Engineering Simulation of Lead–Acid Cell Characteristics and Processes in Batteries

Predicting transient behavior of lead–acid batteries during charge and discharge process is a very important factor in many applications including Hybrid Electric Vehicles (HEV). In this paper, an engineering model based on fundamental chemical and electrochemical relations of lead– acid batteries is introduced. This model is capable to predict transient behavior of lead–acid batteries including charge and discharge cycles. It is also capable to predict acid consumption, SoC and porosity variation of electrodes as well. Since the model is based on electrochemical relations, it gives a good physical understanding of lead–acid phenomena. This model is verified with experimental tests and CFD codes. The results show that the developed model has a good accuracy within a very short time. a Coefficient N Number of electrone A Specific electroactive area, [cm/cm] Na Avogadro number c Acid concentration, [mol/cm] N Mole of acid [mol] e Electric charge of electrone, 1.6× 10−19 [C] q Electric charge [C] ex Exponent in the effective property Q Electrode charge per volume [C/cm] E Battery voltage [V] R Universal gas constant, 8.314 [J/mol ·K] Eoc Open circute voltage [V] Rb Battery ohmic resistance [Ω] F Faraday constant, 96,487, [C/mol] t Time, [sec] i0 Transfer current density, [A/cm] T Temprature [K] I Current, [A] V Electrolyte volume [cm] j Applied current density, [A/cm] x Electrode thickness [cm] k Conductivity of liquid, [S/cm] y Electrode height [cm] MW Molecular weight, g/mol z Electrode width [cm] Greek ε Porosity σ Conductivity of solid matrix [S/cm] φ Electric potential [V] γ Exponent for the exchange current density α Transfer coefficient for the electrode ρ Density of species ξ Exponents for the specific active area Subscripts/Superscripts eff Effective, corrected for tortuosity l Liquid solution ◦ Initial value s Solid phase