This thesis describes the working principle of the lead-acid battery and the associated basic definitions and features. The division of the mathematical models of the battery is presented, and the battery models based on the replacement circuit are additionally explained. Furthermore, battery charging and discharging experiments were performed and, based on the conducted experiments, the characteristics of the dependence of SOC of the batteries on the idle voltage were determined. These characteristics were determined experimentally in the range of SOC 30% - 100% with a step of 10%. After that, the parameters of the lead-acid batteries were determined for various associated mathematical models based on the alternating current circuit, which are available from the literature. For the purpose of determining the parameters of the model, battery voltages were recorded during the experiments, which included battery idle, discharge, charge and rest after discharge and charge to record the dynamics of the battery for all typical operating modes. Such demanding and long-term experiments are necessary in order to calculate the exact values of the parameters, and the model has satisfactory performance. Experimental tests were carried out on two new and one older battery, where the newer batteries were from the same production series, while the older battery was from a different production series. Finally, based on certain parameters and characteristics of the batteries, corresponding simulation models were created in the MATLAB-Simulink software package, where the current measured during the experimental experiments was used as an input variable for a better comparison of the simulated voltage with the real one. To compare the accuracy of the considered models, the integral of the absolute error between the simulated and real voltage was used. In the last chapter, the results of different battery models were analyzed with accurately calculated amounts of model parameters at different percentages of SOC. On the basis of this analysis, the most accurate model was chosen, and the results with approximate parameter values were additionally analyzed for it.