Distance-Based Distributionally Robust Optimization for a Preventive Maintenance Schedule in Hydrothermal Power Systems

This article proposes a distance-based distributionally robust optimization method to determine the optimal preventive maintenance schedule in hydrothermal power systems, with the aim of minimizing the operation cost in the coming year under the uncertainty of natural inflows. The ambiguity set consisting of a family of distributions close to the reference probability distribution, is used to model the uncertainty, where the reference distribution is generated according to predictive information and historical seasonal prediction error, so it is helpful to implicitly reflect the seasonality of natural inflows. The conservatism of the solution can be adjusted by regulating the scale of the ambiguity set. The column and constraint generation algorithm is employed to decompose the proposed min–max–min problem into a master problem and subproblem, where the maintenance decision is determined in the master problem and the operation decisions are made to identify the worst-case probability distribution in the subproblem. The stochastic dual dynamic programming algorithm is applied to further decompose the multistage subproblem into several smaller stage problems. Case studies were conducted on a modified IEEE 30-bus system and real hydrothermal power systems in China to demonstrate the effectiveness of the proposed method.