A Nonlinear Programming Approach to Optimal Static Generation Expansion Planning

This paper shows how a standard nonlinear programming approach can be applied to solve a sophisticated version of the static optimal mix problem in generation planning. The solution of the static mix problem can provide useful insights if the underlying model is able to capture the relevant features of the actual system. The model presented in this paper considers technical minima of thermal capacity, detailed operation models of storage-hydro and pumpedhydro units, a realistic model of capital costs for hydro plants, operating reserve and minimum demand constraints, and also capacity already in existence. The model formulation is in a format that can be directly handled by the well-known Stanford´s MINOS code and can be efficiently solved. A realistic application to the Spanish generation system is presented. The optimal static generation mix problem can be determined by minimizing the cost function that includes the variable costs and the equivalent fixed annual costs of all the technologies in operation during the prescribed horizon year. The technologies considered are: thermal, storage-hydro and pumped-hydro. A number of technical and economical considerations constraint the minimization cost function: i) The sum of all installed available capacities has to exceed the maximum demand by a prescribed reserve margin to acccommodate changes in available capacity or in demand. ii) The sum of all technical minima plus run-of-the river hydro must not exceed the minimum demand plus the base-load capacity devoted to pumping. iii) All the installed capacities must be non-negative.