An analytical model for the CC-CV charge of Li-ion batteries with application to degradation analysis

https://doi.org/10.1016/j.est.2020.101342Get rights and content

Highlights

  • Described the chargeable capacity under a CC-CV profile with an analytical model;

  • Clarified the degradation behaviors of CCCT and CVCT;

  • Developed a new SOH indicator, the CV-CC time ratio;

  • Two partially CC-CV charged circumstances were also studied.

Abstract

While the constant current charge time (CCCT) and constant voltage charge time (CVCT) are increasingly used for the state of health (SOH) estimation of Li-ion batteries, their correlations with battery degradation are not investigated comprehensively. This paper develops an analytical model to quantify the chargeable capacity of a Li-ion battery under a CC-CV profile, in which CCCT and CVCT are identified as two uncoupled parameters. The model is verified using a battery dataset of cycling tests subjected to 19 different test conditions with different discharge currents, ambient temperatures, and rest times. The behaviors of CCCT and CVCT during battery degradation are studied in terms of chargeable capacity fade. A new health indicator, the CV-CC time ratio, is developed for degradation analysis. Two partial CC-CV cases are also considered in the studies: in one case, the partial CC-CV charge starts after different discharged depths, and in the other case, different fast charging policies are executed before the partial CC-CV charge.

Introduction

Li-ion batteries have been increasingly used across diverse applications because of their higher energy density, lower weight, lower self-discharge rate, and longer life compared to other batteries. However, due to the electrochemical characteristics of Li-ion batteries, they are required to work within relatively narrow temperature and voltage windows [1]. This operation range not only slows down battery degradation but also ensures their safety, which is always the critical requirement. The capacity of a Li-ion battery fades with time because of its degradation, thus the performance and reliability of battery-powered devices, such as electric vehicles, cannot be guaranteed over a long duration. Therefore, the state of health (SOH) of Li-ion batteries needs to be monitored in situ during their service life.

The SOH estimation of Li-ion batteries is an intensive research area. Theoretically, it is quantified in terms of capacity loss and/or internal impedance growth. Three categories of SOH estimation methods are widely acknowledged, namely, direct measurement, model-based, and data-driven methods [2,3]. One commonly shared methodology is to identify and quantify the SOH-sensitive parameters. Correspondingly, the SOH estimation of Li-ion batteries includes two aspects: the identification of SOH-sensitive parameters is the precondition, whereas the quantification is achieved by modeling or machine learning with the SOH-sensitive parameters as the features.

The direct measurement methods measure the capacity and internal impedance directly. Coulomb counting is the capacity measurement method [4], whereas internal impedance can be measured by electrochemical impedance spectroscopy (EIS) [5]. Another parameter containing rich information about SOH is open-circuit voltage (OCV), which provides a thermodynamic fingerprint of the electrodes at any given time [6]. Furthermore, incremental capacity analysis (ICA) [7], i.e., dQ/dV = f (V), or differential voltage analysis (DVA) [8], i.e., dV/dQ = f (Q), can be used not only for SOH estimation but also for inferring the degradation modes [9,10], such as loss of lithium inventory (LLI) and loss of anode/cathode active material (LAM). However, direct acquisition of these parameters needs special instruments or high sampling requirements. For example, coulomb counting needs a low C-rate and long-term full charge or discharge, and the differentiation on the voltage or capacity signals amplifies the noise in signals, which limits the practical application of ICA or DVA methods [9]. The model-based and data-driven methods are developed to alleviate the high requirements on data acquisition. The capacity, internal impedance, and other SOH-sensitive parameters can be estimated by adaptive filtering or data-driven algorithms [11]. For a more extensive review of SOH estimation methods, the reader is referred to Refs. [9], [10], [11], [12], [13], [14].

A practical SOH estimation method needs to be compatible with the usage of Li-ion batteries. The constant current and constant voltage (CC-CV) charge profile is widely adopted to charge Li-ion batteries due to its high efficiency and sufficient protection [15]. A study by Pózna et al. [16] shows that the CC-CV charge-discharge cycle can gather most of the information required for battery health estimation. For instance, these charge/discharge curves contain information on SOH and state of charge (SOC) of Li-ion batteries. Lu et al. [17] extracted four geometrical features from the charge current curves and discharge voltage curves to estimate the real battery capacity, Zhang and Guo [18] used the duration of cyclic charge/discharge phases as features for capacity prediction. Among them, the constant current charge time (CCCT) and constant voltage charge time (CVCT) are increasingly used for SOH estimation.

Williard et al. [19] proposed a SOH measure by fusing CCCT and CVCT with capacity and resistance. On the contrary, CVCT was not recognized as a good SOH indicator in Ref. [20], where a remaining useful life prediction model was developed using an integrated SOH indicator with capacity, resistance, and CCCT. In view of the linear correlation between CVCT and normalized capacity, Yang et al. [21] derived a time constant of CV charge current for SOH estimation. By mathematically describing the degradation rule of CV charge current, a CV charge time factor was recognized as a new SOH indicator for Li-ion batteries in Ref. [22]. Moreover, Eddahech et al. [23] revealed that the exponential parameter extracted from the CV charge current has a linear correlation with capacity loss. In short, there are different understandings, even conflicting conclusions, about the SOH modeling with CC-CV charge profile, especially with CVCT. Therefore, a comprehensive study needs to be carried out to guide the use of CCCT and CVCT for SOH estimation. More questions need to be answered. What are the differences between CCCT and CVCT in revealing the SOH of Li-ion batteries? What is the underlying mechanism that relates CCCT and CVCT to SOH? Is there any other effective way for the CC-CV charge to reveal the degradation process?

In this paper, the CC-CV charge profile is studied in terms of the degradation of Li-ion batteries. Incorporating the CV current expression introduced in Ref. [23], an analytical model is developed by approximating the charged capacity. Specifically, changes in CCCT, CVCT, and an exponential parameter B (of the CV current curve) are regarded as the symptoms of degradation. With the same CC-CV profile, the chargeable capacity of a Li-ion battery fades due to its degradation. By approximating the charged capacity with these three parameters, their contributions and correlations with the charged capacity can be clarified so that the degradation analysis can be guided. The generalizability of CCCT and CVCT for SOH estimation is studied from two aspects: i) one large battery dataset of cycling tests subjected to 19 different test conditions, and ii) two partially implemented CC-CV charging cases. The CV-CC time ratio is developed as a new health indicator for degradation analysis. Considering the wide use of the CC-CV profile in charging Li-ion batteries, the results in this study will provoke the development of applicable online SOH estimation methods.

The rest of the paper is organized as follows. Section 2 introduces the CC-CV charge profile and reviews its underlying degradation mechanisms on Li-ion batteries. The analytical model is developed in Section 3 and verified in Section 4 with a vendor dataset. Thereafter, in order to showcase the generalizability of CCCT and CVCT for SOH estimation, two additional datasets are included for a comprehensive study and a new SOH indicator is developed in Section 5. The conclusions are presented in Section 6.

Section snippets

The CC-CV charge profile and its underlying degradation mechanisms

The constant current constant voltage (CC-CV) charge profile over a cycle is presented in Fig. 1(a). Assuming that a battery is discharged to begin with, the battery is charged by a controlled constant current, Ic, that gradually increases the battery voltage. Once the battery voltage reaches a pre-set level Vc, it is kept constant, then the charge current gradually decreases. The charge process stops when the charge current drops below the cut-off level, Id, typically less than 3% of the rated

An analytical model for the CC-CV charge profile

Assuming that the charge current I(t) is known, the charged capacity CAP can be calculated by integrating the charge current with time, i.e., CAP=I(t)dt. As shown in Fig. 1(a), the charged capacity during the CC phase, CAPc, increases linearly within the CCCT, tc, which can be calculated as follows:CAPc=0tcIcdt=Ictc.

As for the CV charged capacity CAPv, according to the expression of CV current proposed in [23], Iv(t)=AeBt+C, the CV charged capacity can be calculated:CAPv=0tvIv(t)dt=0tv(AeB

Verification of the analytical model

A large cycling test dataset of Li-ion batteries from a vendor was introduced (details in the next subsection). The three parameters tc, tv, and B were extracted as features from the current curve in each CC-CV charge cycle to estimate the charged capacity, so the developed analytical model in Eq. (4) was verified by comparing the estimated capacity with the measured value.

A comprehensive study of CCCT and CVCT for degradation analysis

Besides the vendor data, in order to validate the generalizability of CCCT and CVCT for SOH estimation, two partially implemented CC-CV (abbr. partial CC-CV) charges were also considered, which were complemented by two additional open-access datasets. In one dataset, 3 batteries were discharged to different depths to start the CC-CV charge, while in the other, the same CC-CV profile was partially implemented after different fast charging processes.

Conclusions

In order to understand the quantitative relation between the constant current/constant voltage charge time and the degradation of Li-ion batteries, an analytical model was developed to describe the chargeable capacity under constant current and constant voltage (CC-CV) charge profile. Three parameters, constant current charge time (CCCT), constant voltage charge time (CVCT), and parameter B (describing the exponential behavior of CV current curve), were identified contributing to the chargeable

CRediT authorship contribution statement

Haining Liu: Conceptualization, Methodology, Data curation, Formal analysis, Investigation, Software, Validation, Visualization, Writing - original draft. Ijaz Haider Naqvi: Investigation, Writing - review & editing. Fajia Li: Software, Visualization. Chengliang Liu: Writing - review & editing. Neda Shafiei: Data curation. Yulong Li: Writing - review & editing. Michael Pecht: Project administration, Resources, Supervision, Writing - review & editing.

Declaration of Competing Interest

None.

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grant 51605191, in part by the Key Technology Research and Development Program of Shandong under Grant 2019GGX105009, in part by the Postdoctoral Creative Research Program of Shandong Provinceunder Grant 201903072, and in part by the China Scholarship Council under Grant 201808370045.

The authors would like to thank the vendor for providing the battery cycling test data.

References (32)

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