Risk-based Distributionally Robust Energy and Reserve Dispatch with Wasserstein-Moment Metric

With resorting to the tool of distributionally robust optimization, this paper proposes a risk-based distributionally robust approach to address the wind power uncertainty in the energy and reserve dispatch. The proposed model minimizes the total cost including dispatch cost and risk cost. The dispatch cost refers to the cost of scheduling energy and spinning reserve while the risk cost is the expected cost of load shedding and wind spillage. Unlike the previous approach which predefined distribution of random variables, the proposed approach takes the ambiguity of distributions into account. It extracts probabilistic information from historical data of random variables, and constructs ambiguity set to contain possible distributions. Then the worst-case distribution over ambiguity set is used to evaluate risks to hedge against the ambiguity. In this paper, a novel metric - Wasserstein-moment metric (WM-metric) is introduced to construct ambiguity set. Compared with Wasserstein-metric and Moment-metric, WM-metric considers more probabilistic information and thus can further mitigate the conservativeness of ambiguity set. The performance of the proposed approach is tested by a 6-bus system for illustrative purpose.