Distributed energy storage using low-cost valve regulated lead acid (VRLA) batteries becomes a promising solution, especially in prosumer microinstallations. In herein work, the model-based research of VRLA battery in pseudo-random and hybrid power pulse cycles has been presented. The major goal of the article was to develop and compare parametric, analytical, and data-driven models of the battery. There were chosen the dual polarization model and the hybrid recurrent neural network model based on long short-term memory and nonlinear autoregressive with exogenous input model for estimating voltage values and determining nonmeasurable parameters of a VRLA battery for different values of the state of charge. Satisfactory results were obtained for both methods, with the favor of the dual polarization model. Finally, the advantages and disadvantages of both methods are discussed.