Performance comparison of energy supply systems under uncertain energy demands based on a mixed-integer linear model

In designing energy supply systems, several alternatives for design specifications are proposed, and their performances are evaluated and compared. In this paper, a method of comparing performances of two energy supply systems under uncertain energy demands is proposed based on a mixed-integer linear model. Uncertain energy demands are expressed by intervals. The minimum and maximum, and consequently their interval of the difference in the value of a performance criterion are evaluated for all the possible energy demands within their intervals. An optimization problem for this evaluation is formulated as a minimax mixed-integer linear programming one with integer and continuous operation variables. The problem is solved by evaluating upper and lower bounds for the optimal value of the difference in the value of the performance criterion repeatedly. In a case study, the minimum and maximum of the reduction in the annual total cost of a cogeneration system in comparison with a conventional energy supply system are evaluated, and the corresponding energy demands and operational strategies are identified. The influence of the uncertainty in energy demands on these results is also examined. Through the case study, the validity and effectiveness of the proposed method are clarified.