I. A simplified model for determining capacity usage and battery size for hybrid and plug-in hybrid electric vehicles

We develop a simplified model to examine the effect of the shape and magnitude of the battery pulse-power capability on capacity usage and battery size. The simplified model expresses the capacity usage and a dimensionless battery area in terms of a dimensionless energy-to-power ratio and a parameter that characterizes the shape of the pulse-power capability. We also present dimensional results that show how the capacity usage depends on the equivalent-electric range and separator area, and how the battery area depends on the equivalent-electric range. Key results include the presence of a Langmuir-like relationship between the capacity usage and the dimensionless energy-to-power ratio, and a linear relationship between the dimensionless energy-to-power ratio and a dimensionless area, with a slope and offset that depend on the shape of the pulse-power capability. We also found that a flat pulse-power capability curve increases capacity usage and decreases battery size, and that two important parameters for battery design are (U − Vmin)Vmin/R, which reflects the maximum power capability, and Q〈V〉, which reflects the battery energy. The results and analysis contained herein are used to help interpret the results from a combined battery and vehicle model, presented in a companion paper.