The rapid development of electric mobility has made the vehicle traction battery one of the most critical components for range, safety, and lifecycle cost. However, its performance and reliability strongly depend on temperature. A well-designed thermal management strategy must not only prevent overheating or overcooling, but also minimize the energy consumed by the thermal management system itself. In this study, I focus on the coupled problem of temperature control and energy consumption for a vehicle traction battery. I propose a hierarchical battery thermal management architecture, calibrate a high-fidelity AMESim model with physical experiments, and design environment-specific control strategies for low, normal, and high ambient temperatures. Through this work, I aim to provide an effective framework for simultaneously satisfying thermal safety requirements and energy-efficiency goals.
The vehicle traction battery behaves as a multivariable, strongly coupled and nonlinear thermal system. In actual driving cycles, heat generation from electrochemical reactions, Joule losses, polarization losses and side reactions leads to a rapid temperature increase. For a lithium iron phosphate power battery, the operating temperature range is generally recommended to be from 25 °C to 40 °C, while the temperature difference inside a battery pack should be kept below 5 °C. If the temperature exceeds a safety threshold, thermal runaway may be triggered. Conversely, at low temperatures, the internal resistance increases, power capability drops, and charging performance degrades. Therefore, I need to understand the thermal characteristics of the vehicle traction battery before designing an advanced thermal management control strategy.
In this research, I first decompose the total heat generated in a vehicle traction battery into four parts: reaction heat, polarization heat, Joule heat and side-reaction heat. The side-reaction heat is usually ignored because its magnitude is very small. Thus, the total heat generation rate can be expressed by the well-known Bernardi equation. For a single cell, the heat generation rate is written as:
$$\dot{Q}_{gen}=I\left(IR_{e}-T_b\frac{dU_{oc}}{dT_b}\right)$$
where \(I\) is the battery current, \(R_e\) is the equivalent internal resistance, \(T_b\) is the battery temperature, \(U_{oc}\) is the open-circuit voltage, and \(dU_{oc}/dT_b\) is the entropy coefficient. This expression indicates that the instantaneous heat generation of the vehicle traction battery depends on both the operating current and the temperature coefficient of the open-circuit voltage. During discharge, the first term is dominant. During charge, the second term can be negative or positive depending on the electrode material.
For the heat-transfer path, I use heat conduction, convection and radiation equations together with the energy balance principle. The vehicle traction battery is represented by a lumped thermal mass to reduce computational cost. Based on physical experiments and existing correlations, the equivalent heat transfer coefficient between the battery cooling plate and the coolant is given by:
$$h=\frac{Nu\lambda}{d}$$
$$Nu=0.023\,Re^{0.8}Pr^{0.3}$$
$$Re=\frac{ud}{\mu}$$
where \(Nu\), \(Re\), and \(Pr\) are the Nusselt, Reynolds and Prandtl dimensionless numbers, respectively. These equations provide a simplified but sufficiently accurate description of the convective heat removal from a vehicle traction battery.
After deriving the fundamental heat generation and heat-transfer models, I constructed a layered thermal management architecture for the vehicle traction battery. The architecture comprises three fluid loops: a battery cooling loop, a coolant conditioning loop, and an air-conditioning refrigeration loop. In the cooling loop, a two-position three-way valve switches between the radiator branch and the chiller branch. The coolant loop contains an electric water pump and a positive temperature coefficient heater. The refrigeration loop includes a compressor, a condenser, an expansion valve and a liquid-to-refrigerant heat exchanger called the Chiller. A water-glycol mixture with 50% glycol is used as the coolant, and R134a is used as the refrigerant.
To estimate the design load, I considered a demanding high-temperature driving scenario. Assuming the vehicle travels at 120 km/h for 1000 seconds and the battery temperature should be reduced from 40 °C to 30 °C, the required cooling power \(Q_n\) can be computed as:
$$Q_n=\frac{c_{p,b}(T_u-T_d)+Q_{gen}}{t}$$
where \(T_u=40\,^\circ\mathrm{C}\), \(T_d=30\,^\circ\mathrm{C}\), \(t=1000\,\mathrm{s}\), \(c_{p,b}\) is the heat capacity of the battery pack, and \(Q_{gen}\) is the generated heat. For a battery pack with 125 cells in series and 8 cells in parallel, the estimated peak heat generation is around 2474 W, and the required cooling power is approximately 3457 W. Similarly, for a cold-start condition where the battery should be heated from -10 °C to 20 °C in 1500 s, the required heating power is about 1886 W. These load calculations defined the component sizing boundary for the thermal management system of the vehicle traction battery.
I built the entire vehicle model in Simcenter Amesim 2404. The full-vehicle model contains the longitudinal driver model, an electric machine model, an inverter model, a battery package and a vehicle body model. The driver model tracks a prescribed target speed by outputting accelerator and brake commands. The electric motor controller calculates a torque demand based on the accelerator pedal, gear selector, battery state-of-charge, and motor speed. The vehicle parameters are summarized in the table below.
| Parameter | Symbol | Value |
|---|---|---|
| Vehicle mass | \(m_{veh}\) | 1445 kg |
| Rolling resistance coefficient | \(f\) | 0.01 |
| Drag coefficient | \(C_D\) | 0.31 |
| Frontal area | \(A_f\) | 2.09 m² |
| Rotational inertia factor | \(\delta\) | 1.4 |
| Electric machine efficiency | \(\eta_b\) | 0.86 |
| Battery nominal voltage | \(U_b\) | 400 V |
The distributed heat sources in the vehicle were simplified as lumped masses with heat-capacity modules. Since this study focuses on the thermal behavior of the vehicle traction battery, other heat sources were included only to provide a realistic powertrain boundary condition. The interactions among the driving cycle, current load, and battery temperature can then be investigated in a fully closed-loop simulation environment.
A critical step in obtaining reliable simulation results is the calibration of battery sub-models. I carried out experimental tests using a battery test bench including a programmable charge-discharge cycler, a temperature chamber, a data logger, and T-type thermocouples. The vehicle traction battery under test was a lithium iron phosphate prismatic cell. I first measured the open-circuit voltage curve under a low-current discharge profile. The data show that the open-circuit voltage decreases monotonically with the decrease in battery state of charge, which matches the thermodynamic property of the LFP cathode. Table below lists some representative measured points.
| SOC (%) | Open-circuit voltage (V) |
|---|---|
| 100 | 3.32 |
| 80 | 3.30 |
| 60 | 3.27 |
| 40 | 3.23 |
| 20 | 3.17 |
| 0 | 2.50 |
The equivalent internal resistance of the vehicle traction battery was measured through Hybrid Pulse Power Characterization tests. A pulse discharge current \(I_1\) is applied for 20 seconds. The terminal voltage changes from \(U_0\) to \(U_1\) as a result of both ohmic resistance and polarization resistance. The equivalent internal resistance is evaluated by:
$$R=\frac{U_1-U_0}{I_1}$$
I tested the battery at 20 °C, 30 °C and 40 °C, and for several SOC states. The resistance response surface shows that the internal resistance increases sharply when temperature drops below 10 °C and SOC falls below 20%. This result emphasizes that an advanced thermal management strategy for the vehicle traction battery must react to changes in both temperature and SOC.
In addition, I measured the heat capacity of the cell using an insulation-box method. Each surface was covered with a heating film, and the total heating power was 40 W. The temperature rise was recorded for 600 seconds. The equivalent heat capacity was calculated by:
$$C_b=\frac{q\Delta t}{T_1-T_0}$$
During the experiment, the average temperature increased from 14.5 °C to 35.4 °C, and the computed heat capacity was 1142 J/K. Together with the model of open-circuit voltage and internal resistance, this completes the electro-thermal coupling model of the vehicle traction battery.
I conducted a battery discharge validation experiment using a synthetic current profile. The ambient temperature was fixed at 26 °C. The same current boundary conditions were applied in the AMESim model. The simulated battery temperature and terminal voltage agree closely with the experimental results. The temperature error is below 3 °C and the voltage error remains within a narrow band. Thus, the calibrated electro-thermal model is accurate enough for evaluating thermal management algorithms.
In addition to the battery model, I calibrated two heat exchangers: the condenser and the Chiller. For the condenser, the air-side Nusselt number correlation coefficients were tuned by comparing simulation results with experimental data from a wind-tunnel test rig. The table summarizes four calibration test conditions.
| Case | Air velocity (m/s) | Air inlet temperature (°C) | Refrigerant mass flow (kg/h) | Refrigerant inlet temperature (°C) | Inlet pressure (bar) |
|---|---|---|---|---|---|
| 1 | 1.5 | 26 | 101.3 | -4.3 | 2 |
| 2 | 2.5 | 26 | 130.4 | -2.1 | 2 |
| 3 | 4.5 | 26 | 158.9 | 0.2 | 2 |
| 4 | 7 | 26 | 191.3 | 2.5 | 2 |
For each case, the measured heat-transfer rate was compared with the simulation result. The maximum relative error was less than 5%. Similarly, I calibrated the Chiller model using four experimental operating conditions on the coolant side and refrigerant side. Again, the relative errors between experimental and simulated heat-exchange rates were within 5%. These validation results establish a solid physical basis for the subsequent control strategy analysis.
Before investigating the coupling control of the vehicle traction battery thermal management system, I performed a single-factor simulation analysis. In the high-temperature cooling scenario, the ambient temperature was fixed at 30 °C, the initial battery temperature at 30 °C, and the vehicle speed at 60 km/h. The compressor speed was varied from 1000 to 5000 rpm while the water pump speed was fixed at 1500 rpm and the fan was disabled. The results show that a higher compressor speed provides greater cooling capacity but also increases compressor power consumption roughly proportionally in the speed range below 2000 rpm, while at higher speeds the efficiency decreases. A balanced compressor speed range is from 2000 to 4000 rpm for the current vehicle traction battery cooling requirement.
I then varied the water pump speed from 500 to 2500 rpm while keeping the compressor speed fixed at 2000 rpm. The final battery temperature drop changes only slightly when pump speed exceeds 2000 rpm. In contrast, the pump power consumption rises disproportionately. For instance, increasing the pump speed from 2000 to 2500 rpm increases power from about 500 W to 1000 W but only reduces the temperature by another 0.2 °C. Therefore, the recommended pump speed range is from 1000 to 2000 rpm.
For the fan speed, I fixed the compressor speed at 2000 rpm and the pump speed at 1000 rpm. Fan speeds from 750 to 4500 rpm were compared. The resulting battery temperature difference between the lowest and highest fan speeds is only about 0.1–0.2 °C, while the fan power increases from 3.13 W to 673.24 W. This marginal temperature benefit with a dramatic energy cost indicates that the fan is more suitable as an auxiliary actuator.
The single-factor analyses indicate that there are three main manipulated variables: compressor speed \(N_{comp}\), pump speed \(N_{pump}\), and fan speed \(N_{fan}\). To systematically evaluate their joint influences on the temperature and energy consumption of the vehicle traction battery, I applied the optimal Latin hypercube sampling method. The design space is defined as:
$$\Omega=\{(N_{comp},N_{pump},N_{fan})\mid 2000\le N_{comp}\le4000,\;1000\le N_{pump}\le2000,\;1500\le N_{fan}\le2250\}$$
After standardizing the variables to the unit cube, I generated 30 sample points using the maximum-minimum distance criterion. The sampling quality was verified from three aspects: the scatter plot shows that the samples are uniformly distributed in space; the pairwise correlation coefficients are all less than 0.2, indicating good statistical independence; and the distances between sample points follow a concentrated distribution with an average normalized distance of 0.6898 and a minimum distance of 0.195. Moreover, the fan speed has a lower correlation with the other factors, which is beneficial for separating their effects.
For each sample, I ran an AMESim simulation using the NEDC driving cycle at 30 °C ambient temperature and 60 km/h vehicle speed. The battery initial temperature and SOC were set to 30 °C and 90%, respectively. The maximum battery temperature and the total thermal management power consumption were extracted as response variables. Using variance analysis (ANOVA), I estimated the main effects of the three factors. The ANOVA table for the average battery temperature is shown below.
| Source | Sum of squares | DF | Mean square | F value | P value |
|---|---|---|---|---|---|
| Model | 2.07 | 3 | 0.6915 | 152.10 | <0.0001 |
| \(N_{comp}\) | 0.5501 | 1 | 0.5501 | 121.01 | <0.0001 |
| \(N_{pump}\) | 1.08 | 1 | 1.08 | 237.13 | <0.0001 |
| \(N_{fan}\) | 0.002 | 1 | 0.002 | 0.4384 | 0.5137 |
| Residual | 0.1182 | 26 | 0.0045 | ||
| Corrected total | 2.19 | 29 |
For the temperature response, the model F value is 152.10 with a p value below 0.0001. The adjusted coefficient of determination is 0.9399. The pump speed has the largest F value, meaning that it is the dominant factor for controlling the temperature of the vehicle traction battery under the tested conditions. The compressor speed also shows a highly significant effect. In contrast, the fan speed does not significantly affect the battery temperature.
For the total energy consumption response, the ANOVA results are listed in the following table.
| Source | Sum of squares | DF | Mean square | F value | P value |
|---|---|---|---|---|---|
| Model | 5.074E6 | 3 | 1.691E6 | 1994.38 | <0.0001 |
| \(N_{comp}\) | 4.331E6 | 1 | 4.331E6 | 5105.98 | <0.0001 |
| \(N_{pump}\) | 79683.92 | 1 | 79683.92 | 93.95 | <0.0001 |
| \(N_{fan}\) | 40376.73 | 1 | 40376.73 | 47.61 | <0.0001 |
| Residual | 22051.40 | 26 | 848.13 | ||
| Corrected total | 5.097E6 | 29 |
The compressor speed is the most significant factor for energy consumption with an F value of 5105.98, while the pump speed and fan speed are also statistically significant but less influential. These findings confirm that the compressor and the pump are the primary manipulated variables for the coordinated temperature-energy management of the vehicle traction battery. The fan should be used only as an auxiliary actuator. This conclusion directs the design of the control strategies in the subsequent sections.
Based on the factor screening results, I developed a hierarchical control architecture for the vehicle traction battery thermal management system. The controller first determines the thermal management mode based on the ambient temperature and battery temperature. There are three modes: low-temperature heating, normal-temperature cooling, and high-temperature refrigeration.
For the low-temperature mode, the vehicle traction battery must be heated to a target temperature. The positive temperature coefficient heater is the main heat source, and the electric pump drives the warm coolant into the battery cooling plate. I implemented a three-position threshold strategy and a PID control strategy. In threshold control, the heater runs at full power when the battery temperature is below 5 °C and switches off above 6 °C. In PID control, the output power is continuously adjusted based on the error between the desired temperature and the actual battery temperature. The PID output \(u(t)\) is calculated as:
$$u(t)=K_p e(t)+K_i\int_0^t e(\tau)d\tau+K_d\frac{de(t)}{dt}$$
where \(e(t)=T_{ref}-T_b\), \(T_{ref}=5\,^\circ\mathrm{C}\). I simulated the low-temperature condition at an ambient temperature of -10 °C over 2400 seconds. The NEDC cycle was used as the vehicle speed demand. Without heating, the battery temperature remains close to the ambient temperature. With simple threshold control, the heater switches on and off, causing repeated temperature oscillations around 5 °C. With PID control, the PTC heater power smoothly decreases as the battery temperature approaches the target, and the temperature remains stable with only small variation. The accumulated PTC energy consumption for threshold control is 8837 kJ, while the PID control consumes 7921 kJ, a reduction of 10.37%. Thus, the PID algorithm provides more precise heating and better energy conservation during the cold operation of the vehicle traction battery.
For the normal-temperature mode, the ambient temperature is between 6 °C and 30 °C. The objective is to prevent the temperature of the vehicle traction battery from exceeding a safe limit while consuming as little energy as possible. The two actuators are the water pump and the radiator fan. I developed a nonlinear model predictive control strategy to coordinate these two actuators. To implement the nonlinear model predictive controller, I first derive a reduced-order dynamic model of the battery temperature. According to the energy balance, the battery lumped temperature equation is:
$$c_b m_b\frac{dT_b}{dt}=\dot{Q}_g-h_bA_b(T_b-T_{cb})$$
where \(T_{cb}\) is the temperature of the coolant adjacent to the battery. The coolant temperature variation is described by:
$$c_l m_{c,all}\frac{dT_{cb}}{dt}=h_bA_b(T_b-T_{cb})-\dot{m}_c c_l(T_{cb}-T_{cr})$$
where \(T_{cr}\) is the coolant temperature in the radiator. Finally, the radiator coolant equation is:
$$c_l m_{cr}\frac{dT_{cr}}{dt}=\dot{m}_c c_l(T_{cb}-T_{cr})-Q_r$$
The heat rejection \(Q_r\) is approximated by:
$$Q_r=V_{fan} A_r \rho_{air}(T_{cr}-T_{amb})$$
The radiator air velocity is proportional to the fan speed, \(V_{fan}=kN_{fan}\). Therefore, the nonlinear state-space model for the normal-temperature mode can be written as:
$$\dot{x}(t)=f(x(t),u(t),d(t)), \quad y(t)=h(x(t),u(t),d(t))$$
with state vector \(x=[T_b,\;T_{cb},\;T_{cr}]^T\), control input \(u=[\dot{m}_c,\;V_{fan}]^T\), disturbance \(d=\dot{Q}_{gen}\), and output \(y=T_b\).
I validated the predictive model using a Simulink-AMESim co-simulation platform. The ambient temperature was 25 °C and the vehicle followed the NEDC cycle. Both the AMESim high-fidelity model and the reduced predictive model received the same time-varying fan speed and pump speed. The predicted battery temperatures agree within 0.5 °C, confirming the suitability of the model for model predictive control.
The nonlinear model predictive controller solves the following constrained finite-horizon optimization problem at each sampling instant:
$$J=\min \left\{k_1\sum_{i=1}^{N}\left(T_b(k+i)-T_{ref}(k+i)\right)^2+k_2 P_{pump}(k+i)+k_3 P_{fan}(k+i)\right\}$$
subject to the state-space model, pump speed and fan speed limits, and the control constraints \(0\le N_{pump}\le3000\) rpm and \(0\le N_{fan}\le3000\) rpm. In the above objective function, the first term penalizes the battery temperature tracking error, while the second and third terms penalize the water pump and fan energy consumption. Weight parameters \(k_1\), \(k_2\), and \(k_3\) balance control accuracy and energy saving.
I compared three strategies in the normal-temperature condition: threshold control, PID control, and nonlinear model predictive control. In the threshold controller, the pump and fan start at the maximum speed when the battery temperature exceeds 28 °C, and turn off when the temperature drops below 27 °C. The PID controller has two independent PID loops, one for fan speed and one for pump speed. The controlled battery temperature profiles under the five-cycle NEDC simulation are shown in figure needs to be placed here? The figure already inserted earlier. The comparisons are described as follows: without thermal management, the battery temperature continues to rise to 34.5 °C. With threshold control, the temperature oscillates near the upper limit and reaches a maximum of 28.67 °C. The hysteresis causes a delay in activating the cooling system after a sudden load increase. The PID-controlled system shows improved dynamic response but still exhibits an overshoot of 1.72 °C and oscillates during the transition from heating to cooling. The nonlinear model predictive controller maintains the battery temperature near the reference value 27 °C with a maximum temperature of 28.37 °C, and the maximum overshoot is reduced by 20.35% relative to that of PID control.
From the perspective of energy consumption, the patterns of the actuator activities differ substantially. In threshold control, both the pump and fan have on-off behavior and run at maximum speed, leading to the highest cumulative energy use. In PID control, the fan and pump speeds are continually adjusted but still show frequent fluctuations. In nonlinear model predictive control, the controller recognizes when the battery heat generation is small and intentionally reduces or turns off the coolant flow, resulting in an intermittent but energy-efficient operation. The cumulative energy consumptions over the NEDC cycling test are listed below.
| Control strategy | Total thermal management energy (kJ) | Relative saving vs threshold control | Relative saving vs PID control |
|---|---|---|---|
| Threshold control | 10000.87 | — | — |
| PID control | 8585.67 | 14.15% | — |
| NMPC control | 7613.71 | 23.87% | 11.32% |
These results demonstrate that the nonlinear model predictive control strategy successfully lowers the total thermal-management energy consumption while preserving a tighter battery temperature response. The improvement comes from the predictive nature of the algorithm, which anticipates load variations and avoids unnecessary actuator activation.
For the high-temperature mode, the ambient temperature ranges from 31 °C to 40 °C. The thermal management system must provide a large cooling capacity to maintain the vehicle traction battery near a prescribed reference temperature, while avoiding excessive energy consumption. The main actuators are the compressor and the water pump; the condenser fan is maintained at a fixed auxiliary speed. I used an improved nonlinear model predictive control architecture in which the optimization problem is solved with a grey wolf optimizer. The GWO algorithm is a metaheuristic method inspired by the social hierarchy and hunting behavior of grey wolves. The control variables, compressor speed \(N_{comp}\) and water pump speed \(N_{pump}\), are updated iteratively until the objective function converges.
To build the high-temperature prediction model, I derive a simplified two-state model. The battery temperature equation is:
$$c_{p,b} m_b\frac{dT_b}{dt}=\dot{Q}_{gen}+\dot{m}_c c_{p,c}\left(T_{c,in}-T_{c,out}\right)$$
The outlet temperature of the cooling plate is expressed by the uniform-wall-temperature model:
$$T_{c,out}=T_b+\left(T_{c,in}-T_b\right)\exp\left(\frac{-h_bA_b}{\dot{m}_c c_{p,c}}\right)$$
The cooling fluid temperature at the chiller inlet is described by:
$$c_{p,c} m_{c,all}\frac{dT_{c,in}}{dt}=\dot{m}_c c_{p,c}\left(T_{c,out}-T_{c,in}\right)-Q_c^{bat}(N_{comp})$$
The chiller capacity \(Q_c^{bat}\) was fitted as a cubic polynomial function of the compressor speed:
$$Q_c^{bat}=43 N_{comp}^3-241 N_{comp}^2+414 N_{comp}+3939$$
where \(N_{comp}\) is in thousands of revolutions per minute. The coefficient of determination \(R^2\) of the curve fitting is 0.9978, meaning that this algebraic expression accurately reproduces the steady-state cooling capacity. The state vector for this mode is \(x=[T_b,\;T_{c,in}]^T\), the control vector is \(u=[N_{comp},\;N_{pump}]^T\), and the output is \(y=T_b\).
I validated the prediction model for the high-temperature mode through a co-simulation process at an ambient temperature of 35 °C and battery initial temperature of 35 °C. The compressor and pump speed sequences were imposed on the AMESim model and the reduced-order model simultaneously. The maximum error in the battery temperature between the two models is 0.6 °C, which is acceptable for the controller.
The optimization objective for the high-temperature nonlinear predictive controller is designed as:
$$J=\min \left\{k_1\sum_{i=1}^{N}\left(T_b(k+i)-T_{ref}(k+i)\right)^2+k_2P_{comp}(k+i)+k_3P_{pump}(k+i)\right\}$$
with the constraints \(0\le N_{pump}\le3000\) rpm, \(0\le N_{comp}\le4000\) rpm, and the prediction horizon of 20 control intervals. To accelerate convergence, the previous optimal control vector is used as one of the initial grey wolf individuals. The algorithm parameters are: population size 20 and maximum iteration number 20.
I verified the grey-wolf-optimized NMPC strategy through a five-cycle NEDC simulation. The ambient and initial battery temperatures were both set to 35 °C, while the target battery temperature was 27 °C. The threshold controller activates the compressor and pump only when the temperature exceeds 28 °C and deactivates them when the temperature is below 27 °C. This two-position logic causes repeated switching and leads to a temperature ripple. The PID controller adjusts both speeds smoothly but is sensitive to load changes and shows a larger overshoot when the high-speed phase of the NEDC starts. In contrast, the GWO-NMPC controller continuously computes the optimal compressor and pump speeds to minimize the temperature tracking error and energy consumption. The battery temperature under the GWO-NMPC strategy can be held near 27 °C with a smaller root-mean-square error and less overshoot.
For the high-temperature scenario, the accumulated thermal management system energy consumptions under the three strategies are shown in the following table.
| Control strategy | Total energy consumption (kJ) | Relative saving vs threshold control | Relative saving vs PID control |
|---|---|---|---|
| Threshold control | 10580 | — | — |
| PID control | 6165 | 41.74% | — |
| GWO-NMPC control | 5150 | 51.31% | 12.62% |
The compressor and pump speeds in the GWO-NMPC controller are lower on average and adapt in a coordinated manner to the instantaneous heat load. The threshold controller often operates the compressor at its upper speed limit, which is wasteful when the cooling demand is low. The PID controller tracks the temperature with a lag and uses extra energy during transient periods. The GWO-NMPC provides a clear advantage by explicitly incorporating both temperature tracking and energy terms in the same cost function.
It should be noted that the control horizon and weights \(k_1\), \(k_2\), \(k_3\) have a strong influence on the system behavior. In my simulation, I selected the weights by a preliminary tuning study to ensure that the temperature constraint was satisfied with only a small overshoot while preserving a low energy consumption. The proposed tuning method is simple but effective because the three weights correspond to the relative importance of temperature accuracy and each power-consuming component. For engineering deployment, more advanced offline optimization could be used to tune these weights across a wide range of ambient temperatures.
The findings of this study reveal three important aspects of thermal management for the vehicle traction battery. First, the physical model of the battery and cooling circuits must be accurate and validated because the control strategy relies on the prediction model. The AMESim simulation, after calibration with experiments, achieves a temperature error of less than 3 °C in the battery response and a heat-transfer error of less than 5% for the major heat exchangers. Such accuracy is sufficient for the development and verification of model-based controllers.
Second, the optimal Latin hypercube sampling method is a powerful tool to explore the multidimensional parameter space of the thermal management system. By applying orthogonalization and distance-based optimization, I obtained 30 well-distributed samples with no significant correlation among the factor levels. The resulting ANOVA shows that the compressor and pump are essential control variables, while the fan should be treated as an auxiliary variable. This conclusion simplifies the task of controller design and helps reduce the computational burden of real-time optimization.
Third, the environmental mode-specific control strategy provides a practical way to achieve temperature-energy synergy. In low-temperature conditions, the simple PID strategy is sufficient because the PTC heater has a relatively slow response and there is only one dominant heat source. In normal-temperature conditions, nonlinear model predictive control coordinates two actuators and reduces energy consumption by more than 23% compared to threshold control. In high-temperature conditions, the integration of a grey wolf optimizer with NMPC enables fast and reliable minimization of a nonlinear objective function. The controller adjusts compressor and pump speeds continuously to satisfy the strict temperature tracking requirement while lowering the total energy demand of the vehicle traction battery thermal management system.
Although the results are obtained from simulation, the validated system model guarantees a good correspondence with the real physical system. However, several improvements remain possible. First, the battery model uses a lumped parameter approach, which cannot capture internal temperature gradients. For large battery modules, a more detailed thermal model might reveal additional constraints such as maximum local temperature. Second, the effects of battery ageing and parameter drift were not considered. Over time, the internal resistance and heat capacity may change, and the controller should be robust against such variations. Third, the proposed control strategy should be tested on a hardware-in-the-loop platform or in a real electric vehicle to evaluate communication delays and actuator dynamics.
In summary, this research establishes a complete framework for the temperature-energy coordinated thermal management of a vehicle traction battery. I have combined theoretical modeling, experimental calibration, design-of-experiment based factor screening, and advanced control strategies to solve the tradeoff between temperature regulation and energy saving. The developed hierarchical control architecture works in three separate temperature ranges, and the corresponding controllers have been compared with conventional threshold and PID control methods. The quantitative results demonstrate that the nonlinear model predictive control strategy, especially when optimized with the grey wolf algorithm, produces excellent tracking accuracy and significant energy savings. Therefore, the proposed method can be considered a valuable reference for the design of efficient thermal management systems of the vehicle traction battery in real-world electric vehicles.