The rapid transition toward clean energy and electric mobility has placed power battery systems at the core of electric vehicle development. Thermal safety and energy efficiency are the two pillars that determine the practical viability of an electric vehicle. Over the past decade, many studies have focused on battery thermal management systems, but most of them treated temperature regulation and energy consumption as separate design targets. In my work, I aim to unify these two objectives under a single framework. The central question is: how can an EV battery pack remain within its optimal operating temperature window while the cooling and heating system consumes as little electrical energy as possible? This is not a trivial problem because the battery thermal behavior is highly nonlinear and strongly coupled with vehicle driving conditions, ambient temperature, and the operating state of the compressor, pump, and fan. I designed a layered thermal management architecture, developed a high-fidelity simulation platform, screened the dominant control variables, and implemented nonlinear model predictive control strategies for different ambient temperature ranges. My results show that significant energy savings can be achieved without compromising battery temperature control accuracy.
In this paper, I present a comprehensive investigation of a temperature–energy coordinated thermal management system for an EV battery pack. I first describe the theoretical foundations and the physical modeling approach. Then I explain the calibration procedure using experimental data from a lithium iron phosphate battery. Next, I introduce the optimal Latin hypercube sampling method used to identify the most influential control variables. After that, I develop and compare several control strategies for low, normal, and high ambient temperature conditions. The final section gives the conclusion and future research directions.
1. Background and Research Motivation
The global energy crisis and climate change have pushed the automotive industry toward electrification. Electric vehicles rely on rechargeable energy storage systems, and the lithium-ion battery is the most common technology. Among various cathode chemistries, lithium iron phosphate is widely used because of its high thermal stability, long cycle life, and relatively low cost. However, even a thermally stable chemistry can fail if the battery pack is subjected to excessive temperatures or large temperature gradients. The optimum operating range for most lithium-ion batteries is between 20 °C and 40 °C. When the temperature exceeds this range, capacity fade accelerates. When the temperature is below 0 °C, the internal resistance increases significantly, causing power loss and possible lithium plating during charging. Therefore, an effective thermal management system is indispensable.
Traditional thermal management systems usually activate the cooling loop based on a threshold temperature. For example, if the battery temperature exceeds 35 °C, the compressor and pump are switched on at maximum speed. When the temperature falls below a lower threshold, they are switched off. This threshold control is simple but inefficient. It leads to frequent switching, overshoot, and unnecessary energy consumption. More advanced controllers, such as PID, can reduce some of these issues, but they are designed for single-input-single-output systems and do not handle the multivariable, nonlinear, and constrained nature of a battery thermal management system well. Model predictive control offers a more elegant solution, but linear MPC often fails under strong nonlinearities. Nonlinear model predictive control (NMPC) is more accurate, yet it requires a reliable prediction model and a computationally efficient solver.
My research goal is to develop a temperature–energy coordinated control strategy for an EV battery pack. I focus on three typical ambient temperature scenarios: low temperature, normal temperature, and high temperature. For each scenario, I choose suitable actuators and control algorithms. The result is a hierarchical strategy that ensures thermal safety while minimizing the energy consumed by the thermal management system.
2. System Architecture and Theoretical Modeling
The thermal management system investigated in my study belongs to an indirect liquid-cooled architecture. The system consists of three hydraulic loops: a coolant loop, a battery radiator loop, and a vapor-compression refrigeration loop. The coolant loop contains a water pump, a liquid cold plate, a chiller, a two-position three-way valve, and a positive temperature coefficient (PTC) heater. The radiator loop contains a radiator and a fan. The refrigeration loop contains a compressor, a condenser, an expansion valve, and the chiller. The valve connects either the radiator loop or the chiller path into the coolant circuit, depending on the operating mode.
The working principle can be described as follows. In low-temperature conditions, the PTC heater heats the coolant, and the pump drives the warm coolant through the cold plate attached to the battery pack. In moderate-temperature conditions, the radiator is used to dissipate heat to the ambient air, with the fan controlling the air flow rate. In high-temperature conditions, the refrigeration loop is activated, and the chiller transfers heat from the coolant to the refrigerant, which is then rejected by the condenser. The compressor speed determines the refrigeration capacity, while the pump speed controls the coolant flow rate.
3. Battery Electrothermal Coupling Model
The battery pack is discretized by a lumped-parameter model for control purposes. The heat generation rate of a single cell is calculated with the Bernardi equation:
$$
\dot{Q}_{gen} = I \left( I R_e – T_b \frac{\mathrm{d} U_{oc}}{\mathrm{d} T_b} \right)
$$
where \(I\) is the current, \(R_e\) is the equivalent internal resistance, \(T_b\) is the battery temperature, and \(U_{oc}\) is the open-circuit voltage. The entropy coefficient \(\mathrm{d} U_{oc}/\mathrm{d} T_b\) is assumed to be negligible in the simplified model for high-temperature conditions, but it is included in the detailed AMESim model.
The thermal dynamics of the battery pack and coolant can be expressed by the following energy balance equations:
$$
c_{p,b} m_b \frac{\mathrm{d} T_b}{\mathrm{d} t} = \dot{Q}_{gen} – \dot{Q}_{removed}
$$
$$
c_{p,c} m_{c,all} \frac{\mathrm{d} T_{c,in}}{\mathrm{d} t} = \dot{m}_c c_{p,c} \left( T_{c,out} – T_{c,in} \right) – Q_{chiller}
$$
where \(c_{p,b}\) and \(c_{p,c}\) are the specific heat capacities of the battery and coolant, \(m_b\) and \(m_{c,all}\) are the battery mass and coolant mass inside the cold plate, and \(\dot{m}_c\) is the coolant mass flow rate. The heat transfer from the battery to the coolant is modeled as forced convection:
$$
\dot{Q}_{removed} = \dot{m}_c c_{p,c} \left( T_{c,in} – T_b \right) \left[ 1 – \exp\left( – \frac{h_b A_b}{\dot{m}_c c_{p,c}} \right) \right]
$$
where \(h_b\) is the heat transfer coefficient and \(A_b\) is the effective heat transfer area. This formulation is derived from a uniform-wall-temperature model.
In normal-temperature mode, the heat is rejected through the radiator:
$$
c_{p,c} m_{cr} \frac{\mathrm{d} T_{cr}}{\mathrm{d} t} = \dot{m}_c c_{p,c} \left( T_{cb} – T_{cr} \right) – Q_{rad}
$$
$$
Q_{rad} = V_{fan} A_r \rho_{air} c_{p,air} \left( T_{cr} – T_{amb} \right)
$$
where \(V_{fan}\) is the air velocity through the radiator, \(A_r\) is the radiator face area, \(\rho_{air}\) is the air density, and \(T_{amb}\) is the ambient temperature. The relation between fan speed and air velocity is assumed linear:
$$
V_{fan} = k N_{fan}
$$
For the chiller capacity as a function of compressor speed, I fitted a cubic polynomial from simulation data under constant ambient temperature:
$$
Q_{chiller}(N_{comp}) = 43 N_{comp}^3 – 241 N_{comp}^2 + 414 N_{comp} + 3939
$$
The coefficient of determination of this regression is \(R^2=0.9978\), which validates the high fidelity of the fitted model.
4. Power Consumption Models
The energy consumption of the thermal management system is the sum of the power used by the compressor, the pump, the fan, and the PTC heater. The compressor power is a nonlinear function of the compressor speed and the pressure ratio. In my control-oriented model, I correlated the compressor power with the compressor speed via a polynomial fitting. The pump power consumption is proportional to the cube of the coolant mass flow rate:
$$
P_{pump} = k_{pump} \dot{m}_c^3
$$
Similarly, the fan power consumption follows the cubic law with respect to the volumetric flow rate:
$$
P_{fan} = k_{fan} \left( \rho_{air} A_r V_{fan} \right)^3
$$
The PTC heater power is simply the product of voltage and current:
$$
P_{PTC} = U_{PTC} I_{PTC} = I_{PTC}^2 R_{PTC}
$$
In the normal-temperature and high-temperature modes, the compressor and pump are the main controllable loads. In the low-temperature mode, the PTC heater and the pump are dominant. The fan is treated as an auxiliary actuator in most of the analysis.
5. Experimental Calibration and Model Validation
I built a test platform that consisted of a battery cycler, a temperature chamber, and a data acquisition unit. The battery cell was a lithium iron phosphate prismatic cell with a nominal capacity of 20 Ah. I performed several experiments to extract the key parameters of the electrothermal model.
5.1 Open-circuit voltage test
The open-circuit voltage was measured as a function of the state of charge (SOC) by slowly discharging the cell at a low current rate. The obtained curve is shown in the form of a lookup table in the AMESim model. Because the open-circuit voltage is weakly dependent on temperature, I only measured it at 30 °C.
5.2 HPPC test and internal resistance identification
The equivalent internal resistance depends on SOC, temperature, and current direction. I used the hybrid pulse power characteristic (HPPC) test. A single pulse sequence involves a 20 s discharge pulse and a 40 s rest period, followed by a 10 s charge pulse and a rest period. The resistance is computed from the instantaneous voltage drop:
$$
R = \frac{U_1 – U_0}{I_1}
$$
where \(U_0\) is the voltage before the pulse and \(U_1\) is the voltage after the pulse current is applied. I repeated the test at three temperatures (20 °C, 30 °C, and 40 °C) and at SOC steps of 10% or 20%. The resulting response surface showed that the internal resistance increases dramatically at low temperature and low SOC.
5.3 Thermal property test
To obtain the equivalent heat capacity of the cell, I used a thermal flux method. The cell was wrapped in insulating foam, and an electric heating film was attached to all six faces. The total heating power was 40 W, and the heating duration was 600 s. The equivalent heat capacity is:
$$
C_b = \frac{q \, \Delta t}{T_1 – T_0}
$$
In my test, the average temperature rose from 14.5 °C to 35.4 °C, yielding a heat capacity of 1142 J/K for the single cell. This value was then used to scale the heat capacity of the full EV battery pack.
5.4 Battery temperature validation
The AMESim model was validated by comparing the simulated temperature response with the experimental data under the same current profile. The maximum error was less than 3 °C over the entire test period. The voltage response showed similarly good agreement. Therefore, the electrothermal coupling model is accurate enough for control design.
5.5 Heat exchanger calibration
The condenser and the chiller were calibrated using wind-tunnel tests. For the condenser, I varied the air velocity and refrigerant flow rate according to four standard operating conditions. For the chiller, I varied the coolant flow rate while keeping the refrigerant inlet pressure and temperature within a specified range. The calibration was performed in the AMESim heat exchanger calibration module. The relative error between the simulated heat transfer rate and the experimental data was below 5% for both components. Table 1 summarizes the calibration conditions and results.
| Component | Operating conditions | Relative error between simulation and experiment | Calibrated parameters |
|---|---|---|---|
| Condenser | 4 air-side speeds, 4 refrigerant side states | < 5% | Air-side Nusselt correlation coefficients |
| Chiller | 4 coolant flow rates, 4 refrigerant states | < 5% | Two-phase heat transfer correlation coefficients |
6. Key Factor Screening with Optimal Latin Hypercube Sampling
The thermal management system of an EV battery pack has many actuators, but not all of them have the same influence on temperature and energy consumption. In my study, I focused on the compressor speed, pump speed, and fan speed as the primary candidate variables. Before designing the advanced controller, I performed a single-factor analysis to understand the isolated effect of each variable.
6.1 Single-factor effects
The compressor speed determines the refrigeration capacity. Increasing the compressor speed from 1000 rpm to 5000 rpm raised the cooling power and the compressor power simultaneously. The cooling efficiency decreased at high speed. A compressor speed between 2000 and 4000 rpm offers a reasonable balance. The pump speed controls the coolant flow rate and thus the heat transfer coefficient on the battery side. I observed a diminishing marginal benefit above 2000 rpm, while the pump power increased sharply. The fan speed affects the condenser heat rejection. In the tested range, raising the fan speed from 750 rpm to 4500 rpm only changed the battery temperature by about 0.1–0.2 °C, but the fan power increased from 3.13 W to 673.24 W. This indicates that the fan has limited influence on the battery thermal state under the studied conditions and should be considered an auxiliary actuator.
6.2 Design of experiments
Based on the single-factor analysis, I defined the following bounds for the three control variables:
| Factor | Symbol | Lower bound | Upper bound |
|---|---|---|---|
| Compressor speed | \(N_{comp}\) | 2000 rpm | 4000 rpm |
| Pump speed | \(N_{pump}\) | 1000 rpm | 2000 rpm |
| Fan speed | \(N_{fan}\) | 1500 rpm | 2250 rpm |
I implemented the optimal Latin hypercube sampling method in MATLAB. This technique divides each dimension into \(n\) equal probability intervals and then optimizes the sample positions to maximize the minimum distance between points. I generated 30 sample points. The quality of the sampling was verified by checking the distribution in the three-dimensional space, the Pearson correlation matrix, and the distance distribution among points. The maximum absolute correlation coefficient was less than 0.2, indicating good statistical independence.
6.3 Simulation and analysis of variance
Each of the 30 samples was simulated in AMESim under a fixed driving scenario. The ambient temperature was 30 °C, the initial battery temperature was 30 °C, and the vehicle speed was constant at 60 km/h. The simulation duration was 1200 s. I extracted the steady-state battery temperature and the average system power consumption as response variables. Then I used analysis of variance (ANOVA) to quantify the significance of each factor. Table 3 shows the ANOVA results for battery temperature.
| 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 | ||
| Total | 2.19 | 29 |
The \(R^2\) value of the temperature model was 0.9461, and the adjusted \(R^2\) was 0.9399. Both the compressor speed and the pump speed have a significant effect on the battery temperature, with the pump showing the larger F-value in this scenario. The fan speed is not significant for temperature.
Table 4 presents the ANOVA results for system power consumption.
| 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 | ||
| Total | 5.097E6 | 29 |
The compressor speed has the dominant influence on energy consumption. The pump and fan also have significant contributions, but their F-values are much lower. Combining the temperature and energy results, I concluded that the compressor and the pump should be the primary manipulated variables in the high-temperature mode. The fan can be treated as an auxiliary actuator.
7. Control Strategies for Temperature–Energy Synergy
Based on the factor screening, I designed three distinct control strategies for the three ambient temperature ranges. The overall logic is shown in the following state-based decision algorithm:
1. Measure the battery temperature \(T_b\) and the ambient temperature \(T_{amb}\).
2. If \(T_{amb} \le 5\,^\circ\mathrm{C}\), enter the low-temperature heating mode.
3. If \(6\,^\circ\mathrm{C} \le T_{amb} \le 30\,^\circ\mathrm{C}\), enter the normal-temperature cooling mode.
4. If \(T_{amb} \ge 31\,^\circ\mathrm{C}\), enter the high-temperature refrigeration mode.
In each mode, the control law is designed to minimize the temperature tracking error and the total energy consumption.
7.1 Low-temperature mode
In this mode, the PTC heater is the only heat source. The goal is to raise the battery temperature to the target value of 5 °C while minimizing heating energy. Because the heating process is a single-input system, I compared threshold control and PID control.
Threshold control: if \(T_b < 5\,^\circ\mathrm{C}\), the PTC heater operates at full power; if \(T_b > 6\,^\circ\mathrm{C}\), it is switched off. This causes oscillation and overshoot. PID control uses the error \(e(t) = T_{ref} – T_b\) to modulate the heater power continuously. The control input is:
$$
u_{PID}(t) = K_p e(t) + K_i \int_0^t e(\tau) \mathrm{d}\tau + K_d \frac{\mathrm{d} e(t)}{\mathrm{d}t}
$$
I tuned the PID gains by a trial-and-error method in the simulation environment.
7.2 Normal-temperature mode
In normal ambient temperatures, the battery may overheat during high-load driving, so I activate the radiator loop. The manipulated variables are the pump speed \(N_{pump}\) and the fan speed \(N_{fan}\). I designed a nonlinear model predictive controller. The prediction model is built from equations (2)–(5). The state vector is \(\mathbf{x} = [T_b, T_{cb}, T_{cr}]^T\), the control vector is \(\mathbf{u} = [\dot{m}_c, V_{fan}]^T\), and the disturbance is the battery heat generation rate. The optimization problem is:
$$
\min_{\mathbf{u}} \; J = \sum_{i=1}^{N_p} \left[ w_1 \left( T_b(k+i) – T_{ref} \right)^2 + w_2 P_{pump}(k+i) + w_3 P_{fan}(k+i) \right]
$$
subject to:
$$
0 \le \dot{m}_c \le \dot{m}_{c,max}, \quad 0 \le V_{fan} \le V_{fan,max}
$$
The prediction horizon \(N_p\) was set to 10 with a sampling time of 1 second. The optimization problem was solved using an interior-point solver in MATLAB. Only the first element of the optimal control sequence is applied, and the optimization is repeated at every sampling instant.
7.3 High-temperature mode
In high ambient temperatures, the chiller must be activated. The two main actuators are the compressor and the pump. The fan is fixed at a constant speed to simplify the control structure. The state vector is \(\mathbf{x} = [T_b, T_{c,in}]^T\), and the control vector is \(\mathbf{u} = [N_{comp}, N_{pump}]^T\). The battery heat generation is calculated from the driving current. The prediction model is defined by the equations:
$$
c_{p,b} m_b \frac{\mathrm{d} T_b}{\mathrm{d} t} = \dot{Q}_{gen} + \dot{m}_c c_{p,c} \left( T_{c,in} – T_b \right) \left[ 1 – \exp\left( – \frac{h_b A_b}{\dot{m}_c c_{p,c}} \right) \right]
$$
$$
c_{p,c} m_{c,all} \frac{\mathrm{d} T_{c,in}}{\mathrm{d} t} = \dot{m}_c c_{p,c} \left( T_{c,out} – T_{c,in} \right) – Q_{chiller}(N_{comp})
$$
where \(T_{c,out}\) is expressed through the uniform-wall-temperature relation. The objective function becomes:
$$
\min_{\mathbf{u}} \; J = \sum_{i=1}^{N_p} \left[ \lambda_1 \left( T_b(k+i) – T_{ref} \right)^2 + \lambda_2 P_{comp}(k+i) + \lambda_3 P_{pump}(k+i) \right]
$$
The compressor speed is bounded by 0 to 4000 rpm, and the pump speed by 0 to 3000 rpm. The nonlinear optimization problem is solved with the Grey Wolf Optimizer (GWO), a metaheuristic algorithm that mimics the social hierarchy and hunting behavior of grey wolves. The GWO search process is described by the following update equations:
$$
\begin{aligned}
D_{\alpha} &= \left| C_1 \cdot X_{\alpha}(\tau) – X(\tau) \right| \\
D_{\beta} &= \left| C_2 \cdot X_{\beta}(\tau) – X(\tau) \right| \\
D_{\delta} &= \left| C_3 \cdot X_{\delta}(\tau) – X(\tau) \right|
\end{aligned}
$$
$$
X_1 = X_{\alpha}(\tau) – A_1 D_{\alpha}, \quad X_2 = X_{\beta}(\tau) – A_2 D_{\beta}, \quad X_3 = X_{\delta}(\tau) – A_3 D_{\delta}
$$
$$
X(\tau+1) = \frac{X_1 + X_2 + X_3}{3}
$$
The wolf population size was 20, and the maximum number of iterations was 20. To improve convergence, the solution from the previous sampling instant was used as one of the initial population members. The solver was coded as a MATLAB M-function and embedded in a Simulink S-function, which communicated with the AMESim plant model through a co-simulation interface.
8. Model Predictive Control Accuracy Verification
Before applying the NMPC controller, I verified that the simplified prediction model is consistent with the high-fidelity AMESim model. For the normal-temperature mode, I executed a NEDC driving cycle with an ambient temperature of 25 °C. The same control input sequence (pump speed and fan speed) was fed into both models. The maximum deviation between the predicted battery temperature and the AMESim battery temperature was less than 0.5 °C. For the high-temperature mode, I set the ambient and initial battery temperature to 35 °C. The compressor and pump speeds were varied according to a predefined sequence. The maximum temperature error was less than 0.6 °C. These results demonstrate that the prediction model is sufficiently accurate for the NMPC design.
9. Simulation Results and Comparative Evaluation
I evaluated the proposed control strategies under the NEDC driving cycle. The vehicle speed profile was repeated five times for the normal-temperature test to observe long-duration behavior. Table 5 summarizes the control targets and the comparison baselines.
| Ambient condition | Target battery temperature | Actuators | Control strategies compared |
|---|---|---|---|
| Low temperature (-10 °C) | 5 °C | PTC heater, pump | Threshold control, PID control |
| Normal temperature (25 °C) | 27 °C | Pump, fan | Threshold control, PID control, NMPC |
| High temperature (35 °C) | 27 °C | Compressor, pump, fan | Threshold control, PID control, GWO-NMPC |
9.1 Low-temperature results
In the low-temperature case, the ambient temperature was \(-10\,^\circ\mathrm{C}\) and the initial battery temperature was also near \(-10\,^\circ\mathrm{C}\). The NEDC cycle lasted 2400 seconds. The PID controller maintained the battery temperature near 5 °C with a small overshoot, whereas the threshold controller caused a larger oscillation between 4.8 °C and 6.2 °C. The energy consumed by the PTC heater over the whole cycle was 8837 kJ for the threshold control and 7921 kJ for the PID control. Thus, PID reduced the heating energy by 10.37%. I observed that the PID controller’s dynamic adjustment of the heating power avoided unnecessary full-power operation, leading to both better temperature tracking and lower energy consumption.
9.2 Normal-temperature results
In the normal-temperature case, the ambient temperature was 25 °C, and the target temperature was 27 °C. The simulation included five NEDC cycles. Without any cooling, the battery temperature rose to 34.54 °C. With threshold control, the maximum temperature was 28.67 °C with an overshoot of 0.67 °C. The PID control had a maximum temperature of 28.72 °C, which is an overshoot of 1.72 °C. The NMPC controller limited the maximum temperature to 28.37 °C, an overshoot of 1.37 °C. The NMPC controller reduced the maximum tracking error by 20.35% compared to PID. Importantly, the NMPC controller produced a much smoother temperature profile with less oscillation.
Figure 1 shows the actuator responses in the normal-temperature mode. The threshold control switched the fan and pump abruptly between on and off states. The PID control continuously adjusted the speeds but with weak coordination. The NMPC controller coordinated the pump and fan in a complementary manner: at low loads, it increased the pump flow while reducing the fan speed, and at high loads, it used both actuators optimally.
I also compared the cumulative energy consumption. The total energy consumption over the five NEDC cycles was 10000.87 kJ for threshold control, 8585.67 kJ for PID control, and 7613.71 kJ for NMPC. Therefore, NMPC achieved a 23.87% reduction compared to threshold control and an 11.32% reduction compared to PID control. These results confirm that the NMPC strategy is more energy-efficient because it predicts the future thermal load and adjusts the control inputs proactively instead of reactively.
9.3 High-temperature results
In the high-temperature case, the ambient temperature was 35 °C, and the initial battery temperature was also 35 °C. The target was 27 °C. I tested threshold control, PID control, and GWO-NMPC. All three strategies successfully brought the battery temperature down to the target within about 300 seconds. The threshold control exhibited some overshoot and sustained oscillation. The PID controller tracked the target reasonably well but had a large control effort fluctuation. The GWO-NMPC controller provided the smoothest transient response and the smallest deviation around the set point.
Table 6 summarizes the maximum temperature deviation and the energy consumption for each controller.
| Control strategy | Maximum temperature deviation (°C) | Total system energy consumption (kJ) | Relative energy saving vs. threshold |
|---|---|---|---|
| Threshold control | 1.8 | 6872.5 | – |
| PID control | 1.5 | 3829.4 | 44.3% |
| GWO-NMPC | 0.9 | 3346.2 | 51.3% |
The GWO-NMPC controller reduced the energy consumption by 51.31% compared to threshold control and by 12.62% compared to PID control. The main reason for the energy saving is that the NMPC with GWO avoids unnecessary compressor operation. The threshold control frequently switched the compressor between full-on and full-off, which consumes excessive energy and places stress on the mechanical components. The PID controller responded to errors but did not anticipate the future thermal load. In contrast, the GWO-NMPC optimized the compressor and pump speed profiles over the prediction horizon, resulting in a much lower average speed and fewer abrupt changes.
10. Discussion
The results obtained in this study emphasize the importance of considering the coupled dynamics of the EV battery pack and its thermal management system. A key insight from the factor screening is that the fan speed has a negligible effect on battery temperature in the tested range, but it does contribute to energy consumption. Therefore, in the high-temperature mode, I fixed the fan speed and controlled only the compressor and pump. This simplification allowed the GWO-NMPC controller to find better solutions in a lower-dimensional space, improving the convergence speed and the resulting energy efficiency.
Another important observation is that the battery thermal model used in control must be accurate over the whole operating envelope. In the normal-temperature case, the maximum prediction error of 0.5 °C was acceptable, because the temperature constraint was not extremely tight. In the high-temperature case, however, the prediction error of 0.6 °C could have led to a significant constraint violation if the controller had not included a safety margin. I therefore set the reference temperature slightly below the legal limit to prevent overheating. This conservative offset is an engineering compromise that can be adjusted in future work.
The computational burden of the GWO-NMPC controller is worth discussing. With a population size of 20 and 20 iterations, the solution time was about 0.8 seconds in the co-simulation environment. Since the sampling time was 1 second, the solver was barely able to run in real time. In an actual vehicle control unit, a more efficient optimization method or a shorter horizon would be required. Alternatively, a neural-network-based approximate NMPC could be trained offline to approximate the online solver. This is an important direction for future research.
11. Conclusions
In this study, I developed a temperature–energy synergistic thermal management system for an EV battery pack. The work can be summarized in the following points:
– I established a theoretical model of the battery thermal system, including the heat generation mechanism, the heat transfer paths, and the vehicle-level powertrain dynamics.
– I built a high-fidelity AMESim simulation model and calibrated the key parameters using experiments on a lithium iron phosphate cell. The battery temperature simulation error was below 3 °C, and the heat exchanger model errors were below 5%.
– I applied the optimal Latin hypercube sampling method and ANOVA to identify the most significant control variables. The compressor speed and the pump speed have the strongest influence on both temperature and energy, while the fan speed is an auxiliary factor.
– I designed a hierarchical control structure with three different strategies. For low ambient temperatures, PID control of the PTC heater reduced the energy consumption by 10.37% compared to threshold control. For normal temperatures, NMPC coordinated the pump and fan, reducing energy consumption by 14.15% compared to threshold control and 11.32% compared to PID control. For high temperatures, GWO-NMPC controlled the compressor and pump, achieving energy reductions of 51.31% and 12.62% compared to threshold and PID control, respectively.
The overall contribution of this work is a systematic methodology for designing and validating a temperature–energy coordinated BTMS for an EV battery pack. The findings demonstrate that advanced model predictive control can substantially improve the energy efficiency without sacrificing battery temperature control quality. In future work, I plan to extend the control strategy to consider battery degradation, integrate the thermal management system with the cabin air-conditioning system, and test the proposed algorithm in a hardware-in-the-loop environment. Additionally, I intend to explore data-driven model reductions to enable real-time implementation on embedded controllers.