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40 3 Methods for Sizing and Performance of Hybrid-Electric Aircraft ππhπππ‘,πΆπππ£,πππ₯. ππΆπΈ,πππ₯ is obtained according to the performance map of the combustion engine as established in Section 3.2.3.3. ππhπππ‘,πΆπππ£,πππ₯ = ππΏπΆπΈ Β· ππΆπΈ,πππ₯ β ππΆπΈππππ‘πππ (3.9) ππΏπΆπΈ = ππΆπΈ (3.10) ππΆ πΈ ,πππ₯ ππhπππ‘,πΈπππ,πππ₯ is determined with Equation 3.11 by the limiting power between the power of the electrical motor ππΈπ and the ππΈπΈππ·,πππ₯ delivered at the shaft of the electrical motor. In this equation the efficiency chain determined by ππΈπ times the ππππ΄π· is considered. In addition, the electrical power off-take (ππΈπππ,ππππ‘πππ) is taken into account. The maximal power output of the electric energy and power device is set by a controller. The regulation of the controller can be expressed in terms of a power lever of the electrical energy and power device (ππΏπΈπΈππ·). ππhπππ‘,πΈπππ,πππ₯ = min(ππΈπ,ππππ΄π· Β·ππΈπ Β·(ππΏπΈπΈππ· Β·ππΈπΈππ·,πππ₯ βππΈπππ,ππππ‘πππ)) (3.11) ππΈπ is determined in Equation 3.12 according to the power lever of the electric motor (ππΏπΈπ) and ππΈπ,πππ₯. ππΈπ,πππ₯ is calculated according to the power map of the electric motor as described in Section 3.2.3.4. ππΈπ =ππΏπΈπ Β·ππΈπ,πππ₯ (3.12) ππΈπ is determined according to the performance map of the electric motor as detailed in Section 3.2.3.4. ππππ΄π· is calculated according to the layout of the PMAD system as high- lighted in Section 3.2.3.5. The maximum power available at the electrical energy and power device is determined in the case of a battery system according to the maximum power of the battery system (ππ΅ππ‘,πππ₯) which can be established by the terms expressed in Equation 3.5. For a hybrid-electric propulsion system equipped with fuel cells, the maximum power of the fuel cell system ππΉπΆ,πππ₯ is determined according to the number of cells as discussed in Section 3.2.3.6.2. 3.2.4.1.2 Serial Hybrid System The mathematical relations for the determination of the maximum thrust of a serial hybrid-electric propulsion system are formulated in this paragraph. They are based upon a generic serial hybrid-electric propulsion system illustrated in Figure 3.3. In contrast to a parallel system, the maximum thrust of a serial system dependsPDF Image | Conceptual Design Methods Hybrid-Electric Transport Aircraft
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