Cutting planes for security-constrained unit commitment with regulation reserve

With significant economic and environmental benefits, renewable energy is increasingly used to generate electricity. To hedge against the uncertainty due to the increasing penetration of renewable energy, an ancillary service market was introduced to maintain reliability and efficiency, in addition to day-ahead and real-time energy markets. To co-optimize these two markets, a unit commitment problem with regulation reserve (the most common ancillary service product) is solved for daily power system operations, leading to a large-scale and computationally challenging mixed-integer program. In this article, we analyze the polyhedral structure of the co-optimization model to speed up the solution process by deriving problem-specific strong valid inequalities. Convex hull results for certain special cases (i.e., two- and three-period cases) with rigorous proofs are provided, and strong valid inequalities covering multiple periods under the most general setting are derived. We also develop efficient polynomial-time separation algorithms for the inequalities that are in the exponential size. We further tighten the formulation by deriving an extended formulation for each generator in a higher-dimensional space. Finally, we conduct computational experiments to apply our derived inequalities as cutting planes in a branch-and-cut algorithm. Significant improvement from our inequalities over commercial solvers demonstrates the effectiveness of our approach, leading to practical usefulness to enhance the co-optimization of energy and ancillary service markets.