The widespread adoption of electric vehicles (EVs) is a critical pathway toward achieving global carbon neutrality goals. At the heart of this transition lies the performance and reliability of the energy storage system, predominantly powered by lithium ion battery technology. The health of these batteries, quantified as the State of Health (SOH), is paramount for ensuring safety, optimizing performance, and predicting the useful life of the entire system. As a lithium ion battery ages through repeated charge and discharge cycles, its maximum available capacity gradually degrades, primarily due to irreversible losses of active lithium and electrode materials. Accurately and reliably estimating the SOH, therefore, is not just an academic exercise but a practical necessity for effective battery management, thermal control, and charge/discharge strategy optimization.
Current methodologies for SOH estimation can be broadly categorized into three groups: experimental feature analysis, model-based approaches, and data-driven techniques. Experimental methods, such as Incremental Capacity Analysis (ICA) and Differential Voltage Analysis (DVA), extract aging-sensitive features from voltage-capacity curves obtained during standard charging or discharging. Model-based methods, including equivalent circuit models and electrochemical models, attempt to simulate the internal states of the lithium ion battery but often involve complex parameterization. Data-driven techniques, like those employing neural networks or support vector machines, leverage large datasets to learn the mapping between operational data and SOH. While promising, many existing studies focus on single-cell analysis under low current rates (C-rates) with high sampling frequencies. However, real-world applications, especially in electric vehicles, frequently involve battery modules operating at higher C-rates with potentially lower data sampling rates. This gap presents a significant challenge: the performance of traditional feature-based methods like ICA tends to deteriorate under high-current conditions, making accurate SOH assessment difficult.
This article addresses this challenge by proposing and validating an enhanced feature extraction method derived from ICA, termed Regional Capacity Analysis (RCA). The core innovation is shifting the health indicator (HI) from the traditional peak height of the Incremental Capacity (dQ/dV) curve to the “regional capacity”—the capacity released or absorbed within a specific voltage window centered on a key phase transformation peak. We demonstrate that this regional capacity maintains a strong, linear correlation with the SOH of a commercial lithium iron phosphate (LFP) battery module, even under demanding 1C and 2C charge-discharge cycles, where traditional ICA peak analysis fails to provide a robust estimate. The findings underscore the superior robustness and applicability of the RCA method for practical, high-rate lithium ion battery module diagnostics.
Fundamental Concepts and Proposed Methodology
1. Defining State of Health
The State of Health is a dimensionless metric representing the degradation level of a lithium ion battery. From a capacity perspective, which is one of the most direct and widely used indicators, SOH is defined as the ratio of the current maximum available capacity of an aged battery to its nominal or beginning-of-life capacity.
$$ \text{SOH} = \frac{C_{\text{current}}}{C_{\text{nominal}}} \times 100\% $$
where $C_{\text{current}}$ is the maximum discharge capacity that can be obtained from the aged battery under standard conditions, and $C_{\text{nominal}}$ is the rated capacity of the new battery. An SOH of 100% indicates a fresh battery, while an SOH typically reaching 70-80% is often considered the end of useful life for many EV applications.
2. Incremental Capacity Analysis (ICA)
ICA is a powerful differential analysis tool that transforms the voltage plateaus observed on a charge/discharge curve into identifiable peaks on a dQ/dV versus V plot. These peaks correspond to major phase transitions within the electrode materials. For a constant current (I) charge or discharge process, the incremental capacity is calculated as:
$$ \frac{dQ}{dV} \approx \frac{\Delta Q}{\Delta V} = I \cdot \frac{\Delta t}{\Delta V} $$
In practice, the raw voltage (V) and accumulated capacity (Q) data are processed. The voltage data is often smoothed to mitigate noise before numerical differentiation. The resulting ICA curve provides a “fingerprint” of the lithium ion battery‘s electrochemical behavior. As the battery ages, these peaks diminish in height, shift in voltage, and change shape, reflecting loss of active material and increased internal resistance. Traditionally, the height or position of a specific peak (often the most prominent one) is extracted as a Health Indicator (HI) and correlated with SOH. However, a significant limitation is that the shape and clarity of these peaks are highly sensitive to the applied current rate. High C-rates cause polarization, smearing and flattening the ICA peaks, which severely degrades the accuracy of peak-height-based SOH estimation.
3. Regional Capacity Analysis (RCA) – The Proposed Method
To overcome the limitations of traditional ICA under high-rate conditions, we introduce the concept of Regional Capacity Analysis. Instead of relying on the instantaneous value of the dQ/dV peak, which is susceptible to noise and polarization effects, RCA integrates the capacity over a defined voltage range surrounding the peak. This integrated quantity, the regional capacity, is inherently more robust because it aggregates information over a wider operational window, making it less sensitive to local distortions in the voltage curve caused by high currents.
The mathematical procedure for RCA is outlined as follows:
Step 1: Identify the Key Feature Voltage. Perform ICA on the charge or discharge data. Identify the voltage $V_{\text{peak}}$ corresponding to the maximum of the chosen characteristic peak (e.g., the main peak associated with the FePO4/LiFePO4 phase transition in LFP batteries).
Step 2: Define the Regional Voltage Window. Select a symmetric voltage window $\Delta V$ centered on $V_{\text{peak}}$. The start and end voltages of this window are:
$$ V_1 = V_{\text{peak}} – \frac{\Delta V}{2} $$
$$ V_2 = V_{\text{peak}} + \frac{\Delta V}{2} $$
The choice of $\Delta V$ is crucial; a window too narrow may not capture enough aging information, while one too wide may include non-linear regions from other phase transitions.
Step 3: Calculate the Regional Capacity. Locate the capacities $Q_1$ and $Q_2$ on the original voltage-capacity (Q-V) curve corresponding to voltages $V_1$ and $V_2$, respectively. The Regional Capacity $C_r$ is then:
$$ C_r = | Q_2 – Q_1 | $$
This value represents the charge stored or delivered by the lithium ion battery as its voltage traverses the defined region centered on the key phase transition.
Step 4: Establish the SOH Model. For a battery module undergoing aging cycles, extract $C_r$ at different aging states (i.e., different cycle numbers). Calculate the corresponding SOH via capacity calibration tests. Finally, establish a mathematical model, typically linear regression, between the regional capacity $C_r$ and the SOH:
$$ \text{SOH} = k \cdot C_r + b $$
where $k$ and $b$ are fitting parameters. The goodness of fit ($R^2$) indicates the strength of the correlation.
The following table summarizes a comparison between the traditional ICA peak method and the proposed RCA method:
| Aspect | Traditional ICA (Peak Height) | Proposed RCA (Regional Capacity) |
|---|---|---|
| Core Metric | Height of dQ/dV peak ($\Delta Q/\Delta V_{\text{max}}$) | Integrated capacity over voltage window ($C_r$) |
| Sensitivity to Current Rate | High. Peaks flatten and become indistinct at high C-rates. | Low. Integration over a region averages out polarization effects. |
| Robustness to Data Noise | Low. Differentiation amplifies measurement noise. | High. Based on capacity difference from smoothed Q-V curve. |
| Information Content | Point measurement at a specific voltage. | Aggregated measurement over a voltage range related to a phase transition. |
| Suitability for Module SOH | Poor for high rates due to cell inconsistencies affecting peak shape. | Good. The regional capacity effectively reflects the aggregate behavior of cells in the module. |
Experimental Investigation on LFP Battery Modules
1. Test Objects and Setup
The experimental study was conducted on commercial 26650-type cylindrical Lithium Iron Phosphate (LFP) battery modules. Each module had a configuration of 15 cells in parallel and 4 such blocks in series (15P4S), with a nominal module voltage of 12.8V and a rated capacity of 40 Ah. LFP chemistry was chosen due to its widespread use in energy storage and electric vehicles, known for safety and long cycle life, though its relatively flat voltage plateau presents a challenge for feature-based SOH estimation.
The aging tests were performed using a professional battery module test system capable of precise current and voltage control. The ambient temperature was maintained at 25 ± 1°C for all tests. A low sampling frequency of 1/60 Hz was deliberately used to simulate conditions that might be present in some practical battery management systems (BMS).
2. Aging Test Protocols
Two identical LFP battery modules (Module #1 and Module #2) were subjected to different aging regimens to evaluate the proposed method under varying stress conditions.
Preconditioning: Prior to aging, both modules underwent five activation cycles at a low rate of C/5 to stabilize performance.
Cyclic Aging: The modules were then cycled continuously between 0% and 100% State of Charge (SOC) with different constant-current (CC) rates.
- Module #1: Aged using a 1C charge and 1C discharge current rate.
- Module #2: Aged using a more strenuous 2C charge and 2C discharge current rate.
Capacity Calibration: Every 50 aging cycles, the cycling was paused for a reference capacity test. This involved a full charge at C/3 constant current followed by a constant voltage (CV) phase until the current dropped to a cut-off value, and then a full discharge at C/3 constant current. The discharge capacity from this test was used as $C_{\text{current}}$ to calculate the SOH according to the formula in Section 1.3. This process continued until the module’s SOH degraded below approximately 60%.
The detailed steps for the aging cycles and capacity calibration are consolidated in the table below:
| Step | Action | Current / Condition | Stop Criterion |
|---|---|---|---|
| 1 | CC Discharge (Start of Cycle) | 1C (Module #1) or 2C (Module #2) | Module Voltage ≤ 10.8 V |
| 2 | Rest | 30 minutes | – |
| 3 | CC Charge | 1C (Module #1) or 2C (Module #2) | Module Voltage ≥ 14.6 V |
| 4 | CV Charge | Hold at 14.6 V | Current ≤ C/5 |
| 5 | Rest | 30 minutes | – |
| 6-8 | Repeat Steps 1-5 | For 50 full cycles | – |
| 9 | CC Charge (Calibration) | C/3 | Module Voltage ≥ 14.6 V |
| 10 | CV Charge (Calibration) | Hold at 14.6 V | Current ≤ C/30 |
| 11 | Rest | 30 minutes | – |
| 12 | CC Discharge (Calibration) | C/3 | Module Voltage ≤ 10.8 V |
| 13 | Rest | 30 minutes | – |
| 14 | Repeat from Step 1 | – | Until SOH < ~60% |
Results, Analysis, and Model Development
1. Module Aging Behavior
Module #1 (1C Aging): This module completed 1300 cycles. Its SOH declined from an initial 98.95% to 58.85%. The degradation showed a highly linear relationship with cycle number ($R^2$ > 0.98), indicating a consistent aging mechanism under this stress level. The charge/discharge voltage curves exhibited the expected shortening of voltage plateaus and an increase in charge polarization (higher charge voltage) and discharge polarization (lower discharge voltage) over time.
Module #2 (2C Aging): This module degraded much faster, reaching ~53.5% SOH after only 400 cycles. The aging trajectory was best described by a two-stage linear model: a slower initial degradation for the first 200 cycles ($R^2$ = 0.958) followed by an accelerated fade in the latter 200 cycles ($R^2$ = 0.984). The voltage-capacity curves under 2C operation showed more pronounced polarization effects compared to the 1C case, compressing the usable voltage window.
2. SOH Modeling Based on Traditional ICA Peak Height
ICA was performed on the 1C and 2C charge/discharge data from the calibration cycles. For the LFP chemistry under these test conditions, the ICA curves typically showed one dominant peak in the mid-voltage range during both charge and discharge.
1C Results: The height of the main ICA peak ($H_{ICA}$) showed a discernible linear relationship with SOH.
- Charge stage: $R^2$ = 0.8154
- Discharge stage: $R^2$ = 0.8741
While moderately strong, the correlation was not excellent, suggesting other factors were influencing the peak height.
2C Results: The limitations of the peak-height method became starkly apparent. The high current rate caused significant polarization, severely distorting and flattening the ICA peaks.
- Charge stage: The linear fit between $H_{ICA}$ and SOH was very poor, with $R^2$ = 0.1884.
- Discharge stage: The correlation was somewhat better but still weak, with $R^2$ = 0.5767.
This confirms that the traditional ICA peak height is an unreliable health indicator for a lithium ion battery module operating at high C-rates.
3. SOH Modeling Based on Proposed RCA Regional Capacity
The RCA method was then applied to the same datasets. The regional capacity $C_r$ was calculated for four different regional voltage window sizes: $\Delta V$ = 200 mV, 400 mV, 600 mV, and 800 mV, all centered on the voltage of the main ICA peak ($V_{\text{peak}}$).
Analysis for Module #1 (1C Data): A clear, positive linear correlation was found between $C_r$ and SOH for all $\Delta V$ values. Crucially, the goodness of fit ($R^2$) improved consistently as the integration window $\Delta V$ increased. This demonstrates that integrating over a broader, relevant voltage region captures more aging-related information from the lithium ion battery module.
| ΔV (mV) | Charge Stage Model (SOH = k·Cr + b) | R² (Charge) | Discharge Stage Model (SOH = k·Cr + b) | R² (Discharge) |
|---|---|---|---|---|
| 200 | SOH = -157 + 16.0·Cr | 0.7527 | SOH = -3.48 + 6.46·Cr | 0.8402 |
| 400 | SOH = -110 + 9.03·Cr | 0.7581 | SOH = -45.7 + 5.93·Cr | 0.9541 |
| 600 | SOH = -63.1 + 5.95·Cr | 0.9247 | SOH = -37.7 + 4.94·Cr | 0.9395 |
| 800 | SOH = -29.0 + 4.18·Cr | 0.9842 | SOH = -20.5 + 3.91·Cr | 0.9576 |
Analysis for Module #2 (2C Data): The superiority of the RCA method is most evident here. Despite the high-rate, noisy data that crippled the peak-height method, the regional capacity $C_r$ maintained a strong linear relationship with SOH, especially with larger $\Delta V$.
- For $\Delta V$ = 800 mV, the $R^2$ values were 0.8942 (charge) and 0.9882 (discharge).
- Even at 2C, the discharge-stage model achieved a near-perfect linear fit ($R^2$ > 0.98).
This robust performance under high-stress conditions is the key advantage of the RCA approach for assessing the health of a lithium ion battery.
| ΔV (mV) | Charge Stage Model (SOH = k·Cr + b) | R² (Charge) | Discharge Stage Model (SOH = k·Cr + b) | R² (Discharge) |
|---|---|---|---|---|
| 200 | SOH = 55.6 + 1.74·Cr | 0.0517 | SOH = 13.5 + 4.33·Cr | 0.7275 |
| 400 | SOH = 5.62 + 3.76·Cr | 0.3160 | SOH = -19.7 + 4.79·Cr | 0.9766 |
| 600 | SOH = -12.7 + 3.83·Cr | 0.6352 | SOH = -16.8 + 4.13·Cr | 0.9809 |
| 800 | SOH = -18.3 + 3.63·Cr | 0.8942 | SOH = -13.6 + 3.70·Cr | 0.9882 |
4. Comparative Discussion
The experimental results lead to several definitive conclusions regarding SOH estimation for lithium ion battery modules:
1. Failure of Traditional ICA Peak at High Rates: The peak height of the incremental capacity curve is a fragile health indicator. Its correlation with SOH weakens significantly as the charge/discharge current rate increases. At 2C, the method becomes practically unusable for accurate estimation ($R^2$ = 0.1884 for charge), primarily due to voltage polarization obscuring the fine electrochemical features the peak is meant to capture.
2. Superiority and Robustness of Regional Capacity (RCA): In contrast, the regional capacity $C_r$ demonstrates remarkable robustness. It maintains a strong linear correlation with SOH across both 1C and 2C aging tests. The underlying reason is that $C_r$ measures the aggregate charge associated with a major phase transition over a defined voltage span. This integrated measure is less affected by the instantaneous distortions caused by high currents or module inconsistency and more directly related to the total amount of active material available for that reaction, which fades with aging.
3. Optimal Regional Voltage Window: The width of the integration window ($\Delta V$) is a key parameter. The results show a clear trend: larger windows (e.g., 800 mV) generally yield higher $R^2$ values and more stable linear models. A window that is too small (200 mV) may be overly sensitive to local voltage noise and may not fully encompass the capacity change associated with the fading phase transition. Therefore, selecting an appropriately wide $\Delta V$ centered on a stable, characteristic peak voltage is recommended for building reliable RCA-based SOH models.
4. Practical Implication for Module SOH: The successful application of RCA to a commercial LFP module (15P4S) under high-rate cycling is particularly significant. Module-level SOH estimation is complicated by cell-to-cell variations, which can distort traditional feature-based methods. The RCA method, by using an aggregate capacity measure, inherently averages some of these inconsistencies, making it a more practical and reliable tool for real-world battery pack management systems.
Conclusion and Future Perspectives
Accurate State of Health estimation remains a cornerstone for the safe, efficient, and prolonged operation of lithium ion battery systems. This work has addressed a critical practical challenge: reliable SOH assessment under high current-rate operating conditions where traditional diagnostic features often fail. By introducing Regional Capacity Analysis (RCA), we have demonstrated a simple yet powerful enhancement to the well-established Incremental Capacity Analysis framework.
The core finding is that the regional capacity—the capacity exchanged within a defined voltage window centered on a key ICA peak—serves as a far more robust and accurate health indicator than the peak height itself. For a commercial LFP battery module, linear models based on regional capacity achieved excellent correlation with SOH ($R^2 > 0.95$) under both 1C and, most importantly, 2C charge-discharge cycles. In the 2C case, where the traditional peak-height method essentially broke down ($R^2 = 0.188$), the RCA method maintained a very strong relationship ($R^2 = 0.988$ for discharge). This establishes RCA as a highly suitable method for SOH estimation in applications involving high-power demands, such as electric vehicle acceleration or fast charging.
Future research can build upon this work in several directions. First, the method should be validated under more complex, dynamic driving cycle profiles rather than constant-current cycles to ensure its effectiveness in real-world automotive environments. Second, the impact of varying ambient temperature on the RCA-SOH relationship needs investigation, as temperature significantly influences the voltage behavior of a lithium ion battery. Third, exploring adaptive or optimal algorithms for automatically selecting the regional voltage window $\Delta V$ and the peak voltage $V_{\text{peak}}$ could enhance the method’s autonomy and applicability across different battery chemistries and aging paths. Finally, integrating the robust RCA-derived health indicator with machine learning algorithms for remaining useful life (RUL) prediction presents a promising avenue for developing next-generation, prognostic battery management systems. By providing a stable and accurate input feature, RCA can significantly improve the performance of data-driven prognostic models for lithium ion battery packs.