Study Of Mathematical Model For Lithium-ion Battery

Particle-fracture and over-charge and discharge in electrode materials are one of the main reasons for capacity fade of lithium-ion batteries.In general,the former is dependent on the current density on the surface of active particles,while the latter is dependent on the state of charge(SOC).Therefore,in order to figure out the mechanism of capacity fade of lithium-ion batteries,it is necessary to study the current density distribution and SOC in the electrode.Based on the mathematical model for lithium-ion batteries,many studies on current density and SOC across single electrode(e.g.LiCoO₂,LiMn₂O₄ and MCMB) and mixed electrode have been carried out.Mathematical model of LiCoO₂/MCMB battery model was first established. Related material diffusion coefficient and reaction parameters were confirmed by the experimental optimization of voltage and specific capacity,suggesting a higher reliability.Using this mode,current density and SOC of active particles within the LiCoO₂/MCMB cell were modeled.The results showed that different electrode locations had different current densities.Changes both electrode sides were larger than that of the middle electrode,while the maxim discharge current density almost appeared in the discharge end.On the other hand,SOC with the location of the electrodes vary in the discharge process,a maximum depth of discharge-lateral and medial depth of discharge shallow.Also,current density and SOC of active particles within the LiMn₂O₄/MCMB cell were modeled using the same method.Comparing with the LiCoO₂/MCMB cell, although the rules of SOC across electrode in LiMn₂O₄/MCMB were similar with LiCoO₂/MCMB cell,the rules of current density distribution were different from that. Outside particles showed the maxim current density distribution at the beginning of discharge while inside particles had it at the end of discharge.In addition,the particle size's effects were discussed based on multi-sizes model.The smaller particle size was,the smaller current density,which were inclined to be over-charge and over-discharge status. Mixed-electrode mathematical model was established to study current density distribution and SOC across on mixed materials electrode in hybrid batteries.The results show that current density distribution in the negative electrode and concentration gradient changes in solution phase are same with single model of the same battery materials.While the current density distribution and the SOC state on the surface of the particle have a lot of difference:in the early and end discharge,the current density of LiCoO₂ is larger,the current density of LiMn₂O₄ and smaller in the early and end charge.SOC state has differences in the mixed electrode,which is bigger than different place on electrode.The effect of material component on current density distribution and SOC has been carried out.The results showed that the component contents,particle size distribution,discharge rate obviously affected current density distribution,but less affected the SOC.