The current context leads energy system design to very demanding objectives, due to their variety. Indeed, despite an increasing energy demand, environment indicators are becoming always more important. So that for a given service, emission (and then associated consumption as well) is desired to decrease. Improving systems efficiencies is then a important step. Such a problem is formulated as an optimization. It is based on numerical models. Every models differs by definition from reality. This difference can be translated into uncertainties. Usually, they are considered at their most probable value. However, their variation can lead to consequences between a performance decrease and plant inoperability. It is then critical to take into account the deviation due to uncertainties when optimizing an energy system. The optimization problem will be described. It will introduce the description of functions and variables involved in energy system design. The formulation of the optimization under uncertainty will be developed, as well as mathematical methods for uncertainty propagation. Finally, an innovative method taking advantage of the high number of iterations due to the chosen solver will be described. In this study, pinch analysis has been applied. Its limits related to uncertainties treatment will be presented. Methods described here will be applied to an hybrid system of a fuel cell coupled with gas turbines. Results will be compared to a conventional optimization solutions. It will demonstrate that, despite sub-optimal objectives, the sensitivity of the system to uncertainties has been improved.