Multi-Stage Distributionally Robust Stochastic Dual Dynamic Programming to Multi-Period Economic Dispatch with Virtual Energy Storage

A virtual energy storage (VES) model is proposed in this paper to accommodate renewable energy under a special market regulation. Such VESs can provide or consume electricity to the main power grid under the premise that the daily net electricity energy is balanced. Furthermore, a multi-stage distributionally robust optimization (MSDRO) model is set up in this paper to address the temporal uncertainties in the day-ahead economic dispatch model. Compared with the traditional two-stage distributionally robust optimization, the proposed multi-stage approach provides more flexibilities so that the decision variables can be adjusted at each time period, leading to a complex nested formulation. To efficiently solve the MSDRO model, a stochastic dual dynamic programming method is employed to decompose the original large-scale optimization model into several sub-problems in the stages, as two steps: forward pass and backward pass. In the forward pass, the expected cost-to-go function is approximated by piecewise-linear functions and then several samples are used to generate a lower bound; the backward pass will generate Benders' cuts at each stage from the solution of the forward pass. The forward and backward passes are performed iteratively until the convergence is reached. Numerical results on an IEEE 118-bus system and a practical power system in China verify the proposed method.