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For the purpose of attaining the highest performance of energy supply systems, it is important to design the systems optimally in consideration of their operational strategies for seasonal and hourly variations in energy demands. An ap- proach to solve such an optimal design problem with a large number of periods efficiently is to derive an approximate optimal design solution by aggregating periods with a clustering method. However, such an approach does not provide any information on the accuracy for the optimal value of the objective function. The purpose of this paper is to provide a time aggregation method for deriving aprroximate optimal design solutions and evaluting their values of the objective function. Especially, a method of evaluating design solutions is presented here using both methods of evaluating the robustness under uncertain energy demands and solving optimal design problems by a hierarchical approach. A case study is conducted for a cogeneration system with a practical configuration, and it turns out that the proposed approach enables one to evaluate effective lower bounds for the optimal value of the objective function as compared with those obtained by a conventional approach.
In designing energy supply systems, it is important to consider the uncertainty in energy demands, evaluate the robustness in some performance criteria, and heighten the robustness. A robust optimal design method has been previously proposed to maximize the robustness in a single performance criterion against the uncertainty in energy demands based on a mixed-integer linear model. In this paper, as a preliminary step toward multiobjective robust optimal design, a method of evaluating robustness in multiple performance criteria against the uncertainty in energy demands is proposed based on a mixed-integer linear model. The problems of evaluating the robustness in the performance criteria are formulated as bilevel mixed-integer linear programming (MILP) ones. They are solved by evaluating lower and upper bounds for the maximum regrets in the performance criteria alternately and repeatedly with the aid of a solution method based on reformulation and decomposition. In addition, for the purpose of applying the proposed method to practical problems, a hierarchical MILP method is used to efficiently solve some MILP problems in the solution process. Through a case study on a cogeneration system, the robustness in the annual total cost and primary energy consumption is evaluated and its trade-off relationship is clarified.
For the purpose of attaining the highest performance of energy supply systems, it is important to design the systems optimally in consideration of their operational strategies for seasonal and hourly variations in energy demands. An ap- proach to efficiently solve such an optimal design problem with a large number of periods for variations in energy de- mands is to derive an approximate optimal design solution by aggregating periods with a clustering method. However, such an approach does not provide any information on the accuracy for the optimal value of the objective function. The purpose of this paper is to propose a time aggregation approach for deriving suitable aprroximate optimal design solutions and evaluting their values of the objective function accurately. This time aggregation approach is realized by combining a robust optimal design method under uncertain energy demands and a hierarchical approach for solving large scale optimal design problems. A case study is conducted for a cogeneration system with a practical configuration, and it turns out that the proposed approach enables one to evaluate effective upper and lower bounds for the optimal value of the objective function as compared with those obtained by a conventional approach.
In designing energy supply systems, it is important to consider the uncertainty in energy demands, evaluate the robustness in some performance criteria, and heighten the robustness. A robust optimal design method has been previously proposed to maximize the robustness in a single performance criterion against the uncertainty in energy demands based on a mixed-integer linear model. In this paper, as a preliminary step toward multiobjective robust optimal design, a method of evaluating robustness in multiple performance criteria against the uncertainty in energy demands is proposed based on a mixed-integer linear model. The problems of evaluating the robustness in the performance criteria are formulated as bilevel mixed-integer linear programming (MILP) ones. They are solved by evaluating lower and upper bounds for the maximum regrets in the performance criteria alternately and repeatedly with the aid of a solution method based on reformulation and decomposition. In addition, for the purpose of applying the proposed method to practical problems, a hierarchical MILP method is used to efficiently solve some MILP problems in the solution process. Through a case study on a cogeneration system, the robustness in the annual total cost and primary energy consumption is evaluated and its trade-off relationship is clarified. As a result, it turns out how the values of these performance criteria are close to the optimal ones in relation to the uncertainty in energy demands. This work will be an important step toward developing a multiobjective robust optimal design method.
Mixed-integer linear programming (MILP) methods have 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, some strategies have been proposed to enhance the computation efficiency furthermore. As one of the strategies, a method of reducing model by time aggregation has been proposed to search design candidates efficiently in the relaxed optimal design problem at the upper level. In this paper, the hierarchical MILP method with the strategies is extendedly applied to the optimal design of energy supply systems with storage units. Especially, the method of reducing model is extended by aggregating both representative days and sampling times separately in consideration of the characteristics of energy storage units. A case study is conducted on the optimal design of a cogeneration system with a thermal storage tank. Through the study, it turns out the hierarchical MILP method is effective to derive the optimal solutions in short computation times. It also turns out that the model reduction with day and time aggregations is effective to shorten the computation times furthermore when the number of candidates for equipment capacities is relatively small.
Mixed-integer linear programming (MILP) methods have 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, some strategies have been proposed to enhance the computation efficiency furthermore. As one of the strategies, a method of reducing model by time aggregation has been proposed to search design candidates efficiently in the relaxed optimal design problem at the upper level. In this paper, the hierarchical MILP method with the strategies is extendedly applied to the optimal design of energy supply systems with storage units. Especially, the method of reducing model is extended by aggregating both representative days and sampling times separately in consideration of the characteristics of energy storage units. A case study is conducted on the optimal design of a cogeneration system with a thermal storage tank. Through the study, it turns out the hierarchical MILP method is effective to derive the optimal solutions in short computation times. It also turns out that the model reduction with day and time aggregations is effec- tive to shorten the computation times furthermore when the number of candidates for equipment capacities is relatively small.