The following work presents the model-assisted research on Valve-Regulated Lead-Acid (VRLA) Absorbent Glass Mat (AGM) battery in pulse operation cycle. The experimental research was conducted for a constant value of State of Charge (SOC) of the battery, for values ranging from 0.2 to 0.8. Based on the conducted test stand research, the parameters of the battery were identified, which were later used to model the battery using the equivalent circuit based on dual polarization (DP) model with double Resistive-Capacitive (RC) loop. Simulations were performed for the identified parameters of the battery which are described by the general form of the polynomial. The second part contains the research on utilization of Nonlinear AutoRegressive eXogenous (NARX) recurrent neural network to predict SOC and a terminal voltage of the battery. Obtained validation results with the use of the identified parameters of the double RC loop and NARX model were discussed in the following work. The article also features the advantages and disadvantages of NARX model and DP model utilization for the use of in Battery Managements Systems (BMS) and micro-installations based on renewable energy sources. Furthermore, the advantages of the addition of more RC loops to describe the dynamic states of batteries in pulse states were discussed in the article.