Solution of the Economic Dispatch Problem by Spatial decomposition

The overall solution time for the power market simulator FanSi is too high for practical use by power producers, transmission system operators and regulators. The FanSi model formulates optimisation problems in the form of Linear Programming (LP) problems to solve the economic dispatch problem (EDP). We apply the decomposition technique Lagrangian Relaxation (LR) on the EDP with the goal of reducing computation time and obtaining high quality results. The relaxation of the power balance constraints gives separate subproblems for hydropower and thermal power in geographically separated areas, and one market problem. A dual problem is solved and provides Lagrangian multipliers to the subproblems. A bundle method is used to solve the nondifferentiable dual problem. Our results are obtained from a test case with a detailed description of the Northern European power system. We report on the solution quality and speed of the decomposed EDP by comparison with the solution of the LP-problem. Our results show that the solution from the LR underestimates the system costs, the dual solution is shown to provide area power prices with some inaccuracy which is reflected in the solutions of the subproblems. The speed of the decomposed problem relative to the LPproblem varies depending on the EDP to be solved.