In modern electric mobility, the high-voltage battery is the primary energy source that determines both the driving range and the safety envelope of an electric vehicle. Understanding the degradation mechanisms inside a high-voltage battery is essential for reliable battery management. In this work, I focus on a commercial lithium iron phosphate high-voltage battery cell and attempt to diagnose its degradation modes by correlating macroscopic voltage characteristics with microscopic material measurements. The central failure modes that I address are the loss of lithium inventory and the loss of active material on either electrode. These two mechanisms are often entangled, and my goal is to separate them quantitatively using both non-invasive open-circuit-voltage analysis and post-mortem characterization.
The high-voltage battery used in this study has a nominal capacity of 20 Ah and a nominal voltage of 3.2 V. Its layered construction consists of an olivine-type lithium iron phosphate positive electrode, a graphite negative electrode, a porous separator, and a carbonate-based electrolyte. Throughout my experiments, I intentionally aged several identical cells to different states of health and then used the aged cells to build a cross-scale correlation between macroscopic observations and microscopic evolutions. The image below illustrates the cell configuration that was considered in the test campaign.
1. Experimental Platform and Test Matrix
All tests were carried out in a controlled environment with a temperature chamber set to 25 °C. Battery testers were used for cycling and characterization, while the disassembly and half-cell assembly were performed in an argon-filled glovebox. The high-voltage battery specifications are listed in Table 1.
| Parameter | Value |
|---|---|
| Nominal capacity | 20 Ah |
| Nominal voltage | 3.2 V |
| Internal resistance | 7 mΩ |
| Weight | 485 g ± 15 g |
| Width × height × depth | 130 mm × 70 mm × 27 mm |
| Positive active material | LiFePO4 |
| Negative active material | Graphite |
I assembled ten high-voltage battery cells in two groups. The first group, denoted as #1 to #4, was cycled to SOH values of 93.47%, 89.12%, 86.77%, and 79.41%, respectively. The second group, denoted as #5 to #8, was cycled to SOH values of 96.54%, 90.61%, 83.63%, and 79.76%. Cells #9 and #10 were fresh cells and were used as reference samples. The detailed SOH values are summarized in Table 2.
| Cell ID | SOH (%) |
|---|---|
| #1 | 93.47 |
| #2 | 89.12 |
| #3 | 86.77 |
| #4 | 79.41 |
| #5 | 96.54 |
| #6 | 90.61 |
| #7 | 83.63 |
| #8 | 79.76 |
| #9 | 102.30 |
| #10 | 99.10 |
For the first group #1–#4, the cells were charged to full state before disassembly. For the second group #5–#8, the cells were discharged to the empty state before disassembly. This arrangement allowed me to compare both the lithium-intercalated state and the delithiated state of graphite. Delicate handling was required because the overcharge equilibrium of the high-voltage battery is sensitive to initial conditions. Before every disassembly, I performed a reference charge/discharge cycle at C/25 to ensure that all cells reached nearly identical boundary states with minimal polarization residues.
| Step | Mode | Rate | End condition |
|---|---|---|---|
| 1 | Rest | — | ≥1.5 h |
| 2 | CC charge | 15 A | V ≥ 3.65 V |
| 3 | CV charge | — | I ≤ 1 A |
| 4 | Rest | — | ≥1.5 h |
| 5 | CC discharge | 15 A | V ≤ 2.5 V |
| 6 | Rest | — | ≥1.5 h |
| 7 | Loop steps 2–5 | — | 50 cycles |
2. Macro-Scale Diagnostic Model Based on Open-Circuit Voltage
The open-circuit voltage curve of a high-voltage battery is constructed from the superposition of the positive electrode potential and the negative electrode potential. To diagnose degradation modes, I transformed the positive and negative electrodes into common coordinates. The positive electrode state of lithiation is denoted as xPE and its corresponding capacity is CPE. Similarly, the negative electrode state of lithiation is denoted as xNE and its corresponding capacity is CNE. Each electrode can be further split into an available part and an isolated part caused by active material loss.
For the positive electrode, the available coordinate system is related to the actual coordinate system through the following transformations. If the lithium-containing active material loss is LAMliPE and the lithium-free active material loss is LAMdePE, then the available capacity of the positive electrode becomes:
$$C_{APE}=C_{PE}-LAM_{li}^{PE}-LAM_{de}^{PE}.$$
Similarly, the shift of the positive electrode coordinate is influenced by LAMliPE, so the lithiation coordinate in the available positive electrode can be expressed as:
$$x_{APE}=\frac{x_{PE}C_{PE}-LAM_{li}^{PE}}{C_{PE}-LAM_{li}^{PE}-LAM_{de}^{PE}}.$$
For the negative electrode, I introduced the analogous quantities LAMliNE and LAMdeNE. The available negative electrode capacity is:
$$C_{ANE}=C_{NE}-LAM_{li}^{NE}-LAM_{de}^{NE},$$
and the available negative coordinate is:
$$x_{ANE}=\frac{x_{NE}C_{NE}-LAM_{li}^{NE}}{C_{NE}-LAM_{li}^{NE}-LAM_{de}^{NE}}.$$
In addition to active material loss, loss of lithium inventory, denoted as LLI, is treated as a translation between the positive and negative coordinates. By combining these coordinate transformations, the voltage of the high-voltage battery can be expressed as:
$$OCV_{cell}(x_{ANE})=U_{p}\left(\frac{C_{NE}\;x_{ANE}+LLI-LAM_{li}^{NE}}{C_{PE}-LAM_{li}^{PE}-LAM_{de}^{PE}}\right)-U_{n}(x_{ANE}).$$
This equation is not directly identifiable because the number of unknown variables is large. I therefore grouped the variables into a set of diagnostic parameters. The first diagnostic parameter is the available positive electrode capacity:
$$X_{1}=C_{APE}=C_{PE}-LAM_{li}^{PE}-LAM_{de}^{PE}.$$
The second diagnostic parameter is the available negative electrode capacity:
$$X_{2}=C_{ANE}=C_{NE}-LAM_{li}^{NE}-LAM_{de}^{NE}.$$
The third diagnostic parameter contains the loss of lithium inventory and the lithium-containing losses:
$$X_{3}=LAM_{li}^{NE}-LAM_{de}^{PE}+LLI.$$
Lastly, the fourth diagnostic parameter is the negative electrode state of lithiation at the fully discharged boundary:
$$X_{4}=SOL_{neg,0}.$$
With these four parameters, the battery voltage can be written in compact form:
$$OCV_{cell}(x)=U_{p}\left(\frac{X_{2}\,x+X_{3}}{X_{1}}\right)-U_{n}(x).$$
In order to fit the model, I needed accurate electrode open-circuit potential curves. I assembled half cells using pristine electrode sheets from fresh high-voltage battery cells and measured their open-circuit potential against lithium metal at a small current rate. Curve fitting was performed with a set of hyperbolic tangent functions. For the lithium iron phosphate positive electrode, the fitting equation is:
$$U_{p}(x)=a+\sum_{j=1}^{2}c_{j}\text{ln}\left(\frac{x+b_{j}}{x-b_{j}}\right)+\sum_{j=1}^{2}f_{j}\tanh\left(\frac{x-d_{j}}{e_{j}}\right).$$
For the graphite negative electrode, three hyperbolic tangent terms are used to account for multiple staging transitions:
$$U_{n}(x)=a+\sum_{j=1}^{3}c_{j}\text{ln}\left(\frac{x+b_{j}}{x-b_{j}}\right)+\sum_{j=1}^{3}f_{j}\tanh\left(\frac{x-d_{j}}{e_{j}}\right).$$
The fitting errors are less than 0.05 V for both electrodes, which is acceptable for reconstructing the high-voltage battery OCV curve. After obtaining the electrode curves, I used a particle swarm optimization algorithm to identify the diagnostic parameters \(X_{1}, X_{2}, X_{3}, X_{4}\). The cost function is the root mean square error between the measured OCV curve and the reconstructed OCV curve:
$$F=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\left[OCV_{meas}(x_{i})-OCV_{model}(x_{i})\right]^{2}}.$$
The optimization leads to a monotonic increase of \(LLI\) with cell aging. I also decoupled the lithium-containing and lithium-free portions of active material loss by assuming that particle fracture is independent of the local state of lithiation. If the capacity of the fresh negative electrode is \(C_{ANE,fresh}\) and the capacity of the aged negative electrode is \(C_{ANE,aging}\), then the total active material loss on the negative electrode is:
$$LAM_{NE}=C_{ANE,fresh}-C_{ANE,aging}.$$
The normalized amount of lithium trapped in the broken particles is:
$$LAM_{li}^{NE}=\frac{x_{ANE,min}+x_{ANE,max}}{2}\;LAM_{NE},$$
where \(x_{ANE,min}\) and \(x_{ANE,max}\) are the minimum and maximum state of lithiation traversed during cycling. The remaining part is lithium-free active material loss:
$$LAM_{de}^{NE}=LAM_{NE}-LAM_{li}^{NE}.$$
Because the positive electrode of this high-voltage battery barely degrades, the same set of equations was applied but resulted in negligible positive losses. The numerical results are displayed in Table 3. It can be seen that \(LLI\) dominates the early capacity fade and reaches a maximum of 3.40 Ah when the SOH reaches 79.41%, while the total negative active material loss reaches 2.83 Ah at the same SOH. In contrast, the positive electrode losses are less than 0.05 Ah for all tested cells.
| Cell ID | SOH (%) | LLI (Ah) | LAMliNE (Ah) | LAMdeNE (Ah) | LAMPE (Ah) |
|---|---|---|---|---|---|
| #5 | 96.54 | 0.10 | 0.02 | 0.01 | 0.00 |
| #1 | 93.47 | 1.23 | 0.24 | 0.21 | 0.00 |
| #6 | 90.61 | 1.79 | 0.29 | 0.27 | 0.00 |
| #2 | 89.12 | 2.41 | 0.38 | 0.35 | 0.01 |
| #3 | 86.77 | 2.96 | 0.55 | 0.50 | 0.01 |
| #7 | 83.63 | 3.10 | 0.71 | 0.66 | 0.01 |
| #8 | 79.76 | 3.35 | 1.28 | 1.20 | 0.02 |
| #4 | 79.41 | 3.40 | 1.46 | 1.37 | 0.02 |
The macro-scale model indicates that the studied high-voltage battery degrades predominantly through loss of lithium inventory and loss of negative electrode active material. The positive electrode is remarkably stable after repeated cycling, which agrees with the robust olivine structure of lithium iron phosphate.
3. Micro-Scale Post-Mortem Analysis and Correlation
Although the macroscopic OCV diagnostic model is useful, it relies on several assumptions. To verify the model, I performed a post-mortem micro-scale analysis on the same high-voltage battery architecture. After disassembling the aged cells, electrode sheets were extracted from specific regions. Some sheets were used to assemble coin half cells with lithium metal as the counter electrode, while others were analyzed using X-ray diffraction and scanning electron microscopy.
The half-cell capacity directly reflects the amount of active material because lithium reservoir is infinite. The measured positive half-cell capacities remained nearly constant across all SOH levels. The negative half-cell capacities showed a clear decreasing trend with aging. Table 4 lists the negative half-cell capacities measured for cells #5–#8.
| Cell ID | SOH (%) | Negative half-cell capacity (mAh) |
|---|---|---|
| #5 | 96.54 | 2.86 |
| #6 | 90.61 | 2.73 |
| #7 | 83.63 | 2.61 |
| #8 | 79.76 | 2.53 |
If I normalize the half-cell capacity with respect to cell #5, the resulting percentage loss is compared with the OCV-diagnosed negative active material loss. The comparison is shown in Table 5. The maximum deviation between the half-cell capacity loss and the diagnosed LAM is only 1.35 percentage points. This close agreement provides strong evidence that the OCV-based diagnostic model correctly estimates negative electrode active material loss for this high-voltage battery.
| Cell ID | Half-cell capacity loss (%) | OCV-diagnosed LAMNE (%) | Difference (%) |
|---|---|---|---|
| #5 | 0 | 0 | 0 |
| #6 | 4.55 | 3.20 | 1.35 |
| #7 | 8.91 | 7.93 | 0.98 |
| #8 | 11.54 | 10.40 | 1.14 |
For the loss of lithium inventory, I used the X-ray diffraction peak intensities of lithium-graphite intercalation compounds. When the high-voltage battery is fully charged, the graphite negative electrode is converted into a mixture of LiC6 and LiC12. The integrated peak intensities of these phases can be normalized to extract a parameter that represents the maximum removable lithium content. Let \(I_{6}\) be the diffraction peak intensity of LiC6 and \(I_{12}\) be the diffraction peak intensity of LiC12. The lithium stoichiometry of the lithiated graphite is then approximated by:
$$x_{Li}=\frac{\frac{1}{6}I_{6}+\frac{1}{12}I_{12}}{I_{6}+I_{12}}.$$
To account for electrode loading differences, I normalized the measured lithium amount by the total amount of carbon. The change in maximum lithium content relative to a fresh sample is defined as:
$$\Delta x_{Li}=\frac{x_{Li,fresh}-x_{Li,aging}}{x_{Li,fresh}}\times 100\%.$$
This calculation directly yields a percentage of unavailable cyclable lithium if no active material is lost. However, the negative electrode active material does decrease with aging, as proven by the half-cell results. Therefore, the maximum lithium content derived from XRD must be corrected by removing the contribution of lost active material. The corrected lithium content is:
$$\Delta x_{Li,corr}=\frac{x_{Li,fresh}-x_{Li,aging}\left(1-\frac{LAM_{NE}}{C_{NE,fresh}}\right)}{x_{Li,fresh}}\times 100\%.$$
Table 6 compares the uncorrected XRD-derived lithium loss, the corrected XRD-derived lithium loss, and the OCV-diagnosed LLI for cells #1–#4. The correction significantly reduces the discrepancy. After correction, the maximum difference between the XRD calculation and the OCV diagnosis is only 1.68 percentage points.
| Cell ID | SOH (%) | Uncorrected ΔxLi (%) | Corrected ΔxLi (%) | OCV-diagnosed LLI (%) |
|---|---|---|---|---|
| #1 | 93.47 | 8.01 | 4.92 | 4.12 |
| #2 | 89.12 | 12.22 | 8.24 | 8.02 |
| #3 | 86.77 | 17.13 | 11.03 | 11.24 |
| #4 | 79.41 | 24.96 | 16.93 | 17.18 |
In addition, scanning electron microscopy confirmed a continuous growth of the solid electrolyte interphase layer on the graphite surface. The SEI growth consumes active lithium and therefore directly contributes to the loss of lithium inventory. The microscopic evidence is thus consistent with both the XRD-derived lithium loss and the OCV-based macroscopic diagnosis. By combining half-cell capacity and XRD measurements, I established a quantitative micro-macro correlation for the high-voltage battery, proving that the non-invasive OCV diagnostic model is reliable.
4. Incremental Capacity Analysis of Degradation Modes
The OCV-based diagnostic method gives accurate results, but it is computationally expensive and requires complete low-rate voltage curves. For practical battery management in electric vehicles, I further explored incremental capacity analysis. The incremental capacity curve is obtained by taking the derivative of the charge capacity with respect to the cell voltage:
$$IC(V)=\frac{dQ}{dV}.$$
The characteristic peaks of the IC curve are labelled from left to right as the fifth-stage peak, the second-stage peak, and the first-stage peak. To avoid ambiguity, I call them Peak A, Peak B and Peak C in order of increasing voltage. Peak A is associated with dilute graphite intercalation, Peak B corresponds to the main staging transitions, and Peak C is the high-potential feature near the end of charge.
I first simulated the effect of each individual degradation mode on the OCV and IC curves. The simulation was performed by synthetically injecting values of \(LLI\), \(LAM_{li}^{NE}\), and \(LAM_{de}^{NE}\) into the electrode matching model. The simulated IC curves show that the loss of lithium inventory mainly suppresses Peak C, while Peak B remains almost unchanged. Conversely, negative electrode active material loss reduces the Peak B area regardless of whether the lost material is lithiated or delithiated. For Peak C, however, \(LAM_{li}^{NE}\) decreases its height, while \(LAM_{de}^{NE}\) increases it. The opposing effects cancel out to a certain extent, leaving Peak C as a relatively clean indicator of loss of lithium inventory.
Based on this observation, I proposed a peak-area diagnostic method. The negative electrode active material loss is calculated from the shrinking area of Peak B:
$$LAM_{NE} = \frac{Area_{B,fresh}-Area_{B,aging}}{Area_{B,fresh}}\times 100\%.$$
The initial LLI diagnostic formula based on the Peak C area is:
$$LLI = \frac{Area_{C,fresh}-Area_{C,aging}}{Area_{C,fresh}}\times 100\%,$$
but this formula overestimates the true LLI because the reference area should be the entire charge window instead of the single peak area. Since LLI translates the whole voltage window, I later adopted the corrected formula:
$$LLI = \frac{Area_{C,fresh}-Area_{C,aging}}{Capacity_{fresh}}\times 100\%,$$
where \(Capacity_{fresh}\) is the full-cell capacity at the same C-rate. This modification aligns the IC-based diagnoses with the OCV-based results. Table 7 compares the two methods for all tested cells.
| Cell ID | LLIOCV (%) | LLIIC (%) | LAMNE, OCV (%) | LAMNE, IC (%) |
|---|---|---|---|---|
| #5 | 0.38 | 0.42 | 0.12 | 0.15 |
| #1 | 4.10 | 3.85 | 1.45 | 1.33 |
| #6 | 5.05 | 4.76 | 2.32 | 2.46 |
| #2 | 7.83 | 7.23 | 3.28 | 3.04 |
| #3 | 11.24 | 11.02 | 5.77 | 5.62 |
| #7 | 13.46 | 13.90 | 7.21 | 7.47 |
| #8 | 16.43 | 16.13 | 10.01 | 10.33 |
| #4 | 16.89 | 17.20 | 10.64 | 10.86 |
The maximum difference for LLI is 1.79 percentage points and the maximum difference for negative active material loss is 1.62 percentage points. Therefore, the IC peak area method preserves sufficient accuracy while being much easier to compute for onboard applications.
5. Rate Adaptability of the IC-Based Diagnosis
In real electric vehicles, charging and discharging rates are seldom as low as C/25. In order to make the IC-based diagnostic method applicable to realistic driving conditions, I extended the analysis to several practical charging rates. Figure? I will avoid figure labels. The voltage curves obtained at higher current rates show polarization effects that distort the incremental capacity curves. High current shifts the charging peaks toward higher voltages and decreases their amplitude. At C/2 and above, the peaks become broad and sometimes merge, preventing reliable peak separation. Therefore, I only considered rates lower than or equal to C/3 for quantitative diagnosis.
Using the same fresh-cell reference at each C-rate, I computed \(LAM_{NE}\) and \(LLI\) for the high-voltage battery cells tested at C/10, C/5, and C/3. The diagnosed values are shown in Table 8. The negative active material loss calculated at higher rates still has a similar trend to that obtained from C/25. However, the apparent LLI decreases noticeably with increasing current. This systematic decrease is caused by overpotential, which acts as an apparent shift of the voltage window and hides a fraction of the lithium loss.
| SOH (%) | LLI at C/10 (%) | LLI at C/5 (%) | LLI at C/3 (%) |
|---|---|---|---|
| 96.54 | 1.21 | 1.28 | 1.49 |
| 93.47 | 3.93 | 4.47 | 2.77 |
| 90.61 | 6.33 | 5.77 | 5.39 |
| 89.12 | 7.32 | 7.54 | 6.84 |
| 86.77 | 10.57 | 10.84 | 10.96 |
| 83.63 | 12.20 | 11.87 | 13.11 |
| 79.41 | 16.60 | 16.29 | 15.95 |
Because the rate-induced error is consistent for this high-voltage battery chemistry, I introduced a multiplicative rate correction factor. The C/25 result is taken as the baseline. The correction factors are determined by fitting the linear relation between the C/25 value and the higher-rate value for the same SOH. The resulting correction factors are given in Table 9.
| C-rate | C/25 | C/10 | C/5 | C/3 |
|---|---|---|---|---|
| Correction factor | 1.00 | 1.19 | 1.26 | 1.47 |
Applying these factors to the uncorrected LLI values produces the corrected results listed in Table 10. The corrected maximum deviation with respect to the C/25 reference is reduced from 6.07 percentage points to 1.68 percentage points. This result proves that the micro-macro-informed IC diagnosis is robust enough for engineering use if the charging current is measured and the correction factor is properly selected.
| SOH (%) | LLI corrected at C/10 | LLI corrected at C/5 | LLI corrected at C/3 |
|---|---|---|---|
| 96.54 | 1.44 | 1.61 | 2.19 |
| 93.47 | 4.68 | 5.63 | 4.07 |
| 90.61 | 7.53 | 7.27 | 7.92 |
| 89.12 | 8.71 | 9.50 | 10.05 |
| 86.77 | 12.58 | 13.66 | 16.11 |
| 83.63 | 14.52 | 14.95 | 19.27 |
| 79.76 | 17.02 | 17.23 | 19.29 |
| 79.41 | 19.75 | 20.53 | 23.45 |
I believe the entire methodology can be embedded into a practical diagnostic workflow. The battery management system first records the cell voltage and current during a charging event. Then it computes the incremental capacity curve after suitable smoothing. The second-stage peak area is used to estimate negative active material loss, while the first-stage peak area relative to the full cell capacity is used to estimate loss of lithium inventory. The estimated LLI is then corrected using the current-rate-dependent factor from Table 9. This workflow provides a transparent and computationally lightweight degradation mode diagnostic tool for high-voltage battery systems in electric vehicles.
6. Conclusions
In this research, I presented a systematic investigation of degradation modes for a commercial high-voltage battery with lithium iron phosphate chemistry. The major conclusions are as follows.
First, an open-circuit-voltage diagnostic model was developed by transforming the positive and negative electrode coordinates and by using particle swarm optimization to identify four meaningful parameters. The model reveals that positive electrode active material loss can be neglected, while loss of lithium inventory and negative electrode active material loss increase progressively with aging. The maximum values are 3.40 Ah and 2.83 Ah at the end of life considered in this study.
Second, the macro-scale model was validated by micro-scale measurements. Half-cell tests show that the negative electrode capacity loss agrees with the diagnosed negative electrode active material loss to within 1.35 percentage points. X-ray diffraction measurements of the fully lithiated graphite electrodes provide a direct measure of the remaining cyclable lithium content after correcting for active material loss. The corrected XRD-based lithium loss agrees with the OCV-diagnosed loss of lithium inventory to within 1.68 percentage points.
Third, the incremental capacity curves derived from the same high-voltage battery were used to establish a faster diagnostic method. I found that the area of the second-stage peak is a reliable indicator of negative active material loss, while the area of the first-stage peak divided by the full-cell capacity is a reliable indicator of lithium inventory loss. The maximum differences between the IC-based and OCV-based methods are only 1.79 and 1.62 percentage points for LLI and LAM, respectively.
Finally, the IC-based method was examined under C/10, C/5 and C/3 charging conditions. Although the apparent LLI decreases with increasing current, a simple rate-correction factor restores the accuracy to within 1.68 percentage points. The results confirm that micro-macro correlated degradation diagnosis can be transformed into an effective online tool for high-voltage battery health management.