Robust optimal design of energy supply systems under uncertain energy demands based on a mixed-integer linear model

In designing energy supply systems, designers should consider the robustness in performance criteria against the uncertainty in energy demands. In this paper, a robust optimal design method of energy supply systems under uncertain energy demands is proposed using a mixed-integer linear model so that it can consider discrete characteristics for selection and on/off status of operation and piecewise linear approximations for nonlinear performance characteristics of constituent equipment. First, a robust optimal design problem is formulated as a three-level min-max-min optimization one by expressing uncertain energy demands by intervals based on the interval programming, evaluating the robustness in a performance criterion based on the minimax regret criterion, and considering hierarchical relationships among design variables, uncertain energy demands, and operation variables. Then, a special solution method of the problem is proposed especially in consideration of the existence of integer operation variables. In a case study, the proposed method is applied to the robust optimal design of a cogeneration system with a simple configuration. Through the study, the validity and effectiveness of the method is ascertained, and some features of the obtained solutions are clarified.