Fast Stochastic Dual Dynamic Programming for Economic Dispatch in Distribution Systems

The multistage economic dispatch solution is of paramount importance for achieving the optimal unit commitment and the optimal decentralized decision-making in smart grid operations. Through the approximations of the optimal expected cost-to-go functions, the stochastic dual dynamic programming (SDDP) has been shown effective to obtain the optimum for the multistage stochastic programming (SP) problem, while without finite termination guarantee. Thus, we propose a fast stochastic dual dynamic programming (FSDDP) method to accelerate the convergence rate of the SDDP, including updating the candidate points based on the case with the maximum difference between the upper and lower bounds of the optimal value functions, adding a backward-forward-backward inner scheme in the backward pass, and initializing the bounds with finite constant values. We can verify that the FSDDP method enjoys a nice property with a finite convergence guarantee for the multistage SP problems. Numerical tests on 4-, 33-, 34-, 69-, 118- and 123-bus distribution systems have demonstrated that FSDDP can approach the optimal economic performance at significantly improved computational efficiency.

Automated summary

The multistage economic dispatch solution is crucial for achieving optimal unit commitment and decentralized decision-making in smart grid operations. The stochastic dual dynamic programming (SDDP) has been effective in solving the multistage stochastic programming (SP) problem, but lacks a guarantee of finite termination. To address this, we propose a fast stochastic dual dynamic programming (FSDDP) method that accelerates convergence rate by updating candidate points based on the maximum difference between upper and lower bounds of optimal value functions, adding a backward-forward-backward inner scheme, and initializing bounds with finite constant values. Numerical tests on various distribution systems demonstrate that FSDDP can significantly improve computational efficiency while approaching optimal economic performance.