We provide an analysis of batteries subject to controlled power operation on both charge and discharge over the temperature range of -30 to 45 C, consistent with vehicle drive events. The method we develop is applied to a high-power lithium ion cell, thereby allowing us to obtain parameters and overall characteristics useful for (i) representing the battery in vehicle models and (ii) providing a quantitative means of comparing and classifying battery systems. The current and voltage histories are modeled during the constant power discharge, and Ragone plots (energy vs power) as well as discharge and charge times are analyzed. The equations employed are based on an equivalent circuit comprising a parallel resistor- capacitor combination in series with a resistor and the open- circuit potential source. The circuit element values are dependent on temperature and independent of the current and potential. Model calculations are compared with experimental data. Good agreement is obtained for temperatures ranging from 0 to 45 degrees C. More work is needed to clarify phenomena below 0 degrees C. c 2007 The Electrochemical Society.