Battery management systems in hybrid electric vehicle battery packs must estimate values descriptive of the pack's present operating condition. These include: battery state of charge, power fade, capacity fade, and instantaneous available power. The estimation mechanism must adapt to changing cell characteristics as cells age and therefore provide accurate estimates over the lifetime of the pack. In a series of three papers, we propose a method, based on extended Kalman filtering (EKF), that is able to accomplish these goals on a lithium ion polymer battery pack. We expect that it will also work well on other battery chemistries. These papers cover the required mathematical background, cell modeling and system identification requirements, and the final solution, together with results. In order to use EKF to estimate the desired quantities, we first require a mathematical model that can accurately capture the dynamics of a cell. In this paper we "evolve" a suitable model from one that is very primitive to one that is more advanced and works well in practice. The final model includes terms that describe the dynamic contributions due to open-circuit voltage, ohmic loss, polarization time constants, electro-chemical hysteresis, and the effects of temperature. We also give a means, based on EKF, whereby the constant model parameters may be determined from cell test data. Results are presented that demonstrate it is possible to achieve root-mean-squared modeling error smaller than the level of quantization error expected in an implementation. (C) 2004 Elsevier B.V. All rights reserved.