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.

Unit Commitment (UC) is an important problem in power system operations. It is traditionally scoped for 24 hours with one-hour time intervals. To improve system flexibility by accommodating the increasing net-load variability, sub-hourly UC has been suggested. Such a problem is larger and more complicated than hourly UC because of the increased number of periods and reduced unit ramping capabilities per period. The computational burden is further exacerbated for systems with large numbers of virtual transactions leading to dense transmission constraints matrices. Consequently, the state-of-the-art and practice method, branch-and-cut (B&C), suffers from poor performance. In this paper, our recent Surrogate Absolute-Value Lagrangian Relaxation (SAVLR) is enhanced by embedding ordinal-optimization concepts for a drastic reduction in subproblem solving time. Rather than formally solving subproblems by using B&C, subproblem solutions that satisfy SAVLR’s convergence condition are obtained by modifying solutions from previous iterations or solving crude subproblems. All virtual transactions are included in each subproblem to reduce major changes in solutions across iterations. A parallel version is also developed to further reduce the computation time. Testing on MISO’s large cases demonstrates that our ordinal-optimization embedded approach obtains near-optimal solutions efficiently, is robust, and provides a new way on solving other MILP problems.