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3.2 Methods for Sizing and Performance of Hybrid-Electric Aircraft 37 requirement. Adapted from Vratny et al. [111] the sizing of the battery mass according to the electrical energy requirement is expressed in Equation 3.4 assuming a constant ππ΅ππ‘. By integrating ππΈπππ over time, the total electrical energy required by the battery system is determined. As ππΈπππ is the electric power required by the battery system, this parameter does not include the efficiency of the battery itself. Consequently, ππ΅ππ‘ is considered in Equation 3.4 in order to compute the electrical energy supply. The amount of energy available in a battery is char- acterized by the battery state-of-charge (SOC). The SOC expresses the amount of energy available in percent of the total energy. To protect the battery from irremediable damage, the battery must not be discharged below a certain limit. The SOC limit is taken into account in Equation 3.4 with the term πππΆπππππ‘. 1 ππ΅ππ‘π‘πππ¦ππππππ¦ = π Β·π Β·(1βπππΆ π΅ππ‘ π΅ππ‘,ππ¦π π‘ ) β«οΈ π‘πππ π‘ππππ‘πππ ππΈπππ(π‘)Β·ππ‘ (3.4) The maximal power required along the mission profile can turn out to be the criterion for sizing of the battery system mass. In particular, the high power requirement during takeoff or climb can represent the sizing case for the battery mass for transport aircraft sized for short design mission range [10]. The power which can be delivered by a battery is a function of the ππ΅ππ‘,ππ¦π π‘. As a result, delivering a certain power level requires the installation of a given total battery mass, as formulated in Equation 3.5. In other terms, according to the total battery mass and ππ΅ππ‘,ππ¦π π‘, Equation 3.5 determines ππΈπΈππ·,πππ₯. ππ΅ππ‘π‘πππ¦ πππ€ππ = max(ππΈπππ) (3.5) ππ΅ππ‘ Β· ππ΅ππ‘,ππ¦π π‘ Assuming a constant ππ΅ππ‘ is suitable in conceptual design phase [111]. However, in order to enhance the level of fidelity of the battery modelling, the sensitivity of ππ΅ππ‘ was modelled in this thesis based upon a physics-based battery model developed by Vratny et al. [111]. Considering the evolution of ππ΅ππ‘ for a given power demand and SOC implies the evaluation of the voltage level and electric current. The input required by the battery model is the power profile which determines the electric power required ππΈπππ to be delivered by the battery system. According to the required electrical power and the battery SOC, the available output voltage at required discharge rate is calculated using the discharge characteristics of the battery cell [111]. With respect to the discharge rate fulfilling the power requirements, the battery SOC is calculated at each time step. In this way, the battery SOC at the end of the mission is determined. As indicated in Figure 3.2, if the SOC of the battery calculated at the end of the mission for an initial battery mass is below the πππΆπππππ‘, the battery mass is increased iteratively until the SOC constraint is met. The battery mass sized at aircraft level according to the energy requirements is consequently determined by iteration. The description of the iterative sizing loop is detailed in Section 3.2.7. The sizing power criterion of the battery is evaluated with Equation 3.5 according to the πππππ‘PDF Image | Conceptual Design Methods Hybrid-Electric Transport Aircraft
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