Explicit Ensemble Learning Surrogate for Joint Chance-Constrained Optimal Power Flow

TL;DR

The paper tackles uncertainty in power system operation by addressing joint chance-constrained OPF (JCC-OPF) with an explicit ensemble SVM surrogate. It replaces intractable probabilistic line-flow constraints with a data-driven, polyhedral surrogate learned via bootstrap-aggregated linear SVMs and embedded into the DC-OPF through Big-M relaxations. On the IEEE 118-bus system, the surrogate achieves near-optimal costs, with average relative cost penalties around $0.03\%$, while strictly enforcing the prescribed risk level $\alpha$. The approach offers a transparent, scalable framework for risk-aware optimization under renewable uncertainty, with strong interpretability from explicit surrogate hyperplanes and reduced computational burden compared to scenario-based methods.

Abstract

The increasing penetration of renewable generation introduces uncertainty into power systems, challenging traditional deterministic optimization methods. Chance-constrained optimization offers an approach to balancing cost and risk; however, incorporating joint chance constraints introduces computational challenges. This paper presents an ensemble support vector machine surrogate for joint chance constraint optimal power flow, where multiple linear classifiers are trained on simulated optimal power flow data and embedded as tractable hyperplane constraints via Big--M reformulations. The surrogate yields a polyhedral approximation of probabilistic line flow limits that preserves interpretability and scalability. Numerical experiments on the IEEE 118-bus system show that the proposed method achieves near-optimal costs with a negligible average error of $0.03\%$. These results demonstrate the promise of ensemble surrogates as efficient and transparent tools for risk-aware optimization of power systems.

Figures (5)

• Figure 1: Conceptual comparison between the conventional SAA and the proposed surrogate-based formulation for solving the JCC–OPF problem under renewable uncertainty. The proposed method replaces the scenario-based approximation with a data-driven linear surrogate to enhance tractability and interpretability.
• Figure 2: Overall workflow of the proposed ensemble SVM surrogate approach. Data is generated and labeled under wind/load uncertainty using SAA JCC-OPF. An ensemble of linear SVMs is trained via bagging to construct a polyhedral surrogate, which is then embedded into the JCC-OPF formulation through Big–M relaxation. The surrogate JCC-OPF is subsequently solved and benchmarked against the baseline formulation.
• Figure 3: Distribution of the relative cost penalty of the ensemble SVM surrogate with respect to the baseline JCC-OPF. The boxplot summarizes results across 15 test samples, with individual sample points shown in red. The mean and standard deviation are $\mu=0.0335\%$ and $\sigma=0.0089\%$, respectively.
• Figure 4: Cost–reliability tradeoff for the ensemble SVM surrogate across 15 test samples. The $x$-axis shows the relative cost penalty with respect to JCC-OPF, while the $y$-axis indicates the number of ex-post violations. All points lie on the violation budget cap ($\alpha N = 5$), demonstrating that the surrogate enforces the prescribed reliability level while incurring only marginal cost increases.
• Figure 5: Predictive performance of the ensemble surrogate as a function of the number of weak linear SVMs. Accuracy (red line) improves with ensemble size, while the number of false negatives (blue line) decreases. Beyond $M=8$, gains in predictive performance are marginal, suggesting that eight classifiers offer a favorable balance between accuracy and reliability.