Mathematical fitting for the variation in capacity of lithium iron phosphate batteries corresponding to cycles

It is well known that the capacity of lithium iron phosphate (LiFePO\(_{4}\)) batteries decreases as the usage cycles increase. In order to investigate the relationship between the number of charge/discharge cycles and the battery capacity, two batteries were cyclically charged and discharged using an automatic testing system, while simultaneously collecting the capacity data. The tested batteries were composed of different materials and had a capacity of 15 Ah. Each battery was cyclically charged and discharged 800 times. The batteries are analyzed and compared with each other to create fitted curves. The developed mathematical fitting, which consists of both exponential and polynomial terms, is closely responsive to the battery capacity. References W. Su, H. Rahimi-Eichi, W. Zeng and M. -Y. Chow. A survey on the electrification of transportation in a smart grid environment. IEEE Trans. Ind. Inform. , 8:1–10, 2012. doi:10.1109/TII.2011. 2172454 J. Wang, Z. Sun and X. Wei. Performance and characteristic research in LiFePO\(_4\) battery for electric vehicle applications. IEEE Proc. Vehicle Power Propul. Conf. , 1657–1661, 2009. doi:10.1109/VPPC.2009. 5289664 T. Kim and W. Qiao. A hybrid battery model capable of capturing dynamic circuit characteristics and nonlinear capacity effects. IEEE Trans. Energy Conv. , 26:1172–1180, 2011. doi:10.1109/TEC.2011. 2167014 A. Eddahech, O. Briat and J.-M. Vinassa. Determination of lithium-ion battery state-of-health based on constant-voltage charge phase. J. Power Sources , 258:218–227, 2014. doi:10.1016/j.jpowsour. 2014.02. 020 A. Shafiei, A. Momeni and S. S. Williamson. Battery modeling approaches and management techniques for plug-in hybrid electric vehicles. IEEE Proc. Vehicle Power Propul. Conf. , 1–5, 2011. doi:10.1109/VPPC.2011. 6043191 M. Chen and G. A. Rincon-Mora. Accurate electrical battery model capable of predicting runtime and i-v performance. IEEE Trans. Energy Conv. , 21:504–511, 2006. doi:10.1109/TEC.2006. 874229 L. Gao, S. Liu and R. A. Dougal. Dynamic lithium-ion battery model for system simulation. IEEE Trans. Comp. Pack. Tech. , 25:495–505, 2002. doi:10.1109/TCAPT.2002. 803653 O. Erdinc, B. Vural and M. Uzunoglu. A dynamic lithium-ion battery model considering the effects of temperature and capacity fading. IEEE Inter. Conf. Clean Elec. Power , 383–386, 2009. doi:10.1109/ICCEP.2009. 5212025 B. Schweighofer, K. M. Raab and G. Brasseur. Modeling of high power automotive batteries by the use of an automated test system. IEEE T. Instrum. Meas. , 52:1087–1091, 2003. doi:10.1109/TIM.2003. 814827 S. -Y. Lee, W. -L. Chiu, Y. -S. Liao, K. -Y. Lee, J.-H. Chen, H. -J. Lin and K. Li. Modified empirical fitting of the discharge behavior of LiFePO\(_4\) batteries under various conditions. ANZIAM J. , 55:368–383, 2014. doi:10.21914/anziamj.v55i0. 8182 S. Flandrois and B. Simon. Carbon materials for lithium-ion rechargeable batteries. Carbon , 37:165–180, 1999. doi:10.1016/S0008-6223(98)00290-5 H. Li and H. Zhou. Enhancing the performances of Li-ion batteries by carbon-coating: present and future. Chem. Comm. , 48:1201–1217, 2012. doi:10.1039/C1CC14764A J. Wang and X. Sun. Understanding and recent development of carbon coating on LiFePO\(_4\) cathode materials for lithium-ion batteries. Energ. Environ. Sci. , 5:5163–5185, 2012. doi:10.1039/C1EE01263K P. Bai and M. Z. Bazant. Charge transfer kinetics at the solid-solid interface in porous electrodes. Nature Comm. , 5:3585, 2014. doi:10.1038/ncomms4585