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shortened lifetime and/or thermal runaway; maximum DOD of 80% is typical in the literature [137, 23, 138]. At higher discharge rates, internal resistance in the battery becomes significant, and the output voltage will be reduced; therefore, high discharge rates (high power) result in lower total useful energy [136]. The curve of pb versus eb is called a Ragone plot, and it is specific to the cell design/chemistry and pack design. Xue et al. [139] show Ragone curves for Li-ion cells optimized for different C-rates (Figure 8). Vratny et al. [136] contains a related plot of battery “efficiency” (eb,act/eb,0C) as a function of C-rate. 103 102 100 120 140 160 180 200 220 240 gravimetric energy density (W-hr/kg) Pareto front 0.2C cell 2C cell 4C cell 9C cell Ba ̈uerlein [1999] Horiba [2001] Howard [2011] Figure 8: Ragone curves for Li-ion cells optimized for 0.2C–9C rates, with Pareto front (figure from Xue et al. [139]) Cell chemistry significantly contributes to battery characteristics. In general, bat- teries contain a positive electrode (cathode), negative electrode (anode), electrolyte, and various other inactive materials for binding, insulation, and other necessities. Li+ ions are currently favored as a charge carrier because of high potential and lightweight [135]. The theoretical upper limit on cell-level specific energy is determined by the electro- chemical reaction; however, practical considerations ensure that the actual eb is lower than the theoretical maximum. Xue et al. discuss the tradeoff between high specific energy and high specific power [135]. At the cell level, densely-packed active materials result in high eb, but the resulting low porosity and conductivity limit the C-rate (and therefore pb). For a given cell chemistry, a Pareto front exists between specific energy and specific power when considering detailed cell design parameters (Figure 8). Adding inactive materials is also required in order to prevent degradation of eb over repeated charge/discharge cy- cles. Each of these factors causes actual cell specific energy to fall below the theoretical value. At the battery pack level, practical design considerations introduce additional parasitic weight (such as spacing/cooling to contain cells in thermal runaway and bat- tery control electronics [87, 140]). 29 specific power density(W/kg)PDF Image | Electric, hybrid, and turboelectric fixed-wing aircraft
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