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Battery modeling in conceptual aircraft studies often assumes a fixed pack-level eb and pb with constant battery efficiency factor [16]. This approach may be appropriate for long-term advanced technology studies where detailed discharge characteristics of the battery technology are unknown. A higher level of fidelity considers discharge rate effects by constructing an “equivalent circuit” model of the battery. The battery model consists of an internal resistance and possibly capacitance determined from empirical data [17, 136, 141, 142]. Equivalent circuit models introduce a power-dependent battery efficiency factor and create coupling between mission analysis, control strategy, and vehicle weights. Physics-based models considering internal cell design variables have been used to explore coupling between vehicle design and optimal cell design [143]; however, physics-based cell modeling introduces significant computational cost and has not yet been coupled to an aircraft design problem. Avanzini et al. contains a detailed procedure for empirical modeling of a particular battery pack [144]. 5.3 Electrical System Trades Key trade studies for an electric propulsion system include the choice of alternating current (AC) or direct current (DC) in the distribution buses, the nominal system operating voltage, and whether to utilize constant-voltage or variable-voltage DC power for battery-fed hybrid- and all-electric systems. Vratny et al. [145] studied constant and variable system voltage (CSV/VSV) in a hybrid system and concluded that VSV was more efficient overall. High system voltages may be more efficient but incur a weight or safety penalty due to the risk of electrical arcing at high altitude [145, 92]. Paschen’s Law dictates that air gap insulation is safe below 327V, no matter the air density or pressure; therefore, current commercial airplanes restrict electrical bus voltages to 270V or below for intrinsic safety. Electric propulsion concepts will require higher operating voltages in the low kV range, necessitating investment in highly durable and lightweight insulative materials [92, 146, 27]. The literature currently favors DC power distribution, particularly for any appli- cation involving the use of batteries but also for high-power turboelectric [57, 17]. DC power distribution eliminates the need to synchronize the phases of multiple electrical generators and motors and simplifies “throttling” for distributed propulsion applica- tions, but it incurs weight and efficiency penalties due to AC/DC conversion on both ends [147]. Each unit of rated motor power requires an equal unit of inverter and rec- tifier power, plus redundancies for system safety. Using the pe estimates given above, this means that the weight of the power electronics will be on the order of or even heavier than the motors themselves. Regardless, since batteries operate on DC, there is no need to rectify the power; therefore, where electric energy storage is used, DC power distribution will be more favored [148]. An alternative AC power distribution scheme for a turboelectric configuration was devised by Sadey et al. [131] and utilizes doubly-fed induction machines similar to wind turbines. Figures 2c and 2d illustrate the more common DC distribution architecture. For hybrid electric applications involving turbofans, shaft power may be taken off from the low-pressure and/or high-pressure spool. While the high-pressure spool rotates over a narrower range of speeds, operability characteristics of the engine limit 30PDF Image | Electric, hybrid, and turboelectric fixed-wing aircraft
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