Gradient accelerated stochastic dual dynamic programming for economic dispatch in microgrids with energy storages

Multistage stochastic economic dispatch (ED) solutions play a crucial role in obtaining reliable and cost-effective operations. The stochastic dual dynamic programming (SDDP) has been proposed to achieve optimal solutions for multistage stochastic programming (SP) problems under the probabilistic convergence rate. The fast SDDP (FSDDP) method can guarantee finite convergence by solving bilevel problems for generating deterministic updates while suffering from the high computational complexity of large-scale decision-making systems. Thus, we leverage the recent advances in the primal–dual reformulation method of solving bilevel problems, which allows for first-order gradient descent/ascent (GDA) updates. Based on the primal–dual bilevel optimizer (PDBO), we propose the gradient-accelerated SDDP (GA-SDDP) for solving stochastic ED problems. Taking advantage of the finite termination of PDBO for solving bilevel problems, the finite convergence of GA-SDDP is verified by the analysis. Numerical tests on the IEEE 33-bus, 69-bus, and 123-bus systems have shown that GA-SDDP can achieve finite termination compared to SDDP and improved computational performance over FSDDP. • A cost-to-go approximation method is proposed for stochastic economic dispatch. • Minimax reformulation is provided for maximizing gaps between the upper and lower bounds. • The gradient descent/ascent method is developed for the minimax reformulation. • Finite termination of the proposed iterative scheme is presented.