Mathematical modelling and the dynamic simulation of battery storage systems can be challenging and demanding due to the nonlinear nature of the battery chemistry. This paper introduces a new dynamic battery model, with application to state of charge estimation, considering all possible aspects of environmental conditions and variables. The aim of this paper is to present a suitable convenient, generic dynamic representation of rechargeable battery dynamics that can be used to model any Lithium-ion rechargeable battery. The proposed representation is used to develop a dynamic model considering the thermal balance of heat generation mechanism of the battery cell and the ambient temperature effect including other variables such as storage effects, cyclic charging, battery internal resistance, state of charge etc. The results of the simulations have been used to study the characteristics of a Lithium-ion battery and the proposed battery model is shown to produce responses within 98% of known experimental measurements.