achieves the best accuracy and low infeasibility, while -DC significantly improves upon -OPF and offers strong data efficiency; both outperform simple neural networks, especially when training data are scarce. The approach provides a practical, transparent alternative that retains convex optimization guarantees while closely approximating the true -OPF solution, facilitating trust and adoption in real power-system operations.

Abstract

The AC optimal power flow (AC-OPF) problem is essential for power system operations, but its non-convex nature makes it challenging to solve. A widely used simplification is the linearized DC optimal power flow (DC-OPF) problem, which can be solved to global optimality, but whose optimal solution is always infeasible in the original AC-OPF problem. Recently, neural networks (NN) have been introduced for solving the AC-OPF problem at significantly faster computation times. However, these methods necessitate extensive datasets, are difficult to train, and are often viewed as black boxes, leading to resistance from operators who prefer more transparent and interpretable solutions. In this paper, we introduce a novel learning-based approach that merges simplicity and interpretability, providing a bridge between traditional approximation methods and black-box learning techniques. Our approach not only provides transparency for operators but also achieves competitive accuracy. Numerical results across various power networks demonstrate that our method provides accuracy comparable to, and often surpassing, that of neural networks, particularly when training datasets are limited.
Paper Structure (6 sections, 6 equations, 1 figure, 4 tables, 1 algorithm)

This paper contains 6 sections, 6 equations, 1 figure, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Formulations
  3. Learning-based methods
  4. Comparison
  5. Numerical simulations
  6. Conclusions

Figures (1)

  • Figure 1: Visual illustration of how neural networks and our approach work