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

Gonzalo E. Constante-Flores and Antonio J. Conejo

European Journal of Operational Research, 2024, vol. 319, issue 2, 427-441

Abstract: 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.

Keywords: Large scale optimization; OR in energy; Decomposition algorithm; Network reduction; Unit commitment (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:319:y:2024:i:2:p:427-441

DOI: 10.1016/j.ejor.2023.06.013

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