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In order to reduce the conservatism of the robust optimization method and the complexity of the stochastic optimization method and to enhance the ability of power systems to deal with occasional line fault disturbance, this paper proposes a distributionally robust unit commitment (DRUC) model with concentrating solar power (CSP) operational flexibility and N-k safety criterion under distributed uncertainty. According to the limited historical sample data, under the condition of satisfying a certain confidence level, based on the imprecise Dirichlet model (IDM), an ambiguity set is constructed to describe the uncertainty of transmission line fault probability. Through the identification of the worst probability distribution in the ambiguity set, the adaptive robust optimal scheduling problem is transformed into a two-stage robust optimization decision model under the condition of deterministic probability distribution. The CSP flexibility column and constraint generation (C&CG) algorithm is used to process the model and the main problem and subproblem are solved by using the Big-M method, linearization technique, and duality principle. Then, a mixed integer linear programming problem (MILP) model is obtained, which effectively reduces the difficulty of solving the model. Finally, case studies on the IEEE 14 bus system and the IEEE 118 bus system demonstrate the efficiency of the proposed method, such as enhancing the ability of power systems to cope with occasional line fault disturbances and reducing the conservatism of the robust optimization method.

Aiming at the problem that the current dynamic economic dispatch (DED) fails to consider the response risk of spinning reserve caused by the fluctuation and uncertainty of wind power, we work out a DED problem considering time-coupling spinning reserve response risk while the stochasticity and variability arising from RESs are taken into consideration. The developed framwork unified the response risk of reserve caused by forced shutdown of the unit into the response risk caused by time coupling. The expected customer interruption cost (ECOST) and the expected abandoned wind cost considering this reserve response risk are added to the objective function. While seeking the minimum objective function, the system is automatically configured with suitable reserve to ensure the consistency of the system’s response risk in each period. An improved multi-universe parallel quantum genetic algorithm was used to solve the model. Numerical examples and analysis prove the effectiveness and feasibility of the proposed method.