A modeling approach for battery as an Electrical Energy Storage System is proposed in this paper. The model aims to predict non-linear power delivery dynamics, given charge and discharge demand as a controllable input, not only in normal operating range of batteries, but also in extreme cases such as battery over-charging. In order to achieve that, the model is composed of separated voltage and current models. Several non-linear models, including Hammerstein model, non-linear open-circuit voltage characteristics, and Takacs hysteresis model are combined in the voltage and the current model, respectively. The state of charge of the battery can also be estimated in a recursive optimization fashion by the model. The parameterization and estimation methods of the model are described and also demonstrated on experimental data from a lithium iron phosphate (LiFePO4) cell. The experiment validation shows excellent agreement between measured and simulated voltage and current signals provided by the model during both normal operating and over-charging conditions. The contribution of this paper is given by the unique combination of data-based models used to capture linear dynamics, static non-linearity, and non-linear hysteresis effects in a single dynamic voltage/current model to simulate and predict the non-linear dynamic behavior of a battery as an energy storage/delivery system. (C) 2016 Elsevier Ltd. All rights reserved.