A distributionally robust bidding strategy for a wind power plant

•Distributionally robust optimization is applied to bidding strategy optimization.•Ambiguity of the distribution of uncertain wind forecast error is introduced.•The wind power plant is modeled as a price-maker in the day-ahead market and a deviator in the balancing market by using a stochastic bi-level model.•Results of using distributionally robust optimization is compared to that of using stochastic and robust optimization. This paper presents a two-stage distributionally robust model to derive optimal bidding strategies for an aggregated wind power plant (WPP), that participates as a price-maker in the day-ahead market, and a deviator in the balancing market. The market power is realized by using a bi-level model, which is then transformed into a mixed-integer linear programming model using the Karush-Kuhn-Tucker (KKT) optimality conditions and strong duality theory. The uncertainty in wind generation output is characterized by an ambiguity set that defines a family of distributions. The optimal decision is robust to the expectation over the worst-case distribution. With a case study based on a modified Swiss system, we verify the effectiveness of the proposed distributionally robust optimization model and compare its performance to that of robust and stochastic optimization models.