Lithium-ion battery modules (LIBMs) are critical components in modern energy storage systems. However, thermal runaway incidents pose significant risks to system reliability. Existing qualitative models struggle to quantify thermal diffusion probability under dynamic operating conditions. This study proposes a fuzzy reasoning-based method to evaluate thermal diffusion probability in LIBMs, integrating COMSOL simulations, fuzzy logic, and an improved optimization algorithm.
1. Modeling Thermal Diffusion in Lithium-Ion Battery Modules
1.1 Electrochemical-Thermal Coupling Model
A multi-physics model was developed in COMSOL to simulate LIBM behavior under thermal runaway. The model integrates:
- Electrochemical Submodel: Governed by the P2D (pseudo-two-dimensional) equations:∇⋅(σeff∇ϕs)=jLi,∇⋅(Deff∇c)=∂t∂cwhere σeff is effective conductivity, ϕs is solid-phase potential, Deff is diffusion coefficient, and c is lithium concentration.
- Thermal Submodel: Energy conservation equation:ρCp∂t∂T=∇⋅(k∇T)+Qtotalwhere Qtotal includes heat from internal short circuits (Qisc) and side reactions (Qside).
- Internal Short-Circuit Model: Joule heating during thermal runaway:Qisc=Ishort2Rcell,Ishort=RshortVocv−Vmin
1.2 Side Reaction Kinetics
Four key exothermic reactions were modeled (SEI decomposition, anode/electrolyte reactions, etc.):dtdci=Aiexp(−RTEi)ciγi(1−ci)δi
Thermodynamic parameters are summarized in Table 1.
Table 1: Thermodynamic Parameters of Side Reactions
| Reaction | Ai (s⁻¹) | Ei (kJ/mol) | ΔHi (J/g) |
|---|---|---|---|
| SEI decomposition | 1.67×10¹⁵ | 135 | 257 |
| Anode-electrolyte | 2.5×10¹⁹ | 145 | 1718 |
| Electrolyte oxidation | 5.6×10¹⁴ | 120 | 1322 |
| Cathode decomposition | 1.5×10¹⁵ | 160 | 427 |
2. Factors Influencing Thermal Diffusion in LIBMs
2.1 Module Arrangement
Three configurations (Fig. 1a–c) were tested to analyze contact area effects:
Table 2: Thermal Runaway Propagation Under Different Arrangements
| Configuration | Tmax (°C) | Propagation Time (s) |
|---|---|---|
| (a) Compact | 944–992 | 1199–1672 |
| (b) Spaced | 952–999 | 1247–1720 |
| (c) Offset | 947–993 | 1573–2017 |
Reduced contact area in Configuration (c) delayed thermal runaway by 28% compared to (a).
2.2 Heating Methods
Constant, stepwise, and linear heating were applied to trigger thermal runaway:
Table 3: Thermal Response Under Heating Methods
| Heating Method | Tmax (°C) | Propagation Time (s) |
|---|---|---|
| Constant (190°C) | 944–992 | 1199–1672 |
| Stepwise (100→190°C) | 916–1009 | 2654–3079 |
| Linear (0→190°C) | 886–1016 | 3141–3546 |
Slower heating increased temperature gradients between adjacent cells, accelerating heat transfer.
2.3 State of Charge (SOC)
Higher SOC accelerated thermal runaway due to greater active material availability:
Table 4: SOC Impact on Thermal Runaway
| SOC (%) | Tmax (°C) | Propagation Time (s) |
|---|---|---|
| 100 | 944–992 | 1199–1672 |
| 75 | 861–920 | 1234–1785 |
| 60 | 808–864 | 1279–1874 |
A 40% SOC reduction delayed propagation by 32%.
3. Fuzzy Reasoning System for Thermal Diffusion Probability
3.1 Input-Output Variables
A Mamdani-type fuzzy system was designed with:
- Inputs:
- Cell temperature (Tself)
- Inter-cell distance (DN)
- Ambient temperature (Tenv)
- Output: Thermal diffusion probability (Ptr)
Membership functions (MFs) for inputs and output are shown in Fig. 2. Triangular MFs were chosen for computational efficiency.
3.2 Fuzzy Rule Base
Thirty-six rules were formulated based on experimental insights. Examples include:
- Rule 1: IF Tself is High AND DN is Small THEN Ptr is Very High.
- Rule 2: IF Tenv is Medium AND Tself is Medium THEN Ptr is Moderate.
Table 5: Fuzzy Rule Matrix (Simplified)
| Tenv | Tself | DN | Ptr |
|---|---|---|---|
| Low | Low | Large | Very Low |
| High | High | Small | Very High |
3.3 Optimization of Membership Functions
An Improved Dung Beetle Optimizer (IDBO) was developed to refine MF parameters:
- Dynamic Spiral Search: Enhanced global exploration:β=ezrcos(2πr),z=emcos(πl)
- Adaptive Weighting: Balanced exploitation/exploitation:φ1=1−l3,φ2=l3
Table 6: Optimized MF Parameters
| Parameter | μ1 | μ2 | μ3 | μ4 | μ5 | μ6 | μ7 |
|---|---|---|---|---|---|---|---|
| Value | 0.66 | 0.34 | 2.72 | 0.87 | 0.29 | 0.62 | 0.77 |
4. Validation and Comparative Analysis
4.1 Accuracy Metrics
The Pearson Correlation Coefficient (PCC) between Tself and Ptr improved from 0.893 (unoptimized) to 0.978 after IDBO optimization.
Table 7: Algorithm Performance Comparison
| Algorithm | PCC | Convergence Iterations |
|---|---|---|
| PSO | 0.937 | 45 |
| SSA | 0.931 | 38 |
| DBO | 0.902 | 28 |
| IDBO | 0.978 | 22 |
4.2 Case Study: Random Heating Scenario
Under Tenv=145∘C and offset arrangement, the model predicted:
- Cell 1: Ptr=0.984 (Actual Tmax=945∘C)
- Cells 2–4: Ptr<0.45 (No thermal runaway observed)
5. Conclusion
This work presents a fuzzy reasoning-based framework for evaluating thermal diffusion probability in lithium-ion battery modules. Key findings include:
- Module arrangement and heating methods significantly influence heat propagation rates.
- Higher SOC accelerates thermal runaway by increasing reactive material availability.
- The IDBO-optimized fuzzy system achieved a 9.5% improvement in PCC over conventional methods.
This methodology enables real-time risk assessment for lithium-ion battery energy storage systems, enhancing operational safety and reliability. Future work will integrat