Lithium iron phosphate battery have become a cornerstone of modern energy storage systems due to their high safety, long cycle life, and cost-effectiveness. However, the dynamic mechanical behavior of lithium iron phosphate battery during cycling, driven by volume changes in graphite and LFP electrodes, remains a critical factor influencing their performance and longevity. This study presents a novel approach to monitor strain evolution in graphite-LFP pouch cells using fiber Bragg grating (FBG) sensors and establishes a robust framework for estimating the state of charge (SOC) based on strain signals.
Mechanical-Electrochemical Coupling in LFP Batteries
Lithium-ion intercalation and deintercalation in graphite and lithium iron phosphate battery electrodes induce periodic volume changes. The strain evolution in these electrodes is governed by phase transitions and lattice parameter variations. For the LFP cathode, lithium insertion expands the crystal lattice along the a– and b-axes while contracting the c-axis, leading to a net volumetric strain (ΔVLFP) proportional to the lithium concentration (x) in LixFePO4). Similarly, graphite anodes exhibit strain (ΔVAG) during lithiation, transitioning through distinct phases (e.g., dilute stage 1, stage 2L, and stage 2). The total strain (εtotal) in a full cell is expressed as:εtotal=α⋅ΔVLFP+β⋅ΔVAG+γ⋅T+δ⋅σmech
where α and β are material-specific coefficients, T is temperature, and σmech accounts for mechanical constraints.
FBG Sensor Integration and Calibration
We embedded FBG sensors into graphite-LFP pouch cells to measure strain with high precision (Figure 1). The FBG’s Bragg wavelength (λB) shifts in response to strain (ε) and temperature (T):ΔλB=Kε⋅ε+KT⋅ΔT
where Kε = 0.854 pm/με and KT = 10.095 pm/°C (calibrated experimentally, Table 1). A dual-FBG setup decoupled strain and temperature effects: one sensor bonded to the cell surface measured combined effects, while a loose reference sensor isolated temperature contributions.
Table 1. FBG sensitivity coefficients
| Parameter | Value | Error Range |
|---|---|---|
| Kε | 0.854 pm/με | ±2.5 με |
| KT | 10.095 pm/°C | ±0.5°C |
Strain Evolution During Cycling
The graphite-LFP pouch cell exhibited reversible strain hysteresis during charge/discharge cycles (Figure 2). Key observations include:
- Charge Phase:
- Stage 1: Rapid strain increase (0–20% SOC) due to graphite delithiation.
- Stage 2: Strain plateau (20–80% SOC) from phase transitions in graphite (2L→2).
- Stage 3: Sharp strain rise (80–100% SOC) as lithium iron phosphate battery delithiation dominated.
- Discharge Phase:
- Stage 1: Strain drop (100–60% SOC) from lithium iron phosphate battery lithiation.
- Stage 2: Gradual strain increase (60–20% SOC) during graphite staging.
- Stage 3: Rapid strain decrease (20–0% SOC).
Table 2. Strain characteristics at key SOC points
| SOC (%) | Strain (με) | Dominant Process |
|---|---|---|
| 0 | 0 | Fully lithiated graphite |
| 20 | 120 ± 5 | Graphite stage 2L→2 |
| 50 | 190 ± 8 | Mixed LFP/graphite phases |
| 100 | 387 ± 10 | Fully delithiated lithium iron phosphate battery |
SOC Estimation via Strain Signatures
The flat voltage plateau of lithium iron phosphate battery (2.5–3.65 V) complicates voltage-based SOC estimation. Strain signals, however, provide monotonic trends during charging and enable accurate SOC mapping. We developed a piecewise linear model:SOC=⎩⎨⎧a1⋅ε+b1,a2⋅ε+b2,a3⋅ε+b3,0≤ε<120 με120≤ε<190 με190≤ε<387 με
Table 3. Model coefficients and errors
| Segment | a | b | RMSE (%) |
|---|---|---|---|
| 1 | 0.167 | -2.1 | 3.2 |
| 2 | 0.083 | 8.4 | 2.8 |
| 3 | 0.294 | -38.7 | 4.1 |
Validation using subsequent cycles showed <10% SOC estimation error (Figure 3). Strain-based SOC outperformed voltage-based methods in the mid-SOC range (20–80%), where voltage remains stable but strain changes significantly.
Implications for Battery Management Systems
Integrating FBG sensors into lithium iron phosphate batteries enables real-time mechanical-electrochemical monitoring, critical for:
- Early Fault Detection: Anomalous strain patterns (e.g., sudden drops or plateaus) signal electrode degradation or gas generation.
- State of Health (SOH) Tracking: Accumulated irreversible strain correlates with capacity fade.
- Thermal Management: FBG-derived temperature/strain data optimize cooling strategies.
Conclusion
This work demonstrates that strain evolution in lithium iron phosphate batteries is a reliable indicator of SOC, particularly in voltage-insensitive regions. By leveraging FBG sensors, we achieve high-resolution mechanical monitoring without compromising cell integrity. Future studies will extend this framework to multi-cell modules and extreme operating conditions (e.g., fast charging, low temperatures).