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

Highlights: • A robust optimal design method of energy supply systems is proposed. • A mixed-integer linear model is adopted for equipment performance characteristics. • A three level mixed-integer linear programming problem is formulated and solved. • Robust optimal design of a cogeneration system is investigated. • Influence of uncertainty in energy demands on robust optimal design is clarified. 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.