To attain the highest economic and energy saving characteristics of gas turbine cogeneration plants, it is necessary to rationally determine capacities and numbers of gas turbines and auxiliary equipment in consideration of their operational strategies corresponding to seasonal and hourly variations in energy demands. Some optimization approaches based on the mixed-integer linear programming have been proposed to this design problem. However, equipment capacities have been treated as continuous variables, and correspondingly performance characteristics and capital costs of equipment have been assumed to be continuous functions with respect to their capacities. This is because if equipment capacities are treated discretely, the number of integer variables increases drastically, and the problem becomes too difficult to solve. As a result, the treatment of equipment capacities as continuous variables causes discrepancies between existing and optimized values of capacities, and expresses the dependence of performance characteristics and capital costs on capacities with worse approximations. In this paper, an optimal design method is proposed in consideration of discreteness of equipment capacities. A formulation for keeping the number of integer variables as small as possible is presented to solve the optimal design problem easily. This method is applied to the design of a gas turbine cogeneration plant, and its validity and effectiveness are clarified.

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