A model for simulating a lead-acid battery using bond graphs

This paper presents a model of a lead-acid battery developed with bond graphs. The bond graph structure is used to reproduce the behavior of reversible electrochemical cells in charging conditions or in discharging conditions. The work presented here has been applied to the particular case of lead-acid battery, so widely used in the automotive industry as standard 12 V batteries and as traction batteries in electrical or hybrid vehicles.The model considers each half-cell independently. For each half-cell the main electrode reaction and the electrolysis reaction of water are considered, that will be the hydrogen evolution reaction in the negative electrode and the oxygen evolution reaction in the positive.Electrochemical principles are considered in order to consider the main phenomena that appear in the battery, like the equilibrium potential, and the overpotential, modeled by means of the activation or charge transfer and the diffusion mechanisms.Each one of this phenomena are modeled with their corresponding bond graph elements and structures, showing the correspondence between bond graph elements and its physical interpretation in this field.First, an isothermal model has been developed in order to show the behavior of the main phenomena. A more complex model has also been developed including thermal behavior. This model is very useful in the case of traction batteries in electrical and hybrid vehicles where high current intensities appear.Some simulation results are also presented in order to show the accuracy of the proposed models and the differences of behavior if thermal effects are considered.