A robust optimal design method based on the minimax regret criterion is proposed for unit sizing of energy supply plants so that they are robust economically against the uncertainty in energy demands. Equipment capacities and utility contract demands as well as energy flow rates are determined to minimize the maximum regret in the annual total cost and to satisfy all the possible energy demands. This optimization problem is formulated as a kind of multilevel linear programming one, and its solution is derived by repeatedly evaluating lower and upper bounds for the optimal value of the maximum regret in the annual total cost. Through a case study on a gas turbine cogeneration plant for district energy supply, it is shown that determining equipment capacities appropriately is more important under uncertain energy demands rather than certain ones. It is also shown that the ratio of power generating capacity to total power supply capacity decreases with an increase of the uncertainty in energy demands.

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