Robust Approximate Dynamic Programming for Large-Scale Unit Commitment With Energy Storages

The robust unit commitment (UC) is of paramount importance for achieving reliable operations considering the uncertainty of renewable realizations. The typical affine decision rule method and the robust feasible region method may achieve uneconomic dispatches as the dispatch decisions just rely on the current-stage information. Through approximating the future cost-to-go functions, the dual dynamic programming based methods have been shown adaptive to the multistage robust optimization problems, while suffering from high computational complexity. Thus, we propose the robust approximate dynamic programming (RADP) method to promote the computational speed and the economic performance for large-scale robust UC problems. RADP initializes the candidate points for guaranteeing the feasibility of upper bounding the value functions, solves the alternating calculation based bilinear programming to obtain the worst cases, and combines the primal and dual updates for the two-phase robust UC decision-making problem to achieve fast convergence. The finite termination guarantee of the RADP method is verified by the analyses for the multistage robust optimization problems with achieving suboptimal solutions. Numerical tests on 118-bus and 2383-bus transmission systems have demonstrated that RADP can approach the suboptimal economic performance at significantly improved computational efficiency.
Note to Practitioners
—This paper was motivated by solving the large-scale robust UC problem embedded with the multistage economic dispatch with improved computational and economical performance. Compared to the existing methods, this work suggests a RADP-based approach, which is inspired by the robust dual dynamic programming (RDDP) scheme. The proposed RADP owns lower computational complexity when compared with RDDP. As the problem in this work is formulated in a general form, the proposed RADP can be applied to other robust optimization problems such as the inventory management problem with uncertain demands. To apply the method to large-scale decision-making problems, one needs to solve linear programming problems to obtain the finite upper/lower bounds first, and then initialize the upper-bound points based on the feasible region limits of the decision variables. Conduct the forward pass to generate the candidate points and the backward pass to refine the cost-to-go functions. If the application problems have discrete decision variables as in the two-phase UC, one can solve the nonanticipativity constrained problem to obtain discrete solutions before doing the RADP scheme. The analyses and numerical experiments suggest that this approach can achieve suboptimal solutions. In future research, we will address the accelerated multistage robust decision-making with achieving optimal solutions.