Cutting planes for the multistage stochastic unit commitment problem

As renewable energy penetration rates continue to increase in power systems worldwide, newchallenges arise for system operators in both regulated and deregulated electricity markets tosolve the security constrained unit commitment problem with intermittent generation (due torenewables) and uncertain load, in order to ensure system reliability and maintain cost effec-tiveness. In this paper, we study a security constrained multi-stage stochastic unit commitment(MSUC) model, which we use to enhance the reliability unit commitment process for day-aheadand look-ahead power system operations. In our approach, we first develop a scenario tree-baseddeterministic equivalent formulation for the problem, which leads to a large-scale mixed-integerlinear program (MILP). By exploring substructures of the MSUC formulation, we develop sev-eral families of strong valid inequalities. In particular, we obtain (i) a convex hull representationof the minimum up/down time polytope under the stochastic scenario tree setting, (ii) strongvalid inequalities to strengthen the ramping constraints by exploring the sequence independentlifting procedure, and (iii) strong valid inequalities for the general economic dispatch polytope byexploring sequence independent and subadditive approximation properties. Finally, a branch-and-cut algorithm is developed to employ these valid inequalities as cutting planes to solve theMSUC problem. Our computational results verify the effectiveness of the proposed approach.