A distributionally robust energy management of microgrid problem with ambiguous chance constraints and its tractable approximation method

Abstract

As the penetration of intermittent renewable energy increases in microgrid systems, flexible power generation resources cause the power imbalance problem. To improve the absorption of renewable energy and to deal with its uncertainty more effectively, this paper proposes a distributionally robust approximate model for microgrid with ambiguous chance constraints (DR-CCP). First, the distributionally robust model with ambiguous chance constraints is a semi-infinite chance constrained planning problem, which is computationally difficult and inefficient, so the use of Chernoff's inequality to derive a safe tractable approximation form for the ambiguous chance constraint on the basis of a probability distribution for ambiguous sets including bounded perturbations with mean zero, transforms it into a mixed integer linear programming problem that can be directly solved using CPLEX to solve it. Then, the optimal value of the proposed model is used to approximate equivalent conditional value at risk (CVaR), and the relationship with CVaR is established. The optimal solution of our model is employed to construct multiple sets of comparison models, enhancing the richness of numerical experiments. Finally, to validate the feasibility and effectiveness of our proposed model, a series of diverse tests are performed on the IEEE 33-bus power distribution system.