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38 3 Methods for Sizing and Performance of Hybrid-Electric Aircraft efficiency value of the battery calculated by the physics-based battery model. The battery mass interfaced with the aircraft model is finally determined by Equation 3.3. According to the sizing of the battery system, the integration of the physics-based battery model enables determining ππΈπΈππ·,πππ₯ and ππΈπΈππ· with respect to ππΈπππ. 3.2.3.6.2 Methods for Fuel Cells Integration The integration of a fuel cell as an energy and power device in hybrid-electric propulsion systems require the determination of the maximum power of the fuel cell system (ππΉπΆ,πππ₯) and the efficiency of the fuel cell sys- tem (ππΉπΆ) according to the electrical power requirement ππΈπππ. A first order approximation based upon an invariant efficiency value, gravimetric and volumetric specific power as high- lighted in Section 2.2.3.2 can be used in first instance. Higher fidelity representation of the characteristics of the fuel-cells can be achieved with the integration of physics-based models. The mapping of ππΉπΆ can be established for instance on the basis of an analytical model of a fuel cell system developed by Gradwohl [55] according to the work published by Haji [112]. Considering the different types of losses namely the activation losses, the ohmic losses and the concentration losses, the voltage characteristics of a fuel cell is modelled according to the level of current [55]. As a result, the efficiency of the fuel cell is computed according to the amount of losses. In addition, the efficiency of the balance of plant is taken into account to establish the overall efficiency of the fuel cell system [55]. The output power of the fuel cell is calculated as the product of the current and the voltage. According to this analytical model, a multi-dimensional table can be produced with the electrical power required at the fuel cell system as input ππΈπππ and the efficiency of the fuel cell system as output ππΉπΆ. According to ππΉπΆ, the fuel flow of the fuel cell (πΉπΉπΉπΆ) required to provide the electric power during the mission is computed with Equation 3.6. πΉπΉπΉπΆ = ππΈπππ (3.6) ππΉπΆ Β·πΉπ»π The maximal electrical power produced by the fuel cell system during the mission or within the flight envelope sets the fuel cell maximum power requirement ππΉ πΆ,πππ₯ as shown in Equa- tion 3.7. ππΉπΆ,πππ₯ = max(ππΈπππ) (3.7) ππΉπΆ ππΉπΆ,πππ₯ determines the number of cells composing the fuel cell stack [55]. The weight of the fuel cell can be calculated according to methods developed by Gradwohl [55] considering the number of cells and the additional estimated mass resulting from the components of the balance of plant. The coupling of a physics-based model of a fuel cell enables the computation of ππΈπΈππ·,πππ₯ and ππΈπΈππ· according to ππΈπππ to interface the fuel cell performance with the aircraft environment as indicated in Figure 3.2.PDF Image | Conceptual Design Methods Hybrid-Electric Transport Aircraft
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