Modeling Generating Unit Size and Economies of Scale in Capacity Expansion with an Efficient, Real Number Representation of Capacity Additions

The impact of generating unit size on system reliability and production costs is an important concern in utility capacity planning. Previously developed planning tools that model economies of scale allow decision variables that represent capacity additions to take integer values only. The integer restriction limits the choice of optimization algorithms to dynamic or integer programing techniques which are computationally too burdensome and suitable only for analyzing a few capacity expansion options at a time. A new algorithm based on generalized Benders´ decomposition and probabilistic production costing is developed here. To enhance computational efficiency, it utilizes real number variables for capacity addition decisions, at the same time, however, it properly models fractional and multiple unit capacity additions to account for economies of scale and the proper impact of units sizes on system reliability and production costs.