Hydrogen fuel cell gas-electric coordination control and water content constraint management method

Abstract

The application discloses a hydrogen fuel cell gas-electricity coordinated control and water content constraint management method, and belongs to the technical field of fuel cells, and comprises the following steps: analyzing the influence of different load conditions, different gas supply flow and pressure on membrane water content, and establishing a transmembrane water mass flow equation; considering the nonlinear coupling relationship between the air loop and the DC-DC converter, a fuel cell gas-electricity loop dynamic model is constructed; aiming at the dynamic response characteristics of the coupling system on different time scales, a control instruction is designed based on a nonlinear backstepping method, and the coordinated control of the hydrogen fuel cell gas-electricity coupling loop is completed; finally, in view of the problem that the fluctuation of the membrane water content influences the service life of the system, a reference regulation algorithm is introduced, a reference signal is corrected in real time, and the safe constraint management of the membrane water content is realized. The application can reduce the influence of rapid load change on the voltage and membrane water content of the fuel cell system, and improve the operation stability and safety of the system.

Description

Technical Field

[0001] This invention belongs to the field of fuel cell technology, specifically relating to a method for gas-electric coordinated control and water content constraint management of hydrogen fuel cells. Background Technology

[0002] Proton exchange membrane fuel cells (PEMFCs) are complex systems involving multiple timescales and coupled physical fields. Their operation is influenced by the interactions of various physical processes, including gas flow, electrochemical reactions, membrane water transfer, and heat transfer. The dynamic response of the gas supply system plays a crucial role in fuel cell operation. Due to the significant mechanical inertia of components such as the air compressor and the lag in gas flow regulation, the system's response to load changes is relatively slow. Especially under conditions of large load fluctuations, the rapid current adjustment by the DC-DC converter can easily lead to drastic fluctuations in the oxygen concentration, membrane water content, and output voltage within the fuel cell stack, potentially causing oxygen starvation, flooding, and membrane drying, thus affecting system efficiency and lifespan. Therefore, to reduce the impact of rapid load changes on system performance and ensure the system's stability and safety under various operating conditions, research related to the safety control of fuel cell gas-electricity-water coupling systems is urgently needed. This research can effectively improve the system's dynamic and steady-state performance, enhance fuel cell operating efficiency, and extend its lifespan.

[0003] Existing DC-DC control strategies in fuel cell systems rely on linear feedback methods. However, in achieving fuel cell voltage output control, they fail to fully consider the system's nonlinear characteristics and the impact of gas dynamic response on membrane water content and output voltage, making it difficult to meet performance requirements under complex dynamic loads. Furthermore, current work on proton exchange membrane fuel cell control focuses on the control of a single gas supply system, typically neglecting the real-time adjustment of membrane water content within the stack. The stability of membrane water content is crucial to fuel cell performance, lifespan, and safety. Water management in proton exchange membrane fuel cells involves complex water transport mechanisms and multi-scale dynamic processes, making it a highly challenging research problem. Summary of the Invention

[0004] To address the multi-timescale and strongly coupled characteristics of gas dynamics and load current dynamics in proton exchange membrane fuel cells (PEMFCs), and the issue of fluctuating membrane water content within the stack under different load conditions and gas supply, this invention provides a gas-electric coordinated control and water content constraint management method for hydrogen fuel cells. This method aims to achieve coordinated control between the gas supply circuit and the DC-DC converter, as well as safe constraint adjustment of membrane water content under different load conditions.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for coordinated gas-electric control and water content constraint management of hydrogen fuel cells includes the following steps:

[0007] Step 1: Analyze the effects of different load conditions, air supply flow rates, and pressures on membrane water content. To account for the effects of electroosmotic drag and reverse diffusion of water inside the fuel cell stack, a mass flow rate equation for water transport across the membrane is established.

[0008] Step 2: Consider the coupling behavior of gas flow and pressure in the air supply system, as well as the coupling dynamics between the air loop and the DC-DC converter, and construct a nonlinear dynamic model of the gas-electric multi-loop system.

[0009] Step 3: Combining the pneumatic-electric multi-loop nonlinear dynamic model from Step 2, derive the control strategy based on the backstepping method, and design the air compressor input voltage for the air loop respectively. Back pressure valve opening command and the duty cycle of the DC-DC converter This forms a closed-loop control system, enabling coordinated control of the fuel cell gas-electric coupling system.

[0010] Step 4: Linearly discretize the closed-loop control system formed in Step 3 to predict the membrane humidity state information, and design a cascaded reference control algorithm based on this to sequentially adjust the flow reference value. Pressure reference value and load current reference value Make corrections to complete the safety constraint management of membrane water content.

[0011] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0012] (1) During the DC-DC regulation process, the present invention takes into account the impact of the slow time scale air supply system on the output performance of the fuel cell. It can reduce the fluctuation amplitude of the output voltage and stack membrane water content of the fuel cell system when the load changes rapidly, thereby improving the operating efficiency and reliability of the system.

[0013] (2) By indirectly correcting the reference signal values ​​of flow rate, pressure and current, the present invention achieves safe constraint management of membrane water content, effectively avoids flooding and membrane dryness failure conditions, helps maintain the output performance of fuel cell and effectively extends battery life. Attached Figure Description

[0014] Figure 1 This is a flowchart of a hydrogen fuel cell gas-electric coordinated control and water content constraint management method according to the present invention;

[0015] Figure 2 This is a diagram of the fuel cell output voltage of a hydrogen fuel cell gas-electric coordinated control and water content constraint management method according to the present invention.

[0016] Figure 3 This is a reference signal correction diagram for a hydrogen fuel cell gas-electric coordinated control and water content constraint management method according to the present invention.

[0017] Figure 4 This invention relates to the membrane water content constraint situation of a hydrogen fuel cell gas-electric coordinated control and water content constraint management method. Detailed Implementation

[0018] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0019] like Figure 1 As shown, the hydrogen fuel cell gas-electric coordinated control and water content constraint management method of the present invention includes the following steps:

[0020] Step 1: Analyze the effects of different load conditions, air supply flow rates, and pressures on membrane water content. To account for the effects of electroosmotic drag and reverse diffusion of water inside the fuel cell stack, a mass flow rate equation for water transport across the membrane is established.

[0021] Step 2: Consider the coupling behavior of gas flow and pressure in the air supply system, as well as the coupling dynamics between the air loop and the DC-DC converter, and construct a nonlinear dynamic model of the gas-electric multi-loop system.

[0022] Step 3: Combining the system dynamic model from Step 2 (i.e., the pneumatic-electric multi-loop nonlinear dynamic model), derive the control strategy based on the backstepping method, and design the air compressor input voltage for the air loop separately. and back pressure valve opening command and the duty cycle of the DC-DC converter To form a closed-loop control system ( Figure 1 (not shown in the image) to achieve coordinated control of the fuel cell gas-electric coupling system;

[0023] Step 4: Linearly discretize the closed-loop control system formed in Step 3 to predict the membrane humidity state information, and design a cascaded reference governor (RG) algorithm based on this to sequentially adjust the flow-pressure reference vector values. and load current reference value Corrections were made to complete the safety constraint management of membrane water content. Among these, This is a reference value for traffic volume. This is a pressure reference value.

[0024] Specifically, step 1 includes:

[0025] Analysis of the effects of different load conditions, air supply flow rates, and pressures on membrane water content The influence of this is deduce, and the corresponding mathematical representation equation is derived as follows:

[0026] ;

[0027] in, Indicates relative humidity. The mass of water vapor at the cathode of the fuel cell stack. Let be the gas constant of water vapor. For the fuel cell stack temperature, For the cathode flow channel volume, This is the saturated vapor pressure;

[0028] Considering the electroosmotic drag and reverse diffusion of water, the mass flow rate of water transported across the membrane is... Represented as:

[0029] ;

[0030] in, The molar mass of water, The area of ​​the proton exchange membrane. For the number of fuel cell wafers, and These are the mass flow rates of the electroosmotic drag water and the reverse diffusion water, respectively.

[0031] Specifically, step 2 includes:

[0032] Considering the coupled behavior of gas flow and pressure in an air supply system, reveal the compressor speed in the air supply system. Gas supply manifold pressure oxygen mass at the cathode of the fuel cell stack Nitrogen mass water vapor mass and return manifold pressure The interaction between them is further analyzed, and the coupling dynamics between the air loop and the DC-DC converter are further analyzed. Based on the law of conservation of gas mass and the working principle of the DC-DC converter circuit, the nonlinear dynamic model of the gas-electric multi-loop is derived as follows:

[0033] ;

[0034] in, The vector representation formed , Vector representation , For fuel cell current, This is the output voltage of the fuel cell. , and express , and The first derivative, Indicates the cathode gas pressure. This refers to the outlet gas flow rate of the air compressor. The output voltage is a DC-DC converter. , These represent the air compressor input voltage and the back pressure valve opening control command, respectively. Indicates duty cycle, For the gas-electric coupling system model parameters of the fuel cell, The inductance value of the DC-DC converter. This is the resistance value. This is the capacitance value.

[0035] Specifically, step 3 includes:

[0036] Based on the gas-electric coupling dynamic model in step 2, the flow-pressure tracking error of the air path is defined as follows: Current tracking error of DC-DC converter ,in, For flow-pressure vectors, This is a flow-pressure reference value. For the fuel cell current reference value, the virtual controlled variable and stabilization function are designed as follows:

[0037] ;

[0038] in, and These are the virtual controlled variables for the flow-pressure control loop and the current control loop, respectively. and They are respectively and The stabilization function, For process variables, and They are respectively and The first derivative, , For positive design parameters, superscript This is the matrix transpose symbol;

[0039] Define the flow-pressure tracking error of the virtual controlled variable. and virtual controlled variable current tracking error To achieve tracking control of flow rate, pressure, and current status, the air circuit control input signal is designed. and duty cycle update rate for:

[0040] ;

[0041] in, and They are respectively and The first derivative, For process variables, , These are the positive design parameters.

[0042] Specifically, step 4 includes:

[0043] The closed-loop control system formed in step 3 is linearly discretized to obtain the prediction model:

[0044] ;

[0045] in, For the system matrix, express The state variables of the closed-loop control system at all times. express The output value of the closed-loop control system at any given time. This indicates the flow-pressure-current reference signal value to be corrected;

[0046] The design vector reference regulation algorithm obtains the flow-pressure reference value correction signal. :

[0047] ;

[0048] in, To optimize parameters, To satisfy the system state and reference signal set that meets the membrane water content constraint, diag represents a diagonal matrix. Indicates satisfaction The minimum value under the given conditions is i=1,2; Denotes the Euclidean norm;

[0049] A scalar reference regulation algorithm is designed to obtain the current reference value correction signal. :

[0050] ;

[0051] in, This indicates that the optimization parameters are satisfied. The maximum value under the given conditions.

[0052] In summary, the designed cascaded reference regulation algorithm is used to correct the flow-pressure reference vector and the reference current respectively. While meeting the water content constraint management, it reduces the correction of the current reference value and reduces the impact on the output voltage and power of the fuel cell system.

[0053] Example:

[0054] This embodiment uses a proton exchange membrane fuel cell system as an example. The system parameters are shown in Table 1, which are used to define this specific fuel cell system. Considering the system's characteristics of multi-timescale, multi-physics coupling, and strong nonlinearity, it is necessary to use nonlinear control methods to achieve multi-stage loop coordinated control and safety constraint management of membrane water content under variable load conditions.

[0055] Table 1

[0056]

[0057] The specific steps of this embodiment are as follows:

[0058] Step 1: Analyze the effects of different load conditions, air supply flow rates, and pressures on membrane water content. Considering the effects of electroosmotic drag and reverse diffusion of water within the fuel cell stack, the membrane water content is derived. Mathematical characterization equations and water mass flow rates across membranes .

[0059] Step 2: Considering the coupling behavior of gas flow and pressure in the air supply system, as well as the coupling dynamics between the air loop and the DC-DC converter, construct a gas-electric multi-loop nonlinear dynamic model. The specific model parameters are shown in Table 2.

[0060] Table 2

[0061]

[0062] Step 3: Define the system's flow, pressure, and current tracking errors. Design the control command signals for the air compressor input voltage and back pressure valve opening based on the nonlinear backstepping method, as well as the duty cycle update rate of the DC-DC converter. Specific design parameters are as follows: , , , .

[0063] Step 4: Linearly discretize the closed-loop control system formed in Step 3, design a cascaded reference control algorithm, and sequentially adjust the flow-pressure reference vector values. and load current reference value Make corrections to complete the safety constraint management of membrane water content.

[0064] To verify the effectiveness of the multi-loop coordinated control and water management system designed in this invention, simulation verification was performed on the above algorithm. Under variable load conditions, the fuel cell output voltage under the gas-electric coupling system coordinated control strategy is as follows: Figure 2 As shown, solid lines represent coordinated control, and dashed lines represent control strategies that do not consider gas dynamics. Simulation results show that the total overshoot and offset of the output voltage are reduced by 11.21%. To verify the designed reference control algorithm, the membrane humidity was constrained between 0.5 and 0.98. The correction results for the current, pressure, and flow reference signal values ​​are shown below. Figure 3 As shown. The constraint results for membrane humidity are as follows. Figure 4 As shown, the dashed and solid lines represent the changes in membrane humidity with and without the RG correction algorithm, respectively. Simulation results demonstrate that the designed correction algorithm can achieve safe constraint management of membrane water content. Thus, the gas-electric coordinated control and water content constraint management of the hydrogen fuel cell are completed.

[0065] Although the illustrative specific embodiments of the present invention have been described above to enable those skilled in the art to understand the invention, it should be understood that the invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes will be obvious as long as they are within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of the present invention are protected.

Claims

1. A method for coordinated gas-electric control and water content constraint management of a hydrogen fuel cell, characterized in that, Includes the following steps: Step 1: Analyze the effects of different load conditions, air supply flow rates, and pressures on membrane water content. To account for the effects of electroosmotic drag and reverse diffusion of water inside the fuel cell stack, a mass flow rate equation for water transport across the membrane is established. Considering the electroosmotic drag and reverse diffusion of water, the transmembrane water mass flow rate Represented as: ； in, The molar mass of water, The area of ​​the proton exchange membrane. For the number of fuel cell wafers, and These are the mass flow rates of electroosmotic drag water and reverse diffusion water, respectively. Step 2: Consider the coupling behavior of gas flow and pressure in the air supply system, as well as the coupling dynamics between the air loop and the DC-DC converter, and construct a nonlinear dynamic model of the gas-electric multi-loop system. Step 3: Combining the pneumatic-electric multi-loop nonlinear dynamic model from Step 2, derive the control strategy based on the backstepping method, and design the air compressor input voltage for the air loop respectively. Back pressure valve opening command and the duty cycle of the DC-DC converter This forms a closed-loop control system, enabling coordinated control of the fuel cell gas-electric coupling system. Step 4: Linearly discretize the closed-loop control system formed in Step 3 to predict the membrane humidity state information, and design a cascaded reference control algorithm based on this to sequentially adjust the flow reference value. Pressure reference value and load current reference value Make corrections to complete the safety constraint management of membrane water content.

2. The method for coordinated gas-electric control and water content constraint management of a hydrogen fuel cell according to claim 1, characterized in that, Step 1 includes: Analysis of the effects of different load conditions, air supply flow rates, and pressures on membrane water content The influence of this is deduce, and the corresponding mathematical representation equation is derived as follows: ； in, Indicates relative humidity. The mass of water vapor at the cathode of the fuel cell stack. Let be the gas constant of water vapor. For the fuel cell stack temperature, For the cathode flow channel volume, This is the saturated vapor pressure.

3. The method for coordinated gas-electric control and water content constraint management of a hydrogen fuel cell according to claim 2, characterized in that, Step 2 includes: Considering the coupled behavior of gas flow and pressure in an air supply system, reveal the compressor speed in the air supply system. Gas supply manifold pressure oxygen quality at the cathode of the fuel cell stack Nitrogen mass Water vapor mass and return manifold pressure The interaction between them is further analyzed, and the coupling dynamics between the air loop and the DC-DC converter are further analyzed. Based on the law of conservation of gas mass and the working principle of the DC-DC converter circuit, the nonlinear dynamic model of the gas-electric multi-loop is derived as follows: ； in, Vector representation , Represents vector elements, Vector representation , and For vector elements, For fuel cell current, This is the output voltage of the fuel cell. , and express , and The first derivative, , Indicates the cathode gas pressure. This refers to the outlet gas flow rate of the air compressor. The output voltage is a DC-DC converter. and These represent the air compressor input voltage and the back pressure valve opening control command, respectively. Indicates duty cycle, For the model parameters of the fuel cell gas-electric coupling system, The inductance value of the DC-DC converter. This is the resistance value. This is the capacitance value.

4. The method for coordinated gas-electric control and water content constraint management of a hydrogen fuel cell according to claim 3, characterized in that, Step 3 includes: Based on the gas-electric multi-loop nonlinear dynamic model in step 2, the flow-pressure tracking error of the air path is defined as follows: Current tracking error of DC-DC converter ,in, For flow-pressure vectors, This is a flow-pressure reference value. Design a virtual controlled variable and stabilization function for the fuel cell current reference value: ； in, and These are the virtual controlled variables for the flow-pressure control loop and the current control loop, respectively. and They are respectively and The stabilization function, For process variables, and They are respectively and The first derivative, , For positive design parameters, superscript This is the matrix transpose symbol.

5. The method for coordinated gas-electric control and water content constraint management of a hydrogen fuel cell according to claim 4, characterized in that, Step 3 also includes: Define the flow-pressure tracking error of the virtual controlled variable. and virtual controlled variable current tracking error To achieve tracking control of flow rate, pressure, and current status, an air circuit control input signal is designed. and duty cycle update rate for: ； in, and They are respectively and The first derivative, For process variables, , These are the positive design parameters.

6. The method for coordinated gas-electric control and water content constraint management of a hydrogen fuel cell according to claim 5, characterized in that, Step 4 includes: The closed-loop control system formed in step 3 is linearly discretized to obtain the prediction model: ； in, For the system matrix, express The state variables of the closed-loop control system at all times. express The output value of the closed-loop control system at any given time. This indicates the flow-pressure-current reference signal value to be corrected. For flow-pressure reference value correction signal, This is a correction signal for the current reference value.

7. The method for coordinated gas-electric control and water content constraint management of a hydrogen fuel cell according to claim 6, characterized in that, In step 4, the cascaded reference adjustment algorithm includes a vector reference adjustment algorithm; The design vector reference regulation algorithm obtains the flow-pressure reference value correction signal. : ； in, To optimize the parameters, k represents the k-th time. To satisfy the system state and reference signal set that meets the membrane water content constraint, diag represents a diagonal matrix. This indicates that the optimization parameters are satisfied. The minimum value under the given conditions, i=1,2; This represents the Euclidean norm.

8. The method for coordinated gas-electric control and water content constraint management of a hydrogen fuel cell according to claim 7, characterized in that, In step 4, the cascaded reference adjustment algorithm includes a scalar reference adjustment algorithm; A scalar reference regulation algorithm is designed to obtain the current reference value correction signal. : ； in, This indicates that the optimization parameters are satisfied. The maximum value under the given conditions.

9. The method for coordinated gas-electric control and water content constraint management of a hydrogen fuel cell according to claim 8, characterized in that, Traffic reference value Pressure reference value A flow-pressure reference vector is constructed, and the flow-pressure reference vector and reference current are corrected by the designed cascaded reference regulation algorithm. While meeting the water content constraint management, the adjustment of the current reference value is reduced, thereby reducing the impact on the output voltage and power of the fuel cell system.

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