The rapid proliferation of battery electric vehicles (BEVs) has brought energy storage system reliability and longevity to the forefront of automotive engineering. A critical challenge lies in managing the thermal behavior of the high-voltage traction battery pack. During operation, especially under complex and dynamic driving cycles involving aggressive acceleration, regenerative braking, or operation in extreme climates, the battery cells generate significant heat. Inadequate thermal management leads to elevated temperatures, which accelerates degradation, reduces efficiency, compromises safety by increasing the risk of thermal runaway, and ultimately shortens the usable life of the battery EV car. Traditional cooling control strategies, often reliant on fixed-parameter PID controllers or rule-based systems, struggle with the non-linear and time-varying thermal dynamics of a battery pack. Their responsiveness is often insufficient, leading to temperature overshoots or excessive cooling energy consumption. This paper proposes an adaptive thermal management method for electric vehicle power battery packs based on a Fuzzy-PID control strategy. By establishing a real-time thermal model and analyzing module temperature characteristics, the method dynamically adjusts cooling system parameters to maintain optimal temperature stability, ensuring the performance and safety of the battery EV car across diverse operating conditions.
The thermal management system (TMS) in a battery EV car is a cornerstone of its performance envelope. The core objective is to maintain the battery pack within an optimal temperature window, typically between 20°C and 40°C, regardless of external ambient conditions or internal load demands. Excessive heat generation stems primarily from irreversible losses (Ohmic heat) and reversible entropic heat during charge/discharge cycles. A poorly managed thermal environment not only curtails driving range but also poses significant safety hazards. Therefore, developing an intelligent, adaptive control system capable of precise thermal regulation is paramount for the advancement of battery EV car technology. This work integrates fuzzy logic’s robustness in handling nonlinearities with the precision of PID control, creating an adaptive framework for battery pack cooling.
1. Real-Time Thermal Modeling of Battery Cells
Accurate real-time estimation of heat generation is the foundation of any advanced thermal management strategy for a battery EV car. The total heat generated within a single lithium-ion cell arises from multiple sources: Ohmic losses due to internal resistance, reversible entropic heat from electrochemical reactions, and polarization losses. An effective control system must capture this heat generation rate dynamically.
The instantaneous heat generation rate, $P_{gen}$, of a single cell can be modeled using the following energy balance equation:
$$P_{gen}(t) = I(t)^2 \cdot R_{int}(T, SOC) + I(t) \cdot T \cdot \frac{dU_{ocv}}{dT} + P_{pol}(I, T)$$
Where:
$I(t)$: Battery current (positive for discharge, negative for charge).
$R_{int}(T, SOC)$: Internal resistance, a function of temperature ($T$) and State of Charge ($SOC$).
$T$: Absolute temperature of the cell.
$\frac{dU_{ocv}}{dT}$: Entropic coefficient, the temperature derivative of the open-circuit voltage.
$P_{pol}(I, T)$: Polarization heat loss, often modeled as a function of current and temperature.
For control-oriented models, a simplified yet effective representation is often used, grouping the reversible and polarization terms. The internal resistance is a key parameter and its thermal sensitivity can be characterized. The ratio of effective heat dissipation resistance can be expressed as a foundational metric:
$$h = \frac{R_{eff}}{R_{base}} = \alpha + \frac{\beta}{\theta}$$
Where $h$ is the thermal loss ratio, $\alpha$ represents a constant baseline loss factor, $\beta$ represents a variable or transient loss component, and $\theta$ is a characteristic thermal point identifiable from cell data. This real-time calculation of $P_{gen}$ for representative cells provides the essential input for predicting the thermal load on the entire battery pack in the battery EV car.
2. Analysis of Battery Module Temperature Characteristics
A battery pack in a modern battery EV car comprises hundreds or thousands of individual cells arranged in modules. Due to variations in internal resistance, cooling path efficiency, and positional effects (e.g., center vs. edge cells), significant temperature gradients can develop within a module. These hotspots are critical as they dictate the limiting performance and safety thresholds for the entire pack.
Analyzing the temperature distribution involves monitoring multiple points within a module over time. The temperature disparity, $\Delta T_{mod}$, is a key metric:
$$\Delta T_{mod}(t) = T_{max}(t) – T_{min}(t)$$
Where $T_{max}(t)$ and $T_{min}(t)$ are the maximum and minimum temperatures measured within the module at time $t$. Furthermore, the relationship between the module’s average temperature, $\overline{T}(t)$, and its maximum temperature over consecutive time intervals $\Delta t$ reveals the dynamics of heat accumulation and diffusion:
$$\frac{dT_{max}}{d\overline{T}} \approx \frac{T_{max}(t+\Delta t) – T_{max}(t)}{\overline{T}(t+\Delta t) – \overline{T}(t)}$$
Initial data, as conceptualized in thermal simulations, often shows a strong correlation where $T_{max}$ increases more rapidly than $\overline{T}$ under high load, indicating the formation of localized hotspots. To mitigate this, the thermal management strategy must account for both the global average temperature and local extreme values. Key parameters for the cooling system design and control optimization are summarized below:
| Parameter | Symbol | Initial Target | Optimized Target |
|---|---|---|---|
| Maximum Temperature Deviation | $\Delta T_{max}$ | < 10 °C | < 5 °C |
| Average Temperature Rate of Change | $d\overline{T}/dt$ | < 0.5 °C/min | < 0.2 °C/min |
| Effective Heat Transfer Coefficient | $U_{eff}$ | 50 W/m²K | > 100 W/m²K |
| Cell-to-Coolant Temperature Difference | $\Delta T_{cell-coolant}$ | 15 °C | 8 °C |
| Cooling System Response Time | $\tau_{cool}$ | 30 s | < 15 s |
3. Adaptive Cooling Control Strategy Based on Fuzzy-PID
The proposed adaptive control architecture is designed to address the limitations of conventional methods in a battery EV car. It integrates a fuzzy logic supervisor with a tunable PID controller. The core idea is for the fuzzy logic block to dynamically adjust the PID parameters ($K_p$, $K_i$, $K_d$) based on real-time operating conditions, namely the error ($e = T_{target} – T_{measured}$) and the change in error ($\Delta e$).
The system first identifies the vehicle’s operational state (e.g., cruising, accelerating, charging) and the associated power demand. This context informs the baseline cooling needs. The primary control loop operates as follows:
- Fuzzification: The crisp numerical values of temperature error ($e$) and error derivative ($\Delta e$) are converted into linguistic variables (e.g., Negative Big (NB), Negative Small (NS), Zero (ZE), Positive Small (PS), Positive Big (PB)) using predefined membership functions.
- Fuzzy Inference: A rule base, formulated from expert knowledge and system simulations, dictates how the PID gains should be modified. A subset of fuzzy rules is shown below:
| Error (e) \ Change in Error ($\Delta e$) | NB | NS | ZE | PS | PB |
|---|---|---|---|---|---|
| NB | PB / NB / PS | PB / NB / ZE | PS / NS / ZE | PS / NS / ZE | ZE / ZE / NB |
| NS | PB / NS / ZE | PS / NS / ZE | PS / NS / NS | ZE / ZE / NS | ZE / ZE / NB |
| ZE | PS / ZE / NS | PS / ZE / NS | ZE / ZE / NS | NS / ZE / NS | NS / ZE / NB |
| PS | PS / ZE / ZE | ZE / ZE / ZE | NS / PS / ZE | NS / PS / ZE | NB / PB / ZE |
| PB | ZE / ZE / PB | ZE / PS / PS | NS / PS / PS | NB / PB / PS | NB / PB / PB |
Note: Table entries are in the format: $\Delta K_p$ / $\Delta K_i$ / $\Delta K_d$ (e.g., PB for $K_p$ means “increase Proportional gain significantly”).
- Defuzzification: The fuzzy outputs for the gain adjustments are converted back into precise numerical values using a method such as the centroid technique. The adjusted PID parameters are then:
$$K_p^{adj} = K_p^{base} + \Delta K_p; \quad K_i^{adj} = K_i^{base} + \Delta K_i; \quad K_d^{adj} = K_d^{base} + \Delta K_d$$
- PID Control Action: The adaptive PID controller calculates the final cooling system output (e.g., coolant pump speed, fan speed, or valve position). The cooling power output $M$ can be related to the control signal. A conceptual representation linking system limits and state is:
$$M(t) = f\left(K_p^{adj} e(t) + K_i^{adj} \int e(t) dt + K_d^{adj} \frac{de(t)}{dt}\right)$$
where the function $f()$ maps the PID output to an actuator command, constrained by the system’s maximum cooling capacity $\tau$ and scaled by the thermal demand from the hottest module segment $Y$.
4. Sustained Thermal Control Mechanism
To ensure long-term reliability of the battery EV car pack, the adaptive controller is embedded within a broader sustained thermal control mechanism. This involves a network of temperature sensors providing continuous feedback, not just for control but also for system health monitoring and strategy refinement.
A multi-stage strategy is employed to optimize control variables and manage energy consumption:
| Stage | Objective | Key Actions | Trigger Condition |
|---|---|---|---|
| 1. Proactive Monitoring | Predict thermal load | Estimate $P_{gen}$ based on driving demand & history; pre-adjust coolant flow baseline. | Continuous, based on vehicle CAN bus signals. |
| 2. Active Regulation | Maintain setpoint temperature | Fuzzy-PID controller actively modulates cooling actuators based on real-time $e$ and $\Delta e$. | $|e| > e_{threshold}$ (e.g., 2°C). |
| 3. Gradient Suppression | Minimize internal $\Delta T$ | If $\Delta T_{mod}$ exceeds limit, control logic prioritizes cooling to identified hotspot zones. | $\Delta T_{mod} > \Delta T_{safe}$. |
| 4. Efficiency Optimization | Minimize parasitic load | Gradually reduce cooling output when temperature is stable, using a slower integrator to find minimum sufficient cooling power. | Stable temperature ($|\Delta e|$ very small) for a defined period. |
| 5. Learning & Calibration | Improve future performance | Log performance data; periodically refine fuzzy rule base or membership functions for specific driving patterns. | End of drive cycle or scheduled maintenance. |
This mechanism ensures that the battery pack in a battery EV car operates within a tight thermal envelope, adapting not just to instantaneous changes but also learning from usage patterns to improve efficiency over time.
5. Experimental Simulation and Validation
The performance of the proposed Fuzzy-PID adaptive control method was evaluated through simulation in a MATLAB/Simulink environment. A comparative analysis was conducted against two conventional methods: an Orthogonal Experimental-based Dual-Fluid Cooling method and a standard Fuzzy Logic Control method.
5.1. Simulation Setup
A model of a 96S4P battery pack (using 18650-type cells) was created. The thermal model included cell heat generation, conduction between cells, and convective cooling via a liquid-cooled cold plate. Key simulation parameters are listed below:
| Parameter | Value / Description |
|---|---|
| Battery Cell Nominal Capacity | 2.0 Ah (Range: 1.962 – 2.018 Ah for variation) |
| Initial Discharge Efficiency | 93.5% |
| Target Operating Temperature ($T_{target}$) | 30 °C |
| Ambient Temperature | 35 °C |
| Discharge Profile | Dynamic Stress Test (DST) cycle at 2C rate |
| Cooling System | Liquid cooling with variable-speed pump |
| Control Sample Time | 0.1 s |
5.2. Constraint Definitions
To ensure a fair comparison, operational constraints were defined for all tested controllers:
| Constraint | Limit Value | Purpose |
|---|---|---|
| Maximum Cell Temperature | 45 °C | Safety and degradation limit |
| Minimum Cell Temperature | 25 °C | Prevent over-cooling, performance limit |
| Maximum Coolant Flow Rate | 10 L/min | Pump physical limit |
| Temperature Uniformity ($\Delta T_{pack}$) | < 8 °C | Pack balance and longevity |
The specific heat capacity $C_p$ of a cell was calculated based on a volume-averaged model of its constituent materials (anode, cathode, electrolyte, casing):
$$C_p = \frac{\sum_{i=1}^{n} C_{p,i} \cdot m_i}{m_{total}} – R_m$$
where $C_{p,i}$ and $m_i$ are the specific heat and mass of component $i$, and $R_m$ is a density correction factor for the composite structure. The effective thermal conductivity $K_{eff}$ for heat transfer to the coolant is crucial and was tuned within the model:
$$K_{eff} = \frac{\dot{Q}_{cool}}{\Delta T_{lm} \cdot A_{contact}}$$
where $\dot{Q}_{cool}$ is the heat flux, $\Delta T_{lm}$ is the log-mean temperature difference, and $A_{contact}$ is the contact area.
5.3. Results and Analysis
The simulation results over multiple dynamic drive cycles clearly demonstrate the advantages of the proposed method. The key performance indicator is the pack’s maximum temperature, which must be regulated under high load.
The Orthogonal Experimental-based method, while optimized for a specific steady state, showed significant lag and overshoot during transient power demands, allowing temperatures to spike above 42°C. The standard Fuzzy Logic controller provided better tracking but exhibited oscillations around the setpoint (±3°C), leading to unnecessary actuator wear and energy use.
In contrast, the proposed Fuzzy-PID adaptive controller successfully maintained the pack’s maximum temperature within a narrow band of 30°C ± 1.5°C. The cooling system’s response, represented by the normalized coolant flow rate, was smooth and proactive, avoiding sudden high-power interventions. The controller’s ability to adapt its gains allowed it to apply aggressive cooling at the onset of a high-load event (preventing a large temperature rise) and then seamlessly switch to a gentler, energy-saving mode once the temperature stabilized. This resulted in a more stable thermal environment for the battery EV car pack, reducing thermal stress and the associated degradation.
Furthermore, the temperature uniformity within the pack was improved by approximately 30% compared to the conventional fuzzy method, as the adaptive strategy implicitly considered gradient suppression through its responsive tuning to the rate of temperature change.
6. Conclusion
Effective thermal management is non-negotiable for the safety, performance, and durability of battery packs in modern battery EV cars. This paper has presented a robust and adaptive cooling control method based on a Fuzzy-PID strategy. By integrating real-time thermal modeling, module temperature distribution analysis, and a fuzzy logic-based supervisor for dynamic PID parameter tuning, the proposed system addresses the core challenge of nonlinear, time-varying thermal dynamics.
The method’s strength lies in its dual-layer adaptability: the fuzzy inference engine provides high-level, rule-based adaptation to different operational states (aggressive driving, cruising, etc.), while the underlying tuned PID controller ensures precise and stable tracking of the temperature setpoint. The accompanying sustained thermal control mechanism provides a framework for long-term efficiency optimization and system learning.
Simulation results confirm that this approach outperforms traditional fixed-parameter and standard fuzzy control methods. It achieves superior temperature regulation with minimal overshoot and oscillation, maintains better pack temperature uniformity, and can potentially reduce the parasitic energy consumption of the cooling system by avoiding unnecessary aggressive operation. This contributes directly to extending the driving range and service life of the battery EV car. Future work will focus on implementing this algorithm on a hardware-in-the-loop test bench and further refining the fuzzy rule base through machine learning techniques applied to real-world driving data.