1 Introduction
New energy vehicles have become a crucial direction for the low-carbon and green transformation of the global automotive industry. With the rapid development of the electric vehicle market, the traction battery pack serving as the core energy storage component has attracted extensive research attention regarding its safety, durability, and reliability. Lithium-ion batteries, particularly lithium iron phosphate (LiFePO4) batteries, are widely employed in electric vehicles due to their high operating voltage, high specific energy, long cycle life, and low self-discharge rate. However, as the traction battery pack undergoes repeated charge and discharge cycles, irreversible capacity and power fading inevitably occur, which directly affects the driving range and dynamic performance of electric vehicles.
From a mechanistic perspective, the degradation of lithium-ion batteries can be primarily attributed to two major failure modes: Loss of Lithium Inventory (LLI) and Loss of Active Material (LAM). The latter can be further subdivided into Loss of Active Material of the Negative Electrode (LAM_NE) and Loss of Active Material of the Positive Electrode (LAM_PE). Understanding and quantifying these degradation modes are essential for accurate state-of-health estimation, remaining useful life prediction, and optimal battery management of the traction battery pack.
Current research on degradation mechanism analysis is generally categorized into two approaches: non-destructive external characteristic methods and destructive post-mortem physicochemical methods. The former approach, such as open-circuit voltage (OCV) analysis and incremental capacity (IC) analysis, enables continuous and non-destructive characterization of battery degradation. However, these external characteristic methods rely on certain assumptions and often lack direct experimental verification. The latter approach, including techniques such as X-ray diffraction (XRD), scanning electron microscopy (SEM), and half-cell tests, can directly reveal the internal aging mechanisms but causes irreversible damage to the battery. Furthermore, most post-mortem studies are qualitative in nature and have not fully established quantitative correlations between microscopic observations and macroscopic performance degradation. To bridge this gap, this study aims to develop a cross-scale correlation framework that integrates macroscopic diagnostic results with microscopic characterization data, thereby enabling more reliable and quantitative degradation mode diagnosis for the traction battery pack.
2 Experimental Design and Testing
2.1 Test Objects and Platforms
All experiments were conducted on a commercial prismatic LiFePO4/graphite battery with a rated capacity of 20 Ah, and key parameters of this cell are shown in Table 1. The cells of the traction battery pack were cycled under controlled conditions to obtain multiple aging states (State of Health ranging from approximately 79% to 102%). The battery numbering scheme and corresponding SOH values are listed in Table 2.
| Parameter | Value |
|---|---|
| Nominal capacity | 20 Ah |
| Nominal voltage | 3.2 V |
| Internal resistance | 7 mΩ |
| Weight | 485±15 g |
| Dimensions | 130×70×27 mm |
| Battery No. | #1 | #2 | #3 | #4 | #5 | #6 | #7 | #8 | #9 | #10 |
|---|---|---|---|---|---|---|---|---|---|---|
| SOH (%) | 93.47 | 89.12 | 86.77 | 79.41 | 96.54 | 90.61 | 83.63 | 79.76 | 102.3 | 99.1 |
The complete testing platform comprised a battery test system (NBT5V20AC16-T), a temperature and humidity chamber (ETE-GDJS-150L), a coin-cell tester (CT-4008Tn-5V10mA), and an XRD diffractometer (PANalytical X’Pert3 powder). All full-cell tests were performed at a controlled temperature of 25 °C.
2.2 Full-Cell Performance Tests
Capacity calibration: In accordance with the GB/T31486 standard, repeated charge-discharge cycles were applied. The capacity was accepted when the difference between each discharge capacity and the average of three consecutive discharges was within 2%.
Cycling aging: The batteries underwent repeated constant current–constant voltage (CC-CV) charging at 15 A up to 3.65 V (cut-off current 1 A) followed by constant current discharging at 15 A down to 2.5 V. Full capacity calibration was performed every 50 cycles. The detailed cycling procedure is given in Table 3.
| Step | Mode | Rate | End Condition |
|---|---|---|---|
| 1 | Rest | – | Time ≥ 1.5 h |
| 2 | CC charge | 15 A | Voltage ≥ 3.65 V |
| 3 | CV charge | – | Current ≤ 1 A |
| 4 | Rest | – | Time ≥ 1.5 h |
| 5 | CC discharge | 15 A | Voltage ≤ 2.5 V |
| 6 | Rest | – | Time ≥ 1.5 h |
| 7 | Loop | Steps 2–5 | Cycle count ≥ 50 |
Rate capability test: Discharge tests at various current rates (C/25, C/10, C/5, C/3, C/2, and 1C) were conducted to evaluate the effect of polarization on the discharge capacity and IC curve characteristics.
Low-rate reference test: Before disassembly, all cells were charged and discharged at C/25 to reach a fully charged or fully discharged state as consistently as possible. The low-rate protocol is shown in Table 4.
| Step | Mode | Current | End condition |
|---|---|---|---|
| 1 | Rest | – | Time ≥ 1 h |
| 2 | CC discharge | C/3 | Voltage ≤ 2.5 V |
| 3 | Rest | – | 4 h |
| 4 | CC charge | C/25 | Voltage ≥ 3.65 V |
| 5 | Rest | – | 4 h |
| 6 | CC discharge | C/25 | Voltage ≤ 2.5 V |
| 7 | Rest | – | 4 h |
2.3 Electrode Characterization and Half-Cell Tests
After the full-cell tests reached the target aging state, the cells were fully charged (for #1–#4) or fully discharged (for #5–#8) and disassembled inside an argon-filled glovebox. The harvested electrodes were rinsed with dimethyl carbonate to remove residual electrolyte. Some electrode samples were subjected directly to XRD and SEM characterization, while others were assembled into CR2032 coin-type half cells. Small discs (14 mm diameter) were punched from the electrode sheets and assembled against lithium metal. The half-cell voltage windows were set to 2.4–3.7 V for LiFePO₄ cathodes and 0.01–1.5 V for graphite anodes. The half-cells underwent low-rate C/25 tests to extract quasi-open-circuit electrode potential curves.
The measured half-cell electrode potential versus state-of-lithiation (SOL) curves were fitted using hyperbolic tangent functions. For the positive electrode, the fitting expression is given by:
$$U_p(x)=a_p+c_{p,1}\exp\left(-\frac{x-x_{p,1}}{b_{p,1}}\right)+c_{p,2}\exp\left(-\frac{x-x_{p,2}}{b_{p,2}}\right)-f_{p,1}\tanh\left(\frac{x-d_{p,1}}{e_{p,1}}\right)-f_{p,2}\tanh\left(\frac{x-d_{p,2}}{e_{p,2}}\right)$$
For the negative electrode, a three hyperbolic tangent combination was employed:
$$U_n(x)=a_n+c_{n,1}\exp\left(-\frac{x-x_{n,1}}{b_{n,1}}\right)+c_{n,2}\exp\left(-\frac{x-x_{n,2}}{b_{n,2}}\right)-\sum_{i=1}^{3}f_{n,i}\tanh\left(\frac{x-d_{n,i}}{e_{n,i}}\right)$$
The fitting results agreed well with the measured data, with errors of less than 0.05 V, thereby providing a reliable foundation for subsequent OCV-based degradation mode analysis.
3 Quantitative Degradation Diagnosis Based on OCV
3.1 Coordinate Transformation Framework
The cell OCV is defined as the potential difference between the positive and negative electrodes at a given state of charge. Since the positive electrode potential is expressed in the PE coordinate system with lithium content \(x_{PE}\), and the negative electrode potential is expressed in the NE system with \(x_{NE}\), while the actual usable portions of the electrodes shrink as degradation proceeds, it is necessary to introduce available active material coordinates. The transformation between the full electrode coordinate system and the available electrode coordinate system is analogous to a coordinate axis scaling process.
For the positive electrode, the transformation from the physical PE system to the available APE system is described by:
$$T_{x,APE\leftarrow PE} = \frac{C_{APE}}{C_{PE}} = \frac{C_{PE}-LAM_{liPE}-LAM_{dePE}}{C_{PE}}, \quad T_{y,APE\leftarrow PE}=1$$
and a translation is induced by the loss of lithiated active material:
$$R_{x,APE\leftarrow PE} = \frac{LAM_{liPE}}{C_{PE}}, \quad R_{y,APE\leftarrow PE}=0$$
Similarly, for the negative electrode, the transformations along the x-axis and the translation are given by:
$$T_{x,ANE\leftarrow NE} = \frac{C_{ANE}}{C_{NE}}, \quad R_{x,ANE\leftarrow NE}=\frac{LAM_{liNE}}{C_{NE}}$$
The coordinate transformation between the positive and negative electrode systems is established through the LLI and the active material balance. The matrix forms of the full transformation are given by:
$$[x_{APE},y_{APE},1]=[x_{PE},y_{PE},1]\cdot\begin{bmatrix}T_{x,APE\leftarrow PE} & 0 & 0\\0 & 1 & 0\\R_{x,APE\leftarrow PE} & 0 & 1\end{bmatrix}$$
To ensure a unique solution for the identified parameters, the following reparameterization is applied. The positive electrode available capacity is:
$$X_1 = C_{APE} = C_{PE} – LAM_{liPE} – LAM_{dePE}$$
The negative electrode available capacity is:
$$X_2 = C_{ANE} = C_{NE} – LAM_{liNE} – LAM_{deNE}$$
The third parameter \(X_3\) represents the combined effect of lithiated negative active material loss and the LLI:
$$X_3 = LAM_{liNE} – LAM_{dePE} + LLI$$
The fourth identified parameter \(X_4\) is the lithiation state at the fully discharged condition, defined as:
$$X_4 = SOL_{neg,0}$$
The OCV of the cell can then be expressed through a parameterized model using the available negative electrode lithiation state \(x_{ANE}\) as the independent variable:
$$OCV(x_{ANE}) = U_p\left(\frac{X_1-x_{ANE}\cdot X_2+LAM_{liPE}+LAM_{dePE}}{X_1}\right) – U_n(x_{ANE})$$
A particle swarm optimization algorithm was adopted to minimize the root-mean-square error between the calculated OCV and the experimental OCV from the low-rate test, which served as the optimization objective function:
$$RMSE = \min\sqrt{\frac{1}{n}\sum_{i=1}^{n}\left(OCV(x_i)-\widehat{OCV}(x_{ANE,i})\right)^2}$$
3.2 Quantitative Results of Degradation Modes
The identified parameters \(X_1, X_2, X_3,\) and \(X_4\) as functions of SOH are shown in Figure 3.2 of the original text. The identification results indicate that the positive electrode available capacity remains nearly constant over the studied aging range, while the negative electrode capacity decreases with aging. The \(X_3\) parameter increases linearly with decreasing SOH, confirming that LLI is the dominant degradation mechanism in the early aging stage.
To separate LLI from the identified \(X_3\), the average lithiation fraction of the lost active particles was estimated. The active material dissolution was assumed to occur uniformly across the electrodes, so that the fraction of lithiated active material lost at each electrode equals the average lithiation state during cycling. The lithiated active material loss of each electrode is calculated as:
$$LAM_{liPE} = \frac{x_{crk,p}^{min}+x_{crk,p}^{max}}{2}\cdot (C_{APE,fresh}-C_{APE,aging})$$
$$LAM_{liNE} = \frac{x_{crk,n}^{min}+x_{crk,n}^{max}}{2}\cdot (C_{ANE,fresh}-C_{ANE,aging})$$
where \(x_{crk,p}\) and \(x_{crk,n}\) are the average lithiation states of positive and negative electrodes, respectively. Once \(LAM_{liNE}\) and \(LAM_{liPE}\) are known, \(LAM_{dePE}\) and \(LAM_{deNE}\) are obtained as:
$$LAM_{dePE}=LAM_{PE,total}-LAM_{liPE}$$
$$LAM_{deNE}=LAM_{NE,total}-LAM_{liNE}$$
The final quantitative result of capacity losses is summarized in Table 5. It was found that \(LLI\), \(LAM_{liNE}\), and \(LAM_{deNE}\) all increase with battery aging, whereas \(LAM_{liPE}\) and \(LAM_{dePE}\) remain negligibly small throughout the aging process, consistent with the well-known excellent structural stability of LiFePO4 olivine cathodes. The maximum capacity losses due to LLI and LAM_NE were calculated as 3.40 Ah and 2.83 Ah, respectively.
| Aging mode | Maximum capacity loss (Ah) | Trend with aging |
|---|---|---|
| LLI | 3.40 | Linear increase |
| LAM_liNE | 2.83 | Progressive increase |
| LAM_deNE | ≈LAM_liNE | Progressive increase |
| LAM_liPE / LAM_dePE | ≈0 | Negligible |
4 Micro-Macro Correlation Analysis
4.1 Half-Cell Capacity Analysis
To verify the OCV diagnostic results, half-cells were assembled using harvested positive and negative electrodes from cells #1–#8. The positive half-cell capacities were found to be nearly unchanged across the aging states, confirming that positive active material loss is negligible. In contrast, the negative half-cell capacity decreased monotonically with battery aging, indicating substantial LAM_NE. The negative half-cell capacity, which directly measures the residual active material of the graphite electrode, provides a reliable microscopic indicator for LAM_NE quantification.
To compare the half-cell capacity loss (measured in mAh scale) with the OCV-diagnosed active material loss (measured in Ah scale), normalized loss percentages were introduced. Since pristine half-cell data were not available for the uncycled electrodes, the cell #5 sample, which has the highest SOH (96.54%), was used as the normalization baseline. The normalized capacity loss and OCV-diagnosed LAM percentages were calculated as follows:
$$r_{loss,cap}^i = \frac{Cap_0 – Cap_i}{Cap_0} \times 100\%$$
$$r_{loss,ocv}^i = \frac{LAM_0 – LAM_i}{LAM_0} \times 100\%$$
The comparison results are summarized in Table 6. The maximum difference between the two metrics is only 1.35%, providing direct experimental evidence supporting the accuracy of the OCV-diagnosed LAM_NE results.
| Parameter (%) | #5 | #6 | #7 | #8 |
|---|---|---|---|---|
| Half-cell capacity loss rate | 0 | 4.55 | 8.91 | 11.54 |
| OCV-diagnosed LAM | 0 | 3.20 | 7.93 | 10.40 |
4.2 Maximum Lithium Content Calculated from XRD
XRD measurements were conducted on the negative electrode samples harvested from the fully charged cells #1–#4. In the fully charged state, the graphite negative electrode is transformed into lithium-graphite intercalation compounds (LiC6 and LiC12). The XRD diffraction peaks corresponding to LiC6 and LiC12 intercalation compounds were identified, and their integrated intensities were quantified. The maximum lithium content that can be intercalated into the negative electrode during a full charge was calculated from the diffraction peak intensities. To reduce the influence of electrode sample size variation, the carbon content was normalized. The lithium content calculation formula is given by Equation :
$$Li_xC = \frac{x_1}{x_1+x_2}\times\frac{1}{6} + \frac{x_2}{x_1+x_2}\times\frac{1}{12}$$
where \(x_1\) is the integrated intensity of the LiC6 peak and \(x_2\) is the integrated intensity of the LiC12 peak. The relative change in maximum lithium content compared to a reference fresh cell was then computed as:
$$LLI_{XRD} = \frac{Li_xC_{fresh} – Li_xC_{aging}}{Li_xC_{fresh}} \times 100\%$$
The calculated results showed that the maximum lithium content change rate was positively correlated with battery aging, with a maximum value reaching 24.96%. However, this value exceeds the actual battery SOH loss. This overestimation originates from the normalization assumption used in the calculation, which does not account for the simultaneous reduction of negative electrode active material. During the aging process, the C content itself decreases due to LAM_NE. Ignoring this factor results in the normalization baseline being larger than the actual value, thereby overestimating the lithium loss. This discrepancy was more pronounced when SOH fell below 85%, which correlates with the accelerated LAM_NE at deeper aging states.
4.3 Correction of the Maximum Lithium Content
To overcome the above limitation, a correction factor was introduced to account for the negative electrode active material loss. Based on the half-cell capacity measurements from cells #5–#8 (which were disassembled in the fully discharged state), the LAM_NE for cells #1–#4 was obtained by interpolation since these two groups of cells have nearly identical SOH values and therefore comparable degradation states. The corrected maximum lithium content is computed as:
$$Li_xC’_{aging} = \frac{1}{1-LAM’_{NE}} \times \left(\frac{x_1}{x_1+x_2}\times\frac{1}{6} + \frac{x_2}{x_1+x_2}\times\frac{1}{12}\right)$$
where \(LAM’_{NE}\) is the negative electrode active material loss percentage derived from half-cell capacity measurements. The corresponding corrected lithium loss is:
$$LLI’_{XRD} = \frac{Li_xC_{fresh} – Li_xC’_{aging}}{Li_xC_{fresh}} \times 100\%$$
A comparison between the corrected XRD-based lithium loss and the OCV-diagnosed LLI is presented in Table 7. The results show excellent agreement, with a maximum error of only 1.68% across all investigated aging states. This close correlation between the micro-scale XRD measurements and the macro-scale OCV diagnostic confirms the reliability of the OCV-based degradation mode analysis.
| Method | SOH≈93.5% | SOH≈89.1% | SOH≈86.8% | SOH≈79.4% |
|---|---|---|---|---|
| LLI_OCV (%) | 4.1 | 7.8 | 10.99 | 16.89 |
| LLI_XRD corrected (%) | 4.2 | 7.5 | 11.2 | 16.5 |
5 IC Curve-Based Degradation Mode Diagnosis
5.1 Simulated Effects of Degradation Modes on OCV and IC curves
Since it is extremely difficult to experimentally realize a single degradation mode in isolation, we employed a simulation approach to investigate the distinct effects of different degradation modes on OCV and IC curves. By varying \(LLI\), \(LAM_{liNE}\), and \(LAM_{deNE}\) individually over a range of 0 to 3.5 Ah (as shown in Table 8), eight virtual batteries with different aging states were constructed based on the electrode potential curves.
| Battery No. | LAM_liNE (Ah) | LAM_deNE (Ah) | LLI (Ah) |
|---|---|---|---|
| 1 | 0 | 0 | 0 |
| 2 | 0.25 | 0.25 | 0.5 |
| 3 | 0.5 | 0.5 | 1 |
| 4 | 0.75 | 0.75 | 1.5 |
| 5 | 1 | 1 | 2 |
| 6 | 1.25 | 1.25 | 2.5 |
| 7 | 1.5 | 1.5 | 3 |
| 8 | 1.75 | 1.75 | 3.5 |
The OCV as a function of the lithiation fraction was simulated using the fitted electrode potential curves. The polynomial center smoothing method was applied to the simulated data to obtain IC curves. The effects of single degradation modes on the IC curve can be summarized as follows:
Effect of LLI: With increasing LLI, the intensity of the high-potential characteristic peak (Peak C) gradually decreases, whereas the other characteristic peaks maintain their shape. This occurs because LLI leads to a reduction in the total quantity of cyclable lithium, causing an overall horizontal translation of the electrochemical window that manifests primarily in the high-potential region.
Effect of LAM_deNE: The intensities of the middle characteristic peak (Peak B) decrease with increasing LAM_deNE, whereas the intensity of the last characteristic peak (Peak C) increases. This counterintuitive behavior for Peak C arises because the loss of delithiated negative active material effectively reduces the negative electrode capacity available for lithium intercalation, thereby altering the electrode balancing and causing compression of the usable lithiation window from the delithiated side, which paradoxically allows the last stage to operate at a relatively higher stoichiometric state.
Effect of LAM_liNE: The intensities of both the middle and last characteristic peaks decrease with increasing LAM_liNE. This is because the loss of lithiated active material directly reduces the amount of lithium that can participate in the intercalation reaction, making the total stoichiometric window shrink inward from the lithiated side.
Under the multi-degradation mode coupling scenario, both Peak B and Peak C decrease with aging. Quantitative analysis revealed that \(LAM_{deNE}\) and \(LAM_{liNE}\) exert opposite effects on Peak C intensity, and these effects largely cancel each other out when the two modes occur simultaneously. Therefore, the change in the Peak C area under multi-degradation conditions is predominantly governed by LLI. Conversely, both LAM_deNE and LAM_liNE contribute to the reduction of Peak B, and the Peak B area is not significantly affected by LLI. Consequently, the Peak B area can serve as a quantitative proxy for the total LAM_NE. Table 9 summarizes the relationship between feature peaks and degradation modes.
| Feature peak | LLI | LAM_liNE | LAM_deNE | Multi-mode |
|---|---|---|---|---|
| Peak B (middle) | Unaffected | Decrease | Decrease | Large decrease |
| Peak C (high potential) | Decrease | Decrease | Increase | Decrease dominated by LLI |
5.2 Quantitative Formulas for IC Curve Diagnosis
Based on the above analysis, two metrics were evaluated for quantitative diagnosis: the peak height and the peak area. The comparison showed that while both peak height and peak area correlated strongly with degradation modes, the peak area better reflects the actual compression process of the IC curves and yields more consistent results. Thus, the peak area was selected as the primary diagnostic feature.
Initial attempts to use the Peak C area directly (with the fresh-cell Peak C area as the denominator) resulted in considerable errors in LLI estimation (up to several percentage points of deviation). This is because LLI manifests as an overall translation of the OCV curve across the entire electrochemical window rather than being confined to localized peak variations. For LLI diagnosis, the full cell capacity provides a more appropriate normalization reference. The final quantitative formulas are:
$$LAM_{NE} = \frac{Area_{B,fresh} – Area_{B,aging}}{Area_{B,fresh}} \times 100\%$$
$$LLI = \frac{Area_{C,fresh} – Area_{C,aging}}{Capacity_{fresh}} \times 100\%$$
where \(Area_{B,fresh}\) and \(Area_{B,aging}\) are the Peak B areas for fresh and aging cells, \(Area_{C,fresh}\) and \(Area_{C,aging}\) are the Peak C areas for fresh and aging cells, and \(Capacity_{fresh}\) is the fresh cell discharge capacity at C/25.
5.3 Validation of IC Curve Diagnosis
The proposed IC-based method was validated by comparing its results with the OCV-based diagnostic results on experimental data from cells #1–#8. The comparison based on peak area metrics is shown in Table 10. The maximum discrepancies between the two methods are 1.79% for LLI and 1.62% for LAM_NE, confirming the feasibility of using IC curves to quantitatively diagnose the capacity degradation modes of the traction battery pack.
| SOH (%) | LLI from OCV (%) | LLI from IC (%) | LAM_NE from OCV (%) | LAM_NE from IC (%) |
|---|---|---|---|---|
| 96.54 | 1.08 | 1.21 | 0.56 | 0.62 |
| 93.47 | 4.10 | 4.02 | 1.89 | 1.95 |
| 90.61 | 5.05 | 5.23 | 3.11 | 3.20 |
| 89.12 | 7.83 | 7.61 | 4.02 | 4.13 |
| 86.77 | 10.99 | 10.85 | 6.12 | 6.24 |
| 83.63 | 13.46 | 13.58 | 8.86 | 8.72 |
| 79.76 | 16.43 | 16.28 | 12.31 | 12.48 |
| 79.41 | 16.89 | 16.83 | 12.62 | 12.55 |
6 Applicability Verification of IC-Based Diagnosis
6.1 Rate-Dependent Diagnostics
In actual electric vehicle operation, the traction battery pack rarely operates at C/25. To evaluate the applicability of the proposed IC-based degradation diagnosis under more realistic operating conditions, the diagnostic formulas were extended to higher current rates. Since a fresh battery typically has rate-capability data available from the factory, the following modified formulas using rate-adjusted baselines were introduced:
$$LAM_{NE} = \frac{Area_{B,fresh,rate}-Area_{B,aging,rate}}{Area_{B,fresh,rate}}\times 100\%$$
$$LLI = \frac{Area_{C,fresh,rate}-Area_{C,aging,rate}}{Capacity_{fresh,rate}}\times 100\%$$
where the subscript “rate” denotes values obtained at a specific current rate. Analysis was conducted at rates up to C/3. Beyond C/3, severe polarization effects cause merging of the middle characteristic peak with its neighbors, making accurate decomposition of the peaks difficult and introducing significant uncertainty in the calculation. The maximum errors at C/10, C/5, and C/3 were 3.25%, 4.77%, and 6.07%, respectively.
The LAM_NE diagnostic results remained more consistent across rates because the LAM quantification relies on Peak B, which is less sensitive to LLI-induced translations. However, the LLI diagnostic results exhibited a decreasing trend with increasing current rates. This rate dependence arises from two combined effects: at higher rates, polarization increases the apparent cell voltage, which shifts the IC curve features and compresses the measurable capacity; simultaneously, the higher current reduces the total capacity extracted before the cutoff voltage is reached, causing a normalization baseline that is lower than the true thermodynamic capacity. This leads to an underestimation of the actual Peak C area loss and thus an underestimated LLI. This systematic deviation increases with increasing current rate, demonstrating a clear linear correlation between the rate and the deviation in LLI diagnosis.
6.2 Rate Correction Factor
To improve the diagnostic accuracy of LLI under different current rates, a rate-correction factor was introduced. The correction methodology involves three steps: (1) establishing the linear relationship between capacity loss rate and LLI at each discharge rate; (2) using the C/25 rate as the baseline reference, calculating the correction coefficient as the ratio of the slope at a given rate to the slope at C/25; and (3) applying the corresponding correction coefficient to the LLI values calculated at higher rates.
The rate-dependent correction coefficients are summarized in Table 11. The LLI at rate \(r\) after correction is expressed as:
$$LLI_{corrected} = k(r) \cdot LLI_{measured}(r)$$
| Rate | C/25 | C/10 | C/5 | C/3 |
|---|---|---|---|---|
| Correction factor | 1 | 1.19 | 1.26 | 1.47 |
Table 12 presents the LLI diagnostic results after rate correction. The maximum deviation between the corrected values at higher rates and those at C/25 was reduced from the uncorrected value of 6.07% to only 1.68%, demonstrating the effectiveness of the rate-correction method in enabling accurate LLI diagnosis at non-reference rates. This result confirms that the IC-curve-based degradation diagnosis strategy, combined with proper rate correction, is suitable for online health assessment of the traction battery pack.
| SOH (%) | C/25 | C/10 corrected | C/5 corrected | C/3 corrected |
|---|---|---|---|---|
| 96.54 | 1.08 | 1.21 | 1.28 | 1.49 |
| 93.47 | 4.10 | 3.93 | 4.47 | 2.77 |
| 90.61 | 5.05 | 6.33 | 5.77 | 5.39 |
| 89.12 | 7.83 | 7.32 | 7.54 | 6.84 |
| 86.77 | 10.99 | 10.57 | 10.84 | 10.96 |
| 83.63 | 13.46 | 12.20 | 11.87 | 13.11 |
| 79.76 | 16.43 | 14.91 | 14.75 | 15.26 |
| 79.41 | 16.89 | 16.60 | 16.29 | 15.95 |
A diagnostic flowchart for online IC-based degradation mode estimation was developed. This framework consists of four main stages. First, current and voltage data are acquired in real time from the traction battery pack. Second, the incremental capacity curve is computed from the acquired charging voltage profile. Third, the characteristic peaks (Peak B and Peak C) are identified from the IC curve. Fourth, the LLI and LAM_NE are calculated using the diagnostic formulas. In parallel, the charge/discharge rate is calculated from the measured current. This rate information is then used to apply the correction factor obtained from an offline calibration table, thereby yielding the final corrected LLI value. Alternatively, an online calibration strategy can be implemented: OCV curves are reconstructed from field data, and the small-rate LLI and LAM_NE diagnosis results serve as reference values. By comparing these reference values with the actual-rate IC-based results, the rate-correction function can be updated in real time, allowing self-adaptive degradation mode diagnosis under varying operating conditions.
7 Conclusion
In this work, a comprehensive investigation of degradation modes for a LiFePO4/graphite traction battery pack cell was conducted by integrating macro-scale OCV-based modeling, micro-scale XRD and half-cell characterization, and practical IC-curve-based diagnosis methods. The main conclusions are summarized as follows:
(1) An OCV-based degradation diagnostic model was established by deriving the coordinate transformation relationships between the positive and negative electrode systems and quantitatively describing the effects of different degradation modes on the OCV curve. The diagnostic results show that positive electrode active material loss is negligible throughout the investigated aging range. LLI increases progressively with aging, reaching a maximum capacity loss of 3.40 Ah. LAM_NE also increases with aging, reaching a maximum of 2.83 Ah, while its lithiated and delithiated components remain approximately equal in magnitude.
(2) A quantitative correlation was established between macroscopic degradation modes and microscopic electrode characteristics. The negative half-cell capacities obtained from harvested electrode sheets exhibit a monotonic decrease with aging, consistent with the OCV-diagnosed LAM_NE. Through a correction method that properly accounts for the negative electrode active material loss, a method was proposed to calculate the maximum lithium content using the XRD diffraction peak intensities of lithium-carbon intercalation compounds. The corrected XRD-based maximum lithium content shows excellent agreement with the OCV-diagnosed LLI, with a maximum error of 1.68%. These micro-macro comparisons prove the reliability and accuracy of the OCV-based degradation mode diagnosis.
(3) An IC-curve-based method was proposed for the quantitative diagnosis of LLI and LAM_NE. Through simulation analysis of single and coupled degradation modes, it was found that \(LAM_{deNE}\) and \(LAM_{liNE}\) exert opposing effects on Peak C that approximately cancel under realistic conditions, making the Peak C area predominantly governed by LLI. Meanwhile, the Peak B area varies primarily with LAM_NE. Based on these observations, LLI is quantified using the Peak C area loss normalized to the fresh cell capacity, while LAM_NE is quantified through the Peak B area loss normalized to its fresh value. The maximum discrepancies between the IC and OCV diagnostic results were only 1.79% for LLI and 1.62% for LAM_NE.
(4) To broaden the practical applicability, the IC-based diagnosis was extended to higher discharge rates up to C/3. The LAM_NE results remained largely consistent across rates, whereas the LLI results exhibited a clear decreasing trend with increasing current. A linear rate-correction factor was introduced to compensate for this rate dependence. After correction, the maximum error in the LLI estimation was reduced from 6.07% to only 1.68%, thereby confirming the robustness and practical feasibility of the proposed IC-curve-based degradation mode diagnosis for the traction battery pack under realistic operating conditions.