A robust optimal design method, based on the relative robustness criterion, is proposed to conduct the unit sizing of energy supply systems, so that they are robust economically under uncertain energy demands. The values of design variables or equipment capacities, as well as those of operation variables or utility contract demands and energy flow rates, are determined to minimize the maximum normalized regret or the maximum regret rate in the annual total cost and satisfy all the possible energy demands. This optimization problem is formulated as a multi-level nonlinear programming problem, and its solution is obtained by repeatedly evaluating the upper and lower bounds for the optimal value of the maximum regret rate by means of the fractional, the bi-level and the linear programming. Through a case study on a cogeneration system, features of the robust optimal design, based on the relative robustness criterion, are clarified.