A Multilevel Programming Approach to Robust Optimal Design of Energy Supply Systems.

Abstract

A multilevel programming approach is proposed to optimal design of energy supply systems in consideration of their robustness in economic and energy saving characteristics against the energy demand uncertainty. Equipment capacities and utility contract demands are determined so as to minimize the annual total cost for average energy demands, to minimize the difference between the annual operational costs for the worst and average energy demands, to maximize the difference between the annual operational costs for average and the best energy demands, and to satisfy all the possible energy demands. This optimization problem is formulated as a three-level linear programming problem, and its solution is obtained by repeatedly solving a linear and a set of linear and bilevel linear programming problems which give, respectively, lower and upper bounds for the original objective function. Through a numerical case study on a cogeneration system, the effectiveness of this approach is ascertained, and the influence of consideration of the robustness on the cogeneration unit sizing is clarified.