An effective approach for deriving and evaluating approximate optimal design solutions of energy supply systems by time series aggregation

It is important to design multi-energy supply systems optimally in consideration of their operations for variations in energy demands. An approach for efficiently solving such an optimal design problem with a large number of periods for variations in energy demands is to derive an approximate optimal design solution by time series aggregation. However, such an approach does not provide any information on the accuracy for the optimal value of the objective function. In this paper, an effective approach for time series aggregation is proposed to derive an approximate optimal design solution and evaluate a proper gap between the upper and lower bounds for the optimal value of the objective function based on a mixed-integer linear model. In accordance with aggregation, energy demands are relaxed to uncertain parameters and the problem for deriving an approximate optimal design solution and evaluating it is transformed to a three-level optimization problem, and it is solved by applying both the robust and hierarchical optimization methods. A case study is conducted on a cogeneration system with a practical configuration, and it turns out that the proposed approach enables one to derive much smaller gaps as compared with those obtained by a conventional approach.