Temperature control method for fuel cell automobile in summer high-temperature environment

Abstract

The invention discloses a temperature control method for a fuel cell vehicle in a summer high-temperature environment, and belongs to the technical field of fuel cell vehicle control. According to the temperature control method for the fuel cell automobile in the summer high-temperature environment, a thermal coupling model is established, a Pontryagin minimum value principle controller is designed, and the temperature is controlled. The method comprises the following steps: building a control model for fuel cell and cabin thermal management, designing a Pontryagin minimum principle controller, solving a proper costate variable initial value by using a Nelder-Mead algorithm, and further solving an optimal control sequence. When the controller is designed, the influence of the air-conditioning system can be considered, the air-conditioning system and the fuel cell are controlled at the same time, and the method is more practical.

Description

Technical Field

[0001] The invention belongs to the technical field of fuel cell vehicle control. Background Art

[0002] Fossil energy will produce a large amount of carbon dioxide and other harmful gases during use, which will aggravate the greenhouse effect and the degree of environmental pollution. Therefore, it is urgent to find a suitable clean energy to replace fossil energy. Fuel cells are an extremely clean energy. Fuel cells convert the chemical energy of hydrogen and oxygen into electrical energy. The product of this reaction is water, which is extremely environmentally friendly. Therefore, fuel cell vehicles will be the focus of future research.

[0003] There are many factors that affect the performance of fuel cell vehicles, and the temperature of the fuel cell is an extremely critical point. In a high temperature environment, when the heat generated cannot be discharged in time, the temperature of the fuel cell will exceed the normal operating range. When the temperature of the fuel cell is too high, the proton exchange membrane in the fuel cell will become dry or even fall off, eventually causing a safety accident. Therefore, the temperature control of the fuel cell is a very important thing. In fuel cell vehicles, there is thermal coupling between the fuel cell cooling system and the cabin cooling system, so the influence of the cabin must be considered when controlling the temperature of the fuel cell. The thermal management system of a fuel cell vehicle is a complex system with high coupling nonlinearity. The currently commonly used proportional integral differential (PID) controller and rule-based controller are difficult to achieve good control effects.

[0004] In summary, the control of fuel cell thermal management system mainly has the following problems: 1. There is thermal coupling between the fuel cell's thermal management system and the air conditioning system. The impact of the cabin on the fuel cell temperature must be considered when designing the controller. 2. The existing fuel cell temperature integrated control strategies all use PID and rule-based controllers, which makes it difficult to achieve good control effects.

[0005] There is thermal coupling between the condenser of the air conditioning system and the radiator of the fuel cell cooling system. The condenser transfers the heat in the cabin to the outside, so the air temperature passing through the condenser will be higher than the ambient temperature. The heated air passes through the radiator of the fuel cell cooling system, which affects the heat dissipation of the fuel cell. The currently used PID controller and rule-based controller are difficult to solve this complex and coupled temperature control problem. Summary of the invention

[0006] The purpose of the present invention is to establish a thermal coupling model and design a Pontryagin minimum principle controller to control the temperature of a fuel cell vehicle in a high temperature environment in summer.

[0007] The steps of the present invention are: S1. Build the control model of fuel cell and cabin thermal management: Q cl =W cl C cl (T fc -T fcin ) (2) in is the derivative of the fuel cell temperature, Q tot is the total energy generated by the fuel cell, P fc is the electrical energy output by the fuel cell, Q cl is the energy taken away by the coolant, T fcin is the fuel cell inlet coolant temperature, W cl is the coolant flow rate, C cl is the heat capacity of the coolant, m fc is the mass of the fuel cell, C fc is the heat capacity of the fuel cell; The temperature of the coolant at the fuel cell inlet: in is the derivative of the coolant temperature at the fuel cell inlet, W air is the air flow at the radiator, C air is the specific heat capacity of air, T atm is the ambient temperature, is the air temperature at the radiator output, m s is the mass of the radiator, C s is the heat capacity of the radiator; Thermal model of the cabin of a fuel cell vehicle: in is the derivative of the car cabin temperature, Q sol is the radiant energy of the sun through the car window glass, Q car is the heat exchange between the vehicle body and the air in the cabin, Q pas It is the heat dissipation of passengers and drivers, Q ele is the heat dissipation of the electronic components in the cockpit, Q eva is the heat removed by the refrigerant, m air is the quality of the air in the cabin; The heat removed by the evaporator is as follows: Q eva =a oe A oe (T we -Tcab ) (5) where a oe is the heat transfer coefficient of the radiator outer surface, A oe is the external surface area of ​​the heat sink, T we is the temperature of the radiator wall; Evaporator temperature: Where m e is the mass of the evaporator, c e is the heat capacity of the evaporator, a ie is the heat exchange coefficient inside the evaporator, D ie is the diameter of the pipe inside the evaporator, l e is the length of the two-phase state of the refrigerant in the evaporator, T re is the critical temperature of the refrigerant at that pressure; S2. Design the Pontryagin minimum principle controller objective function as follows: Where L1, L2, L3 are temperature weight parameters, T fc * is the ideal temperature of the fuel cell, T fcin * is the ideal temperature of the fuel cell inlet coolant, T cab * It is the ideal temperature for the car cabin; The constructed Hamiltonian function: Where H(x(t),u(t),λ(t),t) is the Hamiltonian function, λ1,λ2,λ3 are the corresponding covariates; Co-variables should satisfy the following conditions: λ1(t f )=0 λ2(t f )=0 λ3(t f )=0 (9) where t f It’s the final moment; The optimal control variable sequence is: H(x * (t),u * (t),λ * (t),t)≤H(x * (t),u(t),λ * (t),t) (10) where x* (t) is the optimal state quantity at time t, u * (t) is the optimal control quantity at time t, λ * (t) is the optimal covariate variable at time t, H(x * (t),u * (t),λ * (t), t) is the Hamiltonian function value where the state, control and co-state variables are all optimal at time t. * (t),u(t),λ * (t), t) is the Hamiltonian function value of the optimal state value, optimal co-state variable value and control variable value at time t; The process of obtaining the initial value of the co-state variable: 1) Initial value setting: Select the sum of the absolute values ​​of the co-state variables as the objective function of the Nelder-Mead algorithm, select four groups of numbers as the four initial values ​​of the co-state variables, calculate the value of the objective function under the four initial values, and reduce them in order of size, recorded as l from small to large min ,l1,l2,l max ; Sort the four groups of initial values ​​according to the size of their corresponding objective functions, and record them as a1, a2, a3, a4 from small to large; 2) The average value of the initial value a o : Calculate the reflection point: a r =a o +α(a o -a1) (12) Where α is the reflection point coefficient; 3) Take the reflection point as the initial value of the co-state variable, denoted as a r , calculate the final value of the objective function, denoted as l new ; Compare the obtained objective function value with the value of the objective function in step 1); 4) If the objective function value in step 3) is l new Greater than or equal to the maximum value l of the objective function in step 1) max , then calculate the contraction point, denoted as a s ; Taking the contraction point as the initial value of the co-state variable, the final objective function value is calculated and recorded as l s ; will l s and l max Compare the size. If l s Less than l max , with the contraction point a s Replace a4 with l s Instead of l max; a1,a2,a3,a s Sort them according to the size of their corresponding objective functions, and re-record them as a1, a2, a3, a4 from small to large. At the same time, sort the recombined objective functions by size; return to step 2) and start the cycle again; the calculation formula of the contraction point is as follows: a s =a o +δ(a4-a o ) (13) Where δ is the contraction point coefficient; If l s Greater than or equal to l max , all initial values ​​except the initial value corresponding to the minimum objective function must be recalculated to obtain a new initial value sequence; the new sequence is used as the initial value of the co-state variable, the corresponding objective function is calculated, and it is sorted according to the value of the objective function. The initial value sequence is a1, a2, a3, a4 from small to large, and the objective function is l from small to large. min ,l1,l2,l max ; Return to step 2) and restart the cycle; the formula for recalculating the initial value is as follows: b2=a1+δ(a2-a1) b3=a1+δ(a3-a1) b4=a1+δ(a4-a1) (14) Among them, b2, b3, b4 are the newly obtained initial value sequences; 5) If l in step 3) new Less than the minimum value l of the objective function in step 1) min , calculate the expansion point, denoted as a e ; Taking the expansion point as the initial value of the co-state variable, the corresponding objective function is calculated and recorded as l e ; The obtained l e and l in step 3) new If l e Less than l new , use a e Replace a1; if l e Greater than or equal to l new , use a r Replace a1; then sort according to the size of the corresponding objective function, and the initial value sequence is recorded as a1, a2, a3, a4 from small to large; return to step 2) and start the cycle again; the calculation formula of the expansion point is as follows: a e =a o +γ(a r -a o ) (15) Where γ is the expansion point coefficient; 6) If l in step 3) new The size of l in step 1) min and l max When between, use a r Replace a1, get a new initial value sequence, and sort it according to the size of its corresponding objective function, and record it as a1, a2, a3, a4 from small to large; return to step 2) and start the cycle again; 7) After the cycle is completed, the optimal control sequence and the corresponding initial values ​​of the co-state variables are obtained.

[0008] The present invention takes into account the coupling between temperatures, and controls the fuel cell temperature, the coolant temperature at the fuel cell inlet, and the cabin temperature at the same time, and has a good control effect. The present invention can take into account the influence of the air conditioning system when designing the controller, and control the air conditioning system and the fuel cell at the same time, which is more practical. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Figure 1 It is the thermal coupling diagram of the fuel cell thermal management system and the air-conditioning cabin thermal management system; Figure 2 It is the algorithm flow chart; Figure 3 This is the operating current diagram of the fuel cell under NEDC conditions; Figure 4 This is the driving speed diagram of a fuel cell vehicle under NEDC conditions; Figure 5 is the fuel cell temperature map; Figure 6 is the coolant temperature diagram at the fuel cell inlet; Figure 7 It is a map of cabin air temperature. DETAILED DESCRIPTION

[0010] The present invention designs a temperature control strategy to solve the two existing problems. The present invention takes into account the thermal coupling between the fuel cell and the cabin, establishes a temperature model of the fuel cell and the cabin, and designs a Pontryagin minimum principle controller based on the temperature model.

[0011] Fuel cell vehicles discharge the heat in the cabin to the outside through the evaporator and condenser of the air conditioning system. In this process, the temperature of the air around the condenser will rise, and the heated air will pass through the radiator of the fuel cell cooling system, thereby affecting the temperature control of the fuel cell. The present invention establishes a thermal coupling model and designs a Pontryagin minimum principle controller to control the temperature.

[0012] The technical solution of the present invention is as follows: 1. A simulation model of the fuel cell and cabin is established in the commercial software AVL / Cruise M. The model mainly consists of two parts: the fuel cell cooling system and the cabin air conditioning system.

[0013] 2. Establish the control model of fuel cell and cabin in Matlab / Simulink. The fuel cell temperature model has four inputs, namely the coolant flow, the air flow at the radiator, the fuel cell operating current and the air temperature at the radiator; and two outputs, namely the fuel cell temperature and the coolant temperature at the fuel cell inlet. The cabin temperature model has four inputs, namely the vehicle's driving speed, the refrigerant flow, the air flow at the condenser and the air flow at the evaporator; and two outputs, namely the air temperature in the cabin and the air temperature at the output of the condenser.

[0014] 3. Design the Pontryagin minimum principle controller based on the established model. The optimization problem can be described as follows: xT k+1 =h(X k ,U k ) U k ∈U Where J is the objective function, U k is the control variable of the system, U is the control constraint, X k is the state variable of the system, f(X k ) is the temperature control cost function, h(X k ,U k ) is the solution function of the control quantity, L is the weight coefficient, and N is the number of prediction steps.

[0015] 4. Export the Pontryagin minimum principle controller in Matlab / Simulink as a functional model unit (FMU) file, import it into the simulation model of AVL / Cruise M, and connect the ports of the controller and the model.

[0016] In fuel cell vehicles, the fuel cell cooling system does not exist independently. The temperature of the fuel cell will be affected by the air conditioning system. The condenser of the air conditioning system will affect the heat dissipation of the fuel cell. Under the interference of the condenser, the temperature of the fuel cell will be 5 to 10 degrees Celsius higher than without the condenser. Therefore, the impact of the air conditioning system on the fuel cell cannot be ignored. In addition, the condenser of the air conditioning system and the radiator of the fuel cell share a fan, so when the fan is controlled, it will affect both the fuel cell and the air conditioning system. This model takes these two points into account. When designing a controller based on this model, the impact of the air conditioning system can be taken into account, and the air conditioning system and the fuel cell can be controlled at the same time, which is more practical.

[0017] The fuel cell and cabin temperature optimization control of the present invention is described in detail below with reference to the accompanying drawings. The present invention designs an optimization controller for controlling the fuel cell and cabin temperature. Figure 1 This is a schematic diagram of the fuel cell and air-conditioning cabin thermal management system of a fuel cell vehicle. The thermal management system consists of two cooling cycles, namely the fuel cell cooling system and the cabin cooling system. The cooling pump is the power source of the fuel cell cooling system. Under the action of the cooling pump, the coolant is sent to the fuel cell, and the coolant and the fuel cell exchange heat, taking away the heat of the fuel cell, and the temperature of the coolant increases; under the action of the cooling pump, the coolant is sent to the radiator, and the coolant exchanges heat with the air at the radiator, dissipates the heat and thus reduces the temperature, and then returns to the fuel cell to cool the fuel cell. The power source of the cabin cooling system is the compressor. In the cabin cooling system, the evaporator is located in the cabin and the condenser is located outside the cabin. The refrigerant undergoes a phase change at the evaporator, from a low-temperature and low-pressure gas-liquid mixed state to a high-temperature and low-pressure gas state. In this process, the refrigerant absorbs heat, thereby cooling the cabin. The high-temperature and low-pressure gaseous refrigerant passes through the compressor and becomes a high-temperature and high-pressure gaseous refrigerant. The high-temperature and high-pressure gaseous refrigerant exchanges heat with the air at the condenser and becomes a high-pressure and low-temperature liquid refrigerant. The high-pressure and low-temperature liquid refrigerant passes through the expansion valve and becomes a low-temperature and low-pressure gas-liquid mixed refrigerant, and then reaches the evaporator to cool the cabin.

[0018] Figure 1 It is the structural diagram of the entire thermal management system. Figure 2 The algorithm flow of the present invention is as follows: 1. Build a fuel cell cabin temperature simulation model in a commercial software. The commercial software used in the present invention is AVL / CruiseM.

[0019] 2. Build a control model for fuel cell and cabin thermal management in Matlab / Simulink. The fuel cell temperature is mainly related to the fuel cell operating current and coolant flow rate, and the formula is as follows: Qcl =W cl C cl (T fc -T fcin ) (2) in is the derivative of the fuel cell temperature, Q tot is the total energy generated by the fuel cell, P fc is the electrical energy output by the fuel cell, Q cl is the energy taken away by the coolant, T fcin is the fuel cell inlet coolant temperature, W cl is the coolant flow rate, C cl is the heat capacity of the coolant, m fc is the mass of the fuel cell, C fc is the heat capacity of the fuel cell.

[0020] The temperature of the coolant at the fuel cell inlet is mainly related to the coolant flow rate and the air flow rate at the radiator. The formula is as follows: in is the derivative of the coolant temperature at the fuel cell inlet, W air is the air flow at the radiator, C air is the specific heat capacity of air, T atm is the ambient temperature, is the air temperature at the radiator output, m s is the mass of the radiator, C s is the heat capacity of the heat sink.

[0021] The thermal model of the cabin of a fuel cell vehicle is relatively complex because its energy comes from many sources. The cabin temperature is affected by solar radiation, environmental heat exchange, human body heat dissipation, and heat dissipation of electronic devices in the vehicle. The formula is as follows: in is the derivative of the car cabin temperature, Q sol is the radiant energy of the sun through the car window glass, Q car is the heat exchange between the vehicle body and the air in the cabin, Q pas It is the heat dissipation of passengers and drivers, Q ele is the heat dissipation of the electronic components in the cockpit, Q eva is the heat removed by the refrigerant, m air is the quality of the air in the cabin.

[0022] The air conditioning system exchanges heat with the air in the cabin through the evaporator. The refrigerant in the evaporator changes from a low-temperature gas-liquid mixture to a high-temperature gas state. In this process, a large amount of heat is absorbed, thereby reducing the temperature of the evaporator. The evaporator and the hot air in the cabin further exchange heat, reducing the temperature of the cabin. The heat taken away by the evaporator is as follows: Q eva =a oe A oe (T we -T cab )(5) where a oe is the heat transfer coefficient of the radiator outer surface, A oe is the external surface area of ​​the heat sink, T we is the temperature of the radiator wall.

[0023] The temperature of the evaporator is mainly affected by two parts: one is the heat exchange between the evaporator and the air in the cabin, and the other is the heat exchange between the refrigerant and the evaporator. In the evaporator, the heat exchange between the refrigerant and the evaporator mainly occurs in the two-phase region, that is, the region where the refrigerant is a gas-liquid mixture, so the formula is as follows: Where m e is the mass of the evaporator, c e is the heat capacity of the evaporator, a ie is the heat exchange coefficient inside the evaporator, D ie is the diameter of the pipe inside the evaporator, l e is the length of the two-phase state of the refrigerant in the evaporator, T re is the critical temperature of the refrigerant at this pressure.

[0024] 3. Design a Pontryagin minimum principle controller based on the control model of Matlab / Simulink. There are three control variables in the controller, namely the fuel cell coolant flow, the air flow at the radiator, and the refrigerant flow in the air conditioning system. The fuel cell temperature, the coolant temperature at the fuel cell inlet, and the cabin temperature are selected as state variables. The working current of the fuel cell and the driving speed of the car are interference variables. The objective function of the controller is as follows: Where L1, L2, L3 are temperature weight parameters, T fc * is the ideal temperature of the fuel cell, T fcin * is the ideal temperature of the fuel cell inlet coolant, T cab * It is the ideal temperature for the car cabin.

[0025] The constructed Hamiltonian function is as follows: where H(x(t),u(t),λ(t),t) is the Hamiltonian function and λ1,λ2,λ3 are the corresponding covariates.

[0026] Co-variables should satisfy the following conditions: λ1(t f )=0 λ2(t f )=0 λ3(t f )=0 (9) where t f is the final moment, the derivative of the costate variable is the negative partial derivative of the Hamiltonian function with respect to the corresponding state variable, and the value of the costate variable at the final moment must be 0.

[0027] The control problem of the present invention is to find the optimal control variable sequence to minimize the value of the objective function. The optimal problem is transformed into the problem of finding the extreme value of the Hamiltonian function, that is, to find the optimal control variable sequence to minimize the Hamiltonian function, as shown in the following formula: H(x * (t),u * (t),λ * (t),t)≤H(x * (t),u(t),λ * (t),t) (10) where x * (t) is the optimal state quantity at time t, u * (t) is the optimal control quantity at time t, λ * (t) is the optimal covariate variable at time t, H(x * (t),u * (t),λ * (t), t) is the Hamiltonian function value where the state, control and co-state variables are all optimal at time t. * (t),u(t),λ * (t), t) is the Hamiltonian function value of the optimal state value, optimal co-state variable value and control variable value at time t.

[0028] The optimal control sequence can be obtained by partial derivative of the Hamiltonian function on the control variable. The current problem is how to find the appropriate initial value of the co-state variable. The present invention uses the Nelder-Mead algorithm to find the appropriate initial value of the co-state variable, and then finds the optimal control sequence. The algorithm is an algorithm for finding the local minimum of a multivariate function. Its advantage is that it does not require the function to be differentiable and can converge to the local minimum quickly.

[0029] The workflow is as follows: 1) Initial value setting. Select the sum of the absolute values ​​of the co-state variables as the objective function of the Nelder-Mead algorithm, select four groups of numbers as the four initial values ​​of the co-state variables, calculate the value of the objective function under the four initial values, and reduce them in order of size, recorded as l from small to large. min ,l1,l2,l max . Sort the four groups of initial values ​​according to the size of their corresponding objective functions, and record them as a1, a2, a3, and a4 from small to large.

[0030] Establish a loop. When in the loop, calculate the mass points of the four sets of initial values, that is, the average value of the initial values, recorded as a o The calculation formula is as follows:

[0031] Calculate the reflection point using the following formula: a r =a o +α(a o -a1) (12) Where α is the reflection point coefficient.

[0031] 3) Take the reflection point as the initial value of the co-state variable, denoted as a r , calculate the final value of the objective function, denoted as l new . Compare the obtained objective function value with the value of the objective function in step 1).

[0032] If the objective function value in step 3) is l new Greater than or equal to the maximum value l of the objective function in step 1) max , then calculate the contraction point, denoted as a s Taking the contraction point as the initial value of the co-state variable, the final objective function value is calculated and recorded as l s . s and l max Compare the size. If l s Less than l max , with the contraction point a s Replace a4 with l s Instead of l max . s Sort them according to the size of their corresponding objective functions, and re-record them as a1, a2, a3, a4 from small to large. At the same time, sort the recombined objective functions by size. Return to step 2) and start the cycle again. The calculation formula of the contraction point is as follows: a s =a o +δ(a4-ao ) (13) where δ is the pinch point coefficient.

[0033] If l s Greater than or equal to l max , all initial values ​​except the initial value corresponding to the minimum objective function must be recalculated to obtain a new initial value sequence. The new sequence is used as the initial value of the covariate variable, the corresponding objective function is calculated, and it is sorted according to the value of the objective function. The initial value sequence is a1, a2, a3, a4 from small to large, and the objective function is l from small to large. min ,l1,l2,l max . Go back to step 2) and restart the cycle. The formula for recalculating the initial value is as follows: b2=a1+δ(a2-a1) b3=a1+δ(a3-a1) b4=a1+δ(a4-a1) (14) Among them, b2, b3, b4 are the newly obtained initial value sequences.

[0034] If l in step 3) new Less than the minimum value l of the objective function in step 1) min , calculate the expansion point, denoted as a e Taking the expansion point as the initial value of the co-state variable, the corresponding objective function is calculated and recorded as l e . The obtained l e and l in step 3) new If l e Less than l new , use a e Replace a1. If l e Greater than or equal to l new , use a r Replace a1. Then sort according to the size of the corresponding objective function, and the initial value sequence is recorded as a1, a2, a3, a4 from small to large. Return to step 2) and start the cycle again. The calculation formula of the expansion point is as follows: a e =a o +γ(a r -a o )(15) where γ is the expansion point coefficient.

[0035] If l in step 3) new The size of l in step 1) min and l max When between, use a rReplace a1, get a new initial value sequence, and sort it according to the size of its corresponding objective function, and record it as a1, a2, a3, a4 from small to large. Return to step 2) and start the cycle again.

[0036] After the loop is completed, the optimal control sequence and the corresponding initial values ​​of the co-state variables are obtained.

[0037] Export the designed Pontryagin minimum principle controller as an FMU file and import it into the software AVL / CruiseM. Connect the FMU controller module and the model port through the bus. Set the corresponding simulation step size and simulation time, and perform simulation verification.

[0038] Through the simulation results, the following conclusions can be drawn: Figure 3 and Figure 4 They are the fuel cell operating current and the driving speed of the fuel cell vehicle under NEDC conditions respectively. Figure 5 , Figure 6 and Figure 7 They are the temperature of the fuel cell, the temperature of the coolant at the inlet of the fuel cell, and the temperature of the car cabin under this working condition. In the controller of the present invention, the ideal temperature of the fuel cell is 65°C, the ideal temperature of the coolant at the inlet of the fuel cell is 55°C, and the ideal temperature of the car cabin is 25°C. Figure 5 It can be seen that the temperature of the fuel cell dropped rapidly from the initial 70°C to 65°C, and was then stably controlled at 65°C. Figure 6 The initial temperature of the coolant at the fuel cell inlet is 55°C, and there are large fluctuations in this temperature. The reason for this is that the temperature of the air passing through the condenser varies greatly, which will affect the heat dissipation at the radiator and thus affect the temperature of the coolant at the fuel cell inlet. Figure 7 It can be seen that the temperature of the car cabin drops from 40℃ to 25℃, and the cooling process is relatively stable.

[0039] In summary, the Pontryagin minimum principle controller in the present invention can achieve temperature control.

[0040] The innovation of the present invention is: 1. A fuel cell temperature model was established in the simulation software AVL / Cruise M and Matlab / Simulink. The model takes into account the impact of the air-conditioning cabin system on the fuel cell temperature and reflects the coupling relationship between the two.

[0041] 2. A Pontryagin minimum principle controller was designed. This controller takes into account the coupling between temperatures and simultaneously controls the fuel cell temperature, the coolant temperature at the fuel cell inlet, and the cabin temperature, and the control effect is good.

Claims

1. A temperature control method for a fuel cell vehicle in a high temperature environment in summer, characterized in that: S1. Build the control model of fuel cell and cabin thermal management: Q cl =W cl C cl (T fc -T fcin ) (2) in is the derivative of the fuel cell temperature, Q tot is the total energy generated by the fuel cell, P fc is the electrical energy output by the fuel cell, Q cl is the energy taken away by the coolant, T fcin is the fuel cell inlet coolant temperature, W cl is the coolant flow rate, C cl is the heat capacity of the coolant, m fc is the mass of the fuel cell, C fc is the heat capacity of the fuel cell; The temperature of the coolant at the fuel cell inlet: in is the derivative of the coolant temperature at the fuel cell inlet, W air is the air flow at the radiator, C air is the specific heat capacity of air, T atm is the ambient temperature, is the air temperature at the radiator output, m s is the mass of the radiator, C s is the heat capacity of the radiator; Thermal model of the cabin of a fuel cell vehicle: in is the derivative of the car cabin temperature, Q sol is the radiant energy of the sun through the car window glass, Q car is the heat exchange between the vehicle body and the air in the cabin, Q pas It is the heat dissipation of passengers and drivers, Q ele is the heat dissipation of the electronic components in the cockpit, Q eva is the heat removed by the refrigerant, m air is the quality of the air in the cabin; The heat removed by the evaporator is as follows: Q eva =a oe A oe (T we -T cab ) (5) where a oe is the heat transfer coefficient of the radiator outer surface, A oe is the external surface area of ​​the heat sink, T we is the temperature of the radiator wall; Evaporator temperature: Where m e is the mass of the evaporator, c e is the heat capacity of the evaporator, a ie is the heat exchange coefficient inside the evaporator, D ie is the diameter of the pipe inside the evaporator, l e is the length of the two-phase state of the refrigerant in the evaporator, T re is the critical temperature of the refrigerant at that pressure; S2. Design the Pontryagin minimum principle controller objective function as follows: Where L1, L2, L3 are temperature weight parameters, T fc * is the ideal temperature of the fuel cell, T fcin * is the ideal temperature of the fuel cell inlet coolant, T cab * It is the ideal temperature for the car cabin; The constructed Hamiltonian function: Where H(x(t),u(t),λ(t),t) is the Hamiltonian function, λ1,λ2,λ3 are the corresponding covariates; Co-variables should satisfy the following conditions: λ1(t f )=0 λ2(t f )=0 λ3(t f )=0 (9) where t f It’s the final moment; The optimal control variable sequence is: H(x * (t),u * (t),λ * (t),t)≤H(x * (t),u(t),λ * (t),t) (10) where x * (t) is the optimal state quantity at time t, u * (t) is the optimal control quantity at time t, λ * (t) is the optimal covariate variable at time t, H(x * (t),u * (t),λ * (t), t) is the Hamiltonian function value where the state, control and co-state variables are all optimal at time t. * (t),u(t),λ * (t), t) is the Hamiltonian function value of the optimal state value, optimal co-state variable value and control variable value at time t; The process of obtaining the initial value of the co-state variable: 1) Initial value setting: Select the sum of the absolute values ​​of the co-state variables as the objective function of the Nelder-Mead algorithm, select four groups of numbers as the four initial values ​​of the co-state variables, calculate the value of the objective function under the four initial values, and reduce them in order of size, recorded as l from small to large min ,l1,l2,l max ; Sort the four groups of initial values ​​according to the size of their corresponding objective functions, and record them as a1, a2, a3, a4 from small to large; 2) The average value of the initial value a o : Calculate the reflection point: a r =a o +α(a o -a1) (12) Where α is the reflection point coefficient; 3) Take the reflection point as the initial value of the co-state variable, denoted as a r , calculate the final value of the objective function, denoted as l new ; Compare the obtained objective function value with the value of the objective function in step 1); 4) If the objective function value in step 3) is l new Greater than or equal to the maximum value l of the objective function in step 1) max , then calculate the contraction point, denoted as a s ; Taking the contraction point as the initial value of the co-state variable, the final objective function value is calculated and recorded as l s ; will l s and l max Compare the size. If l s Less than l max , with the contraction point a s Replace a4 with l s Instead of l max ; a1,a2,a3,a s Sort them according to the size of their corresponding objective functions, and re-record them as a1, a2, a3, a4 from small to large. At the same time, sort the recombined objective functions by size; return to step 2) and start the cycle again; the calculation formula of the contraction point is as follows: the s =a o +δ(a4-a o ) (13) Where δ is the contraction point coefficient; If l s Greater than or equal to l max , all initial values ​​except the initial value corresponding to the minimum objective function must be recalculated to obtain a new initial value sequence; the new sequence is used as the initial value of the co-state variable, the corresponding objective function is calculated, and it is sorted according to the value of the objective function. The initial value sequence is a1, a2, a3, a4 from small to large, and the objective function is l from small to large. min ,l1,l2,l max ; Return to step 2) and restart the cycle; the formula for recalculating the initial value is as follows: b2=a1+δ(a2-a1) b3=a1+δ(a3-a1) b4=a1+δ(a4-a1) (14) Among them, b2, b3, b4 are the newly obtained initial value sequences; 5) If l in step 3) new Less than the minimum value l of the objective function in step 1) min , calculate the expansion point, denoted as a e ; Taking the expansion point as the initial value of the co-state variable, the corresponding objective function is calculated and recorded as l e ; The obtained l e and l in step 3) new If l e Less than l new , use a e Replace a1; if l e Greater than or equal to l new , use a r Replace a1; then sort according to the size of the corresponding objective function, and the initial value sequence is recorded as a1, a2, a3, a4 from small to large; return to step 2) and start the cycle again; the calculation formula of the expansion point is as follows: a e =a o +γ(a r -a o ) (15) Where γ is the expansion point coefficient; 6) If l in step 3) new The size of l in step 1) min and l max When between, use a r Replace a1, get a new initial value sequence, and sort it according to the size of its corresponding objective function, and record it as a1, a2, a3, a4 from small to large; return to step 2) and start the cycle again; 7) After the cycle is completed, the optimal control sequence and the corresponding initial values ​​of the co-state variables are obtained.

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