Electrochemical batteries are complex devices to model whose static and dynamic responses are highly dependent on the value of its internal and external variables. This paper aims to determine the different importance of considering three of them (state of charge, hysteresis and room temperature) on the battery modeling accuracy. The battery model used in the paper is based on an electrical model composed of three different circuits: the current-voltage circuit, the state of charge circuit and the hysteresis circuit. The first circuit models the polarization of the battery, based on a second order Thévenin model. The last two circuits model the cycling and the hysteresis battery processes. Circuit parameters are dependent of the internal and external variables considered. Finally, the proposed model and characterization tests have been carried out and validated for a single cell of Ni-Cd of 11 Ah of capacity.