This paper presents a novel electrochemical lithium-ion cell model which can be used in battery control units. Based on classical single-particle approaches, a lumped-parameter nonlinear model is developed that is able to predict accurately the terminal voltages for arbitrary loads, and even for potentiostatic operation. The key features of the extended model are: (1) an incorporation of the electrolyte potential, (2) a modal decomposition of the partial differential equation for the lithium-ion concentration in the liquid phase, (3) a functional handling of the SOC-dependent diffusivity in the insertion materials of both electrodes, and (4) a consideration of temperature-dependent kinetic processes. The prediction quality of the model is verified by means of various experimental load cases applied to the investigated high-power 18650 cell.