This paper presents an approximate time-domain solution for physics-based electrochemical lithium-ion cell battery models. The time-domain solution is represented in state-space form and can be easily used for the design of a state estimator or controller. It uses an interconnection-of-system approach to derive a state-space representation of a battery impedance model and provides a reduced order model based via the balanced truncation method. Simulation results are also provided to show the performance of the proposed model in the frequency domain. (C) 2014 Elsevier B.V. All rights reserved.