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This paper proposes a two-stage robust optimization approach to solve the N-k contingency-constrained unit commitment (CCUC) problem. In our approach, both generator and transmission line contingencies are considered. Compared to the traditional approach using a given set of components as candidates for possible failures, our approach considers all possible component failure scenarios. We consider the objectives of minimizing the total generation cost under the worst-case contingency scenario and/or the total pre-contingency cost. We formulate CCUC as a two-stage robust optimization problem and develop a decomposition framework to enable tractable computation. In our framework, the master problem makes unit commitment decisions and the subproblem discovers the worst-case contingency scenarios. By using linearization techniques and duality theory, we transform the subproblem into a mixed-integer linear program (MILP). The most violated inequalities generated from the subproblem are fed back into the master problem during each iteration. Our approach guarantees a globally optimal solution in a finite number of iterations. In reported computational experiments, we test both primal and dual decomposition approaches. Our computational results verify the effectiveness of our proposed approach. [ABSTRACT FROM PUBLISHER]

With the increasing penetration of wind power into the power grid, maintaining system reliability has been a challenging issue for ISOs/RTOs, due to the intermittent nature of wind power. In addition to the traditional reserves provided by thermal, hydro, and gas generators, demand response (DR) programs have gained much attention recently as another reserve resource to mitigate wind power output uncertainty. However, the price-elastic demand curve is not exactly known in advance, which provides another dimension of uncertainty. To accommodate the combined uncertainties from wind power and DR, we allow the wind power output to vary within a given interval with the price-elastic demand curve also varying in this paper. We develop a robust optimization approach to derive an optimal unit commitment decision for the reliability unit commitment runs by ISOs/RTOs, with the objective of maximizing total social welfare under the joint worst-case wind power output and demand response scenario. The problem is formulated as a multi-stage robust mixed-integer programming problem. An exact solution approach leveraging Benders' decomposition is developed to obtain the optimal robust unit commitment schedule for the problem. Additional variables are introduced to parameterize the conservatism of our model and avoid over-protection. Finally, we test the performance of the proposed approach using a case study based on the IEEE 118-bus system. The results verify that our proposed approach can accommodate both wind power and demand response uncertainties, and demand response can help accommodate wind power output uncertainty by lowering the unit load cost. [ABSTRACT FROM PUBLISHER]

This paper presents a new approach for the contingency-constrained single-bus unit commitment problem. The proposed model explicitly incorporates an n - K security criterion by which power balance is guaranteed under any contingency state comprising the simultaneous loss of up to K generation units. Instead of considering all possible contingency states, which would render the problem intractable, a novel method based on robust optimization is proposed. Using the notion of umbrella contingency, the robust counterpart of the original problem is formulated. The resulting model is a particular instance of bilevel programming which is solved by its transformation to an equivalent single-level mixed-integer programming problem. Unlike previously reported contingency-dependent approaches, the robust model does not depend on the size of the set of credible contingencies, thus providing a computationally efficient framework. Simulation results back up these conclusions. [ABSTRACT FROM PUBLISHER]