The rapid global shift toward environmental sustainability and reduced carbon emissions has propelled the adoption of electric vehicles (EV cars) as a mainstream alternative to traditional internal combustion engine vehicles. EV cars offer significant advantages in terms of cleanliness and energy efficiency, aligning with international goals for a greener future. However, the widespread commercialization of EV cars faces critical challenges, particularly in the performance and efficiency of thermal management systems. Effective thermal management is essential for ensuring the safety, longevity, and operational reliability of key components, such as power batteries, while also maintaining occupant comfort in the cabin. The integration of cabin and battery thermal domains in EV cars presents a complex, multi-objective control problem, characterized by dynamic coupling, nonlinearities, and conflicting goals, such as minimizing energy consumption and maximizing thermal stability. This paper addresses these challenges by proposing a collaborative control strategy that combines neural networks with model predictive control (MPC) to optimize the thermal management system in EV cars, enhancing both energy efficiency and thermal comfort.
Thermal management systems in EV cars are pivotal for managing the heat generated by power batteries during charging and discharging cycles, as well as for regulating the cabin temperature to ensure passenger comfort. Unlike conventional vehicles, EV cars operate under strict energy constraints, where inefficient thermal control can lead to reduced driving range, battery degradation, and compromised safety. The integration of cabin and battery cooling into a unified system offers potential energy savings and structural simplification, but it introduces intricate dynamic interactions. For instance, the cabin temperature is influenced by external factors like solar radiation and ambient conditions, while the battery temperature depends on internal heat generation from electrochemical reactions. Traditional control methods, such as proportional-integral-derivative (PID) control, have been widely used due to their simplicity and robustness in stable conditions. However, PID control often struggles with the nonlinear and time-varying dynamics of integrated thermal systems in EV cars, leading to issues like overshoot, slow response, and higher energy consumption. In contrast, advanced strategies like MPC, which utilize predictive models to anticipate system behavior and optimize control actions, have shown promise in handling such complexities. This study leverages a nonlinear auto-regressive exogenous (NARX) neural network within an MPC framework to dynamically adjust compressor speed and refrigerant flow distribution, aiming to reduce energy usage while maintaining precise temperature control in EV cars.
The thermal management system for EV cars, as modeled in this research, focuses on a coupled cabin-battery configuration operating in high-temperature cooling mode. The system employs a dual-branch design to independently manage the cabin environment and battery thermal needs, using refrigerant-based direct cooling. The high-pressure side (represented by red lines in the schematic) and low-pressure side (blue lines) facilitate heat transfer from critical areas inside the EV car to the external environment. Key components include the compressor, evaporators, expansion valves, and flow control valves, which work in concert to regulate temperatures. The cabin model accounts for heat exchange mechanisms, such as solar radiation, convective heat transfer, and internal loads from occupants, while the battery model simulates heat generation from internal resistance and entropy changes during operation. The dynamic behavior of these components is captured using a lumped-parameter approach in the AMESim simulation platform, which allows for real-time analysis of thermal interactions in EV cars under varying driving conditions.
To mathematically represent the thermal dynamics, the cabin temperature is governed by heat balance equations. The convective heat transfer coefficient, which combines natural and forced convection, is calculated as:
$$h_{\text{conv}} = \left( h_{\text{forced}}^3 – h_{\text{free}}^3 \right)^{1/3}$$
where \( h_{\text{conv}} \) is the overall convective heat transfer coefficient, \( h_{\text{forced}} \) is the forced convection coefficient, and \( h_{\text{free}} \) is the natural convection coefficient. The wall temperature \( T_w \) in the cabin is derived from:
$$\frac{dT_w}{dx} = \frac{f_s – f_{\text{ext}} – f_{\text{int}}}{m c_p}$$
with \( f_s = \alpha s_{\text{ext}} q_{\text{sol}} \) representing solar radiation heat flux, \( f_{\text{ext}} = h_{\text{conv,ext}} s_{\text{ext}} (T_w – T_{\text{ext}}) \) as external convective heat flux, and \( f_{\text{int}} = h_{\text{conv,int}} s_{\text{int}} (T_w – T_{\text{int}}) \) as internal convective heat flux. Here, \( \alpha \) is the solar absorption coefficient, \( s_{\text{ext}} \) and \( s_{\text{int}} \) are surface areas, \( q_{\text{sol}} \) is solar radiation intensity, and \( T_{\text{ext}} \) and \( T_{\text{int}} \) are external and internal temperatures, respectively. The parameters for the cabin model are summarized in Table 1, which includes values for solar radiation, volume, and thermal properties relevant to EV cars.
| Parameter | Value |
|---|---|
| Solar Radiation (W/m²) | 700 |
| Solar Absorption Coefficient | 0.75 |
| Volume (m³) | 4 |
| Wall Specific Heat Capacity (kJ/K) | 7 |
| External Heat Exchange Area (m²) | 8 |
For the power battery in EV cars, the heat generation rate is a critical factor, primarily composed of Joule heating and reversible entropy heat. The simplified heat generation equation is:
$$q = \frac{I}{V} \left[ (U_{\text{OCV}} – U) + T_{\text{bat}} \frac{dU_{\text{OCV}}}{dT_{\text{bat}}} \right]$$
where \( I \) is the current, \( V \) is the battery volume, \( U_{\text{OCV}} \) is the open-circuit voltage, \( U \) is the operating voltage, and \( T_{\text{bat}} \) is the battery temperature. The total internal resistance \( R_{\text{total}} \), which includes ohmic and polarization resistances, is expressed as:
$$R_{\text{total}} = \sum_{i=1}^{3} \left( a_i \beta^i T_{\text{bat}}^{3-i} + b_i \beta^i + c_i T_{\text{bat}}^{3-i} \right)$$
with \( a, b, c \) as empirical coefficients and \( \beta \) as the state of charge. The battery voltage dynamics are described by:
$$\frac{dU}{dt} = \frac{I – \frac{U_{\text{OCV}}}{R}}{C_f}$$
and the open-circuit voltage is approximated as:
$$U_{\text{OCV}} = a_0 + a_1 \beta + a_2 \beta^2 + a_3 \beta^3 + a_4 \beta^4$$
In this study, a lithium iron phosphate (LFP) battery pack is used, with a nominal capacity of 124 Ah and voltage of 3.2 V, configured into modules for simulation. The battery pack parameters, such as total energy and weight, are essential for accurately modeling thermal behavior in EV cars. Validation of the system model against experimental data showed good agreement, with an average relative error of 3.66% for mass flow rate and 3.18% for compressor power consumption, confirming the model’s reliability for control strategy development in EV cars.
The proposed control strategy for EV cars integrates MPC with a NARX neural network to optimize compressor speed, thereby reducing energy consumption while minimizing temperature deviations in the cabin and battery. The MPC formulation is based on a state-space representation:
$$\mathbf{x}(k+1) = \mathbf{A} \mathbf{x}(k) + \mathbf{B_u} \mathbf{u}(k) + \mathbf{B_v} \mathbf{v}(k)$$
$$\mathbf{y}(k) = \mathbf{C} \mathbf{x}(k)$$
where \( \mathbf{x}(k) \) is the state vector, \( \mathbf{u}(k) \) is the input vector (compressor speed), \( \mathbf{v}(k) \) is the measurable disturbance vector, and \( \mathbf{y}(k) \) is the output vector (temperatures). The matrices \( \mathbf{A} \), \( \mathbf{B_u} \), \( \mathbf{B_v} \), and \( \mathbf{C} \) are derived from system identification. The objective function for MPC minimizes tracking errors and control effort over a prediction horizon \( p \) and control horizon \( m \):
$$\min J(k) = \sum_{i=1}^{p} \| \mathbf{w}(k+i|k) – \tilde{\mathbf{y}}(k+i|k) \|_{\mathbf{q}_i}^2 + \sum_{j=1}^{m} \| \Delta \mathbf{u}(k+j|k) \|_{\mathbf{r}_j}^2$$
Here, \( \mathbf{w} \) is the desired output, \( \tilde{\mathbf{y}} \) is the predicted output, and \( \mathbf{q}_i \) and \( \mathbf{r}_j \) are weighting matrices. The compressor speed is constrained between 1000 and 5000 rpm to ensure practical operation in EV cars. Additionally, PID controllers are employed for regulating expansion valve openings based on superheat and flow distribution valve openings based on temperature, creating a hierarchical control structure that enhances system responsiveness.
The NARX neural network is trained using data from the China Light-Duty Vehicle Test Cycle (CLTC-P) driving profile, which includes variables like suction pressure, discharge pressure, vehicle speed, valve openings, and evaporator outlet temperature. The network predicts cabin temperature, providing state estimates to the MPC controller. Training, validation, and testing sets are split in a 70:15:15 ratio, resulting in prediction errors as low as 0.2°C, which significantly improves the accuracy of MPC’s future state predictions for EV cars. The integration of NARX with MPC enables proactive adjustments to compressor operations, accounting for dynamic disturbances and nonlinearities in EV cars.
Simulation studies were conducted under the CLTC-P cycle, which lasts 1800 seconds and includes low, medium, and high-speed phases, with an average speed of 29.0 km/h and a maximum speed of 114.0 km/h. This cycle represents real-world driving conditions for EV cars, with idle periods accounting for 22.1% of the time. The ambient temperatures tested were 35°C, 40°C, and 45°C, with a cabin target temperature of 25°C. The performance of the MPC strategy was compared against a conventional PID controller in terms of temperature stability, energy efficiency, and thermal comfort. Thermal comfort was evaluated using the Predicted Mean Vote (PMV) index, which ranges from -3 (cold) to +3 (hot), with values near 0 indicating neutral comfort. The simulation parameters are listed in Table 2, highlighting key operational settings for EV cars.
| Parameter | Value |
|---|---|
| Ambient Temperature (°C) | 35, 40, 45 |
| Target Temperature (°C) | 25 |
| Compressor Speed Range (rpm) | 1000–5000 |
| Driving Cycle | CLTC-P |
Under MPC control, the cabin temperature demonstrated superior regulation compared to PID. For instance, at an initial ambient temperature of 35°C, the MPC strategy reduced the overshoot by 0.9°C, achieving stability around 25°C within approximately 290 seconds, whereas PID control exhibited oscillations between 23°C and 26°C. Similarly, at 40°C and 45°C, MPC eliminated overshoot entirely and maintained temperature within ±0.5°C of the target after 600 seconds, while PID showed persistent fluctuations. The PMV analysis revealed that MPC quickly brought the thermal sensation to near-neutral levels (PMV between 0.4 and 0.78) across all temperatures, ensuring comfort in EV cars. In contrast, PID control resulted in higher PMV values initially, indicating discomfort due to slower response and larger deviations.
Energy consumption was assessed using the unit energy consumption per temperature drop, defined as \( e = \frac{P}{\Delta T} \), where \( P \) is compressor power and \( \Delta T \) is the temperature reduction. The results, summarized in Table 3, show that MPC consistently achieved lower energy consumption per unit cooling compared to PID. At 35°C, MPC reduced energy use by 7.2%, at 40°C by 2.4%, and at 45°C by 3.5%. Although the absolute compressor power was higher for MPC at 45°C (1787 W vs. 1261 W for PID), the greater temperature drop (4.7°C vs. 3.2°C) resulted in better cooling efficiency, highlighting MPC’s ability to prioritize battery safety in extreme conditions for EV cars. The compressor speed profiles under MPC control exhibited smoother transitions and lower fluctuations after the initial cooling phase, contributing to energy savings and reduced mechanical stress in EV cars.
| Ambient Temperature (°C) | PID Control | MPC Control | Reduction (%) |
|---|---|---|---|
| 35 | 221.5 | 205.5 | 7.2 |
| 40 | 283.1 | 276.2 | 2.4 |
| 45 | 394.1 | 380.2 | 3.5 |
In conclusion, the collaborative control strategy integrating NARX neural networks with MPC offers significant advantages for thermal management in EV cars. It enhances temperature stability by minimizing overshoot and fluctuations, improves energy efficiency by optimizing compressor operations, and ensures passenger comfort through precise PMV control. The validation against experimental data and comparisons with PID control underscore the robustness of this approach for real-world applications in EV cars. Future work could explore adaptive MPC techniques or incorporate additional variables, such as humidity and occupancy, to further refine thermal management systems for EV cars, ultimately supporting the sustainable evolution of electric mobility.