Abstract
A robust optimal design method for multistage expansion of energy supply systems based on the relative robustness criterion is proposed so that they are robust economically against the uncertainty in energy demands which increase stepwise with construction of buildings. Equipment capacities and utility contract demands as well as energy flow rates for each expansion period are determined to minimize the maximum normalized regret or the maximum regret rate in the levelized annual total cost and satisfy all the possible energy demands for the overall planning period. This optimization problem is formulated as a kind of multilevel linear programming problem, and its solution is obtained by repeatedly evaluating upper and lower bounds for the optimal value of the maximum regret rate by means of the fractional, the bilevel, and the linear programming. Through a numerical case study on a cogeneration system, the relationship between the optimal equipment capacities and the uncertainty in energy demands or the number of years for expansion periods is clarified.
