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

## DOI:

https://doi.org/10.21914/anziamj.v59i0.12657## 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**

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## Published

2018-11-11

## Issue

## Section

Proceedings Engineering Mathematics and Applications Conference