Multi-stage robust scheduling of battery energy storage for distribution systems based on uncertainty set decomposition

This paper proposes a multi-stage robust optimization method for battery energy storage (BES) scheduling, considering high-dimensional uncertainties associated with distributed renewable energy sources. To guarantee multi-stage operation security, all possible realizations of uncertainties should be considered as infinite constraints, which will make the problem not tractable in general. To tackle this issue, a decomposition-based solution method is proposed in this paper. The main idea is to decompose the uncertainty set as the sum of several small uncertainty sets (each for one BES). Then, the solution of the original complex problem can be obtained by tackling several relatively independent sub-problems, each of which corresponds to only one BES and one decomposed uncertainty set. The proposed decomposition rule is straightforward to implement, achieving high computational efficiency. Besides, unlike the conventional robust optimization method that relies on explicitly affine decision rules, the decision policy of the proposed method is not limited to linear functions. When uncertainties are observed, decisions are adaptively optimized by solving a simple programming. In this way, the optimality of the dispatch decision is improved. Extensive case studies are tested on a realistic microgrid, the IEEE 33-bus system, and the IEEE 69-bus system. Results show that compared with existing robust optimization methods, the average operation cost is reduced by about 3.23 %–5.80 % by using the proposed method.