Interpretable Machine Learning for DC Optimal Power Flow With Feasibility Guarantees

The increased uncertainty due to the integration of stochastic renewable energy sources necessitates solving Optimal Power Flow (OPF) problems repeatedly and with greater granularity. Machine learning methods hold significant potential to reduce the computing time for OPF problems by learning a mapping from varying input loads to decisions, thus bypassing the need for an optimization solver during inference. However, current machine learning methods for OPF lack interpretability and may produce infeasible decisions, which impedes their adoption by industry stakeholders. To this end, we propose a novel approach for interpretable learning of OPF solutions with feasibility guarantees. Specifically, we develop prescriptive decision trees that learn a piecewise affine mapping from input data to the solutions of a constrained optimization problem, using robust optimization to ensure that decisions are feasible. One important contribution of our work is the development of a tree-based learning method that utilizes non-orthogonal splits informed by domain knowledge, including network congestion and the merit order curve. By incorporating this information, we enhance both the interpretability and performance of the model. We further present a surrogate learning algorithm to handle large-scale problems. The proposed approach is evaluated on several test networks, up to 300 buses, under different types of uncertainty and operating conditions, and is compared to neural network-based models, which do not guarantee feasibility. Notably, our results demonstrate that interpretable, shallow prescriptive trees perform comparably to neural network-based models, which are considered the current state of the art. To the best of our knowledge, this work is the first to introduce an interpretable machine learning approach for directly learning OPF solutions.