1 Introduction
As the use of fossil fuels in traditional automobiles is decreasing year by year, and the environmental pollution caused by vehicle exhaust emissions has not been effectively improved, the development of new energy vehicles is rapid. Among them, hydrogen fuel cell vehicles have received widespread attention due to their advantages such as high efficiency and cleanliness. Proton exchange membrane fuel cells (PEMFCs) have advantages such as high energy conversion efficiency, low-temperature operation, high reliability, and zero emissions, and have broad application prospects in the automotive field.
The operating temperature of the fuel cell stack is one of the key factors affecting its output performance and lifespan. On the one hand, excessively high temperatures will lead to increased liquid water evaporation, causing dehydration of the proton exchange membrane and affecting fuel cell performance; on the other hand, excessively low temperatures will reduce liquid water evaporation, slowing down the chemical reaction rate and degrading fuel cell performance. Generally, the normal operating range of a fuel cell stack is 60–100 °C, but PEMFCs generate a large amount of heat during operation, thus requiring effective thermal management.
Currently, the main control methods for PEMFC thermal management include PI (Proportion Integration) control, state feedback control, predictive control, and fuzzy control. O'Keefe et al. designed a PI controller to control the temperature of a water-cooled fuel cell. This controller regulates the operating temperature of the fuel cell stack by adjusting the water flow rate entering the stack. PI control is simple in principle and easy to use, and traditional PI control is widely used in PEMFC thermal management. However, PI control has drawbacks such as slow response speed and long settling time. In addition, state feedback control and predictive control methods have also been applied to PEMFC thermal management, but the inherent nonlinear characteristics of fuel cells and the uncertainty of parameters make their application challenging. Fuzzy control has a fast response speed and strong anti-interference ability, and is particularly suitable for controlling systems with lag, and has been applied by many scholars to PEMFC thermal management. Wang et al. designed a fuzzy control method to control the stack temperature by adjusting the fan speed. Comparison with PI control shows that fuzzy control has superior performance. Hu Peng et al. considered overcoming interference from external loads and adopted a fuzzy controller with integral to adjust the cooling water flow in real time. The results showed that this method could control the temperature of the fuel cell stack within a reasonable range in real time. However, the design of the fuzzy control mainly relies on expert experience. Therefore, to fully utilize the advantages of fuzzy control, it is necessary to optimize the fuzzy control method to achieve higher accuracy.
Furthermore, to verify the effectiveness of PEMFC thermal management methods, most current literature uses a step load signal approach. However, hydrogen fuel cell vehicles experience acceleration, constant speed, and deceleration during actual driving, resulting in more frequent and complex changes in operating conditions. Therefore, a load suitable for hydrogen fuel cell vehicles is needed to verify the PEMFC thermal management method.
This paper proposes a fuzzy control method for PEMFC thermal management to stabilize the inlet and outlet temperatures of the fuel cell stack at target values. Simultaneously, aiming to minimize the error between the inlet and outlet temperatures and the target temperatures, and to shorten the response time of the control system, the membership function of the fuzzy controller is optimized using a genetic algorithm. While the genetic algorithm-based optimization of fuzzy control has been applied in other fields, its application in PEMFC thermal management is still rare. This paper selects a hydrogen fuel cell hybrid vehicle from Autonomous and designs a rule-based energy management strategy. Two standard operating conditions are used as verification conditions for the proposed thermal management method to validate it, and its performance is compared with that of the unoptimized fuzzy control. The results show that in controlling the inlet and outlet temperatures of the PEMFC fuel cell stack, the optimized fuzzy control is significantly superior to the unoptimized fuzzy control, exhibiting better temperature regulation capability, better reduction of external load disturbances, and smaller deviation from the setpoint.
2 PEMFC Thermal Management System Model
The PEMFC thermal management system model designed in this paper includes a dynamic temperature model of the fuel cell stack, a water tank model, and a radiator model. During the operation of a hydrogen fuel cell vehicle, the PEMFC generates a significant amount of heat while providing power. To maintain the stack's operating temperature within a reasonable range, the cooling water pump and radiator work together to remove excess heat. In this PEMFC thermal management system, the heat generated by the stack is first carried to the water tank by the cooling water pump through controlled cooling water flow, and then to the radiator. The radiator then dissipates the heat into the air by controlling its airflow, as shown in Figure 1. This paper assumes that the temperature in the cooling water is uniform, and uses the cooling water temperature at the stack outlet as the stack outlet temperature, and the radiator outlet temperature as the stack inlet temperature. Furthermore, this paper assumes that other auxiliary systems are operating normally and do not affect the stack's operating temperature.
2.1 Dynamic Temperature Model of the Fuel Cell Stack
Hydrogen fuel cell vehicles require a large amount of power from the PEMFC during operation. As power is generated, the temperature of the stack also changes. Based on the law of conservation of energy, a dynamic temperature model of the PEMFC stack is established. Its energy includes the total electrochemical reaction power Qreact, the electrical power consumed by the load Pst, the heat power Qin/Qout carried in/out by the anode and cathode gases, the heat power Qcl carried away by the cooling water, and the heat power Qamb radiated outward from the stack, as shown in formula (1):
Where mst is the mass of the fuel cell stack; Cst is the specific heat capacity of the fuel cell stack; and Tst is the outlet temperature of the fuel cell stack cooling water, which is often regarded as the fuel cell stack temperature in engineering.
The total power of the electrochemical reaction is expressed as:
(2)
Where n is the number of battery cells; F is the Faraday constant; is the enthalpy change of the reaction; and Ist is the output current of the battery stack.
Figure 1 Schematic diagram of thermal management system
In a PEMFC (Polymerized Electric Magnetic Reactor) reactor, gas flows in and out of the reactor stack during the reaction process. The heat carried away by the gas is equal to the heat of the gas venting from the stack minus the heat of the gas entering the stack. Based on the heat balance formula and the equation of state for gases under ideal conditions, the heat of the gas entering the stack can be expressed as:
(3)
Where, is the anode hydrogen inlet flow rate; CH is the specific heat capacity of hydrogen; is the anode water vapor flow rate; CHO is the specific heat capacity of water vapor; is the anode gas inlet temperature; is the cathode air inlet flow rate; Cair is the specific heat capacity of air; is the cathode inlet water vapor flow rate; is the cathode inlet temperature; T0 is the ambient temperature.
According to the heat balance formula, the heat of the gas at the fuel cell outlet can be expressed as:
(4)
Wherein, is the anode outlet gas flow rate; is the anode gas outlet temperature; is the anode outlet water vapor flow rate; is the cathode oxygen outlet flow rate; is the cathode nitrogen outlet flow rate; CN is the nitrogen specific heat capacity; is the cathode outlet water vapor flow rate; is the cathode water outlet flow rate; is the cathode water outlet flow rate; is the specific heat capacity of liquid water; and is the cathode gas outlet temperature.
The electrical power consumed by the load is equal to the product of the stack output voltage Vst and the current Ist.
Specifically, as shown in formula (5):
Figure 2. Polarization curves of fuel cells
This paper uses the fuel cell stack model in Autonomous to predict the output voltage and output power of a single cell. During power generation, a single cell inevitably incurs losses, namely activation loss, ohmic loss, and concentration loss. The actual output voltage of a PEMFC is equal to the thermodynamic electromotive force minus these three losses. The polarization curve of the fuel cell is shown in Figure 2.
The heat Qcl carried away by the cooling water is shown in formula (6):
(6)
Where Wcl is the cooling water flow rate; Ccl is the specific heat capacity of the cooling water; and Tst.in is the inlet temperature of the fuel cell stack cooling water.
The heat dissipation Qamb from the fuel cell stack is shown in formula (7):
(7)
Where k is the heat transfer coefficient; Ast is the surface area of the PEMFC.
2.2 Water Tank Model
The water tank in the PEMFC thermal management system is a device for storing cooling water and also reduces the water pressure in the entire cooling water circulation system, preventing excessive water pressure from damaging the thermal management system. This paper assumes that the inlet cooling water temperature of the water tank is approximately equal to the outlet cooling water temperature Tst of the fuel cell stack. The outlet cooling water temperature of the water tank is TW.out. Assuming that the water mixes quickly, the water tank model is as shown in formula (8):
(8)
Where mW is the mass of the water tank; CW is the specific heat capacity of the water tank; CPcl is the specific heat capacity of the cooling water; and hW is the natural thermal conductivity coefficient of the water tank.
2.3 Heatsink Model
The radiator is an important component in the thermal management system, which can reduce the temperature of the water flow through heat exchange with the air. This paper assumes that the water tank outlet temperature TW.out is approximately equal to the temperature entering the radiator, and considers the radiator outlet temperature as the fuel cell inlet temperature Tst.in. The radiator model is shown in formula (9):
(9)
Where Wa is the air mass flow rate; CPa is the specific heat capacity of air; and Tr.a is the air temperature at the radiator outlet, which is considered as the average of the cooling water temperatures at the radiator inlet and outlet.
3. Design of PEMFC thermal management control method
3.1 Design of Fuzzy Control Method
This paper establishes two Mandani-type two-dimensional fuzzy controllers to control the inlet and outlet temperatures of the fuel cell stack. For the control of the fuel cell stack outlet temperature, based on the fuel cell stack selected in this paper...
Figure 4. Block diagram of the fuzzy controller based on genetic algorithm
Table 1. Fuzzy control rules for cooling water flow rate and radiator air volume (W/W)
The target outlet temperature Tref.st of the fuel cell stack is set to 80 ℃. The error between the actual outlet temperature and the target temperature, as well as the rate of change of the temperature error, are used as the inputs to the fuzzy controller, and the cooling water flow rate is used as the output. For the fuel cell stack inlet temperature control, the target inlet temperature Tref.st.in is set to 75 ℃. The error between the actual inlet temperature and the target temperature, as well as the rate of change of the temperature error, are used as the inputs to the fuzzy controller, and the radiator airflow is used as the output. The overall fuzzy control schematic diagram is shown in Figure 3.
When controlling the fuel cell stack outlet temperature, the input and output quantities of the fuzzy control are divided into five fuzzy subsets: NB (negative large), NS (negative small), ZO (zero), PS (positive small), and PB (positive large). The fuzzy universe of discourse for the fuel cell stack outlet temperature error and the rate of change of temperature error is selected as [-3, 3], and the fuzzy universe of discourse for the cooling water flow rate is selected as [0, 1]. Similarly, when designing the fuel cell stack inlet temperature controller, the fuzzy universe of discourse for the fuel cell stack inlet temperature error and the rate of change of temperature error is selected as [-3, 3], and the fuzzy universe of discourse for the radiator airflow is selected as [0, 1].
This paper proposes using a genetic algorithm to optimize the membership function of the fuzzy controller, as shown in Figure 4. The unoptimized membership function uses a uniformly distributed membership function with a triangular shape, as shown in Figure 5. This paper designs a fuzzy inference system using ifthen fuzzy control rules, formulating 25 fuzzy rules for each controlled variable. Table 1 shows the control rules for the fuel cell stack inlet/outlet controller. After fuzzy inference, defuzzification is performed using a weighted average method.
3.2 Optimization based on genetic algorithm
This paper proposes using a genetic algorithm to optimize the center and width of the membership function of a fuzzy controller, thereby improving the accuracy and stability of the fuzzy controller.
3.2.1 Genetic Encoding
This paper aims to optimize the membership function. First, the parameters to be optimized are determined, and the membership function is encoded, as shown in Figure 5. There are 33 input and output parameters to be optimized, encoded using real numbers, hence the corresponding encoding is {x1 x2 x3 x4 … x33}. The membership function of the fuel cell stack inlet fuzzy controller in this paper is consistent with that of the unoptimized fuel cell stack outlet fuzzy controller; therefore, the genetic algorithm optimization process is only introduced for the fuzzy controller at the fuel cell stack outlet.
3.2.2 Selecting the fitness function
Fitness is a measure of the quality of individuals in a population, and its performance directly affects the overall performance of the genetic algorithm. The ITAE (Integral Time-Weighted Absolute Error) performance index has advantages such as fast response speed and short adjustment time. This paper selects the ITAE performance index as the fitness function to adjust the parameters of the fuzzy controller, as shown in formula (10):
(10)
Where t is time; Tref is the reference target temperature; and Tst is the stack temperature.
3.2.3 Individual selection, crossover, and variation
Figure 5. Input and output membership functions and parameters to be optimized.
Table 2 Vehicle and Powertrain Parameters
(1) Selection operation. Using the roulette wheel selection method, i.e., a selection strategy based on fitness ratios, the probability of individual i being selected is:
(11)
Where Fi and Fj are the fitness values of individuals i and j, respectively; N is the number of individuals in the population.
(2) Crossover operation. Since individuals are encoded using real numbers, the crossover operation uses the real number crossover method. The method for crossing over the k-th chromosome ck and the i-th chromosome ci at position j is as follows:
(12)
Where b is a random number in the range [0, 1].
(3) Mutation operation. The method for mutagenesis of the j-th gene cij of the i-th individual is as follows:
(13)
Where cmax is the upper bound of gene cij; cmin is the lower bound of gene cij; r2 is a random number; b is the current iteration number; Gmax is the maximum number of evolutions; and r is a random number in [0, 1].
4 Simulation Results
To verify the effectiveness of the proposed PEMFC thermal management control method, a hydrogen fuel cell hybrid electric vehicle was selected. A simple energy management strategy was designed for the hybrid system of fuel cell and battery. Based on the content of Sections 2 and 3, the proposed method was simulated in a computer simulation environment.
4.1 Simulation Conditions
4.1.1 Hydrogen fuel cell vehicles and driving conditions
To make the simulation results more closely resemble the operating state of the fuel cell in a hydrogen fuel cell vehicle during operation, this paper selects a hydrogen fuel cell vehicle from the Autonomous software, where the fuel cell serves as the primary power source and the battery as the auxiliary power source. Table 2 shows the vehicle and powertrain parameters. This paper uses two operating cycles: WLTC (The Worldwide Harmonized Light Vehicles Test Cycles) and HWFET (Highway Fuel Economy Test). The WLTC cycle is part of the globally unified light vehicle test cycle, replacing the NEDC (New European Driving Cycle) test cycle, and includes four speed ranges. Figure 6 shows the two cycle periods and the relationship between speed and time.
Figure 6. WLTC and HWFET speed curves
Figure 7. Fuel cell efficiency curves and fuel cell operating efficiency points under two operating conditions.
4.1.2 Energy Management Strategy
Hydrogen fuel cell vehicles have two power sources: a fuel cell and a battery. This paper designs a rule-based energy management strategy with the goal of maximizing the fuel cell's efficiency. The fuel cell efficiency curve shows that the fuel cell operates optimally in both high-power and low-power driving conditions:
(1) When the vehicle power demand is 0 < Pdem < PFCmin, the battery efficiency is low, as shown in Figure 7. Based on the fuel cell efficiency curve, the fuel cell operating threshold is determined, and the minimum fuel cell power PFCmin, the maximum fuel cell power PFCmax, and the fuel cell output power PC corresponding to the low fuel cell efficiency are introduced, along with the vehicle power demand Pdem. At the same time, in order to keep the battery SOC operating in a reasonable range, based on the battery characteristics, battery charge and discharge thresholds are introduced, namely the upper limit SOC (SOCmax) and the lower limit SOC (SOCmin).
Under energy recovery conditions:
(1) When the vehicle's power demand Pdem ≤ 0, the vehicle is in a braking or stopped state. If the battery SOC > SOCmax, energy will no longer be recovered, corresponding to the charging protection mode.
(2) When the vehicle power demand Pdem ≤ 0, if the battery SOC ≤ SOCmax, in order to maintain the life and efficiency of PEMFC, the fuel cell operates in the minimum power mode, and the lithium battery will recover energy, corresponding to the lithium battery recovery mode.
Under driving conditions:
(1) When the vehicle's power demand is 0 < Pdem < PFCmin, if the battery SOC ≥ SOCmax, the vehicle's power demand will be entirely provided by the fuel cell, corresponding to the power follower mode. If the battery SOC < SOCmax, the fuel cell will operate at a constant power of PFCmin, corresponding to the minimum power mode.
(2) When the vehicle's power demand is PFCmin ≤ Pdem < PC, if the battery SOC ≤ SOCmin, the fuel cell must not only meet the load power requirement but also charge the battery, corresponding to the fast charging mode. If the battery SOC > SOCmin, the battery will no longer be charged, corresponding to the power follower mode.
(3) When the vehicle's power demand is PC ≤ Pdem < PFCmax, if the battery SOC ≤ SOCmin, the fuel cell will provide all the power, corresponding to the power follower mode. If the battery SOC > SOCmin, the fuel cell's efficiency reaches near the threshold due to the high vehicle power demand. At this point, the efficiency drops rapidly, and the vehicle's power demand will be shared by the battery and the fuel cell. The fuel cell will operate at a constant power PC, corresponding to the constant power mode.
(4) When the vehicle's power demand Pdem > PFCmax, in order to protect the fuel cell, the output power of the fuel cell is PFCmax, and the remaining power demand is provided by the battery, which corresponds to the maximum power mode.
In the rule-based energy management strategy formulation presented in this paper, the test conditions determine the values of the logic threshold parameters. Simultaneously, they determine the power allocation between the fuel cell and the battery. Figure 8 shows the schematic diagram of the rule-based energy management strategy.
Figure 8. Rule-based energy management strategy
4.2 Results Analysis
4.2.1 PEMFC Output Power Results
Figure 7 shows the fuel cell operating efficiency points and fuel cell curves under two operating conditions.
Figure 9 shows the power output results of the energy management strategies under HWFET and WLTC operating conditions. As can be seen from Figures 7 and 9, the power required by the vehicle is provided by both the battery and the fuel cell, with the PEMFC providing the main operating power, while the fuel cell's efficiency point remains in the high-efficiency range.
Figure 9 Power Output Curve
4.2.2 Membership Function Optimization Results
The WLTC (Worldwide Transmission Test) cycle is currently the most widely used and realistic driving cycle for vehicles. This paper selects this cycle and uses a genetic algorithm to optimize the fuzzy controllers applied at the fuel cell stack inlet and outlet. The population size and generation number of the genetic algorithm are set to 100, with a crossover rate of 0.9 and a mutation rate of 0.1. Figure 10 shows the optimized membership function of the fuzzy controllers at the fuel cell stack inlet and outlet.
Figure 10 Optimized membership function
4.2.3 Results of fuel cell stack inlet and outlet temperature control
Figure 11 shows the inlet and outlet temperature curves of the fuel cell stack under HWFET and WLTC operating conditions. It can be seen that under genetic fuzzy control, the difference between the outlet and inlet temperatures remains at around 5 ℃, and the errors between the inlet and outlet temperatures and the set target temperatures are both within -1 to 1 ℃.
As shown in Table 3, the maximum deviations of the fuel cell stack inlet and outlet temperatures all decreased after optimization of fuzzy control. Compared to fuzzy control, the fuzzy controller optimized by the genetic algorithm has a faster response speed and smaller error.
Figure 11 Inlet and outlet temperature curves under two operating conditions
Table 3 Thermal management parameters under two operating conditions
Figure 12 shows the heat removed by the cooling water under two operating conditions. As the load increases, the fuel cell generates more heat. Therefore, to ensure the stack operates in a stable and safe temperature environment, both the cooling water flow rate and the radiator airflow will increase with the load, resulting in a greater amount of heat removed by the cooling water. Conversely, when the load decreases, both the cooling water flow rate and the radiator airflow decrease, and the amount of heat removed by the cooling water also decreases accordingly, as shown in Figures 12 and 13. Considering that the cooling water pump cannot be frequently started and stopped in practical applications, a minimum water flow rate will be set for both operating conditions.
Figure 12. Heat removed by cooling water under two operating conditions
Figure 13 Cooling water flow rate and radiator air volume under two operating conditions
4. Discussion and Analysis
Changes in fuel cell stack temperature affect the output performance and safety of hydrogen fuel cell vehicles, thus requiring appropriate thermal management methods to maintain the stack temperature at a reasonable operating temperature. In this paper, fuel cells exhibit nonlinearity and parameter uncertainty, and stack temperature changes are lag-dependent. This paper proposes using fuzzy control to control the stack inlet and outlet temperatures. However, fuzzy control design relies heavily on expert experience; therefore, this paper further proposes applying a genetic algorithm to optimize the membership function of the fuzzy controller. Currently, the method of using genetic algorithms to optimize fuzzy control is relatively mature and has been applied to other fields; this paper applies this method to PEMFC thermal management. By using genetic algorithm-optimized fuzzy control, under HWFET conditions, compared to unoptimized fuzzy control, the maximum deviations between the stack inlet and outlet temperatures and the target temperature were reduced by 0.9 ℃ and 1.1 ℃, respectively. Under WLTC conditions, compared to unoptimized fuzzy control, the maximum deviations between the stack inlet and outlet temperatures and the target temperature were reduced by 1.28 ℃ and 1.23 ℃, respectively.
Currently, the workload for verifying thermal management methods typically uses a step load signal.
However, vehicle operating conditions change frequently, requiring corresponding adjustments to the workload of the PEMFC. To address this issue, this paper proposes a new load model: selecting a vehicle from Autonomous and conducting energy management under two different road conditions to determine the required workload of the PEMFC. This workload is then used as the verification workload for the thermal management method.
The limitation of this paper is that, although the control model is simplified, the process of the fuel cell stack temperature rising from room temperature to the target temperature is neglected. Furthermore, the PEMFC thermal management model established in this paper is relatively simple; a bypass valve could be added in the next step, and large and small circulation loops could be set up to make the model more complete. When the fuel cell stack temperature is relatively low, the small circulation loop is activated to heat the cooling water, and the temperature of the cooling water entering the fuel cell stack is controlled by the bypass valve, thereby rapidly raising the fuel cell stack temperature to a reasonable operating temperature. When the fuel cell stack temperature exceeds the target temperature, the large circulation loop is activated to cool the fuel cell stack.
5. Conclusion
This paper proposes a fuzzy control method for controlling the inlet and outlet temperatures of a fuel cell hybrid electric vehicle (PEMFC) stack, focusing on thermal management. To improve the temperature adjustment capability of the stack, a genetic algorithm is used to optimize the fuzzy controller. To verify the proposed control method, a fuel cell hybrid electric vehicle (FCEV) was selected, and an energy management strategy was designed to operate the PEMFC in its high-efficiency region. The proposed thermal management method was validated under both HWFET and WLTC standard operating conditions. Results show that the fuzzy control method optimized by the genetic algorithm exhibits better performance when the workload changes continuously. The temperature difference between the stack outlet and inlet is maintained at approximately 5 °C, and the errors between the inlet and outlet temperatures and the target temperature are both within -1 to 1 °C. Furthermore, compared to the unoptimized fuzzy control, the errors between the stack inlet and outlet temperatures and the target temperature are reduced. The proposed method demonstrates stronger responsiveness to the stack inlet and outlet temperatures under both test conditions, effectively correcting dynamic temperature errors and improving the control accuracy of the thermal management method.
author:
Zhao Zhenrui 1,2 Ouyang Huiying 2,3 Tian Guofu 1 Zheng Chunhua 2
1. School of Mechanical Engineering, Shenyang University of Technology
2 Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences
3. This article from the School of Engineering at Southern University of Science and Technology is reprinted from "Integrated Technology".
