Adaptive robust optimization framework for day-ahead microgrid scheduling

This paper proposes a framework to address day-ahead scheduling of a microgrid (MG) with wind, solar and micro-turbine distributed generators as well as batteries, considering the associated uncertainties and AC power flow constraints. The problem uncertainties are wind and solar generations, demand, and grid electricity price. The uncertainties are modelled using bounded intervals within adaptive robust optimization method. Unlike previous robust models presented for MG scheduling, our proposed adaptive robust model optimizes both wait and-see and here-and-now decisions simultaneously which leads to obtaining a better operating point. In order to make wait-and-see and here-and-now decisions and immunize the model against worst case realizations, the proposed MG scheduling model has been formulated as a tri-level optimization framework. In the first level, here-and-now commitment decisions are made (these are decisions made before realization of uncertainties). In the second stage, the worst case realization of the uncertain parameters is determined. In the third level, the wait-and-see recourse decisions are made (these are decisions made after realization of uncertainties). Since there are before uncertainty-realization decisions, worst uncertainty-realization determination, and after uncertainty-realization decisions, the proposed model becomes a tri-level optimization framework. The proposed adaptive robust tri-level MG scheduling model, the proposed solution approach including AdptRob and ConvAC problems, and the proposed out-of-sample analysis are the main contributions of this paper. A convexified AC power flow model is used in the proposed framework for modeling the distribution network. The 69-bus distribution test system is used to test the proposed adaptive robust model as well as the proposed solution approach which converges very fast. Moreover, the results of the out-of-sample analysis shows that the proposed adaptive robust model results in lower expected cost and lower cost variance.