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Mixed-integer linear programming (MILP) methods have been applied widely to optimal design of en- ergy supply systems in consideration of multi-period operation. A hierarchical MILP method has been proposed to solve such optimal design problems efficiently. An original problem has been solved by dividing it into a relaxed optimal design problem at the upper level and optimal operation problems which are independent of one another at the lower level. In addition, some strategies have been pro- posed to enhance the computation efficiency furthermore. In this paper, a method of reducing model by time aggregation is proposed as a novel strategy to search design candidates efficiently in the relaxed optimal design problem at the upper level. In addition, the previous strategies are modified in accor- dance with the novel strategy. This method is realized only by clustering periods and averaging energy demands for clustered periods, while it guarantees to derive the optimal solution. Thus, it may decrease the computation time at the upper level. Through a case study on the optimal design of a gas turbine cogeneration system, it is clarified how the model reduction is effective to enhance the computation efficiency in comparison and combination with the modified previous strategies.
The mixed-integer linear programming (MILP) method has been applied widely to optimal design of energy supply systems. A hierarchical MILP method has been proposed to solve such optimal design problems efficiently. In addition, a method of reducing model by time aggregation has been proposed to search design candidates accurately and efficiently at the upper level. In this paper, the hierarchical MILP method and model reduction by time aggregation are applied to the multiobjective optimal design. The methods of clustering periods by the order of time series, by the k-medoids method, and based on an operational strategy are applied for the model reduction. As a case study, the multiobjective optimal design of a gas turbine cogeneration system is investigated by adopting the annual total cost and primary energy consumption as the objective functions, and the clustering methods are compared with one another in terms of the computation efficiency. It turns out that the model reduction by any clustering method is effective to enhance the computation efficiency when importance is given to minimizing the first objective function, but that the model reduction only by the k-medoids method is effective very limitedly when importance is given to minimizing the second objective function.