Security-constrained unit commitment: A decomposition approach embodying Kron reduction

We address the day-ahead scheduling of electricity production units throughout a network imposing N-1 security constraints, which ensures uneventful operation under any single-branch failure. For realistic electric energy systems, this optimization problem, which is mixed-integer linear or nonlinear but convex, involves millions of continuous variables, millions of constraints, and thousands of binary variables. This problem is intractable if state-of-the-art branch-and-cut solvers are used. As a solution methodology, we propose a Benders-type decomposition technique with a dynamically enriched master problem. Such master problem incorporates scheduling (binary) decisions and decisions pertaining to under-contingency operating conditions. The subproblems represent the operation of the system under no failure and single-branch failure. As the algorithm progresses, the master problem incorporates additional under-contingency operating conditions, which increases its computational burden. We use Kron reduction to compact (reducing variables and constraints) the description of the under-contingency operating conditions in the master problem without losing accuracy, which renders major computational gains. The methodology proposed allows solving, within reasonable computing times, instances intractable with state-of-the-art branch-and-cut solvers and decomposition algorithms.