Synergistic Integration of Machine Learning and Mathematical
Optimization for Unit Commitment
Abstract
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 “good enough” subproblem
solutions of deterministic UC. Compared to original UC, a subproblem is
much easier to learn. Nevertheless, predicting good-enough subproblem
solutions is still challenging because of the “jumps” of binary
decisions and many types of constraints. To overcome these issues,
subproblem dimensionality is reduced via aggregating multipliers.
Multiplier distributions are novelly specified based on “jumps” for
effective learning. Loss functions are innovatively designed to improve
prediction qualities. Ordinal Optimization and branch-and-cut are used
as backups for unfamiliar cases. Furthermore, online self-learning is
seamlessly integrated with offline learning to exploit solutions from
daily operations. Results on the IEEE 118-bus system and the Polish
2383-bus system demonstrate that continual learning keeps on improving
the subproblem-solving process with near-optimality of the overall
solutions maintained. Our method opens a new direction to solve
complicated UC.