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Energies 2018, 11, 217 5 of 26 The power density of cables does not directly depend on the power rating, but on the maximum current that is conducted and the cable length. A nickel-plated aluminum cable already tested in an aircraft context is chosen with 0.00324 kg per A per m and an efficiency of 98.5% [38]. One of the main differences between the conventional system and the battery-based aircraft is that the consumption of jet fuel leads to less weight during flight, whereas the battery mass remains constant. Some technologies as the Lithium-Air (Li-Air) battery even gain weight. The performance of the battery depends on the materials used—especially for the electrode and electrolyte [16]. Electrochemical batteries are energy storage systems that do not allow an independent design of the installed power and energy. Installation of additional system power is always associated with additional energy of the system, which is due the integral structure of the battery. A good measure for battery performance in this regard is the power-to-energy ratio (P/E-ratio), which relates the batteries peak power to the according energy capacity. Inherently, a design tradeoff between a high power, high energy performance respectively, is given. Therefore, it is important to choose a battery technology, with its specific ratio of power and energy, in accordance with the requirements of the application. Current technologies as the Lithium-Ion (Li-Ion) batteries, which are used for electric vehicles, reach gravimetric energy densities of only 0.3 kWh/kg [5]. Technologies such as Lithium-Sulfur (Li-S) and Metal-Air batteries are in a practical prototype and early stage demonstrator phase, respectively [24]. Gravimetric energy densities of Li-S can theoretically reach 2.6 kWh/kg (Yang et al., 2010), but commercially produced batteries are expected to be realized with 0.65 kWh/kg [39,40]. The power density varies significantly from 0.4 [16] to 1 kW/kg [41]. The suggested potential of Li-Air storages varies significantly. Assumptions of gravimetric energy densities are around 1 kWh/kg [17]. The business case of batteries also depends on the lifetime cycles of the battery system. First tests proved that the Li-S systems are able to last for 1500 cycles in this stadium of development [42]. 2.3. Sizing and Operation Strategy A propulsion operation strategy is defined to determine the optimal power and energy rating of the conventional and electrical propulsion components according to the overall goal setting and the operation of these in each mission phase. 2.3.1. Degree of Hybridization (DoH) The degree of hybridization HP describes the power ratings of the electric motor PEM,max and the gas turbine PGT,max depending on the required total system power PTotal,max: HP = PEM,max = PEM,max (1) PTotal,max PEM,max + PGT,max with PGT,max = (1 − HP) PTotal,max. (2) In the conventional case, HP = 0, only two gas turbines are used. A FEA, HP = 1, has four wingtip propellers. The choice of propulsion architecture depends on a basic decision, if the operation of the aircraft can depend on ground charging infrastructure at airports or not. Otherwise, the battery has to be recharged in flight by the gas turbine and a generator, which requires additional fuel. As the weight of the propulsion system is the critical limitation of the technological feasibility of hybrid electric aircraft, a strategy including on-ground charging is chosen. On board re-charging causes higher weights for the additional components and fuel. Consequently, the gas turbine and electric motors are not connected (Figure 1) and the power rating of the battery is calculated with the efficiency of the electric system ηElec: PBat,max = PEM,max . (3) ηElecPDF Image | Design of Operation Strategies for Hybrid Electric Aircraft
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