Solving the conic formulation of the security-constrained unit commitment problem via decomposition

The security-constrained unit commitment problem seeks the minimum cost schedule of electricity generation units that meets demand over a 24h horizon and remains robust to failures of the transmission branches of the network linking generators and loads. Due to the size of realistic problems, which involve millions of variables and constraints, state-of-the-art solution techniques rely on linearizing the physical laws governing energy flows through branches and applying decomposition methods. We formulate this problem using high fidelity second order conic expressions for energy flows, yielding a large-scale mixed integer second order conic problem. We solve it using a decomposition procedure that separates the problem into a master problem and a large number of subproblems, and that combines Benders and column and constraint generation ideas, along with an accurate outer linearization for the master problem. We conduct computational experiments on realistic case studies to demonstrate the efficiency of the proposed methodology. For a number of realistic instances, we compare our results with those obtained using state-of-the-art commercial solvers.