PEMFC system modeling method and device for decoupling multiple physical quantities of electricity, heat and water

Abstract

The invention discloses a PEMFC system modeling method and device for decoupling multiple physical quantities of electricity, heat and water. The device comprises an electricity-heat-water independent model building module, an electricity-heat-water coupling model building module, a key parameter extraction module and a key parameter decoupling module, wherein the key parameter extraction module comprises a heat transmission model for building a fuel cell stack meeting heat balance; establishing a water transportation model in the proton exchange membrane meeting water balance; establishing an electrochemical model of the fuel cell stack; constructing a comprehensive model of an electricity-heat-water multi-physical quantity coupled proton exchange membrane fuel cell system; mutually coupled key parameters including fuel cell stack temperature, water content and output voltage are extracted; analyzing the change characteristics of the temperature, the water content and the output voltage characteristic of the fuel cell stack under the condition that the external operation working condition is changed; and decoupling is carried out, so that key parameter extraction of the proton exchange membrane fuel cell system is realized. According to the invention, the complexity of model operation can be reduced.

Description

Technical Field

[0001] The present invention relates to the field of multi-energy flow modeling of proton exchange membrane fuel cells (PEMFCs), and particularly to a modeling method and device for proton exchange membrane fuel cells that decouple multiple physical quantities. Background Art

[0002] Proton exchange membrane fuel cells (PEMFCs) have attracted wide attention due to their advantages such as high energy conversion efficiency, high power density, green cleanliness, and low operating temperature. As a highly potential energy storage technology, PEMFCs are currently mainly applied to transportation, aerospace, and residential combined heat and power systems. However, during the operation of proton exchange membrane fuel cells, there are interactions and couplings among multiple physical fields such as heat, water, and electricity. There are a large number of physical quantities in multiple fields and the working principle is complex. Therefore, a large number of literatures have carried out research on the modeling of proton exchange membrane fuel cells. The literature "Dynamic Modeling and Characteristic Analysis of Proton Exchange Membrane Fuel Cells" constructs an equivalent circuit model of PEMFC to analyze the dynamic operating characteristics of proton exchange membrane fuel cells. However, the parameter modeling method based on the equivalent circuit model does not reflect the response of the internal characteristics of the fuel cell. The literature "Dynamic Response Analysis and Economic Evaluation of Factors Affecting Fuel Cell Life" analyzes the factors affecting the life of proton exchange membrane fuel cells such as thermal management, water management, and load cycling, but the constructed three-dimensional two-phase PEMFC model does not consider the important role of the thermal field. The literature "Research on the Optimization of Operating Conditions of Proton Exchange Membrane Fuel Cells at High Current Densities" is based on the geometric model of proton exchange membrane fuel cells and establishes a three-dimensional single-channel PEMFC model that can reflect the internal flow channels, porous media diffusion, water phase change and flow, and electrochemical reactions of PEMFCs. However, the construction process of this model lacks an analysis of the coupling mechanism among multiple physical fields. The literature "Multi-Physical Field Modeling and Model Parameter Sensitivity Analysis of Proton Exchange Membrane Fuel Cells" constructs a quasi-one-dimensional stack dynamic model that can reflect the multi-field coupling relationship of "electricity-thermal-flow" inside the fuel cell. However, this stack model lacks the role of external auxiliary equipment such as the cooling system under actual operating conditions. In summary, the current models of proton exchange membrane fuel cells lack the construction of the coupling relationship among multiple physical fields of heat, water, and electricity, which makes it difficult to decouple the problems of internal and external electrical characteristics under the condition of connecting a DC load to a proton exchange membrane fuel cell. In view of this situation, taking the PEMFC stack system connected to a DC load as an example, it is necessary to extract the key parameters of the PEMFC stack system and design a modeling method for proton exchange membrane fuel cells that decouples multiple physical quantities of electricity, heat, and water. Summary of the Invention

[0003] For a proton exchange membrane fuel cell stack system for an external DC load, fully considering the multi-physical coupling operation mechanism of heat-water-electricity inside the fuel cell, the present invention proposes a modeling method and device for a PEMFC system decoupling multi-physical quantities of electricity-heat-water. By extracting the key parameters of multi-physical quantities, namely the operating temperature, water content, and single fuel cell terminal voltage of the fuel cell stack, analyzing the internal operating characteristics of the fuel cell when the external operating conditions change, decoupling the multi-physical fields, and realizing the process design for constructing a comprehensive model of a proton exchange membrane fuel cell decoupling multi-physical quantities of electricity-heat-water.

[0004] The present invention is implemented by the following technical solutions:

[0005] In the first aspect, a modeling method for a PEMFC system decoupling multi-physical quantities of electricity-heat-water proposed by the present invention includes:

[0006] Establish a heat transfer model of a fuel cell stack that satisfies heat balance. The heat transfer model of the fuel cell stack takes the external parameters of operating current and output voltage as input parameters and the stack temperature as the output parameter;

[0007] Establish a water transport model in a proton exchange membrane that satisfies water balance. The water transport model in the proton exchange membrane takes the external parameters of operating current and stack temperature as input parameters and the water content as the output parameter;

[0008] Establish an electrochemical model of the fuel cell stack as shown in the following formula:

[0009] U cell =E 0 -U act -U conc -U oh

[0010] In the formula, E 0 is the open circuit voltage, U act is the activation polarization overpotential, U oh is the ohmic polarization overpotential, concentration polarization overpotential, U conc is the concentration polarization overpotential;

[0011] Using the heat transfer model of the fuel cell stack, the water transport model in the proton exchange membrane, and the electrochemical model of the fuel cell stack, construct a comprehensive model of a proton exchange membrane fuel cell system coupled with multi-physical quantities of electricity-heat-water. This comprehensive model is composed of a coupled heat transfer model, water transport model, and electrochemical model. Taking the operating temperature of the fuel cell stack, the water flux of the membrane output by the water transport model, and the water content λ of the membrane as the inputs of the comprehensive model, and performing subsequent processing through the electrochemical model, including the reversible voltage according to the operating temperature T of the fuel cell stack stand the equivalent electronic impedance of the battery. The open-circuit voltage is determined based on the operating temperature of the fuel cell stack, the absolute pressure of hydrogen, the partial pressure of oxygen, and the operating current of the fuel cell stack. The activation polarization overpotential is determined based on the operating temperature of the fuel cell stack, the partial pressure of oxygen, and the operating current of the fuel cell stack. The concentration polarization overpotential is determined based on the operating temperature T of the fuel cell stack st and the operating current of the fuel cell stack. The ohmic polarization overpotential is determined based on the equivalent area A of the membrane, the equivalent electronic impedance of the battery, the thickness of the membrane, and the water content of the membrane. Finally, the single-cell fuel cell terminal voltage U cell and the operating current of the fuel cell stack are output by the comprehensive model;

[0012] According to the comprehensive model of the proton exchange membrane fuel cell with electro-thermal-hydraulic multi-physical quantity coupling, the mutually coupled key parameters are extracted, including the temperature of the fuel cell stack, the water content, and the output voltage;

[0013] Using the comprehensive model of the proton exchange membrane fuel cell with electro-thermal-hydraulic multi-physical quantity coupling to extract the key parameters of thermal-hydraulic-electricity, the fuel cell stack temperature, water content, and output voltage characteristics are analyzed under the condition of changing external operating conditions;

[0014] Decoupling is performed according to the characteristics of the fuel cell stack temperature, water content, and output voltage changing with different time scales of external conditions to realize the extraction of key parameters of the proton exchange membrane fuel cell system.

[0015] In some embodiments, the expression of the thermal balance of the fuel cell stack is as follows:

[0016]

[0017] In the formula, m stack is the mass of the stack, C p,stack is the equivalent specific heat capacity of the stack, T st is the temperature of the stack, is the change rate of the total chemical energy of the reactants with time, P elec is the electric power output by the fuel cell, is the sensible heat power of the reaction, is the heat power discharged by the stack coolant, is the heat power consumed by convection.

[0018] In some embodiments, the expression of the water transport balance in the proton exchange membrane is as follows:

[0019]

[0020] In the formula, is the water flux inside the fuel cell, is the internal resistance of the fuel cell and the moisture flux of reverse diffusion, ρ m and M m are the density and molar mass of the membrane, is the molar mass of water, λ is the water content, which is the number of water molecules adsorbed by each sulfonic acid group in the proton exchange membrane, ▽λ is the gradient of the water content, and the physical meaning of the water content gradient is how the water content changes with position. F is the Faraday constant, D I is the diffusion coefficient of water in the membrane, n d is the resistivity.

[0021] In some embodiments, where the open-circuit voltage E 0 has the following formula:

[0022]

[0023] In the formula, ΔG is the change in Gibbs free energy of the hydrogen / oxygen combustion reaction, ΔH is the calorific value of hydrogen, ΔS is the entropy change during the reaction, p H2 and p O2 are the partial pressures of hydrogen on the anode catalyst layer surface and oxygen on the cathode catalyst layer surface, respectively;

[0024] The activation polarization overpotential U act has the following empirical formula:

[0025]

[0026] In the formula, U act is the activation polarization overpotential, ξ 1 , ξ 2 , ξ 3 , ξ 4 are parameter coefficients based on electrochemistry, kinetics, and thermodynamics, is the oxygen concentration at the cathode gas-liquid interface, and the pressure of oxygen participating in the reaction

[0027] The ohmic polarization overpotential U oh has the following formula:

[0028] U oh = IR oh = I(R M + R c )

[0029] In the formula, U oh is the ohmic polarization overpotential, R oh is the equivalent ohmic resistance of the fuel cell, that is, the resistance of the non-ideal electrode, the conductive plate, and the transfer of protons through the membrane. R M is the equivalent proton resistance of the fuel cell, R cis the impedance that hinders the passage of electrons through the membrane;

[0030] The equivalent proton resistance R M is given by the following formula:

[0031]

[0032] where l is the thickness of the membrane, σ m is the conductivity of the membrane, A is the effective area of the membrane, j is the current density, λ is the water content of the fuel cell, and T st is the operating temperature of the fuel cell;

[0033] The concentration polarization overpotential U conc is given by the following formula:

[0034]

[0035] where U conc is the concentration overpotential of the fuel cell, R is the ideal gas constant, F is the Faraday constant, z is the number of electrons transferred per unit amount of reactant gas participating in the reaction, and I and I max are the fuel cell current and the limiting current, respectively.

[0036] In some embodiments, for the integrated model of the electro-thermal-hydraulic multi-physical proton exchange membrane fuel cell with an external DC load, the key parameters of the proton exchange membrane fuel cell system extracted by decoupling, including the fuel cell stack temperature, water content, and output voltage, are all affected by the change of the external operating current.

[0037] In a second aspect, a PEMFC system modeling device for decoupling electro-thermal-hydraulic multi-physical quantities proposed by the present invention includes an electro-thermal-hydraulic independent model construction module, an electro-thermal-hydraulic coupling model construction module, a key parameter extraction module, and a key parameter decoupling module; wherein:

[0038] The electro-thermal-hydraulic independent model construction module is used to establish a heat transfer model of the fuel cell stack that satisfies the heat balance. The heat transfer model of the fuel cell stack takes the external parameters of the operating current and output voltage as input parameters and the stack temperature as the output parameter; establish a water transport model in the proton exchange membrane that satisfies the water balance. The water transport model in the proton exchange membrane takes the external parameters of the operating current and stack temperature as input parameters and the water content as the output parameter; and, establish an electrochemical model of the fuel cell stack as shown in the following formula:

[0039] U cell =E 0 -U act -U conc -U oh

[0040] where E0 is the open-circuit voltage, U act is the activation polarization overpotential, U oh is the ohmic polarization overpotential, concentration polarization overpotential, U conc is the concentration polarization overpotential;

[0041] The electro-thermal-hydraulic coupling model construction module is used to construct an integrated model of a proton exchange membrane fuel cell system with multi-physical quantity coupling of electricity, heat, and water by using the heat transfer model of the fuel cell stack, the water transport model in the proton exchange membrane, and the electrochemical model of the fuel cell stack. The integrated model consists of a coupled heat transfer model, water transport model, and electrochemical model. Taking the operating temperature of the fuel cell stack, the water flux of the membrane output by the water transport model, and the water content λ of the membrane as the inputs of the integrated model, subsequent processing is performed through the electrochemical model, including the reversible voltage determined according to the operating temperature T of the fuel cell stack st and the equivalent electronic impedance of the battery. The open-circuit voltage is determined according to the operating temperature of the fuel cell stack, the absolute pressure of hydrogen, the partial pressure of oxygen, and the operating current of the fuel cell stack. The activation polarization overpotential is determined according to the operating temperature of the fuel cell stack, the partial pressure of oxygen, and the operating current of the fuel cell stack. The concentration polarization overpotential is determined according to the operating temperature T of the fuel cell stack st and the operating current of the fuel cell stack. The ohmic polarization overpotential is determined according to the equivalent area A of the membrane, the equivalent electronic impedance of the battery, the thickness of the membrane, and the water content of the membrane. Finally, the single-cell fuel cell terminal voltage U cell and the operating current of the fuel cell stack are output by the integrated model;

[0042] The key parameter extraction module is used to extract the mutually coupled key parameters including the fuel cell stack temperature, water content, and output voltage according to the integrated model of the proton exchange membrane fuel cell with multi-physical quantity coupling of electricity, heat, and water;

[0043] The key parameter decoupling module is used to use the integrated model of the proton exchange membrane fuel cell with multi-physical quantity coupling of electricity, heat, and water to extract the fuel cell stack temperature, water content, and output voltage characteristics of the proton exchange membrane fuel cell model with key parameters of heat-water-electricity coupling under the condition of analyzing the change of the external operating conditions; and decouple according to the change characteristics of the fuel cell stack temperature, water content, and output voltage characteristics at different time scales of the external conditions to realize the extraction of the key parameters of the proton exchange membrane fuel cell system.

[0044] In some embodiments, the expression of the heat balance of the fuel cell stack is as follows:

[0045]

[0046] In the formula, m stackis the mass of the stack, C p,stack is the equivalent specific heat capacity of the stack, T st is the temperature of the stack is the rate of change of the total chemical energy of the reactants with time, P elec is the electric power output of the fuel cell is the sensible heat power of the reaction is the heat power discharged by the stack coolant is the heat power consumed by convection

[0047] In some embodiments, the expression for the water transport balance in the proton exchange membrane is as follows:

[0048]

[0049] In the formula, is the water flux inside the fuel cell is the water flux of the internal resistance force and reverse diffusion inside the fuel cell, ρ m and M m are the density and molar mass of the membrane is the molar mass of water, λ is the water content, which is the number of water molecules adsorbed by each sulfonic acid group in the proton exchange membrane, ▽λ is the gradient of the water content, and the physical meaning of the water content gradient is how the water content changes with position. F is the Faraday constant, D I is the diffusion coefficient of water in the membrane, n d is the resistivity

[0050] In some embodiments, wherein the open circuit voltage E 0 has the following formula:

[0051]

[0052] In the formula, ΔG is the change in Gibbs free energy of the hydrogen / oxygen combustion reaction, ΔH is the calorific value of hydrogen, ΔS is the entropy change during the reaction, p H2 and p O2 are the partial pressures of hydrogen on the anode catalyst layer surface and oxygen on the cathode catalyst layer surface, respectively;

[0053] The activation polarization overpotential U act has the following empirical formula:

[0054]

[0055] In the formula, U act is the activation polarization overpotential, ξ 1 , ξ 2 , ξ 3 , ξ 4 are the parameter coefficients based on electrochemistry, kinetics, and thermodynamics is the oxygen concentration at the cathode gas-liquid interface, and the pressure of the oxygen participating in the reaction

[0056] The ohmic polarization overpotential U oh The formula is as follows:

[0057] U oh = IR oh = I(R M + R c )

[0058] In the formula, U oh is the ohmic polarization overpotential, R oh is the equivalent ohmic resistance of the fuel cell, that is, the resistance of the non-ideal electrode, the conductive plate, and the proton transfer through the membrane, R M is the equivalent proton resistance of the fuel cell, R c is the impedance that hinders the electron from passing through the membrane;

[0059] The equivalent proton resistance R M The formula is as follows:

[0060]

[0061] In the formula, l is the thickness of the membrane, σ m is the conductivity of the membrane, A is the effective area of the membrane, j is the current density, λ is the water content of the fuel cell, T st is the operating temperature of the fuel cell;

[0062] The concentration polarization overpotential U conc The formula is as follows:

[0063]

[0064] In the formula, U conc is the concentration overpotential of the fuel cell, R is the ideal gas constant, F is the Faraday constant, z is the number of electrons transferred by the reaction gas per unit amount of substance participating in the reaction, I and I max are the fuel cell current and the limiting current respectively.

[0065] In some embodiments, the comprehensive model of the electro-thermal-hydraulic multi-physical quantity coupled proton exchange membrane fuel cell is externally connected to a DC load. The key parameters of the proton exchange membrane fuel cell system extracted by decoupling, including the fuel cell stack temperature, water content, and output voltage, are all affected by the change of the external operating current

[0066] Compared with the prior art, the present invention has the following remarkable advantages:

[0067] 1) Implement the internal multi - physical process simplified modeling design for analyzing the operating characteristics of key parameters of the PEMFC system for heat - water - electricity in specific scenarios;

[0068] 2) Use the key parameters of the PEMFC system extracted by decoupling from the comprehensive model of the proton exchange membrane fuel cell coupled with electricity - heat - water to analyze the influence relationship of external changes in the power system on the interior, and reduce the computational complexity;

[0069] 3) The analysis shows that when the external load current (operating condition) changes rapidly in a short time below the second level, the temperature and water content of the PEMFC system stack change little, and the impact on the operation of the PEMFC system is also very small. Description of the Drawings

[0070] Figure 1 is the topological diagram of the heat model of the proton exchange membrane fuel cell stack of the prior art;

[0071] Figure 2 is the topological diagram of the water transport model of the proton exchange membrane fuel cell of the prior art;

[0072] Figure 3 is the topological diagram of the electrochemical model of the proton exchange membrane fuel cell of the prior art;

[0073] Figure 4 is the topological diagram of the proton exchange membrane fuel cell system model (PEMFC) coupled with electricity - heat - water of the embodiment of the present invention;

[0074] Figure 5 is the overall flow chart of the modeling method of the PEMFC system for decoupling electricity - heat - water multi - physical quantities of the present invention;

[0075] Figure 6 is the module diagram of the modeling device of the PEMFC system for decoupling electricity - heat - water multi - physical quantities of the present invention;

[0076] Figure 7 is the operating polarization curve of the comprehensive model of the proton exchange membrane fuel cell system for decoupling electricity - heat - water multi - physical quantities constructed by using the method of the present invention. Detailed Embodiments

[0077] The following further elaborates on the present invention with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely for explaining the present invention and are not used to limit the present invention.

[0078] As Figure 1 shown, U cell is the terminal voltage of a single fuel cell, T st is the operating temperature of the fuel cell stack, N is the number of fuel cells connected in series in the stack, I is the operating current of the fuel cell stack, Tincool (T outcool ) is the coolant inlet (outlet) temperature, T is the gas inlet temperature, T amb is the ambient temperature, is the stoichiometric ratio of hydrogen (oxygen), is the proportion of cathode oxygen in the inlet gas, is the coolant mass flow rate. In the thermal model of a proton exchange membrane fuel cell stack, the heat generation unit and the heat dissipation unit are taken as the outputs. The heat generation unit includes the total reaction heat power of the fuel cell stack and the output electric power of a single fuel cell. The total reaction heat power of the fuel cell stack is determined according to the number of fuel cells N connected in series in the stack and the operating current I of the fuel cell stack. The output electric power of a single fuel cell is determined according to the terminal voltage U cell of a single fuel cell. The heat dissipation unit includes the sensible heat power, the conduction heat power, and the heat dissipation power of the cooling system. Among them, the sensible heat power is determined according to the gas inlet temperature T, the stoichiometric ratio of hydrogen (oxygen) the operating temperature T st of the fuel cell stack, and the ambient temperature T amb . The conduction heat power is determined according to the operating temperature T st of the fuel cell stack and the ambient temperature T amb . The heat dissipation power of the cooling system is determined according to the coolant inlet (outlet) temperature T incool (T outcool ) and the coolant mass flow rate .

[0079] As Figure 2 shown, in the water transport model of a proton exchange membrane fuel cell, T st is the operating temperature of the fuel cell stack, I is the operating current of the fuel cell stack, s is the volume fraction of liquid water, is the water concentration, λ is the water content of the membrane, is the water flux of the membrane, D I is the diffusion coefficient of water in the membrane, P sat is the saturation pressure of water vapor, a is the water activity, n d is the resistivity coefficient. The water transport model of a proton exchange membrane fuel cell takes the reverse diffusion water flux and the electroosmotic water flux as the outputs. Among them, the reverse diffusion water flux is determined according to the operating temperature T st of the fuel cell stack and the volume fraction s of liquid water. The electroosmotic water flux is determined according to the operating current I of the fuel cell stack, the volume fraction s of liquid water, the water concentration a, n d , and finally the water flux

[0080] The expression of water activity a is as follows:

[0081]

[0082] The saturation pressure P of water vapor sat has the following expression

[0083]

[0084] As Figure 3 shown, in the electrochemical model of a proton exchange membrane fuel cell, U cell is the terminal voltage of a single fuel cell, T st is the operating temperature of the fuel cell stack, is the absolute pressure of hydrogen, is the absolute pressure of oxygen, is the partial pressure of hydrogen, is the partial pressure of oxygen, I is the operating current of the fuel cell stack, A is the equivalent area of the membrane, R c is the equivalent electronic impedance of the cell, l is the thickness of the membrane, λ is the water content of the membrane, j is the current density, and j = I / A. The reversible voltage is determined according to the operating temperature T st of the fuel cell stack and the equivalent electronic impedance R c of the cell. The open circuit voltage is determined according to the operating temperature T st of the fuel cell stack, the absolute pressure of hydrogen the partial pressure of oxygen and the operating current I of the fuel cell stack. The activation polarization overpotential is determined according to the operating temperature T st of the fuel cell stack, the partial pressure of oxygen and the operating current I of the fuel cell stack. The concentration polarization overpotential is determined according to the operating temperature T st of the fuel cell stack and the operating current I of the fuel cell stack. The ohmic polarization overpotential is determined according to the equivalent area A of the membrane, the equivalent electronic impedance R c of the cell, the thickness l of the membrane and the water content λ of the membrane. The final model outputs the terminal voltage U cell of a single fuel cell and the operating current I of the fuel cell stack.

[0085] As Figure 5 shown, in the comprehensive model of the electro-thermal-hydraulic multi-physical quantity coupled proton exchange membrane fuel cell system of the present invention, T st is the operating temperature of the fuel cell stack, N is the number of fuel cells connected in series in the stack, T incool (T outcool ) is the coolant inlet (outlet) temperature, T is the gas inlet temperature, T atm is the ambient temperature, is the stoichiometric ratio of hydrogen (oxygen), is the proportion of cathode oxygen in the inlet gas, is the coolant mass flow rate, C H20 is the water concentration, λ is the water content of the membrane, and s is the liquid water volume fraction, is the water flux of the membrane, is the absolute pressure of hydrogen, is the absolute pressure of oxygen, is the partial pressure of hydrogen, is the partial pressure of oxygen, U cell is the single - cell fuel cell terminal voltage, I is the operating current of the fuel cell stack, A is the equivalent area of the membrane, R c is the equivalent electronic impedance of the fuel cell, and l is the thickness of the membrane. The thermal model includes a heat - generating unit and a heat - dissipating unit. The heat generation follows the relationship Q heat =Q tott -W elec where Q tot is the total chemical energy of the reactants (J), and W elec is the output electric power of the fuel cell. The heat dissipation follows the relationship Q heatsink =Q sen +Q cool +Q conv where Q sen is the sensible heat and latent heat of the reaction, Q cool is the heat discharged by the coolant of the stack, and Q conv is the heat consumed by convection. This comprehensive model takes the operating temperature T of the fuel cell stack output by the heat transfer model st and the water flux of the membrane output by the water transfer model and the water content λ of the membrane as the inputs of the electrochemical model, and finally the model outputs the single - cell fuel cell terminal voltage U cell and the operating current I of the fuel cell stack.

[0086] Taking the proton exchange membrane fuel cell system as an example, the specific steps of the PEMFC system modeling method for decoupling multi - physical quantities of electricity - heat - water proposed by the present invention are as follows:

[0087] Step S1, establish a heat transfer model of the fuel cell stack that satisfies heat balance. The heat transfer model of the fuel cell stack takes the external parameters of operating current and output voltage as input parameters and the stack temperature as the output parameter; as Figure 1 shown, the heat transfer model takes the operating current I of the fuel cell stack and the single - cell fuel cell terminal voltage U cellLet [[input parameter]] be the input parameter, the fuel cell stack temperature be the output, and the thermal balance of the fuel cell stack be defined by Equation (1). The thermal model of the PEMFC is divided into two parts: heat generation and heat dissipation. The difference between heat generation and heat dissipation leads to the temperature rise of the fuel cell stack. According to the laws of thermodynamics, the expression for the thermal balance of the fuel cell stack is as follows:

[0088]

[0089] In the formula, m stack is the mass of the stack (kg), C p,stack is the equivalent specific heat capacity of the stack (J / kg·K), T st is the temperature of the stack (K), is the rate of change of the total chemical energy of the reactants with time (W), P elec is the electric power output by the fuel cell (W), is the sensible heat power of the reaction (W), is the heat power discharged by the stack coolant (W), is the heat power consumed by convection (W);

[0090] Step S2: Establish a water transport model in the proton exchange membrane that satisfies the water balance. The external parameters of the water transport model in the proton exchange membrane, namely the operating current and the stack temperature, are input parameters, and the water content is the output parameter; as Figure 2 shown, the external parameters output by the thermal model include the operating current I of the fuel cell stack and the operating temperature T of the fuel cell stack st as the input, and the water flux of the membrane is the output of the water transport model; the water transport balance is defined according to Equation (2). The water transport in the proton exchange membrane is the balance achieved by the water flux in the membrane between the resistance force effect and the reverse diffusion. The expression for the water transport balance is as follows:

[0091]

[0092] In the formula, is the moisture flux inside the fuel cell, is the moisture flux of the internal resistance force (permeation) and reverse diffusion in the fuel cell, ρ m and M m are the density and molar mass of the membrane, is the molar mass of water, λ is the water content, which is the number of water molecules adsorbed by each sulfonic acid group in the proton exchange membrane, ▽λ is the gradient of the water content, and the physical meaning of the water content gradient is how the water content changes with position. F is the Faraday constant, D I is the diffusion coefficient (rate) of water in the membrane, n d is the resistance coefficient;

[0093] Step S3: Establish an electrochemical model of the fuel cell stack (PEMFC), which is represented by the open-circuit voltage and polarization phenomenon. According to the electrochemical model of the proton exchange membrane fuel cell defined by formula (3), as Figure 3 shown, using the external parameters output by the water model and the thermal model, namely the operating current I of the fuel cell stack, the operating temperature T of the fuel cell stack st and the water content λ as inputs, and the output voltage is the output of the electrochemical model; Formula (3) is as follows:

[0094] U cell =E 0 -U act -U conc -U oh (3)

[0095] Among them, the open-circuit voltage E 0 is as shown in formula (4-1):

[0096]

[0097] In the formula, ΔG is the change in Gibbs free energy of the hydrogen / oxygen combustion reaction, ΔH is the calorific value of hydrogen, ΔS is the entropy change of the reaction process, and are the partial pressures of hydrogen on the anode catalyst layer surface and oxygen on the cathode catalyst layer surface, respectively.

[0098] The activation polarization overpotential U act The empirical formula is as shown in formula (4-2):

[0099]

[0100] In the formula, U act is the activation polarization overpotential, ξ 1 , ξ 2 , ξ 3 , ξ 4 are parameter coefficients based on electrochemistry, kinetics, and thermodynamics, which need to be identified from the stack polarization curve, is the oxygen concentration at the cathode gas-liquid interface, and the pressure of the oxygen participating in the reaction

[0101] The ohmic polarization overpotential U oh is as shown in formula (4-3):

[0102]

[0103] In the formula, U oh is the ohmic polarization overpotential, R oh is the equivalent ohmic resistance of the fuel cell, that is, the resistance of the non-ideal electrode, the conductive plate, and the proton transfer through the membrane, R Mis the equivalent proton resistance of the fuel cell, R c is the impedance that hinders the passage of electrons through the membrane.

[0104] The equivalent proton resistance RM is shown in Equation (4-4):

[0105]

[0106] where l is the thickness of the membrane, σ m is the conductivity of the membrane, A is the effective area of the membrane, j is the current density (j = I / A), λ is the water content of the fuel cell, and T st is the operating temperature of the fuel cell.

[0107] The concentration polarization overpotential U conc is shown in Equation (4-5):

[0108]

[0109] where U conc is the concentration overpotential of the fuel cell, R is the ideal gas constant, F is the Faraday constant, z is the number of electrons transferred per unit amount of reacting gas participating in the reaction, and I and I max are the fuel cell current and the limiting current, respectively.

[0110] Step S4: Combining the water transport model, heat transport model, and electrochemical model of the proton exchange membrane fuel cell stack defined in steps S1, S2, and S3, the constructed comprehensive model of the proton exchange membrane fuel cell with multi-physical quantity coupling of electricity, heat, and water is as Figure 4 shown; the constructed comprehensive model of the proton exchange membrane fuel cell system with multi-physical quantity coupling of electricity, heat, and water consists of a coupled heat transport model, water transport model, and electrochemical model. Using the operating temperature T st of the fuel cell stack, the water flux of the membrane output by the water transport model, and the water content λ of the membrane as the inputs of the comprehensive model, subsequent processing is performed through the electrochemical model, including determining the reversible voltage based on the operating temperature T st of the fuel cell stack and the equivalent electron impedance R c of the battery, determining the open circuit voltage based on the operating temperature T st of the fuel cell stack, the absolute pressure of hydrogen the partial pressure of oxygen and the operating current I of the fuel cell stack, determining the activation polarization overpotential based on the operating temperature T st of the fuel cell stack, the partial pressure of oxygen and the operating current I of the fuel cell stack, and determining the concentration polarization overpotential based on the operating temperature T st, determined by the operating current I of the fuel cell stack, j is the current density, and the ohmic polarization overpotential is determined by the equivalent area A of the membrane, the equivalent electronic impedance R of the cell c , the thickness l of the membrane, and the water content λ of the membrane. Finally, the single-cell fuel cell terminal voltage U is output by the comprehensive model cell and the operating current I of the fuel cell stack;

[0111] Step S5: According to the comprehensive model of the electro-thermal-hydraulic multi-physical quantity coupled proton exchange membrane fuel cell, the key parameters of the thermal-hydraulic-electricity interaction of the PEMFC system with an external DC load are extracted, which are the fuel cell stack temperature, water content, and output voltage respectively, and they are all affected by the change of the external operating current;

[0112] Step S6: Use the comprehensive model of the electro-thermal-hydraulic multi-physical quantity coupled proton exchange membrane fuel cell to analyze the change characteristics of the fuel cell stack temperature, water content, and output voltage characteristics under the change of the external operating conditions. Specifically, the electrochemical reaction process of the PEMFC will affect the heat conduction and water transport processes. For example, according to the polarization characteristic curve of the fuel cell, as the operating current increases, the output voltage decreases, resulting in an increase in the operating temperature and a decrease in the water content. Conversely, the operating temperature and water content will change the output voltage by affecting the polarization voltage.

[0113] Step S7: Decouple according to the change characteristics of the fuel cell stack temperature, water content, and output voltage characteristics at different time scales under different external conditions. After decoupling, the key variables of the comprehensive model of the electro-thermal-hydraulic multi-physical quantity coupled proton exchange membrane fuel cell are relatively independent to realize the extraction of the key parameters of the proton exchange membrane fuel cell system. Specifically, first analyze the response characteristics of the stack temperature and water content when the PEMFC operating conditions (operating current) change at different time scales (seconds, minutes, hours). On this basis, analyze the influence of different orders of magnitude changes in the stack temperature and water content on the output voltage, and obtain the change characteristics of the physical quantities in each field under different operating conditions, so as to realize the decoupling at multiple time scales of seconds, minutes, and hours.

[0114] Analysis shows that when the external load current (operating conditions) changes rapidly in a short time below the second level, the temperature and water content of the PEMFC stack change little and have little impact on the operation of the PEMFC system.

[0115] As Figure 6 shown, the decoupled electro-thermal-hydraulic multi-physical quantity PEMFC system modeling device of the present invention is used to execute the decoupled electro-thermal-hydraulic multi-physical quantity proton exchange membrane fuel cell modeling method of the present invention. The device includes an electro-thermal-hydraulic independent model construction module, an electro-thermal-hydraulic coupling model construction module, a key parameter extraction module, and a key parameter decoupling module; among them:

[0116] The electro-thermal-water independent model construction module is used to establish a heat transfer model of a fuel cell stack that satisfies thermal equilibrium. The heat transfer model of the fuel cell stack takes the external parameters of operating current and output voltage as input parameters and the stack temperature as the output parameter; establish a water transport model in the proton exchange membrane that satisfies water balance. The water transport model in the proton exchange membrane takes the external parameters of operating current and stack temperature as input parameters and the water content as the output parameter; and, establish an electrochemical model of the fuel cell stack as shown in the following formula:

[0117] U cell =E 0 -U act -U conc -U oh

[0118] In the formula, E 0 is the open-circuit voltage, U act is the activation polarization overpotential, U oh is the ohmic polarization overpotential, concentration polarization overpotential, U conc is the concentration polarization overpotential;

[0119] The electro-thermal-water coupling model construction module is used to utilize the heat transfer model of the fuel cell stack, the water transport model in the proton exchange membrane, and the electrochemical model of the fuel cell stack to construct a comprehensive model of a proton exchange membrane fuel cell system with multi-physical quantity coupling of electro-thermal-water. This comprehensive model is composed of a coupled heat transfer model, water transport model, and electrochemical model. Taking the operating temperature of the fuel cell stack, the water flux of the membrane and the water content λ of the membrane output by the water transport model as the input of the comprehensive model, and performing subsequent processing through the electrochemical model, including that the reversible voltage is determined according to the operating temperature T st of the fuel cell stack and the equivalent electronic impedance of the battery, the open-circuit voltage is determined according to the operating temperature of the fuel cell stack, the absolute pressure of hydrogen, the partial pressure of oxygen, and the operating current of the fuel cell stack, the activation polarization overpotential is determined according to the operating temperature of the fuel cell stack, the partial pressure of oxygen, and the operating current of the fuel cell stack, the concentration polarization overpotential is determined according to the operating temperature T st of the fuel cell stack and the operating current of the fuel cell stack, the ohmic polarization overpotential is determined according to the equivalent area A of the membrane, the equivalent electronic impedance of the battery, the thickness of the membrane, and the water content of the membrane. Finally, the single-cell fuel cell terminal voltage U cell and the operating current of the fuel cell stack are output by the comprehensive model;

[0120] The key parameter extraction module is used to extract the mutually coupled key parameters including the fuel cell stack temperature, water content, and output voltage according to the comprehensive model of the proton exchange membrane fuel cell with multi-physical quantity coupling of electro-thermal-water;

[0121] A key parameter decoupling module is used to extract the key parameters of heat - water - electricity from the comprehensive model of a proton exchange membrane fuel cell with electro - thermal - water multi - physical quantity coupling, analyze the variation characteristics of the temperature, water content, and output voltage characteristics of the fuel cell stack under the change of the external operating conditions; and decouple according to the variation characteristics of the fuel cell stack temperature, water content, and output voltage characteristics at different time scales of the external conditions to achieve the extraction of key parameters of the proton exchange membrane fuel cell system.

[0122] For the system of the proton exchange membrane fuel cell's external circuit, when the system operating conditions change, there are problems such as complex multi - physical quantity coupling in the multi - physical field of heat - water - electricity and large computational amount. Therefore, the present invention reduces the computational complexity during model construction and facilitates the analysis of the influence of external changes in the power system on the inside.

[0123] The present invention is based on the comprehensive model of the proton exchange membrane fuel cell as shown in Figure 4 and obtains the polarization characteristic curve of the PEMFC as shown in Figure 7 .

[0124] It should be noted that although the present invention has been shown and described with reference to specific exemplary embodiments of the present invention, those skilled in the art should understand that the present invention is not limited to the above - mentioned embodiments. The above content is only an embodiment of the present invention, and its purpose is not to limit the systems and methods proposed by the present invention. The protection scope of the present invention is defined by the claims. Without departing from the spirit and scope of the present invention, various obvious modifications or changes in form and details made by those skilled in the art without deviating from the scope and spirit of the present invention shall fall within the protection scope of the present invention.

Claims

1. A PEMFC system modeling method for decoupling multiple physical quantities of electricity, heat and water, characterized in that: include: Establishing a heat transfer model for a fuel cell stack that satisfies thermal balance, wherein the heat transfer model for the fuel cell stack uses external parameters, operating current and output voltage, as input parameters and uses stack temperature as an output parameter; A water transport model in a proton exchange membrane that satisfies water balance is established, wherein the external parameters of the water transport model in the proton exchange membrane include operating current and stack temperature as input parameters, and water content as output parameter; The electrochemical model of the fuel cell stack is established as follows: IN cell =E0-U act -IN conc -IN oh Where E0 is the open circuit voltage, U act is the activation polarization overpotential, U oh is the ohmic polarization overpotential, the concentration polarization overpotential, U conc is the concentration polarization overpotential; The heat transfer model of the fuel cell stack, the water transport model in the proton exchange membrane and the electrochemical model of the fuel cell stack are used to construct a comprehensive model of the proton exchange membrane fuel cell system with coupled electric-heat-water multi-physical quantities. The comprehensive model is composed of a coupled heat transfer model, a water transfer model and an electrochemical model. The operating temperature of the fuel cell stack, the water flux of the membrane output by the water transfer model and the water content λ of the membrane are used as inputs of the comprehensive model. The electrochemical model is used for subsequent processing, including the reversible voltage according to the operating temperature T of the fuel cell stack. st and the battery equivalent electronic impedance, the open circuit voltage is determined according to the fuel cell stack operating temperature, the absolute pressure of hydrogen, the partial pressure of oxygen and the fuel cell stack operating current, the activation polarization overpotential is determined according to the fuel cell stack operating temperature, the partial pressure of oxygen and the fuel cell stack operating current, and the concentration polarization overpotential is determined according to the fuel cell stack operating temperature T st , the fuel cell stack operating current, the ohmic polarization overpotential is determined according to the equivalent area A of the membrane, the battery equivalent electronic impedance, the thickness of the membrane and the water content of the membrane. Finally, the comprehensive model outputs the single-chip fuel cell terminal voltage U cell and fuel cell stack operating current; According to the comprehensive model of the proton exchange membrane fuel cell coupled with multiple physical quantities of electricity, heat and water, the key parameters of mutual coupling including fuel cell stack temperature, water content and output voltage are extracted; The comprehensive model of the proton exchange membrane fuel cell coupled with multiple physical quantities of electricity, heat and water is used to extract the proton exchange membrane fuel cell model of the key parameters of heat, water and electricity to analyze the change characteristics of the fuel cell stack temperature, water content and output voltage characteristics when the external operating conditions change; The temperature, water content and output voltage of the fuel cell stack are decoupled according to their changing characteristics under different time scales of external working conditions, so as to realize the extraction of key parameters of the proton exchange membrane fuel cell system.

2. The PEMFC system modeling method for decoupling electricity, heat and water multi-physical quantities according to claim 1 is characterized in that: The thermal balance of the fuel cell stack is expressed as follows: In the formula, m stack is the mass of the battery stack, C p,stack is the equivalent specific heat capacity of the stack, T st is the temperature of the battery stack, is the rate of change of the total chemical energy of the reactants with time, P elec is the electrical power output of the fuel cell, is the sensible heat power of the reaction, is the heat power discharged by the stack coolant, is the heat power consumed by convection.

3. The PEMFC system modeling method for decoupling electricity, heat and water multi-physical quantities according to claim 1 is characterized in that: The expression of water transport balance in the proton exchange membrane is as follows: In the formula, is the water flux inside the fuel cell, is the internal resistance of the fuel cell and the water flux of reverse diffusion, ρ m and M m are the density and molar mass of the membrane, is the molar mass of water, λ is the water content, and is the number of water molecules adsorbed by each sulfonic acid group in the proton exchange membrane. is the gradient of water content. The physical meaning of water content gradient is how water content changes with position. F is the Faraday constant. D I is the diffusion coefficient of water in the membrane, n d is the resistivity.

4. The PEMFC system modeling method for decoupling electricity, heat and water multi-physical quantities according to claim 1 is characterized in that: in, The formula of the open circuit voltage E0 is as follows: In the formula, ΔG is the change in Gibbs free energy of hydrogen / oxygen combustion reaction, ΔH is the calorific value of hydrogen, and ΔS is the entropy change of the reaction process. and are the partial pressure of hydrogen on the surface of the anode catalyst layer and the partial pressure of oxygen on the surface of the cathode catalyst layer respectively; The activation polarization overpotential U act The empirical formula is as follows: Where U act is the activation polarization overpotential, ξ1, ξ2, ξ3, ξ4 are parameter coefficients based on electrochemistry, kinetics and thermodynamics, C O2 is the oxygen concentration at the cathode gas-liquid interface, and the pressure of the oxygen participating in the reaction is P O2 ; The ohmic polarization overpotential U oh The formula is as follows: U oh =AND oh =I(R M +R c ) Where U oh is the Ohmic polarization overpotential, R oh is the equivalent ohmic resistance of the fuel cell, i.e. the resistance of non-ideal electrodes and conductive plates as well as proton transfer through the membrane, R M is the equivalent proton resistance of the fuel cell, R c The resistance that hinders the passage of electrons through the membrane; The equivalent proton resistance R M The formula is as follows: Where l is the thickness of the film, σ m is the conductivity of the membrane, A is the effective area of ​​the membrane, j is the current density, λ is the water content of the fuel cell, T st is the operating temperature of the fuel cell; The concentration polarization overpotential U conc The formula is as follows: Where U conc is the concentration overpotential of the fuel cell, R is the ideal gas constant, F is the Faraday constant, z is the number of electrons transferred per unit mass of the reaction gas, I and I max are the fuel cell current and the limiting current respectively.

5. The PEMFC system modeling method for decoupling electricity, heat and water multi-physical quantities according to claim 1 is characterized in that: The comprehensive model of the proton exchange membrane fuel cell with coupled electricity, heat and water multiple physical quantities is connected to an external DC load. The key parameters of the proton exchange membrane fuel cell system extracted by decoupling include the fuel cell stack temperature, water content and output voltage, which are all affected by changes in the external operating current.

6. A PEMFC system modeling device for decoupling multiple physical quantities of electricity, heat and water, characterized in that: It includes an electric-thermal-water independent model building module, an electric-thermal-water coupled model building module, a key parameter extraction module and a key parameter decoupling module; among which: The electric-heat-water independent model building module is used to establish a heat transfer model of a fuel cell stack that satisfies thermal balance, wherein the heat transfer model of the fuel cell stack uses external parameters of operating current and output voltage as input parameters and uses stack temperature as output parameter; establish a water transport model in a proton exchange membrane that satisfies water balance, wherein the external parameters of the water transport model in the proton exchange membrane use operating current and stack temperature as input parameters and water content as output parameter; and establish an electrochemical model of a fuel cell stack as shown in the following formula: IN cell =E0-U act -IN conc -IN oh Where E0 is the open circuit voltage, U act is the activation polarization overpotential, U oh is the ohmic polarization overpotential, the concentration polarization overpotential, U conc is the concentration polarization overpotential; The electric-thermal-water coupling model building module is used to construct a comprehensive model of the proton exchange membrane fuel cell system with electric-thermal-water multi-physical quantity coupling by using the heat transfer model of the fuel cell stack, the water transport model in the proton exchange membrane and the electrochemical model of the fuel cell stack. The comprehensive model is composed of a coupled heat transfer model, a water transfer model and an electrochemical model. The operating temperature of the fuel cell stack, the water flux of the membrane output by the water transfer model and the water content λ of the membrane are used as inputs of the comprehensive model. The electrochemical model is used for subsequent processing, including the reversible voltage according to the operating temperature T of the fuel cell stack. st and the battery equivalent electronic impedance, the open circuit voltage is determined according to the fuel cell stack operating temperature, the absolute pressure of hydrogen, the partial pressure of oxygen and the fuel cell stack operating current, the activation polarization overpotential is determined according to the fuel cell stack operating temperature, the partial pressure of oxygen and the fuel cell stack operating current, and the concentration polarization overpotential is determined according to the fuel cell stack operating temperature T st , the fuel cell stack operating current, the ohmic polarization overpotential is determined according to the equivalent area A of the membrane, the battery equivalent electronic impedance, the thickness of the membrane and the water content of the membrane. Finally, the comprehensive model outputs the single-chip fuel cell terminal voltage U cell and fuel cell stack operating current; The key parameter extraction module is used to extract mutually coupled key parameters including fuel cell stack temperature, water content and output voltage according to the comprehensive model of the proton exchange membrane fuel cell coupled with multiple physical quantities of electricity, heat and water; The key parameter decoupling module is used to extract the heat-water-electricity key parameters of the proton exchange membrane fuel cell model using the comprehensive model of the proton exchange membrane fuel cell coupled with the electric-heat-water multi-physical quantities to analyze the changing characteristics of the fuel cell stack temperature, water content and output voltage characteristics when the external operating conditions change; and to decouple the changing characteristics of the fuel cell stack temperature, water content and output voltage characteristics under different time scales of external conditions to realize the extraction of key parameters of the proton exchange membrane fuel cell system.

7. The PEMFC system modeling device for decoupling electricity, heat and water multi-physical quantities according to claim 6, characterized in that: The thermal balance of the fuel cell stack is expressed as follows: In the formula, m stack is the mass of the battery stack, C p,stack is the equivalent specific heat capacity of the stack, T st is the temperature of the battery stack, is the rate of change of the total chemical energy of the reactants with time, P elec is the electrical power output of the fuel cell, is the sensible heat power of the reaction, is the heat power discharged by the stack coolant, is the heat power consumed by convection.

8. The PEMFC system modeling device for decoupling electricity, heat and water multi-physical quantities according to claim 6, characterized in that: The expression of water transport balance in the proton exchange membrane is as follows: In the formula, is the water flux inside the fuel cell, is the internal resistance of the fuel cell and the water flux of reverse diffusion, ρ m and M m are the density and molar mass of the membrane, is the molar mass of water, λ is the water content, and is the number of water molecules adsorbed by each sulfonic acid group in the proton exchange membrane. is the gradient of water content. The physical meaning of water content gradient is how water content changes with position. F is the Faraday constant. D I is the diffusion coefficient of water in the membrane, n d is the resistivity.

9. The PEMFC system modeling device for decoupling electricity, heat and water multi-physical quantities according to claim 6, characterized in that: in, The formula of the open circuit voltage E0 is as follows: Where ΔG is the change in Gibbs free energy of hydrogen / oxygen combustion reaction, ΔH is the calorific value of hydrogen, ΔS is the entropy change of the reaction process, and p H2 With p O2 are the partial pressure of hydrogen on the surface of the anode catalyst layer and the partial pressure of oxygen on the surface of the cathode catalyst layer respectively; The activation polarization overpotential U act The empirical formula is as follows: Where U act is the activation polarization overpotential, ξ1, ξ2, ξ3, ξ4 are parameter coefficients based on electrochemistry, kinetics and thermodynamics, C O2 is the oxygen concentration at the cathode gas-liquid interface, and the pressure of the oxygen participating in the reaction is P O2 ; The ohmic polarization overpotential U oh The formula is as follows: U oh =AND oh =I(R M +R c ) Where U oh is the Ohmic polarization overpotential, R oh is the equivalent ohmic resistance of the fuel cell, i.e. the resistance of non-ideal electrodes and conductive plates as well as proton transfer through the membrane, R M is the equivalent proton resistance of the fuel cell, R c The resistance that hinders the passage of electrons through the membrane; The equivalent proton resistance R M The formula is as follows: Where l is the thickness of the film, σ m is the conductivity of the membrane, A is the effective area of ​​the membrane, j is the current density, λ is the water content of the fuel cell, T st is the operating temperature of the fuel cell; The concentration polarization overpotential U conc The formula is as follows: Where U conc is the concentration overpotential of the fuel cell, R is the ideal gas constant, F is the Faraday constant, z is the number of electrons transferred per unit mass of the reaction gas, I and I max are the fuel cell current and the limiting current respectively.

10. The PEMFC system modeling device for decoupling electricity, heat and water multi-physical quantities according to claim 6, characterized in that: The comprehensive model of the proton exchange membrane fuel cell with coupled electricity, heat and water multiple physical quantities is connected to an external DC load. The key parameters of the proton exchange membrane fuel cell system extracted by decoupling include the fuel cell stack temperature, water content and output voltage, which are all affected by changes in the external operating current.

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