Synergistic Integration of Machine Learning and Mathematical Optimization for Unit Commitment

Unit Commitment (UC) is important for power system operations. With increasing challenges, e.g., growing intermittent renewables and intra-hour net load variability, traditional mathematical optimization could be time-consuming. Machine learning (ML) is a promising alternative. However, directly learning good solutions is difficult in view of the combinatorial nature of UC. This paper synergistically integrates ML within our recent decomposition and coordination method of Surrogate Lagrangian Relaxation to learn subproblem solutions of deterministic UC. Compared to the original problem, a subproblem is much easier to learn. Nevertheless, because of many types of constraints, finding “good enough” subproblem solutions for a given set of multipliers is still challenging. To overcome this, dimensionality is reduced via aggregating multipliers and removing unnecessary variables. Multiplier distributions are novelly specified for effective training. Furthermore, to exploit solutions obtained in daily operations, offline supervised learning and online self-learning are unified at the switching of the innovatively designed loss functions. Although testing of this first attempt to integrate two methods is limited to the IEEE 118-bus system, results demonstrate that ML obtains good-enough subproblem solutions efficiently, leading to near-optimal overall solutions. Our method opens a new direction for integrating ML and mathematical optimization to solve complicated UC and beyond.