This paper presents for the first time an impedance-based non-linear model for lead-acid batteries that is applicable in all operational modes. An overcharging model describes the accumulation and depletion of the dissolved Pb2+ ions. This physical model has been added to the earlier presented model to expand the model validity. To properly represent the charge acceptance during dynamic operation, a concept of “hardening crystals” has been introduced in the model. Moreover, a detailed gassing and oxygen recombination model has been integrated. A realistic simulation of the overcharging behavior is now possible. The mathematical description is given in the paper. Simplifications are introduced that allow for an efficient implementation and for model parameterization in the time domain. A comparison between experimental data and simulation results demonstrates the achieved accuracy. The model enhancement is of major importance to analyze charging strategies especially in partial-cycling operation with limited charging time, e.g. in electrically assisted or hybrid cars and autonomous power supply systems.