Single particle models (SPM) are usually limited to low currents, which is a serious constrain for the usage of such models into vehicular battery management systems. The present study develops a physics-based ordinary differential equation (ODE) model, which is called extended single particle model (ESPM). In order to maintain the physical significance of the ODE model, a first-principle electrochemical partial differential equations (PDE) model is directly converted into an ODE model using volume-average method. The simulation results show that the ESPM model achieves an accuracy improvement of at least 14% when compared to the standard SPM for various levels of current inputs with only slight increase in computation time. The developed model paves the way for further improvements towards high-current, electrochemical ODE models with high physical significance and low computation burden.