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A hierarchical optimization approach to robust design of energy supply systems based on a mixed-integer linear model

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  • Yokoyama, Ryohei
  • Kamada, Hiroki
  • Shinano, Yuji
  • Wakui, Tetsuya

Abstract

In designing energy supply systems, designers should heighten the robustness in performance criteria against the uncertainty in energy demands. In this paper, a robust optimal design method using a hierarchical mixed-integer linear programming (MILP) method is proposed to maximize the robustness of energy supply systems under uncertain energy demands based on a mixed-integer linear model. A robust optimal design problem is formulated as a three-level min-max-min MILP one by expressing uncertain energy demands by intervals, evaluating the robustness in a performance criterion based on the minimax regret criterion, and considering relationships among integer design variables, uncertain energy demands, and integer and continuous operation variables. This problem is solved by evaluating upper and lower bounds for the minimum of the maximum regret of the performance criterion repeatedly outside, and evaluating lower and upper bounds for the maximum regret repeatedly inside. Different types of optimization problems are solved by applying a hierarchical MILP method developed for ordinary optimal design problems without and with its modifications. In a case study, the proposed approach is applied to the robust optimal design of a cogeneration system. Through the study, its validity and effectiveness are ascertained, and some features of the obtained robust designs are clarified.

Suggested Citation

  • Yokoyama, Ryohei & Kamada, Hiroki & Shinano, Yuji & Wakui, Tetsuya, 2021. "A hierarchical optimization approach to robust design of energy supply systems based on a mixed-integer linear model," Energy, Elsevier, vol. 229(C).
    • Handle: RePEc:eee:energy:v:229:y:2021:i:c:s0360544221005922
    DOI: 10.1016/j.energy.2021.120343
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