Lagrangian Relaxation With Incremental Proximal Method for Economic Dispatch With Large Numbers of Wind Power Scenarios

Scenario-based approaches have been widely employed in stochastic economic dispatch with wind power integration. However, due to computational limitations, the number of wind power scenarios usually need to be reduced to a small subset of all available scenarios. The limited number of scenarios could affect the objective performance related to the correlations and uncertainties of wind power, especially when the influence of extreme scenarios needs to be accounted for. To increase the computational efficiency of economic dispatch problem with a large number of scenarios, we propose a Lagrangian relaxation with incremental proximal method to solve the dispatch problem. This approach combines the benefit of Lagrangian relaxation, which allows the problem to be decomposed into a large number of smaller problems and the proximal method, which lead to much faster convergence. In addition, we also propose a multipliers and primal variables initialization method to further reduce the convergence time. Results of case studies show that this framework greatly reduces the computation time and the system cost of economic dispatch compared with the traditional approaches.