Modified empirical fitting of the discharge behavior of LiFePO\(_4\) batteries under various conditions

A mathematical model is developed by fitting the discharge curve of a new LiFePO\(_4\) battery and then used to investigate the relationship between the discharge time and the closed-circuit voltage. This model consists of exponential and polynomial terms where the exponential term dominates the discharge time of a battery and the polynomial term dominates the change in the closed-circuit voltage. Time shift and time scale processes modify the exponential and polynomial terms, respectively, so that the model is suitable for batteries under various conditions. References W. Su, H. Eichi, W. Zeng and M.-Y. Chow, A survey on the electrification of transportation in a smart grid environment, IEEE Intl. Conf. Ind. I. 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 Vehicle Power 1657–1661, 2009. doi:10.1109/VPPC.2009.5289664 A. Shafiei, A. Momeni and S. S. Williamson, Battery modeling approaches and management techniques for plug-in hybrid electric vehicles, IEEE Vehicle Power 1–5, 2011. doi:10.1109/VPPC.2011.6043191 P. Bai, D. A. Cogswell and M. Z. Bazant, Suppression of phase separation in LiFePO\(_4\) nanoparticles during battery discharge, Nano Lett. 11:4890–4896, 2011. doi:10.1021/nl202764f H. L. Chan and D. Sutanto, A new battery model for use with battery energy storage systems and electric vehicle power systems, IEEE Power Eng. Soc. 1:470–475, 2000. doi:10.1109/PESW.2000.850009 T. Kim and W. Qiao, A hybrid battery model capable of capturing dynamic circuit characteristics and nonlinear capacity effects, IEEE T. Energy Conver. 26:1172–1180, 2011. doi:10.1109/TEC.2011.2167014 D. N. Rakhmatov and S. B. K. Vrudhula, An analytical high-level battery model for use in energy management of portable electronic systems, IEEE ICCAD 488–493, 2001. doi:10.1109/ICCAD.2001.968687 V. Srinivasan and J. Newman, Discharge model for the lithium iron-phosphate electrode, J. Electrochem. Soc. 151:A1517–A1529, 2004. doi:10.1149/1.1785012 V. Rao, G. Singhal, A. Kumar and N. Navet, Battery model for embedded systems, VLSI Des. 105–110, 2005. doi:10.1109/ICVD.2005.61 S. Dargavillez and T. W. Farrell, Predicting active material utilization in LiFePO\(_4\) electrodes using a multiscale mathematical model, J. Electrochem. Soc. 157:A830–A840, 2010. doi:10.1149/1.3425620 R. Rao, S. Vrudhula and D. N. Rakhmatov, Battery modeling for energy-aware system design, Computer 36:77–87, 2003. doi:10.1109/MC.2003.1250886 M. Chen and G. A. Rincon-Mora, Accurate electrical battery model capable of predicting runtime and i-v performance, IEEE T. Energy Conver. 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 T. Compon. Pack. T. 25:495–505, 2002. doi:10.1109/TCAPT.2002.803653 V. Agarwal, K. Uthaichana, R. A. DeCarlo and L. H. Tsoukalas, Development and validation of a battery model useful for discharging and charging power control and lifetime estimation, IEEE T. Energy Conver. 25:821–835, 2010. doi:10.1109/TEC.2010.2043106 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