A distributionally robust model for reserve optimization considering contingency probability uncertainty

Spinning reserve is an important resource for power system to deal with the possible contingencies and uncertainties of renewable energy and load. Traditionally, the spinning reserve requirement is calculated by a deterministic or probabilistic method. When the contingency probability is considered, usually a fixed statistical value is applied, and the uncertainty of contingency probability is ignored due to the lack of statistical samples. This paper proposes a new distributionally robust reserve optimization model considering the uncertainty of contingency probability. The ambiguity set of contingency probability is further analyzed based on the deterministic relationship between contingency probability and equipment outage rate. When the uncertainty of equipment outage rate is described by interval, the distributionally robust model finally boils down to a robust-stochastic optimization model. The proposed model is recast as a mixed integer linear programming problem based on dual theory, epigraph reformulation and KKT condition. The effectiveness and validity of the proposed method are illustrated on the IEEE-RTS system.