A two-stage distributionally robust CVaR-constrained framework and its approximations for self-scheduling microgrid

• This paper proposes an approach to decide on a robust renewable energy output and operation at different time scales strategy in microgrid. • Kullback-Leibler distributional robust output of renewable energy considering conditional value-at-risk is in the microgrid scheduling model. • The distributionally robust constraint of renewable energy output is computably reformulated by utilizing Jensen’s inequality and Taylor’s approximation theory. • The two-stage microgrids with energy storage and direct load control are formulated to achieve operation at different time-scales. • The two-stage model is reformulated as a single-stage mixed-integer linear program problem by utilizing Dual-relax and McCormick relaxation theory. This paper proposes a two-stage distributionally robust conditional value-at-risk constrained (TS-DR-CVaR) framework and its computable approximations for the economic self-scheduling of microgrid problems considering the uncertainty of renewable energy sources and direct load control operation at different time-scales. The main challenges in solving the TS-DR-CVaR model are two-stage decision and Kullback-Leibler distributional robust output of renewable energy considering conditional value-at-risk. To overcome these challenges, first, the distributionally robust constraint of renewable energy output is computably reformulated by utilizing Jensen’s inequality and Taylor approximation theory. And then the two-stage model is reformulated as a single-stage mixed-integer linear program problem by utilizing dual-relax and McCormick relaxation methods. Finally, by controlling the risk value and confidence in the approximate TS-DR-CVaR model, the consumption of renewable energy sources can be improved, and the economic operation and security scheduling of the microgrid can be realized. Simulation results demonstrate the correctness and effectiveness of the proposed approximate TS-DR-CVaR models. This framework provides a comprehensive solution to address the uncertainty of renewable energy sources in microgrids and enables both economical and robust scheduling schemes.