Evaluation of Li-ion cell performance and life requires the ability to predict behavior at extreme conditions, such as low temperatures and high C-rates. Most electrochemical models assuming constant electrolyte diffusion properties fail to accurately predict the electrode and electrolyte potential at such conditions. This study presents a physics-based Extended Single Particle Model (ESPM) designed specifically for accurately predicting the behavior of a Li-ion cell at extreme conditions, incorporating concentration-dependent properties in the electrolyte diffusion dynamics. Since the proposed model aims at supporting long-term simulation, virtual design and optimization studies, minimization of the computational complexity is achieved through analytical Model Order Reduction (MOR) based on a Galerkin projection method. Results show that the implementation of the concentration-dependent diffusion properties leads to significant improvement of model accuracy at extreme conditions. The Reduced Order Model (ROM) can be simulated significantly faster than numerical methods with no loss of accuracy, supporting simulation of long-term usage cycles (10-year) and remaining useful life calculations. (C) The Author(s) 2016. Published by ECS. This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 License (CC BY, http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse of the work in any medium, provided the original work is properly cited. All rights reserved.