The correlation between the capacity fade of LiFePO4 batteries and cycle life

Abstract

A new model is developed by fitting the capacity of LiFePO$_4$ batteries, which can be used to investigate the relationship between capacity fade, state of health (SoH), electrochemical reactions and the number of cycles. The equation for the proposed model based on modified Thevenin circuit, Butler-Volmer kinetics and regression analysis consists of a constant term, a sine-exponential term and an exponential term. The constant term represents the rated capacity of a battery, while the sine-exponential term represents the variation in capacity in the active status and the exponential term represents the variation in capacity in the stable status. The model is divided into two parts. The first part is represented by the sine-exponential term, responsive to the activation of electrolyte and electrodes in the first 180 cycles; the second part can be described by the exponential term, estimating the capacity from cycle 180 to cycle 2000. In addition, the comparison between the model and mean absolute percentage error (mape) is able to predict the serious decay of capacity. The MAPE is only 0.47% for the tested battery. The proposed model also successfully estimates the capacity of a tested battery where the number of cycles is 2000 with the error of 0.90%. The results mean that the model is able to closely describe the correlation between capacity and the cycle numbers. References

• M. Zhao, G. Huang, W. Zhang, H. Zhang and X. Song, Electrochemical behaviors of limn1-xfexpo4\(/\)c cathode materials in an aqueous electrolyte with/without dissolved oxygen, Energy and Fuels 27 (2013), 2:1162-1167. doi:10.1021/ef301893b
• Y.-C. Wang, F.-M. Ni and T.-L. Lee, Hybrid modulation of bidirectional three-phase dual-active-bridge dc converters for electric vehicles, Energies 9 (2016), no. 7, 492. doi:10.3390/en9070492
• A. H. N. Galapitage and P. Pudney, Scheduling electric vehicles with shared charging stations, ANZIAM Journal 57 (2016), 208. doi:10.21914/anziamj.v57i0.10443
• T. Zhu, H. T. Min, Y. B. Yu, Z. M. Zhao, T. Xu, Y. Chen, X. Y. Li and C. Zhang, An optimized energy management strategy for preheating vehicle-mounted li-ion batteries at subzero temperatures, Energies 10 (2017), no. 2. doi:24310.3390/en10020243
• K. M. Tsang and W. L. Chan, State of health detection for lithium ion batteries in photovoltaic system, Energ Convers Manage 65 (2013), 7-12. doi:10.1016/j.enconman.2012.07.006
• Z. Rao, S. Wang, M. Wu, Z. Lin and F. Li, Experimental investigation on thermal management of electric vehicle battery with heat pipe, Energ Convers Manage 65 (2013), 92-97. doi:0.1016/j.enconman.2012.08.014
• A. Nikolian, Y. Firouz, R. Gopalakrishnan, J.-M. Timmermans, N. Omar, P. van den Bossche and J. van Mierlo, Lithium ion batteries-development of advanced electrical equivalent circuit models for nickel manganese cobalt lithium-ion, Energies 9 (2016), no. 5, 360. doi:10.3390/en9050360
• Z. Gao, C. Chin, W. Woo and J. Jia, Integrated equivalent circuit and thermal model for simulation of temperature-dependent lifepo_4 battery in actual embedded application, Energies 10 (2017), no. 1, 85. doi:10.3390/en10010085
• 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 Journal textbf55 (2014), 368. doi:10.21914/anziamj.v55i0.8182
• C.-Y. Chung, K.-Y. Lee, T.-J. Kuo, Z.-Y. Lin, S.-D. Wu, C. Fu, Mathematical fitting for the variation in capacity of lithium iron phosphate batteries corresponding to cycles, ANZIAM Journal 57 (2016), 291. doi:10.21914/anziamj.v57i0.10436
• T. Zahid and W. Li, A comparative study based on the least square parameter identification method for state of charge estimation of a lifepo_4 battery pack using three model-based algorithms for electric vehicles, Energies 9 (2016), no. 9, 720. doi:10.3390/en9090720
• T. Sasaki, Y. Ukyo and P. Novak, Memory effect in a lithium-ion battery, Nat Mater 12 (2013), no. 6, 569-575. doi:10.1038/nmat3623
• B. R. Tiwari and M. M. Ghangrekar, Enhancing electrogenesis by pretreatment of mixed anaerobic sludge to be used as inoculum in microbial fuel cells, Energy \(and\) Fuels 29 (2015), no. 5, 3518-3524. doi:10.1021/ef5028197
• P. Bai and M. Z. Bazant, Charge transfer kinetics at the solid-solid interface in porous electrodes, Nat Commun 5 (2014), 3585. doi:10.1021/ef990039t
• A. Eddahech, O. Briat and J.-M. Vinassa, Determination of lithium-ion battery state-of-health based on constant-voltage charge phase, Journal of Power Sources 258 (2014), 218-227. doi:10.1016/j.jpowsour.2014.02.020
• R. Castaing, Y. Reynier, N. Dupre, D. Schleich, S. J. S. Larbi, D. Guyomard and P. Moreau Degradation diagnosis of aged li4ti5012-lifepo_4 batteries, Journal of Power Sources 267 (2014), 744-752. doi:10.1016/jpowsour.2014.06.002
• H. Bulter, F. Peters, J. Schwenzel and G. Wittstock, In situ quantification of the swelling of graphite composite electrodes by scanning electrochemical microscopy, J Electrochem Soc 163 (2016), no. 2, A27-A34. doi:10.1149/2.1061514jes