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This paper provides a mathematical model (linear mixed integer program) for the problem of selecting an expansion plan over a planning horizon for an electric utility system. The objective function that is chosen is the minimization of the net present value of the capital investment cost associated with the construction of power plants and transmission lines plus the operating costs of the system. The restrictions associated with the problem are the requirement to satisfy the forecasted demands of the systems for electrical energy plus the physical restrictions that result from having limited capital resources and plant site limitations. The model provides construction expansion schedules for power plants and transmission lines (i.e. what capacity to build, where the additional capacity is to be located, and when it is to be completed). Additionally, an approximate operating schedule for plants and transmission lines is provided. An application of the modeling technique to a regional electrical utility system illustrating the formulation methods and the results that can be obtained is given.