A Critical Review of Chance-constrained Optimization and Applications to Power Systems

Chance-constrained optimization is one of the major approaches for decision making in uncertain environments. Motivated by the uncertainties from deepening penetration of renewable energy resources in power systems, we provide a critical review of three major solutions to chance-constrained optimization problems: (1) scenario approach; (2) sample average approximation; and (3) convex approximation. We evaluate each solution in three aspects: (1) optimality; (2) conservativeness; and (3) complexity. Case studies based on power system problems (DC optimal power flow, optimal reactive power dispatch) are provided to examine the performance of each solution.

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