This paper presents an improved impedance-based non-linear simulation model for lead–acid batteries. The parameterization of impedance-based models is difficult for operation profiles with high Ah throughput in short times. Such conditions result in non-steady-state conditions and do not allow precise measurements of impedance parameters. Therefore, the model has been extended by an electrolyte transport model which describes the generation and the transport of sulfuric acid inside the porous electrodes. This expands the model validity as higher Ah throughputs can be simulated now. A description of the Matlab/Simulink implementation and its parameterization in the time domain is given. Furthermore, the advantages and the limits of the improved model are discussed. The model allows for precise modeling of automotive batteries, both in conventional applications and in vehicles with electrically assisted propulsion. It is therefore an important tool for the design of automotive power nets.