CN113903956A - Proton exchange membrane fuel cell modeling method and device - Google Patents
Proton exchange membrane fuel cell modeling method and device Download PDFInfo
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- 239000012528 membrane Substances 0.000 title claims abstract description 233
- 239000000446 fuel Substances 0.000 title claims abstract description 104
- 238000000034 method Methods 0.000 title claims abstract description 48
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 claims abstract description 189
- 239000000376 reactant Substances 0.000 claims abstract description 108
- 230000004913 activation Effects 0.000 claims abstract description 32
- 230000032895 transmembrane transport Effects 0.000 claims abstract description 19
- 230000005540 biological transmission Effects 0.000 claims abstract description 13
- 230000032258 transport Effects 0.000 claims description 15
- 230000010287 polarization Effects 0.000 claims description 12
- 238000012546 transfer Methods 0.000 claims description 9
- 238000009826 distribution Methods 0.000 claims description 8
- 239000007788 liquid Substances 0.000 claims description 8
- 230000004044 response Effects 0.000 claims description 8
- 229920006395 saturated elastomer Polymers 0.000 claims description 8
- 230000008859 change Effects 0.000 claims description 7
- 238000009792 diffusion process Methods 0.000 claims description 5
- 238000005370 electroosmosis Methods 0.000 claims description 5
- 238000012545 processing Methods 0.000 claims description 5
- 230000003068 static effect Effects 0.000 claims description 5
- 238000004134 energy conservation Methods 0.000 claims description 3
- 206010016807 Fluid retention Diseases 0.000 claims 1
- 238000004364 calculation method Methods 0.000 abstract description 15
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- UFHFLCQGNIYNRP-UHFFFAOYSA-N Hydrogen Chemical compound [H][H] UFHFLCQGNIYNRP-UHFFFAOYSA-N 0.000 description 6
- QVGXLLKOCUKJST-UHFFFAOYSA-N atomic oxygen Chemical compound [O] QVGXLLKOCUKJST-UHFFFAOYSA-N 0.000 description 6
- 239000001301 oxygen Substances 0.000 description 6
- 229910052760 oxygen Inorganic materials 0.000 description 6
- 238000004422 calculation algorithm Methods 0.000 description 5
- 239000001257 hydrogen Substances 0.000 description 5
- 229910052739 hydrogen Inorganic materials 0.000 description 5
- 239000000463 material Substances 0.000 description 4
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- 230000036961 partial effect Effects 0.000 description 3
- LFQSCWFLJHTTHZ-UHFFFAOYSA-N Ethanol Chemical compound CCO LFQSCWFLJHTTHZ-UHFFFAOYSA-N 0.000 description 2
- 238000004458 analytical method Methods 0.000 description 2
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- 229910052757 nitrogen Inorganic materials 0.000 description 2
- 230000036284 oxygen consumption Effects 0.000 description 2
- 230000004043 responsiveness Effects 0.000 description 2
- 238000012795 verification Methods 0.000 description 2
- MYMOFIZGZYHOMD-UHFFFAOYSA-N Dioxygen Chemical compound O=O MYMOFIZGZYHOMD-UHFFFAOYSA-N 0.000 description 1
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
- H01M8/00—Fuel cells; Manufacture thereof
- H01M8/04—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids
- H01M8/04298—Processes for controlling fuel cells or fuel cell systems
- H01M8/04305—Modeling, demonstration models of fuel cells, e.g. for training purposes
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
- H01M8/00—Fuel cells; Manufacture thereof
- H01M8/10—Fuel cells with solid electrolytes
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
- Y02E60/30—Hydrogen technology
- Y02E60/50—Fuel cells
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Abstract
The disclosure relates to a modeling method and device for a proton exchange membrane fuel cell. Wherein, the method comprises the following steps: establishing an anode model/cathode model according to mass conservation of an anode/cathode reactant; establishing a proton exchange membrane water transmission model according to the transmembrane transport volume of water in the proton exchange membrane; establishing a voltage model according to the positive correlation relationship between the external voltage of the proton exchange membrane fuel cell and the open-circuit voltage and the negative correlation relationship between the external voltage and the activation voltage drop, the ohmic voltage drop and the concentration voltage drop; and optimizing the input quantity and the output quantity of each model to establish a proton exchange membrane fuel cell model. The proton exchange membrane fuel cell is modeled based on the anode model, the cathode model, the proton exchange membrane water model and the voltage model, and the proton exchange membrane fuel cell model is greatly simplified and the calculation efficiency is improved by adopting a parameter coupling and empirical formula introduction mode.
Description
Technical Field
The disclosure relates to the field of new energy application, in particular to a proton exchange membrane fuel cell modeling method and device.
Background
Fuel cells are an electrochemical device that can convert chemical energy in reactants into electrical energy and are widely recognized as a possible future alternative to conventional power sources. Currently, the application of fuel cells is emphasized, firstly, global greenhouse effect forces people to seek clean energy, and secondly, the technologies of preparation, transportation, storage and the like of the current cell fuel are mature day by day. The charge and discharge process of the fuel cell is reversible, which makes it possible to use it as a long-term power source. The reactants used in the fuel cell are reducing agents for the anode, and usually hydrogen, ethanol, etc.; and the oxidant for the cathode, typically air, and sometimes pure oxygen. The two electrodes are separated by a dielectric layer, such as a proton exchange membrane.
In order to study and describe the operating state of proton exchange membrane fuel cells, researchers have proposed many different models. The distribution parameters are classified into one-dimensional, two-dimensional and three-dimensional models according to the spatial dimension. One-dimensional and two-dimensional mathematical models can better describe the performance of the single battery, but for a large-scale battery pack power supply, a three-dimensional model is needed for description. The existing three-dimensional model is based on different three-dimensional flow channels, describes and models a large number of free variables in the proton exchange membrane fuel cell, needs a large amount of calculation and complex logical relations, and has low response speed and poor simulation effect.
Accordingly, there is a need for one or more methods to address the above-mentioned problems.
It is to be noted that the information disclosed in the above background section is only for enhancement of understanding of the background of the present disclosure, and thus may include information that does not constitute prior art known to those of ordinary skill in the art.
Disclosure of Invention
It is an object of the present disclosure to provide a proton exchange membrane fuel cell modeling method and apparatus that overcomes, at least to some extent, one or more of the problems due to the limitations and disadvantages of the related art.
According to one aspect of the present disclosure, there is provided a proton exchange membrane fuel cell modeling method, including:
establishing an anode model according to the mass conservation of an anode reactant at an anode, wherein the anode model takes the transmembrane flow rate of water of a proton exchange membrane, the flow rate of the anode reactant, the relative humidity of the anode, the pressure of the anode and the ambient temperature as input quantities, and takes the relative humidity of the anode side of the proton exchange membrane and the output pressure of the anode reactant as output quantities;
establishing a cathode model according to the mass conservation of a cathode reactant at a cathode, wherein the cathode model takes the transmembrane water flow rate of a proton exchange membrane, the flow rate of the cathode reactant, the relative humidity of the cathode, the pressure of the cathode, the ambient temperature and the content of the cathode reactant as input quantities, and takes the relative humidity of the cathode side of the proton exchange membrane and the output pressure of the cathode reactant as output quantities;
establishing a proton exchange membrane water transmission model according to the transmembrane transport volume of water in a proton exchange membrane, wherein the proton exchange membrane water transmission model takes the relative humidity of the anode side of the proton exchange membrane and the relative humidity of the cathode side of the proton exchange membrane as input and takes the transmembrane flow rate of water in the proton exchange membrane and a membrane water constant as output;
establishing a voltage model according to the positive correlation relation between the external voltage and the open-circuit voltage of the proton exchange membrane fuel cell and the negative correlation relation between the external voltage and the activation voltage drop, the ohmic voltage drop and the concentration voltage drop, wherein the voltage model takes a membrane water constant, an anode reactant output pressure and a cathode reactant output pressure as input quantities, and takes an external voltage as an output quantity;
respectively establishing dynamic relations between input quantity and output quantity of an anode model, a cathode model and a proton exchange membrane water transmission model, establishing a steady-state relation between anode pressure and anode reactant output pressure and between cathode pressure and cathode reactant output pressure, optimizing the dynamic relations between the input quantity and the output quantity of the anode model, the cathode model and the proton exchange membrane water model, and establishing a proton exchange membrane fuel cell model.
In an exemplary embodiment of the present disclosure, the method further comprises:
and calculating the energy distribution of the proton exchange membrane fuel cell based on energy conservation, establishing an energy model, and calculating the energy distribution of the proton exchange membrane fuel cell.
In an exemplary embodiment of the present disclosure, the establishing an anode model further includes:
when the anode model is established, the anode model is established by calculating the flow of the anode reactant and the consumption of the anode reactant on the assumption that the variable of an anode outlet valve is zero, the liquid water reserve of the anode is zero, and the water mass when the anode gaseous water mass is less than or equal to the anode saturated water pressure.
In an exemplary embodiment of the present disclosure, the establishing the cathode model further includes:
when the cathode model is established, the mass of cathode gaseous water is 1.5 times of that of cathode saturated water at atmospheric pressure, the flow of the cathode reactant is calculated through approximate linear processing, the output pressure of the cathode reactant is obtained, and then the cathode model is established.
In an exemplary embodiment of the present disclosure, the establishing the proton exchange membrane water transport model further includes:
and analyzing the transmembrane transport mode of electroosmosis and diffusion generated by water concentration gradient, introducing an empirical formula for calculating the membrane water constant, and further establishing a proton exchange membrane water transport model.
In an exemplary embodiment of the present disclosure, the establishing the voltage model further includes:
according to the positive correlation relation between the external voltage and the open-circuit voltage of the proton exchange membrane fuel cell and the negative correlation relation between the external voltage and the activation voltage drop, the ohmic voltage drop and the concentration voltage drop, an open-circuit voltage model, an activation voltage drop model, an ohmic voltage drop model and a concentration voltage drop model are respectively established, and then a voltage model is established.
In an exemplary embodiment of the present disclosure, the method further comprises:
establishing an open-circuit voltage model taking anode pressure, cathode pressure and temperature in the battery as input quantities based on Gibbs free energy change characteristics;
introducing an activation voltage drop empirical formula based on a Butler-fop-Johnmer equation, and establishing an activation voltage drop model;
establishing an ohmic voltage drop model taking the thickness, the conductivity and the water constant of the proton exchange membrane as input quantities based on the ohmic polarization;
and introducing a concentration voltage drop empirical formula based on the positive correlation relationship of current density, mass transfer speed and reactant concentration gradient, and establishing a concentration voltage drop model.
In an exemplary embodiment of the present disclosure, the method further comprises:
analyzing the influence of the selection of the working point of the proton exchange membrane fuel cell on the working performance of the proton exchange membrane fuel cell according to the voltage static characteristic of the voltage model of the proton exchange membrane fuel cell;
and analyzing influence factors of the response capability of the proton exchange membrane fuel cell based on Euler algorithm simulation according to the voltage dynamic characteristics of the proton exchange membrane fuel cell voltage model.
In one aspect of the present disclosure, there is provided a proton exchange membrane fuel cell modeling apparatus, comprising:
the anode model establishing module is used for establishing an anode model according to the mass conservation of an anode reactant at the anode, wherein the anode model takes the water transmembrane flow rate of the proton exchange membrane, the anode reactant flow, the anode relative humidity, the anode pressure and the ambient temperature as input quantities, and takes the anode side relative humidity of the proton exchange membrane and the anode reactant output pressure as output quantities;
the cathode model establishing module is used for establishing a cathode model according to the mass conservation of a cathode reactant at the cathode, wherein the cathode model takes the water transmembrane flow rate of the proton exchange membrane, the cathode reactant flow, the cathode relative humidity, the cathode pressure, the environment temperature and the cathode reactant content as input quantities and takes the cathode side relative humidity of the proton exchange membrane and the cathode reactant output pressure as output quantities;
the proton exchange membrane water model establishing module is used for establishing a proton exchange membrane water model according to transmembrane transport volume of water in a proton exchange membrane, wherein the proton exchange membrane water model takes relative humidity on the anode side of the proton exchange membrane and relative humidity on the cathode side of the proton exchange membrane as input, and takes transmembrane water flow rate and a membrane water constant of the proton exchange membrane as output;
the voltage model establishing module is used for establishing a voltage model according to the positive correlation relation between the external voltage and the open-circuit voltage of the proton exchange membrane fuel cell and the negative correlation relation between the external voltage and the activation voltage drop, the ohmic voltage drop and the concentration voltage drop, wherein the voltage model takes a membrane water constant, the output pressure of an anode reactant and the output pressure of a cathode reactant as input quantities, and takes the external voltage as an output quantity;
the fuel cell model generation module is used for respectively establishing the dynamic relations of the input quantity and the output quantity of the anode model, the cathode model and the proton exchange membrane water model, establishing the steady-state relation of the anode pressure and the anode reactant output pressure and the steady-state relation of the cathode pressure and the cathode reactant output pressure, optimizing the dynamic relations of the input quantity and the output quantity of the anode model, the cathode model and the proton exchange membrane water model, and establishing the proton exchange membrane fuel cell model.
A proton exchange membrane fuel cell modeling method in an exemplary embodiment of the present disclosure, the method comprising: establishing an anode model/cathode model according to the mass conservation of the anode/cathode reactant at the anode; establishing a proton exchange membrane water model according to the transmembrane transport volume of water in the proton exchange membrane; establishing a voltage model according to the positive correlation relationship between the external voltage of the proton exchange membrane fuel cell and the open-circuit voltage and the negative correlation relationship between the external voltage and the activation voltage drop, the ohmic voltage drop and the concentration voltage drop; and optimizing the input quantity and the output quantity of each model to establish a proton exchange membrane fuel cell model. The proton exchange membrane fuel cell is modeled based on the anode model, the cathode model, the proton exchange membrane water model and the voltage model, the proton exchange membrane fuel cell model is greatly simplified by adopting a mode of parameter approximate coupling and introducing an empirical formula, and the simulation verification has higher responsiveness.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosure.
Drawings
The above and other features and advantages of the present disclosure will become more apparent by describing in detail exemplary embodiments thereof with reference to the attached drawings.
FIG. 1 shows a flow chart of a proton exchange membrane fuel cell modeling method according to an exemplary embodiment of the present disclosure;
FIG. 2 illustrates a proton exchange membrane fuel cell mass transfer schematic of a proton exchange membrane fuel cell modeling method according to an exemplary embodiment of the present disclosure;
FIG. 3 shows a proton exchange membrane fuel cell gross model schematic of a proton exchange membrane fuel cell modeling method according to an exemplary embodiment of the present disclosure;
FIG. 4 shows a schematic block diagram of a proton exchange membrane fuel cell modeling apparatus in accordance with an exemplary embodiment of the present disclosure;
Detailed Description
Example embodiments will now be described more fully with reference to the accompanying drawings. Example embodiments may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of example embodiments to those skilled in the art. The same reference numerals denote the same or similar parts in the drawings, and thus, a repetitive description thereof will be omitted.
Furthermore, the described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a thorough understanding of embodiments of the disclosure. One skilled in the relevant art will recognize, however, that the embodiments of the disclosure can be practiced without one or more of the specific details, or with other methods, components, materials, devices, steps, and so forth. In other instances, well-known structures, methods, devices, implementations, materials, or operations are not shown or described in detail to avoid obscuring aspects of the disclosure.
In the present exemplary embodiment, a proton exchange membrane fuel cell modeling method is first provided; referring to fig. 1, the modeling method of the proton exchange membrane fuel cell may include the steps of:
step S110, establishing an anode model according to the mass conservation of an anode reactant at the anode, wherein the anode model takes the water transmembrane flow rate of a proton exchange membrane, the flow rate of the anode reactant, the relative humidity of the anode, the pressure of the anode and the ambient temperature as input quantities, and takes the relative humidity of the anode side of the proton exchange membrane and the output pressure of the anode reactant as output quantities;
step S120, establishing a cathode model according to the mass conservation of a cathode reactant at the cathode, wherein the cathode model takes the water transmembrane flow rate of the proton exchange membrane, the flow rate of the cathode reactant, the cathode relative humidity, the cathode pressure, the environment temperature and the cathode reactant content as input quantities, and takes the cathode side relative humidity of the proton exchange membrane and the cathode reactant output pressure as output quantities;
step S130, establishing a proton exchange membrane water model according to the transmembrane transport volume of water in the proton exchange membrane, wherein the proton exchange membrane water model takes the relative humidity of the anode side of the proton exchange membrane and the relative humidity of the cathode side of the proton exchange membrane as input, and takes the transmembrane flow rate of water in the proton exchange membrane and a membrane water constant as output;
step S140, establishing a voltage model according to the positive correlation relation between the external voltage and the open-circuit voltage of the proton exchange membrane fuel cell and the negative correlation relation between the external voltage and the activation voltage drop, the ohmic voltage drop and the concentration voltage drop, wherein the voltage model takes a membrane water constant, the output pressure of an anode reactant and the output pressure of a cathode reactant as input quantities, and takes the external voltage as an output quantity;
step S150, respectively establishing dynamic relations of input quantity and output quantity of the anode model, the cathode model and the proton exchange membrane water model, establishing steady-state relations of anode pressure and anode reactant output pressure and cathode reactant output pressure, optimizing the dynamic relations of the input quantity and output quantity of the anode model, the cathode model and the proton exchange membrane water model, and establishing the proton exchange membrane fuel cell model.
A proton exchange membrane fuel cell modeling method in an exemplary embodiment of the present disclosure, the method comprising: establishing an anode model/cathode model according to the mass conservation of the anode/cathode reactant at the anode; establishing a proton exchange membrane water model according to the transmembrane transport volume of water in the proton exchange membrane; establishing a voltage model according to the positive correlation relationship between the external voltage of the proton exchange membrane fuel cell and the open-circuit voltage and the negative correlation relationship between the external voltage and the activation voltage drop, the ohmic voltage drop and the concentration voltage drop; and optimizing the input quantity and the output quantity of each model to establish a proton exchange membrane fuel cell model. The proton exchange membrane fuel cell is modeled based on the anode model, the cathode model, the proton exchange membrane water model and the voltage model, the proton exchange membrane fuel cell model is greatly simplified by adopting a mode of parameter approximate coupling and introducing an empirical formula, and the simulation verification has higher responsiveness.
Next, the proton exchange membrane fuel cell modeling method in the present example embodiment will be further explained.
In the present exemplary embodiment, a proton exchange membrane fuel cell mass transfer schematic is shown in fig. 2, where the subscript re denotes the fraction consumed and produced by the chemical reaction and m denotes the transmembrane transport fraction, regardless of the cell's spatial structure.
The complete model of the proton exchange membrane fuel cell comprises submodels including an anode model, a cathode model, an exchange membrane water model, a voltage model for determining response and an energy module for calculating temperature.
The mass transfer condition inside the proton exchange membrane fuel cell model and the influence on the external observed quantity voltage are mainly shown in figure 3. Outside of the frame Ia，TeCurrent density (a/cm2), cell temperature (K), respectively, are global variables. The temperature T of the battery is given in the text by an energy model according to the conservation of energyeA calculation is performed, and the model will be described later.
To simplify the analysis in this model, the following assumptions were made:
the reactants are saturated with water vapor; the membrane is completely soaked by water; the partial pressure of the reactants in the flow channel depends on the inlet flow, consumption, etc.; the model is lumped and one-dimensional; the system is isothermal, and the temperature of the whole galvanic pile is uniform; the total pressure inside the flow field is uniform and variations in the reactant partial pressure can affect the system.
In step S110, an anode model may be established according to the mass conservation of the anode reactant at the anode, where the anode model takes the transmembrane water flow rate of the proton exchange membrane, the anode reactant flow rate, the anode relative humidity, the anode pressure, and the ambient temperature as input quantities, and takes the anode side relative humidity of the proton exchange membrane and the anode reactant output pressure as output quantities.
In an embodiment of the present example, the establishing an anode model further includes:
when the anode model is established, the anode model is established by calculating the flow of the anode reactant and the consumption of the anode reactant on the assumption that the variable of an anode outlet valve is zero, the liquid water reserve of the anode is zero, and the water mass when the anode gaseous water mass is less than or equal to the anode saturated water pressure.
In the present exemplary embodiment, the hydrogen gas of the anode is supplied from a hydrogen gas tank in the model. The hydrogen tank is excellent in rapidity, and therefore the pressure difference between the two electrodes can be made small by appropriate control. In addition, the assumption at the anode is similar to that at the cathode, and the calculation method is also similar.
Assuming herein that the anode has no outlet valve, the following equation is obtained:
liquid water is not retained in the anode, and the quality of water is also limited by:
mw，an＝msat，an，msat，an＜mw，an (3)
the anode inlet flow rate was calculated as follows:
Wan，in＝ln(kan·(pan，in-pan)+1) (4)
Wi，an，in＝Wan，in·xi，an，in (5)
the consumption (generation) of chemical reaction is equivalent to the calculation of flow rate, and by using the electrochemical principle, the following formula is provided:
in step S120, a cathode model may be established according to the conservation of mass of the cathode reactant at the cathode, where the cathode model takes the transmembrane water flow rate of the proton exchange membrane, the cathode reactant flow rate, the cathode relative humidity, the cathode pressure, the ambient temperature, and the cathode reactant content as input quantities, and takes the cathode side relative humidity and the cathode reactant output pressure of the proton exchange membrane as output quantities.
In the embodiment of the present example, when the cathode model is established, the mass of cathode gaseous water is 1.5 times of the mass of water at the cathode saturated water pressure, and the cathode reactant flow rate is calculated by approximate linear processing to obtain the cathode reactant output pressure, so as to establish the cathode model.
In the present exemplary embodiment, the cathode model describes the state of the cathode reactant, including mass, humidity, pressure. The model is based on conservation of mass and aerodynamic properties of the air.
In the model, the oxygen mass of the cathode is calculated using mass continuity
Quality of nitrogen
Quality of water
In the model, data of the cathode is represented using subscript ca. W represents the flow rate in kg/s; d is relative humidity, dimensionless quantity, tableShowing the ratio of the actual water vapor pressure to the saturated water vapor pressure; p is pressure, in Pa; y is data unique to the cathode, representing the oxygen content, which is the ratio of the amount of oxygen species to the amount of air species; this value in air is 0.2. In the establishment of the model, since the temperatures are considered to be uniform, all the temperature amounts in the model are Ta。Wm，wIs the exchange membrane water flow, which is calculated by an exchange membrane water model. Because a zero-dimensional model is established, meanwhile, for convenience of analysis, data such as pressure, temperature, humidity and the like in the cathode are assumed to be consistent. Meanwhile, when the relative humidity is less than 1, the state of water is only gaseous: when the relative humidity is greater than 1, the excess water will be present as a liquid. In the model, a certain amount of water is allowed to be present in the electrodes, while the excess water is removed entirely. From the mass continuity, there is the following equation at the cathode to describe the mass change:
(7) oxygen O on the left side of each of the three equations (8) to (8)2Nitrogen gas N2The rate of change of water (using the subscript w); the right side of the equation is the calculation of the substance. In the formula, the subscript in represents the inflow, out represents the outflow, re represents the reaction consumption or production, and m represents the transmembrane transport. The flow rate for transport across the membrane will be calculated in the exchange membrane water transport model. The outflow speed W of liquid water is assumed in the simulationl，ca，outIt was 0 kg/s. The calculation of the flow rate will be described below.
The gas in the flow channel can be described by an ideal gas equation, and meanwhile, the relation between the mass and the pressure of each substance can be obtained respectively according to the definition.
piV＝niRT (10)
mi＝Mini (11)
In the formulae (10) and (11), n represents the amount of a substance, M represents the mass of a substance, M represents the molar mass of a substance, and subscript i represents different substances, respectively.
psatSaturated water pressure is a function of temperature. The model is calculated by using Emanuel formula as follows:
the water in the cathode will have two states, a gaseous state and a liquid state. Let the mass of cathode gaseous water be mw，ca，gMass of liquid water is mw，ca，lThe mass of water at saturated water pressure is msat，caThe numerical value can be calculated by the equations (10) and (12). Then setting the maximum capacity of cathode water as mmax，ca. The water in the cathode is calculated as follows:
in the model, take mca，max＝1.5mca，sat。
The pressure of the cathode is dry air pa，caAnd the pressure p of waterw，caAnd (4) summing.
pca＝pa，ca+pw，ca (14)
The drying air contains oxygen and nitrogen.
The relative humidity was:
in calculating the inlet-outlet flow rate, the kinetic properties of the gas are generally used. Considering that the pressure difference between the inlet and the outlet and the inside of the flow channel is not large in the working process, the approximate linear processing is generally carried out, namely the following formula is adopted:
W＝k·Δp (18)
where k is a coefficient. In practical cases, when the pressure difference Δ p is large, the flow rate W increases more and more slowly and finally reaches a constant value, so the approximate non-linear equation described in equation (19) is used in the model.
W＝ln(k·Δp+1) (19)
Both describe mainly the flow rate W when Δ p is small and therefore have little effect on the response of the model. The calculations on the cathode model are as follows: wca，in＝ln(kca，in·(pca，in-pca)+1) (20)
The inlet flow rates for each material are calculated below. Note that the flow rate W in equation (19) is a mass flow rate, and therefore, it is necessary to calculate the mass ratio of the inlet material when solving the flow rates of the respective components. From the ideal gas equation, the formula can be derived
pica，in∝ni，ca，in (21)
xi，ca，in∝Wi，ca，in∝mi，ca，in∝Mi，ca，in·ni，ca，in(∑ixi，ca，in＝1) (22)
Wi，ca，in＝Wca，in·xi，ca，in (23)
Where the subscript i represents the different components. It should be noted that the mass m of the inflowing gasi，inAnd flow velocity Wi，inHave similar physical meanings; x in the formulai，inIt represents the mass ratio of the corresponding component. The flow rates of the respective components are finally given by the formula (23).
The consumption (generation) of chemical reaction is equivalent to the calculation of flow rate, and by using the electrochemical principle, the following formula is provided:
in the formula SefIs the effective area of the exchange membrane.
Flow velocity W at the outletca，outThe calculation of (a) is similar.
Wca，out＝ln(kca，out·(pca-pca，out)+1) (26)
pi，ca，out∝ni，ca，out (27)
xi，ca，out∝Wi，ca，out∝mi，ca，out∝Mi，ca，out·ni，ca，out(∑ixi，ca，out＝1) (28)
Wi，ca，out＝Wca，out·xi，ca，out (29)
The outlet pressure in the cathode model is a controlled quantity in the battery system, but is a free quantity in the present model. The processing method will be discussed in the final model.
In step S130, a proton exchange membrane water transport model may be established according to the transmembrane transport volume of water in the proton exchange membrane, where the proton exchange membrane water transport model takes the anode side relative humidity of the proton exchange membrane and the cathode side relative humidity of the proton exchange membrane as input, and takes the transmembrane flow rate of water in the proton exchange membrane and the membrane water constant as output.
In an embodiment of the present example, the establishing the proton exchange membrane water transport model further includes:
and analyzing the transmembrane transport mode of electroosmosis and diffusion generated by water concentration gradient, introducing an empirical formula for calculating the membrane water constant, and further establishing a proton exchange membrane water transport model.
In the present exemplary embodiment, the exchange membrane water transport model is primarilyTo describe the degree of membrane wetting and to calculate the water transport across the membrane. In the exchange membrane water transmission model, the input d is the relative humidity inside two poles; output Wm，wFlow rate of water across the membrane, cmThis value affects the ohmic drop of the cell for the membrane water constant.
Since here a similar treatment of the two pressure levels has been done, two main transmembrane transports of water are considered here:
one effect is electro-osmosis. The protons move in the form of hydrated protons while undergoing transmembrane transport. The number of water molecules carried by each proton is defined by the electroosmotic resistance factor ndAnd (6) determining.
In the formula Nw，eThe density of the water flow generated by electroosmosis is expressed in units of (mol/(s · cm 2)).
Another effect is diffusion by water concentration gradients. Since the humidity is different on both sides, a water concentration gradient exists. This concentration gradient will cause water to flow from high concentrations to low concentrations.
In the formula DwV represents water concentration as a water diffusion coefficient. In conjunction with the above two equations, the membrane water flow rate can be written as (positive with anode flow to cathode):
Ww，m＝n·Nw·Sef·Mw (33)
the water constant of the exchange membrane is the average value of the water constants of the two poles. The water constant of both poles is a function of the relative humidity d. The following equations are all empirical equations established based on experimental data for Nafion 117 exchange membranes.
The water concentration at the membrane surface is a function of the water constant. In the formula (38), ρm，dryIs the dry density of the exchange membrane, Mm，dryIs the dry molar mass of the membrane.
In step S140, a voltage model may be established according to a positive correlation between an external voltage and an open-circuit voltage of the pem fuel cell and a negative correlation between the external voltage and an activation voltage drop, an ohmic voltage drop, and a concentration voltage drop, where the voltage model takes a membrane water constant, an anode reactant output pressure, and a cathode reactant output pressure as input quantities, and takes an external voltage as an output quantity.
In an embodiment of the present example, the establishing the voltage model further includes:
according to the positive correlation relation between the external voltage and the open-circuit voltage of the proton exchange membrane fuel cell and the negative correlation relation between the external voltage and the activation voltage drop, the ohmic voltage drop and the concentration voltage drop, an open-circuit voltage model, an activation voltage drop model, an ohmic voltage drop model and a concentration voltage drop model are respectively established, and then a voltage model is established.
In an embodiment of the present example, the method further comprises:
establishing an open-circuit voltage model taking anode pressure, cathode pressure and temperature in the battery as input quantities based on Gibbs free energy change characteristics;
introducing an activation voltage drop empirical formula based on a Butler-fop-Johnmer equation, and establishing an activation voltage drop model;
establishing an ohmic voltage drop model taking the thickness, the conductivity and the water constant of the proton exchange membrane as input quantities based on the ohmic polarization;
and introducing a concentration voltage drop empirical formula based on the positive correlation relationship of current density, mass transfer speed and reactant concentration gradient, and establishing a concentration voltage drop model.
In an embodiment of the present example, the method further comprises:
analyzing the influence of the selection of the working point of the proton exchange membrane fuel cell on the working performance of the proton exchange membrane fuel cell according to the voltage static characteristic of the voltage model of the proton exchange membrane fuel cell;
and analyzing influence factors of the response capability of the proton exchange membrane fuel cell based on Euler algorithm simulation according to the voltage dynamic characteristics of the proton exchange membrane fuel cell voltage model.
In the present example embodiment, in this subsection, the voltage of a pem fuel cell is discussed. Under the working state, the external voltage U of the battery0There are several major components: open circuit voltage EnActivating voltage drop UoutOhmic voltage drop UohmAnd concentration voltage drop Ucon. External voltage see formula (39):
U0＝En-Uact-Uohm-Ucon (39)
in the exemplary embodiment, the activation voltage drop is modeled as the maximum potential that would be obtained if the PEM fuel cell discharge were reversible, which is the reversible voltage of the PEM fuel cell, and which is also the open-circuit voltage E mentioned aboven. Since the reaction is reversible, it is believed that all of the chemical energy consumed is converted to electrical energy.
The maximum electrical energy that can be provided by a chemical reaction at a constant temperature is determined by the gibbs free energy change (Δ G) of the reaction, which is derived from equations (40) - (42).
Welec＝ΔG＝ΔH-TΔS (40)
Welec＝-2FEn (41)
In the formula WelecFor the generated electrical energy, Δ H is the enthalpy of generation, T is the temperature, and Δ S is the entropy change. Formula (41) indicates 1mol H per consumption2Transporting 2mol electrons, F is the Faraday constant. Δ H is a function of temperature T, Δ S is temperature T, and reactant gas pressure
As a function of (c). After calculation and arrangement, a formula can be obtained.
In the formula TaIs ambient temperature in K;
respectively, oxygen pressure and hydrogen pressure, in atm. Here, the unit of the atmospheric pressure in the voltage calculation alone is atm, and Pa is used as a unit in other models. T isaIs ambient temperature, TeIs the battery temperature.
In the present exemplary embodiment, the ohmic drop is modeled by consuming a certain amount of energy to activate the reactant, a process also referred to as activation polarization; and this portion of energy is irreversible, the voltage drop resulting from it is called the activation voltage drop. There is activation polarization at both poles of the pem fuel cell, and the final activation voltage drop is the sum of the two.
The activation voltage drop is typically calculated using the Butler-Volmer equation. The formula is as follows:
in the formula i0To exchange the current density, αRd、αOxThe reaction coefficient, E, is the voltage actually output under the influence of the activation polarization. The activation pressure drop formula derived from this formula is as follows:
in actual use, many of the parameters in the formula are difficult to determine. Some semi-empirical formulas can be derived from the mechanism. Formula (46) is introduced here:
the parameters in the formula are usually fitted according to the experimental results. Here a set of existing data is used.
TABLE 1 parameters in the activation overvoltage equation
The calculations in the formula use the liquid phase concentration of the reactants, which is calculated as follows:
in the present exemplary embodiment, the ohmic voltage drop is caused by the resistive effect of the pem fuel cell on the movement of electrons, a phenomenon also known as ohmic polarization. This voltage drop follows ohm's law, i.e. is linear with the current.
Uohm＝Ia·Rohm (49)
Wherein R isohmIs equivalent resistance in omega cm2. The resistance has a large relationship with both temperature and humidity. Numerous studies have shown that the main part affecting the electrical resistance is the proton exchange membrane. RohmIs calculated as follows:
ba＝0.005139cm-0.00326 (50.c)
in the formula tmIs the thickness of the exchange membrane in cm2，dmIs electrical conductivity, cmThe exchange membrane water constant is called membrane water constant for short. The membrane water constant will be calculated in the exchange membrane water transport model.
In the present exemplary embodiment, the concentration voltage drop is modeled by what is also referred to as concentration polarization, whose main influencing factor is current. Considering that the reactant concentration near the electrode decreases very rapidly when the current is large, the battery works approximately at low concentration, the current density is in positive correlation with the mass transfer speed, and the mass transfer speed is in direct proportion to the reactant concentration gradient. As such, the maximum current of the battery is limited. This is the reason why the rich differential pressure will occur. According to the mechanism, there is the following formula
Wherein α is the conversion coefficient of current, ImaxIs the maximum current density. In actual use, the parameters in the formula are difficult to obtain, so an empirical formula is used:
Ucon＝qa·exp(qb0Ia) (52.a)
qa＝1.1×10-4-1.2×10-6(Te-273) (52.b)
qb0＝8 (52.c)
equation (52.a) does not take into account the effect of reactant pressure on concentration pressure drop. And in fact, the reactant concentration versus the maximum current density ImaxThe influence of (a) is large. There is therefore the following modified equation:
Ucon＝qa·exp(qbIa) (53.a)
qa＝1.1×10-4-1.2×10-6(T-273) (53.b)
in the embodiment of the present example, according to the voltage static characteristic of the voltage model of the pem fuel cell, the influence of the operating point selection of the pem fuel cell on the operating performance of the pem fuel cell is analyzed, and the dominant polarization effects are different in different current segments of the polarization curve of the pem fuel cell. When the current density is 0-0.2A/cm2The activation polarization plays a dominant role, causing a very large and rapid voltage drop; at a current density of 0.2-0.8A/cm2Ohmic polarization plays a dominant role; when the current rises again, the concentration drop rises rapidly and the battery operating state becomes worse. The power density of the pem fuel cell can be calculated using equation (54), and the efficiency can be calculated from equation (56). The power rises first and then falls with the current density. It is important to select a suitable operating point.
P＝UoIa (54)
η＝Uo/En (55)
In the embodiment of the example, according to the voltage dynamic characteristics of the voltage model of the proton exchange membrane fuel cell, influence factors of the response capability of the proton exchange membrane fuel cell are analyzed based on Euler algorithm simulation, and the dynamic characteristics of the voltage model are established on the basis of a static model. In this context, the "double electric layer" phenomenon is mainly considered, which plays an important role in the response capability of the voltage model.
When the proton exchange membrane fuel cell works, charged substances with opposite polarities are generated in the reaction cross section of the two poles, and the structure can be understood as a parallel plate capacitor. This effect causes it to act like a capacitor-limiting the variation of the voltage. Therefore, in the voltage dynamic model, the existence of the parallel capacitance is considered.
Ract，Rohm，RconRespectively, the corresponding equivalent resistances, CdIs a capacitance as in the above. However, studies have shown that the equivalent capacitance CdIs a variable and its calculation is very complex. Let Requ＝Ract+RconThis part is connected in parallel with the capacitor. Partial simulation with RequApproximating as a constant resistance, taking Cd1-10F. To better characterize this phenomenon, the most basic equations will be calculated herein. The equation is as follows
In the formula RequFunction f for volt-ampere characteristicsUIs described, IcThen represents a flow through CdThe magnitude of the current density of (2). Due to the presence of the capacitor, UequDo not mutate, therefore IequAnd also does not mutate. Since the equation is not expressed explicitly, it is difficult to solve directly, and the key to the solution is Iequ. The algorithm is discrete in the simulation, and the Euler algorithm can be used for reference by processing the equation. The calculation is as follows:
Iequ2-Iequ1＝a(t)·Δt (59)
in the formula (58), a (t) is the rate of increase of the current as a function of time;
is the derivative of voltage with respect to current and is therefore easy to find since the analytical formula is known. lequ1Current of the previous moment, Iequ2For the current at the next moment, Δ t is the simulated step size. Finally solve to obtain IequBrought back to U (56)equ。
In an embodiment of the present example, the method further comprises:
and calculating the energy distribution of the proton exchange membrane fuel cell based on energy conservation, establishing an energy model, and calculating the energy distribution of the proton exchange membrane fuel cell.
In the embodiment of the present example, the energy model calculates the battery temperature based on the conservation of energy. In the model, it is assumed that the inlet temperature is consistent, the temperature in the battery is consistent, and the ambient temperature is consistent.
According to the energy distribution in the fuel cell. The temperature is calculated as shown in equation (67).
PE＝nIaSefEn (61)
Pload＝nIaSefUo (63)
Pair＝(Te-Ta)kE (64)
P in formula (67)EIs the total power of the battery, PinIndicating the thermal power, P, due to the input gasloadFor consuming energy by load, PairRepresents the heat dissipation power to air, CEIs the thermal capacity of the battery. Assuming that the inlet air is sufficiently mixed with the gas in the flow channel in equation (62), this energy is fully divided equally throughout the cell, CgThe molar heat capacity unit of the gas is J/mol/K, ngThe total amount of intake air of the two poles is represented and calculated by the flow. K in formula (65)ERepresenting the heat transfer coefficient to air. Considering that the single cells of the proton exchange membrane fuel cell are similar, the heat dissipation amount mainly depends on the temperature gradient and the heat dissipation area. The parameters in the formula can be calculated by inspecting some batteries which are already put into use. As shown in the following table:
TABLE 2 parameters in the energy model
in step S150, a dynamic relationship between the input and output of the anode model, the cathode model, and the proton exchange membrane water transport model may be respectively established, a steady-state relationship between the anode pressure and the anode reactant output pressure, and a steady-state relationship between the cathode pressure and the cathode reactant output pressure may be established, the dynamic relationship between the input and output of the anode model, the cathode model, and the proton exchange membrane water transport model may be optimized, and the proton exchange membrane fuel cell model may be established.
In the present exemplary embodiment, according to the model in fig. 3. In order to reduce the variation, facilitate the control, reduce the pressure difference of two poles at the same time, do the following treatment.
The outlet pressure of the cathode follows the inlet pressure in a certain proportion.
pca，out＝0.8pca，in (66)
Since the anode does not exhaust gas, the inlet pressure of the anode can be approximately considered as its internal pressure in the steady state condition.
pan＝pan，in (67)
The anode inlet pressure is relatively well controlled. In order to reduce the pressure difference of the two poles, the pressure at the inlet of the anode is made to follow the pressure of the cathode by considering the observability of data; the cathode pressure is obtained by a sensor.
pan，in＝0.9pca+pw，an，in (68)
Whether the battery is electrified or not has great influence on the flow of water. In the water flow model, there is a two-pole inlet and water generated at the cathode, and since there is no outlet at the anode, the only output is the cathode outlet. Water can flow between the two electrodes through the exchange membrane. When gas is just fed, the anode is a quick valve, gas is fed quickly, and water saturation is achieved first; subsequently, the cathode also reaches water saturation very quickly due to transmembrane transport. But at this time, since the cathode pressure is lower than the cathode intake pressure, but the inside of the cathode has reached water saturation, the outflow amount of water is greater than the inflow at the cathode; the relative humidity of the cathode is reduced, the relative humidity can not be kept in a state of 1, the relative humidity of the anode is reduced, and air is not basically introduced into the anode. However, after the current is applied, the hydrogen consumption in the anode and the oxygen consumption in the cathode cause the air inflow at the two electrodes to rise, and simultaneously, the water flow rate rises, so that the water vapor at the two electrodes reaches the approximate saturation. Because the current brings water to be transported across the membrane in a directional way, when the water reaches a steady state, the two poles have extremely small humidity difference, and the difference is related to the current.
Whether the battery is electrified or not has great influence on the flow of water. In the water flow model, there is a two-pole inlet and water generated at the cathode, and since there is no outlet at the anode, the only output is the cathode outlet. Water can flow between the two electrodes through the exchange membrane. When gas is just fed, the anode is a quick valve, gas is fed quickly, and water saturation is achieved first; subsequently, the cathode also reaches water saturation very quickly due to transmembrane transport. But at this time, since the cathode pressure is lower than the cathode intake pressure, but the inside of the cathode has reached water saturation, the outflow amount of water is greater than the inflow at the cathode; the relative humidity of the cathode is reduced, the relative humidity can not be kept in a state of 1, the relative humidity of the anode is reduced, and air is not basically introduced into the anode. However, after the current is applied, the hydrogen consumption in the anode and the oxygen consumption in the cathode cause the air inflow at the two electrodes to rise, and simultaneously, the water flow rate rises, so that the water vapor at the two electrodes reaches the approximate saturation. Because the current brings water to be transported across the membrane in a directional way, when the water reaches a steady state, the two poles have extremely small humidity difference, and the difference is related to the current.
In the embodiment of the present example, the meaning of the parameters and symbols in the formula is shown in table 1, and the meaning of the parameters in the model is shown in table 2:
TABLE 1
TABLE 2
It should be noted that although the various steps of the methods of the present disclosure are depicted in the drawings in a particular order, this does not require or imply that these steps must be performed in this particular order, or that all of the depicted steps must be performed, to achieve desirable results. Additionally or alternatively, certain steps may be omitted, multiple steps combined into one step execution, and/or one step broken down into multiple step executions, etc.
In addition, in the example embodiment, a proton exchange membrane fuel cell modeling apparatus is also provided. Referring to fig. 4, the modeling apparatus 400 for a pem fuel cell may include: an anode model building module 410, a cathode model building module 420, a proton exchange membrane water model building module 430, a voltage model building module 440, and a fuel cell model generation module 450. Wherein:
an anode model establishing module 410, configured to establish an anode model according to mass conservation of an anode reactant at an anode, where the anode model takes water transmembrane flow rate of a proton exchange membrane, anode reactant flow rate, anode relative humidity, anode pressure, and ambient temperature as input quantities, and takes anode side relative humidity of the proton exchange membrane and anode reactant output pressure as output quantities;
a cathode model establishing module 420, configured to establish a cathode model according to mass conservation of a cathode reactant at the cathode, where the cathode model takes water transmembrane flow rate of the proton exchange membrane, cathode reactant flow rate, cathode relative humidity, cathode pressure, ambient temperature, and cathode reactant content as input quantities, and takes cathode side relative humidity and cathode reactant output pressure of the proton exchange membrane as output quantities;
the proton exchange membrane water model establishing module 430 is used for establishing a proton exchange membrane water model according to the transmembrane transport volume of water in the proton exchange membrane, wherein the proton exchange membrane water model takes the relative humidity of the anode side of the proton exchange membrane and the relative humidity of the cathode side of the proton exchange membrane as input, and takes the transmembrane flow rate of water in the proton exchange membrane and the membrane water constant as output;
a voltage model establishing module 440, configured to establish a voltage model according to a positive correlation between an external voltage and an open-circuit voltage of the pem fuel cell and a negative correlation between the external voltage and an activation voltage drop, an ohmic voltage drop, and a concentration voltage drop, where the voltage model takes a membrane water constant, an anode reactant output pressure, and a cathode reactant output pressure as input quantities, and takes an external voltage as an output quantity;
the fuel cell model generating module 450 is configured to respectively establish a dynamic relationship between input and output of the anode model, the cathode model, and the proton exchange membrane water model, establish a steady-state relationship between anode pressure and anode reactant output pressure, and between cathode pressure and cathode reactant output pressure, optimize the dynamic relationship between input and output of the anode model, the cathode model, and the proton exchange membrane water model, and establish the proton exchange membrane fuel cell model.
The specific details of each module of the proton exchange membrane fuel cell modeling apparatus are already described in detail in the corresponding proton exchange membrane fuel cell modeling method, and therefore are not described herein again.
It should be noted that although several modules or units of the pem fuel cell modeling apparatus 400 are mentioned in the above detailed description, such partitioning is not mandatory. Indeed, the features and functionality of two or more modules or units described above may be embodied in one module or unit, according to embodiments of the present disclosure. Conversely, the features and functions of one module or unit described above may be further divided into embodiments by a plurality of modules or units.
Furthermore, the above-described figures are merely schematic illustrations of processes involved in methods according to exemplary embodiments of the invention, and are not intended to be limiting. It will be readily understood that the processes shown in the above figures are not intended to indicate or limit the chronological order of the processes. In addition, it is also readily understood that these processes may be performed synchronously or asynchronously, e.g., in multiple modules.
Other embodiments of the disclosure will be apparent to those skilled in the art from consideration of the specification and practice of the disclosure disclosed herein. This application is intended to cover any variations, uses, or adaptations of the disclosure following, in general, the principles of the disclosure and including such departures from the present disclosure as come within known or customary practice within the art to which the disclosure pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the disclosure being indicated by the following claims.
It will be understood that the present disclosure is not limited to the precise arrangements described above and shown in the drawings and that various modifications and changes may be made without departing from the scope thereof. The scope of the present disclosure is to be limited only by the terms of the appended claims.
Claims (9)
1. A method of modeling a proton exchange membrane fuel cell, the method comprising:
establishing an anode model according to the mass conservation of an anode reactant at an anode, wherein the anode model takes the transmembrane water flow rate of a proton exchange membrane, the flow of the anode reactant, the relative humidity of the anode, the pressure of the anode and the ambient temperature as input quantities, and takes the relative humidity of the anode side of the proton exchange membrane and the pressure of the anode reactant as output quantities;
establishing a cathode model according to the mass conservation of a cathode reactant at a cathode, wherein the cathode model takes the transmembrane water flow rate of a proton exchange membrane, the flow rate of the cathode reactant, the relative humidity of the cathode, the pressure of the cathode, the ambient temperature and the content of the cathode reactant as input quantities, and takes the relative humidity of the cathode side of the proton exchange membrane and the output pressure of the cathode reactant as output quantities;
establishing a proton exchange membrane water transmission model according to the transmembrane transport volume of water in a proton exchange membrane, wherein the proton exchange membrane water model takes the relative humidity of the anode side of the proton exchange membrane and the relative humidity of the cathode side of the proton exchange membrane as input, and takes the transmembrane flow rate of water in the proton exchange membrane and a membrane water constant as output;
establishing a voltage model according to the positive correlation relation between the external voltage and the open-circuit voltage of the proton exchange membrane fuel cell and the negative correlation relation between the external voltage and the activation voltage drop, the ohmic voltage drop and the concentration voltage drop, wherein the voltage model takes a membrane water constant, an anode reactant output pressure and a cathode reactant output pressure as input quantities, and takes an external voltage as an output quantity;
respectively establishing dynamic relations of input quantity and output quantity of an anode model, a cathode model and a proton exchange membrane water transmission model, establishing a steady-state relation between anode pressure and anode reactant output pressure and between cathode pressure and cathode reactant output pressure, optimizing the dynamic relations of the input quantity and the output quantity of the anode model, the cathode model and the proton exchange membrane water transmission model, and establishing a proton exchange membrane fuel cell model.
2. The method of claim 1, wherein the method further comprises:
and calculating the energy distribution of the proton exchange membrane fuel cell based on energy conservation, establishing an energy model, and calculating the energy distribution of the proton exchange membrane fuel cell.
3. The method of claim 1, wherein the establishing an anode model further comprises:
when the anode model is established, the anode model is established by calculating the flow rate of the anode reactant and the consumption of the anode reactant on the assumption that the variable of an anode outlet valve is zero, the liquid water retention of the anode is zero, and the water mass when the mass of the anode gaseous water is less than or equal to the anode saturated water pressure.
4. The method of claim 1, wherein said modeling the cathode further comprises:
when the cathode model is established, the mass of cathode gaseous water is 1.5 times of that of cathode saturated water at atmospheric pressure, the flow of the cathode reactant is calculated through approximate linear processing, the output pressure of the cathode reactant is calculated, and then the cathode model is established.
5. The method of claim 1, wherein the establishing a proton exchange membrane water transport model further comprises:
and analyzing the transmembrane transport mode of electroosmosis and diffusion generated by water concentration gradient, introducing an empirical formula for calculating the membrane water constant, and further establishing a proton exchange membrane water transport model.
6. The method of claim 1, wherein the establishing a voltage model further comprises:
according to the positive correlation relation between the external voltage and the open-circuit voltage of the proton exchange membrane fuel cell and the negative correlation relation between the external voltage and the activation voltage drop, the ohmic voltage drop and the concentration voltage drop, an open-circuit voltage model, an activation voltage drop model, an ohmic voltage drop model and a concentration voltage drop model are respectively established, and then a voltage model is established.
7. The method of claim 6, wherein the method further comprises:
establishing an open-circuit voltage model taking anode pressure, cathode pressure and temperature in the battery as input quantities based on Gibbs free energy change characteristics;
introducing an activation voltage drop empirical formula based on a Butler-fop-Johnmer equation, and establishing an activation voltage drop model;
establishing an ohmic voltage drop model taking the thickness, the conductivity and the water constant of the proton exchange membrane as input quantities based on the ohmic polarization;
and introducing a concentration voltage drop empirical formula based on the positive correlation relationship of current density, mass transfer speed and reactant concentration gradient, and establishing a concentration voltage drop model.
8. The method of claim 6, wherein the method further comprises:
analyzing the operating point of the proton exchange membrane fuel cell according to the voltage static characteristic of the voltage model of the proton exchange membrane fuel cell, and selecting the influence on the operating performance of the proton exchange membrane fuel cell;
and analyzing influence factors and reasons of the response capability of the proton exchange membrane fuel cell according to the voltage dynamic characteristics of the proton exchange membrane fuel cell voltage model.
9. A proton exchange membrane fuel cell modeling apparatus, comprising:
the anode model establishing module is used for establishing an anode model according to the mass conservation of an anode reactant at the anode, wherein the anode model takes the water transmembrane flow rate of the proton exchange membrane, the anode reactant flow, the anode relative humidity, the anode pressure and the ambient temperature as input quantities, and takes the anode side relative humidity of the proton exchange membrane and the anode reactant output pressure as output quantities;
the cathode model establishing module is used for establishing a cathode model according to the mass conservation of a cathode reactant at the cathode, wherein the cathode model takes the water transmembrane flow rate of the proton exchange membrane, the cathode reactant flow, the cathode relative humidity, the cathode pressure, the environment temperature and the cathode reactant content as input quantities and takes the cathode side relative humidity of the proton exchange membrane and the cathode reactant output pressure as output quantities;
the proton exchange membrane water transmission model establishing module is used for establishing a proton exchange membrane water transmission model according to the transmembrane transport volume of water in a proton exchange membrane, wherein the proton exchange membrane water transmission model takes the anode side relative humidity of the proton exchange membrane and the cathode side relative humidity of the proton exchange membrane as input, and takes the transmembrane flow rate of water in the proton exchange membrane and a membrane water constant as output;
the voltage model establishing module is used for establishing a voltage model according to the positive correlation relation between the external voltage and the open-circuit voltage of the proton exchange membrane fuel cell and the negative correlation relation between the external voltage and the activation voltage drop, the ohmic voltage drop and the concentration voltage drop, wherein the voltage model takes a membrane water constant, the output pressure of an anode reactant and the output pressure of a cathode reactant as input quantities, and takes the external voltage as an output quantity;
the fuel cell model generation module is used for respectively establishing the dynamic relations of the input quantity and the output quantity of the anode model, the cathode model and the proton exchange membrane water transmission model, establishing the steady-state relation of the anode pressure and the anode reactant output pressure and the steady-state relation of the cathode pressure and the cathode reactant output pressure, optimizing the dynamic relations of the input quantity and the output quantity of the anode model, the cathode model and the proton exchange membrane water transmission model, and establishing the proton exchange membrane fuel cell model.
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