Nowadays, many aircraft manufacturers are working on new airplanes to reduce the environmental footprint and therefore meet greenhouse gas reduction targets. The concept of more electric aircraft is one of the solutions to achieve this goal. For this aircraft architecture, several electrical devices are used in order to supply propulsive and non-propulsive functions. This paper focuses on the sizing of a direct hybridization system to supply a non-propulsive function in an aircraft. It is composed of a High-Temperature Proton Exchange Membrane Fuel Cell (HT-PEMFC) and a lithium-ion (Li-ion) battery. This sizing is based on a static model of each storage device. The accuracy of these models is compared with dynamic models during a simulation for an aeronautical mission. Static models are implemented in a genetic algorithm to achieve two goals: on the one hand, satisfy the mission profile, and on the other hand, minimize the mass of the system. Other criteria, such as battery and fuel cell aging estimation, are considered. The obtained results show that the direct hybridization system allows protecting the fuel cell against an accelerated aging.