The rapid growth of renewable energy integration and grid flexibility demands has positioned lithium-ion battery modules (LIBMs) as critical components in modern energy storage system (ESS). However, thermal runaway propagation within LIBMs remains a significant safety challenge, threatening system reliability and operational continuity. Existing qualitative models inadequately address the dynamic and quantitative assessment of thermal diffusion risks under time-varying conditions. This study proposes a novel fuzzy reasoning-based method enhanced by an improved dung beetle optimizer (IDBO) to evaluate thermal diffusion probability in LIBMs, enabling real-time risk assessment and mitigation strategies.
1. Thermal Diffusion Modeling in LIBMs
1.1 COMSOL-Based Simulation Framework
A multi-physics model was developed using COMSOL Multiphysics to simulate thermal runaway propagation in LIBMs. The model integrates four sub-models:
- Electrochemical Model: Describes lithium-ion intercalation dynamics using the pseudo-two-dimensional (P2D) framework.
- Internal Short-Circuit Model: Quantifies joule heating during separator collapse.
- Side Reaction Model: Accounts for heat generation from decomposition reactions (SEI, electrolyte, electrodes).
- 3D Thermal Model: Solves energy conservation equations to predict temperature distribution.
The coupled governing equations are:ρCp∂T∂t=∇⋅(kbat∇T)+QVbatρCp∂t∂T=∇⋅(kbat∇T)+VbatQ
where Q=qisc+qside+qchemQ=qisc+qside+qchem represents total heat generation from internal short circuits (qiscqisc), side reactions (qsideqside), and electrochemical processes (qchemqchem).
1.2 Critical Factors Influencing Thermal Diffusion
Simulations evaluated three key factors:
Table 1: Impact of Arrangement Configurations on Thermal Diffusion
| Arrangement | TmaxTmax (°C) | tpropagationtpropagation (s) |
|---|---|---|
| Configuration A | 992 | 1672 |
| Configuration B | 999 | 1720 |
| Configuration C | 993 | 2017 |
Key findings:
- Reduced contact area between cells (Configuration C) delays thermal propagation by 18% compared to Configuration A.
- Maximum temperatures (TmaxTmax) remain consistent (±1.5%), emphasizing the dominant role of heat transfer geometry.
Table 2: Effect of Heating Modes on Thermal Runaway
| Heating Mode | TmaxTmax (°C) | tpropagationtpropagation (s) |
|---|---|---|
| Constant Temperature | 992 | 1672 |
| Stepwise Heating | 1009 | 3079 |
| Linear Heating | 1016 | 3546 |
Slow heating modes (e.g., linear heating) delay thermal runaway but increase TmaxTmax in the final cell by 2.4%.
Table 3: SOC-Dependent Thermal Behavior
| SOC (%) | TmaxTmax (°C) | tpropagationtpropagation (s) |
|---|---|---|
| 100 | 992 | 1672 |
| 75 | 920 | 1785 |
| 60 | 864 | 1874 |
Higher SOC accelerates thermal diffusion due to increased reactive material availability, reducing propagation time by 12% at SOC=100% compared to SOC=60%.
2. Fuzzy Reasoning System for Thermal Diffusion Probability Assessment
2.1 System Architecture
The fuzzy inference system (FIS) maps three inputs to a thermal diffusion probability (PtrPtr):
- Cell Temperature (TselfTself)
- Inter-Cell Distance (DNDN)
- Ambient Temperature (TenvTenv)
Membership Functions and Rules
- Triangular membership functions defined for inputs and output.
- 36 fuzzy rules derived from experimental data and literature:
- Rule Example: IF TselfTself is High AND DNDN is Small AND TenvTenv is High, THEN PtrPtr is Very High.
2.2 Optimization of Membership Functions Using IDBO
Traditional optimization algorithms (PSO, SSA, DBO) were outperformed by the proposed IDBO, which incorporates:
- Dynamic Spiral Search: Enhances exploration using:
β=ezr⋅cos(2πr),z=em⋅cos(πl)β=ezr⋅cos(2πr),z=em⋅cos(πl)
- Adaptive Weighting: Balances global and local search:
ϕ1=1−l3,ϕ2=l3ϕ1=1−l3,ϕ2=l3
Table 4: Performance Comparison of Optimization Algorithms
| Algorithm | PCC Score | Convergence Iterations |
|---|---|---|
| IDBO | 0.978 | 35 |
| DBO | 0.902 | 48 |
| PSO | 0.937 | 42 |
| SSA | 0.931 | 50 |
The IDBO-optimized FIS achieved a 9.1% higher Pearson correlation coefficient (PCC) than the baseline model.
3. Validation and Practical Implications
3.1 Case Study: Random Operational Conditions
Under experimental conditions (heating temperature=145°C, arrangement=Configuration C), the IDBO-FIS predicted:
Table 5: Thermal Runaway Probability Assessment
| Cell ID | PtrPtr | TmaxTmax (°C) |
|---|---|---|
| No.1 | 0.984 | 945 |
| No.2 | 0.25 | 56 |
| No.3 | 0.44 | 87 |
| No.4 | 0.19 | 32 |
The results align with COMSOL simulations, confirming the model’s accuracy.
3.2 Engineering Applications
- Risk Mitigation: Reducing inter-cell contact area delays propagation by 15–20%.
- Operational Guidelines: Avoid constant high-temperature heating; prefer stepwise protocols.
- SOC Management: Limit SOC to <75% in high-risk environments.
4. Conclusion
This study presents a robust framework for evaluating thermal diffusion probability in lithium-ion battery modules using fuzzy reasoning and advanced optimization. Key contributions include:
- A COMSOL-based multi-physics model identifying critical factors (arrangement, heating mode, SOC).
- An IDBO-optimized FIS achieving a PCC of 0.978, outperforming traditional algorithms.
- Practical insights for enhancing energy storage system safety through design and operational adjustments.
Future work will integrate real-time sensor data and machine learning to further refine predictive accuracy. By addressing thermal risks in lithium-ion battery systems, this approach supports the safe scaling of renewable energy infrastructure globally.