CN114678568B - Modeling method for proton exchange membrane fuel cell - Google Patents
Modeling method for proton exchange membrane fuel cell Download PDFInfo
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- 239000000446 fuel Substances 0.000 title claims abstract description 270
- 238000000034 method Methods 0.000 title claims abstract description 40
- 239000012528 membrane Substances 0.000 title claims abstract description 25
- 239000003990 capacitor Substances 0.000 claims abstract description 37
- UFHFLCQGNIYNRP-UHFFFAOYSA-N Hydrogen Chemical compound [H][H] UFHFLCQGNIYNRP-UHFFFAOYSA-N 0.000 claims abstract description 33
- 239000001257 hydrogen Substances 0.000 claims abstract description 32
- 229910052739 hydrogen Inorganic materials 0.000 claims abstract description 32
- 239000001301 oxygen Substances 0.000 claims abstract description 25
- 229910052760 oxygen Inorganic materials 0.000 claims abstract description 25
- QVGXLLKOCUKJST-UHFFFAOYSA-N atomic oxygen Chemical compound [O] QVGXLLKOCUKJST-UHFFFAOYSA-N 0.000 claims abstract description 24
- 230000007613 environmental effect Effects 0.000 claims description 6
- 239000003054 catalyst Substances 0.000 claims description 5
- 230000010354 integration Effects 0.000 claims description 5
- 238000012546 transfer Methods 0.000 claims description 5
- 238000006243 chemical reaction Methods 0.000 claims 1
- 230000005611 electricity Effects 0.000 abstract description 6
- 238000010586 diagram Methods 0.000 description 10
- 239000003792 electrolyte Substances 0.000 description 10
- NBIIXXVUZAFLBC-UHFFFAOYSA-N Phosphoric acid Chemical compound OP(O)(O)=O NBIIXXVUZAFLBC-UHFFFAOYSA-N 0.000 description 8
- 230000004907 flux Effects 0.000 description 5
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- BVKZGUZCCUSVTD-UHFFFAOYSA-L Carbonate Chemical compound [O-]C([O-])=O BVKZGUZCCUSVTD-UHFFFAOYSA-L 0.000 description 3
- OKKJLVBELUTLKV-UHFFFAOYSA-N Methanol Chemical compound OC OKKJLVBELUTLKV-UHFFFAOYSA-N 0.000 description 3
- KWYUFKZDYYNOTN-UHFFFAOYSA-M Potassium hydroxide Chemical compound [OH-].[K+] KWYUFKZDYYNOTN-UHFFFAOYSA-M 0.000 description 3
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- 230000000694 effects Effects 0.000 description 2
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- VNWKTOKETHGBQD-UHFFFAOYSA-N methane Chemical compound C VNWKTOKETHGBQD-UHFFFAOYSA-N 0.000 description 2
- 238000004377 microelectronic Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 2
- 239000004215 Carbon black (E152) Substances 0.000 description 1
- 238000004458 analytical method Methods 0.000 description 1
- 239000003245 coal Substances 0.000 description 1
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- 239000010416 ion conductor Substances 0.000 description 1
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- OBTSLRFPKIKXSZ-UHFFFAOYSA-N lithium potassium Chemical compound [Li].[K] OBTSLRFPKIKXSZ-UHFFFAOYSA-N 0.000 description 1
- STJUJXONQFLCOP-UHFFFAOYSA-L lithium;sodium;carbonate Chemical compound [Li+].[Na+].[O-]C([O-])=O STJUJXONQFLCOP-UHFFFAOYSA-L 0.000 description 1
- 238000013178 mathematical model Methods 0.000 description 1
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- 150000003460 sulfonic acids Chemical class 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
- H01M8/04694—Processes for controlling fuel cells or fuel cell systems characterised by variables to be controlled
- H01M8/04858—Electric variables
- H01M8/04925—Power, energy, capacity or load
- H01M8/04947—Power, energy, capacity or load of auxiliary devices, e.g. batteries, capacitors
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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
- H01M8/04992—Processes for controlling fuel cells or fuel cell systems characterised by the implementation of mathematical or computational algorithms, e.g. feedback control loops, fuzzy logic, neural networks or artificial intelligence
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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 embodiment of the invention discloses a modeling method of a proton exchange membrane fuel cell. The method comprises the following steps: constructing a dynamic model of the fuel cell stack according to the temperature of the fuel cell and the parallel capacitor; constructing an electrolytic cell dynamic model based on the fuel supplied by the electrolytic cell to the fuel cell stack and the operating temperature of the electrolytic cell; adjusting the output voltage and frequency of the fuel cell stack to target values by a two-stage converter; and converting the direct current voltage of the output fuel cell stack to an alternating current voltage by a single-phase four-phase inverter; the flow of hydrogen and oxygen into the fuel cell stack is controlled by a controller. By the method, alternating current can be generated, and then the proton exchange membrane fuel cell can be applied to power supply for household electricity.
Description
Technical Field
The invention relates to the field of fuel cells, in particular to a modeling method of a proton exchange membrane fuel cell.
Background
A distributed power supply is a power generation source directly connected to a distribution network or consumer, wherein the voltage level of the distributed power supply ranges from 400 volts up to 33 kw, with a capacity in the range of a few watts up to 100 megawatts.
There are a variety of fossil and renewable energy based tools, which may be internal combustion engines, microturbines, fuel cells, diesel generators, wind turbines, solar cells, etc., and energy storage tools for distributed generation to expand the global trend of energy consumption and decentralized production at the consumer site. Among them, a fuel cell is an electrochemical cell that generates electric energy, and is composed of two conductors called electrodes and a conductive film between the electrodes, the conductive film between the two electrodes being called an electrolyte. Among them, the fuel cells are classified into the following types according to the types of electrolyte used: solid oxide fuel cells, molten carbonate fuel cells, phosphoric acid fuel cells, alkaline fuel cells, and proton exchange membrane fuel cells. Nowadays, with the development of fuel technology, fuel cells are widely used in various industries such as microelectronics, electric vehicles, small ships, scouts, buses, home and business applications, cogeneration production, and the like. Proton Exchange Membrane (PEM) fuel cells have the advantage of fast start-up, availability to provide partial load, etc., as compared to other types of fuel cells. Thus, the home load profile can be modified by using PEM fuel cells. However, there is no method for effectively modeling a proton exchange membrane fuel cell in the prior art.
In summary, how to effectively model a fuel cell and improve accuracy of the model is a problem that needs to be solved at present.
Disclosure of Invention
In view of this, the embodiment of the invention provides a modeling method for a proton exchange membrane fuel cell, which can generate alternating current, so that the proton exchange membrane fuel cell can be applied to power supply for domestic electricity.
In a first aspect, an embodiment of the present invention provides a method for modeling a proton exchange membrane fuel cell, the method including:
constructing a dynamic model of the fuel cell stack according to the temperature of the fuel cell and the parallel capacitor;
constructing an electrolytic cell dynamic model based on the fuel supplied by the electrolytic cell to the fuel cell stack and the operating temperature of the electrolytic cell;
adjusting the output voltage and frequency of the fuel cell stack to target values by a two-stage converter; and converting the direct current voltage of the output fuel cell stack to an alternating current voltage by a single-phase four-phase inverter;
the flow of hydrogen and oxygen into the fuel cell stack is controlled by a controller.
Optionally, the constructing a dynamic model of the fuel cell stack according to the temperature of the fuel cell and the parallel capacitor includes:
according to the parameters of the fuel cell stack and the electrochemical thermodynamic principle, the output voltage v of the single fuel cell is determined as follows:
V＝E-υ act +η ohmic
wherein E is the lossless open-circuit voltage in the single fuel cell, V act An active pressure drop at an anode and a cathode in the fuel cell; η (eta) ohmic Is burnt byOhmic voltage loss in the material cell.
Optionally, the total output voltage V of the fuel cell stack is obtained according to the output voltage V of the single fuel cell stack ：
V stack ＝n*V
The fuel cell group consists of n single fuel cells which are connected in series, wherein n is a positive integer.
Alternatively, E is determined by the following formula:
wherein P is H2 And P O2 Respectively hydrogen partial pressure and oxygen partial pressure; t is the temperature of the fuel cell;
the v is determined by the following formula act ：
Wherein i is the current of the single fuel cell; zeta type 1 、ζ 2 、ζ 3 、ζ 4 Is a model parameter;oxygen concentration at the catalyst surface;
η is determined by the following formula ohmic ：
η ohmic ＝-i*R in
R in ＝0.01605-3.5*10 -5 *T+8*10 -5 *i
Wherein i is the current of the single fuel cell; t is the temperature of the fuel cell.
Optionally, the method further comprises: the heat balance in the fuel cell stack is determined according to the following equation:
Q I ＝Q S +Q L
wherein Q is S For environmental heat loss, Q L Is internal heat loss.
Optionally, the method further comprises: q is determined according to the following formula I ：
Q is determined according to the following formula S ：
Q is determined according to the following formula L ：
Q L ＝i 2 (R a +R int )*n
Wherein C is t Is the heat capacity of the fuel cell, T is the temperature of the fuel cell; ta is ambient temperature; i is the current of the single fuel cell; r is R a Is the fuel cell resistance; n is the number of single fuel cells.
Alternatively, the cross-sectional area of the electrode used in the capacitor is 500 to 2000 times the cross-sectional area of the fuel cell electrode.
Optionally, the capacitor is a low pass filter and is expressed by the following formula:
wherein C is 108.75mF millivolts, R c Is a series resistance R s Is nonsensical resistance.
Optionally, the building an electrolytic cell dynamic model based on the temperature at which the electrolytic cell supplies fuel to the fuel cell stack and the electrolytic cell operates includes:
determining the rate of hydrogen produced by the electrolyzer according to Faraday's lawThe method comprises the following steps:
wherein i is e For the cell current, n n The number of the electrolytic cells; η (eta) F Is Faraday efficiency; f is Faraday constant.
Optionally, the transfer function G of the controller r (s) is:
wherein K is p The proportional magnification of the controller; t (T) i Is the integration time; t (T) d Is the differential time.
In a second aspect, an embodiment of the present invention provides an apparatus for modeling a proton exchange membrane fuel cell, the apparatus comprising:
the fuel cell modeling module is used for constructing a dynamic model of the fuel cell stack according to the temperature of the fuel cell and the parallel capacitor;
the electrolyzer modeling module is used for constructing an electrolyzer dynamic model based on the temperature at which the electrolyzer supplies fuel to the fuel cell stack and the electrolyzer operates;
a converter modeling module for adjusting an output voltage and a frequency of the fuel cell stack to target values through a two-stage converter; and converting the direct current voltage of the output fuel cell stack to an alternating current voltage by a single-phase four-phase inverter;
a controller modeling module for controlling the flow of hydrogen and oxygen into the fuel cell stack via a controller.
Optionally, the fuel cell modeling module is further configured to determine, according to parameters of the fuel cell stack and an electrochemical thermodynamic principle, an output voltage V of the single fuel cell as:
V＝E-υ act +η ohmic
wherein E is the lossless open-circuit voltage in the single fuel cell, V act An active pressure drop at an anode and a cathode in the fuel cell; η (eta) ohmic Is the ohmic voltage loss in the fuel cell.
Optionally, the fuel cell modeling module is further configured to obtain a total output voltage V of the fuel cell stack according to the output voltage V of the single fuel cell stack ：
V stack ＝n*V
The fuel cell group consists of n single fuel cells which are connected in series, wherein n is a positive integer.
Optionally, the fuel cell modeling module is further configured to determine E by:
wherein P is H2 And P O2 Respectively hydrogen partial pressure and oxygen partial pressure; t is the temperature of the fuel cell;
the v is determined by the following formula act ：
Wherein i is the current of the single fuel cell; zeta type 1 、ζ 2 、ζ 3 、ζ 4 Is a model parameter;oxygen concentration at the catalyst surface;
η is determined by the following formula ohmic ：
η ohmic ＝-i*R in
R in ＝0.01605-3.5*10 -5 *T+8*10 -5 *i
Wherein i is the current of the single fuel cell; t is the temperature of the fuel cell.
Optionally, the fuel cell modeling module is further configured to determine a heat balance in the fuel cell stack according to the following formula:
Q I ＝Q S +Q L
wherein Q is s For environmental heat loss, Q L Is internal heat loss.
Optionally, the fuel cell modeling module is further configured to determine Q according to the following formula I ：
Q is determined according to the following formula S ：
Q is determined according to the following formula L ：
Q L ＝i 2 (R a +R int )*n
Wherein C is t Is the heat capacity of the fuel cell, T is the temperature of the fuel cell; ta is ambient temperature; i is the current of the single fuel cell; r is R a Is the fuel cell resistance; n is the number of single fuel cells.
Alternatively, the cross-sectional area of the electrode used in the capacitor is 500 to 2000 times the cross-sectional area of the fuel cell electrode.
Optionally, the capacitor is a low pass filter and is expressed by the following formula:
wherein C is 108.75mF milliV, R c Is a series resistance R s Is nonsensical resistance.
Optionally, the electrolytic cell modeling module is further configured to:
determining the rate of hydrogen produced by the electrolyzer according to Faraday's lawThe method comprises the following steps:
wherein i is e For the cell current, n n The number of the electrolytic cells; η (eta) F Is Faraday efficiency; f is Faraday constant.
Optionally, the transfer function G of the controller r (s) is:
wherein K is p The proportional magnification of the controller; t (T) i Is the integration time; t (T) d Is the differential time.
According to the embodiment of the invention, a dynamic model of the fuel cell stack is built according to the temperature of the fuel cell and the parallel capacitor, the dynamic model of the electrolytic cell is built based on the temperature of the fuel cell stack supplied with fuel by the electrolytic cell and the operation of the electrolytic cell, and the output voltage and the frequency of the fuel cell stack are adjusted to target values through a two-stage converter; and converting the direct-current voltage of the output fuel cell stack into alternating-current voltage through a single-phase four-phase inverter, and controlling the flow of hydrogen and oxygen entering the fuel cell stack through a controller, so that stable voltage can be output and alternating current can be generated, and further the proton exchange membrane fuel cell can be applied to power supply for household electricity.
Drawings
The above and other objects, features and advantages of the present invention will become more apparent from the following description of embodiments of the present invention with reference to the accompanying drawings, in which:
fig. 1 is a schematic view of a fuel cell system in an embodiment of the invention;
FIG. 2 is a schematic diagram of a method of modeling a proton exchange membrane fuel cell in an embodiment of the invention;
FIG. 3 is a schematic diagram of the output voltage waveforms of a fuel cell with and without a supercapacitor;
FIG. 4 is a schematic diagram of an inverter output voltage in an embodiment of the invention;
FIG. 5 is a schematic diagram of a filtered load voltage in an embodiment of the invention;
fig. 6 is a schematic diagram of load current in an embodiment of the invention.
Detailed Description
The present disclosure is described below based on examples, but the present disclosure is not limited to only these examples. In the following detailed description of the present disclosure, certain specific details are set forth in detail. The present disclosure may be fully understood by those skilled in the art without a review of these details. Well-known methods, procedures, flows, components and circuits have not been described in detail so as not to obscure the nature of the disclosure.
Moreover, those of ordinary skill in the art will appreciate that the drawings are provided herein for illustrative purposes and that the drawings are not necessarily drawn to scale.
Unless the context clearly requires otherwise, the words "comprise," "comprising," and the like throughout the application are to be construed as including but not being exclusive or exhaustive; that is, it is the meaning of "including but not limited to".
In the description of the present disclosure, it is to be understood that the terms "first," "second," and the like are used for descriptive purposes only and are not to be construed as indicating or implying relative importance. Furthermore, in the description of the present disclosure, unless otherwise indicated, the meaning of "a plurality" is two or more.
With the development of fuel technology, fuel cells are widely used in various industries such as microelectronics, electric vehicles, small ships, scouts, buses, home and business applications, cogeneration production, and the like. Fuel cells have many benefits, including in particular:
A. from the energy system point of view, the efficiency is high. For example, PEM fuel cells have an efficiency of 40-60% in generating electricity while the efficiency of generating electricity and thermal energy is increased to 85%.
B. From the power control point of view, easy adjustment is possible. For example, the output power may be controlled by controlling the reactants (hydrogen and oxygen).
C. The environmental compatibility is strong. If hydrogen is used as the primary fuel, its output is only water and, because of the absence of mechanical parts, they are free of noise pollution.
D. The fuel has flexibility. Among these, hydrogen fuel can be obtained from various sources, such as water, natural gas, coal, methanol, hydrocarbon fuel, and the like.
E. The unit energy production has portability and portability. Fuel cells have the highest energy storage density compared to batteries, electrochemical capacitors and supercapacitors.
Further, the fuel cells can be classified into 5 types according to the type of electrolyte used, respectively: solid Oxide Fuel Cells (SOFCs), molten Carbonate Fuel Cells (MCFCs), phosphoric Acid Fuel Cells (PAFCs), alkaline Fuel Cells (AFCs), and Proton Exchange Membrane Fuel Cells (PEMFCs). Among them, solid Oxide Fuel Cells (SOFC) use oxygen ion conductor solid oxide as an electrolyte. Molten Carbonate Fuel Cells (MCFCs) use molten lithium-potassium or lithium-sodium carbonate as the electrolyte. Phosphoric Acid Fuel Cells (PAFCs) use concentrated phosphoric acid as an electrolyte. Alkaline Fuel Cells (AFCs) typically use alkaline potassium hydroxide solutions as the electrolyte. Proton Exchange Membrane Fuel Cells (PEMFCs) typically use perfluorinated or partially fluorinated sulfonic acid type proton exchange membranes as the electrolyte.
PEM fuel cells (PEMFC) have the advantages of fast start-up, availability to provide partial load, etc., compared to other types of fuel cells. Thus, the home load profile can be modified by using PEM fuel cells. Due to the low load demand, the electrical energy of the national grid is delivered to the electrolyzer, and the hydrogen required for the fuel cell is produced during peak hours and stored in a hydrogen tank. Hydrogen storage is not an easy matter and has many technical problems and costs. In other words, in the case of hydrogen gas, a simple storage system method is not applicable due to high pressure supply, explosion problems, etc., and a hydrogen storage technology is one of complex technologies combined with nanotechnology, metal hybridization, etc.
In view of the above, the present invention proposes a strategy for supplying fuel to a fuel cell using an electrolytic cell. Further, the cell strategy may be used during midnight operation. Thus, each consumer in the home sector can produce the partial load they need during peak hours and remove the partial peak load from the global power grid. Further, this strategy will result in a smoothing of the global network daily load curve.
Fig. 1 is a schematic view of a fuel cell system in an embodiment of the present invention, as shown in fig. 1, a polymer electrolyte fuel cell including: a fuel cell stack 110, a supply pipe section 120, a reformer or fuel processor 130, a cooling system 140, wherein the supply pipe section 120 comprises a hydrogen supply pipe 121, an air supply pipe 122. Specifically, the fuel enters a reformer or fuel processor 130 and a cooling system 140 with fans is used to blow air into the cells of the fuel cell stack 110.
FIG. 2 is a schematic diagram of a method for modeling a proton exchange membrane fuel cell according to an embodiment of the present invention, as shown in FIG. 2, and the embodiment of the present invention provides a method for modeling a proton exchange membrane fuel cell, which mainly includes:
s201: constructing a dynamic model of the fuel cell stack according to the temperature of the fuel cell and the parallel capacitor;
s202: constructing an electrolytic cell dynamic model based on the fuel supplied by the electrolytic cell to the fuel cell stack and the operating temperature of the electrolytic cell;
s203: adjusting the output voltage and frequency of the fuel cell stack to target values by a two-stage converter; and converting the direct current voltage of the output fuel cell stack to an alternating current voltage by a single-phase four-phase inverter;
s204: the flow of hydrogen and oxygen into the fuel cell stack is controlled by a controller.
According to the embodiment of the invention, stable voltage can be output and alternating current can be generated, so that the proton exchange membrane fuel cell can be applied to power supply for household electricity.
In an alternative embodiment, constructing a dynamic model of the fuel cell stack based on the fuel cell temperature and the parallel capacitors includes:
according to the parameters of the fuel cell stack and the electrochemical thermodynamic principle, determining the output voltage V of the single fuel cell as follows:
V＝E-υ act +η ohmic
wherein E is the lossless open-circuit voltage in the single fuel cell, V act An active pressure drop at an anode and a cathode in the fuel cell; η (eta) ohmic Is the ohmic voltage loss in the fuel cell.
Specifically, E is the lossless open circuit voltage in a single fuel cell
Wherein Δg accounts for the change in gibbs free energy in joules per mole (j/mol), Δs is the entropy change in joules per mole (j/mol) in the above formula. F is the faraday constant and,and->The hydrogen partial pressure and the oxygen partial pressure are expressed in units of atmospheric air, respectively. R is the general constant of the gas; t is the fuel cell temperature, T ref Is a reference temperature in kelvin (e.g., 25 ℃).
In an alternative embodiment, using the standard pressure and temperature Δs, a Δg value is obtained, and E is determined based on the above equation and by:
wherein P is H2 And P O2 Respectively hydrogen partial pressure and oxygen partial pressure; t is the temperature of the fuel cell.
The v is determined by the following formula act ：
Wherein i is the current of the single fuel cell; zeta type 1 、ζ 2 、ζ 3 、ζ 4 Is a model parameter;oxygen concentration at the catalyst surface;
η is determined by the following formula ohmic ：
η ohmic ＝-i*R in
R in ＝0.01605-3.5*10 -5 *T+8*10 -5 *i
Wherein i is the current of the single fuel cell; t is the temperature of the fuel cell.
In an alternative embodiment, multiple individual fuel cells may be combined together to form a fuel cell stack in order to provide a higher voltage. Obtaining the total output voltage V of the fuel cell stack according to the output voltage V of the single fuel cell stαck ：
V stack ＝n*V
The fuel cell group consists of n single fuel cells which are connected in series, wherein n is a positive integer.
Specifically, according to henry's law, the concentration of insoluble oxygen in the gas/liquid interfaceThe method comprises the following steps:
based on experimental analysis, the parametric equation for determining the overpressure caused by activity and internal resistance is:
R in ＝0.01605-3.5*10 -5 *T+8*10 -5 *i
where i is the current in the single fuel cell and the resistance of the single fuel cell is:
from the steady fuel cell model, the continuous current, cell temperature, hydrogen pressure, and oxygen pressure will affect the output voltage of the cell. The voltage drop across the fuel cell can be compensated for by increasing the cell pressure and the dynamic behavior of the fuel cell voltage can be simulated by adding a capacitor to the stabilized fuel cell model.
The effect of double layer charge is simulated by using a capacitor or resistor in parallel. The differential equation describing the fuel cell voltage is:
ohmic voltage loss η in fuel cells ohmi2 The method comprises the following steps:
η ohmic ＝-i*R in
the fuel cell stack is composed of n single fuel cells connected in series, and then the total voltage is:
V stack ＝n*V
the rates of hydrogen and oxygen in a fuel cell depend on the input and output fluxes and the current output from the fuel cell and the volume of the electrodes. If the inlet and outlet flux rates are specified in moles per second, the gas pressure inside the fuel cell dehumidifier can be obtained using the molar equation. For fuel cell anodes:
wherein V is a The volume of the anode is expressed as liter; UA is the cross-sectional area of the flux;is the molar flux rate; r is the global constant of the gas; t is the temperature of the fuel cell; />Is the molar density; f is the faraday constant.
Likewise, for a fuel cell cathode:
wherein V is c Is the volume of the anode. For example, it may be assumed that the volume of the anode and cathode is 2 liters.
In an alternative embodiment, the balance of total thermal energy in the fuel cell stack:
Q I ＝Q S -Q L
wherein Q is I As internal heat energy (stored heat energy), Q S For environmental heat loss, Q L Is internal heat loss.
Specifically, internal heat loss Q L The method comprises the following steps:
Q L ＝i 2 (R a +R int )*n
then the first time period of the first time period,
wherein C is t As the heat capacity of the fuel cell, in the present embodiment, the heat capacity of the fuel cell may be set to 10000 ℃, and T is the temperature of the fuel.
Then the first time period of the first time period,
ta is the ambient temperature, which in this embodiment may be set to 25 ℃.
Further, the large-capacity capacitor is an energy storage device having a battery-like structure, and the capacitor has two electrodes inside an electrolyte, respectively. The electrodes are made of a material having a very porous cross section. In an alternative embodiment, the cross-sectional area of the electrodes used in the capacitor is 500-2000 times larger than the cross-sectional area of the battery electrodes.
If high power is required, large capacity capacitors can be used in a short time, for example, these capacitors can be used in automobiles using fuel cells. In particular, the capacitor is considered a low voltage device. Typically, the voltage of the capacitor is about 2.5 volts. But in a capacitor bank with a large voltage, the capacity of the large-capacity capacitor varies in the range of 10-2700 farads or more.
To obtain the required voltage at the fuel cell output, 4 capacitors may be connected in series. For example, the series resistance of the selected capacitor is 4 milliamperes, the leakage current is 10 milliamperes, assuming that the leakage current of the capacitor is constant. Specifically, the bulk capacitor is modeled by a series capacitance with a resistor. For example, 4 large capacity capacitor cases are connected in series, the total capacity is 108.75 farads, the series resistance is 16mm, and the capacitor module with the characteristics is connected in parallel with the fuel cell to reduce voltage fluctuation caused by abrupt load change.
The bulk capacitance is written as a low pass filter:
wherein C is 108.75mF millivolts, R c Is a series resistance R s Is nonsensical resistance. For example, c= 108.75mF millivolts, series resistance R c =4 millivolts, nonsensical resistor, R s =0.01W watts.
The decomposition into hydrogen and oxygen can be achieved by using an electric current between two electrodes with separate aqueous electrolytes. The entire electrolysis process can be expressed as:
h2o+electrical energy=h2 (g) +0.5O2 (g)
In one possible embodiment, an electrolyzer system consists of several electrolyzers connected in series. The current characteristics of the cell voltage depend on the temperature at which it flows and are non-linear and obtained by curve fitting. The rate of hydrogen generation in the electrolyzer unit is proportional to the rate of electron transfer at the electrodes, according to faraday's law, determining the rate of hydrogen generation by the electrolyzerThe method comprises the following steps:
wherein i is e For the cell current, n n The number of the electrolytic cells; η (eta) F Is Faraday efficiency; f is Faraday constant. The faraday efficiency may be the ratio between the maximum value of hydrogen produced in practice and the theoretical value in the electrolyzer. Assuming that the cell has a separate cooling system that maintains the temperature at 40 ℃, i.e. the cell is operated at a temperature of 40 ℃, the faraday efficiency is determined as:
the hybrid system is designed to use the network alone, and the two-stage converter module is designed to adjust the output voltage and frequency to desired standard values. The first step involves a boost converter that converts the variable DC value of the fuel cell to a higher constant DC voltage value in parallel with a bulk capacitor. Here, the converter is controlled by a PID controller to keep the voltage constant at 200 volts. This is achieved by adjusting the duty cycle by the following equation:
since the proposed design is a system separate from the mains, the inverter in voltage control mode is contrary to the current control method that is typically applied to inverters connected to mains. The pulse width modulated inverter uses a single phase voltage source to operate a PID controller that adjusts the module to 120 volts and 50 hertz. The triangular carrier has a frequency of 8 khz.
The need for a controller is felt due to the nonlinear nature of the system and the long response to load changes, as well as the presence of significant persistent errors. The general transfer function of the controller is as follows:
wherein K is p The proportional magnification of the controller; t (T) i Is the integration time; t (T) d Is the differential time.
Further, the mathematical model created by the proton exchange membrane fuel cell modeling method described in the above embodiment can be simulated in Simulink of Matlab software by changing the amount of load connected to the system in Matlab software. Wherein, this model system is made up of 8 main subcomponents: a fuel cell stack, an electrolyzer, a supercapacitor, an inverter, a booster, a hydrogen reservoir, and a hydrogen-oxygen mass flow controller. And determining mathematical representations of the sub-components by the proton exchange membrane fuel cell modeling method described in the above embodiments.
FIG. 3 is a schematic diagram of the output voltage waveforms of a fuel cell with and without a supercapacitor; FIG. 4 is a schematic diagram of an inverter output voltage in an embodiment of the invention; FIG. 5 is a schematic diagram of a filtered load voltage in an embodiment of the invention; fig. 6 is a schematic diagram of load current in an embodiment of the invention.
In a specific embodiment, to find the response of the fuel cell to a load step disturbance, the load current is increased over time from a base value of 15 amps to 21 amps. The model system response indicates the optimal performance of the controller and supercapacitor. Two modes of using and not using supercapacitors are shown in the form of load voltage curves. The voltage drop at the initial time of the output of the fuel cell with the supercapacitor is in the period in which the initial current enters with the flux, but after a while the voltage across it creates a stable condition.
Then, the response of the fuel cell to the periodic load fluctuation is determined. In this case, a constant load of 10 amperes and an oscillating load in the range of 5 amperes were applied to the fuel cell at intervals of 2 seconds. As shown in fig. 3, the output voltage waveforms of the fuel cell with and without the supercapacitor are shown. The response of the fuel cell to the load had fluctuations in the range of 3 volts, while the closing of the supercapacitor reduced the amplitude of these fluctuations by about 0.5 volts.
Since the voltage applied to the load is ac, a single-phase inverter must be used to convert the DC output voltage of the fuel cell to ac. Therefore, the proton exchange membrane fuel cell of the embodiment of the invention uses a 4-pulse inverter. As shown in fig. 4-6, fig. 4, 5 and 6 show the inverter output voltage, the filtered load voltage and the load current, respectively.
The embodiment of the invention provides a proton exchange membrane fuel cell modeling device, which comprises:
the fuel cell modeling module is used for constructing a dynamic model of the fuel cell stack according to the temperature of the fuel cell and the parallel capacitor;
the electrolyzer modeling module is used for constructing an electrolyzer dynamic model based on the temperature at which the electrolyzer supplies fuel to the fuel cell stack and the electrolyzer operates;
a converter modeling module for adjusting an output voltage and a frequency of the fuel cell stack to target values through a two-stage converter; and converting the direct current voltage of the output fuel cell stack to an alternating current voltage by a single-phase four-phase inverter;
a controller modeling module for controlling the flow of hydrogen and oxygen into the fuel cell stack via a controller.
In an embodiment, the fuel cell modeling module is further configured to determine, according to parameters of the fuel cell stack and electrochemical thermodynamic principles, an output voltage V of the single fuel cell as:
V＝E-υ act +η ohmic
wherein E is the lossless open-circuit voltage in the single fuel cell, V act An active pressure drop at an anode and a cathode in the fuel cell; η (eta) ohmic Is the ohmic voltage loss in the fuel cell.
In an embodiment, the fuel cell modeling module is further configured to obtain a total output voltage V of the fuel cell stack according to the output voltage V of the single fuel cell stack ：
V sstack ＝n*V
The fuel cell group consists of n single fuel cells which are connected in series, wherein n is a positive integer.
In an achievable embodiment, the fuel cell modeling module is further configured to determine E by:
wherein P is H2 And P O2 Respectively hydrogen partial pressure and oxygen partial pressure; t is the temperature of the fuel cell;
the v is determined by the following formula act ：
Wherein i is the current of the single fuel cell; zeta type 1 、ζ 2 、ζ 3 、ζ 4 Is a model parameter;oxygen concentration at the catalyst surface;
η is determined by the following formula ohmic ：
η ohmic ＝-i*R in
R in ＝0.01605-3.5*10 -5 *T+8*10 -5 *i
Wherein i is the current of the single fuel cell; t is the temperature of the fuel cell.
In an achievable embodiment, the fuel cell modeling module is further configured to determine the heat balance in the fuel cell stack according to the following formula:
Q I ＝Q S +Q L
wherein Q is S For environmental heat loss, Q L Is internal heat loss.
Optionally, the fuel cell modeling module is further configured to determine Q according to the following formula I ：
Q is determined according to the following formula s ：
Q is determined according to the following formula L ：
Q L ＝i 2 (R a +R int )*n
Wherein C is t Is the heat capacity of the fuel cell, T is the temperature of the fuel cell; ta is ambient temperature; i is the current of the single fuel cell; r is R a Is the fuel cell resistance; n is the number of single fuel cells.
In one possible embodiment, the cross-sectional area of the electrode used in the capacitor is 500-2000 times the cross-sectional area of the fuel cell electrode.
In one possible embodiment, the capacitor is a low pass filter and is expressed by the following formula:
wherein C is 108.75mF millivolts, R c Is a series resistance R s Is nonsensical resistance.
In an achievable embodiment, the cell modeling module is further configured to:
determining the rate of hydrogen produced by the electrolyzer according to Faraday's lawThe method comprises the following steps:
wherein i is e For the cell current, n n The number of the electrolytic cells; η (eta) F Is Faraday efficiency; f is Faraday constant.
In an embodiment, the transfer function G of the controller r (s) is:
wherein K is p Is the proportion of the controller to be amplified by timesA number; t (T) i Is the integration time; t (T) d Is the differential time.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, and various modifications and variations may be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. A method of modeling a proton exchange membrane fuel cell, the method comprising:
constructing a dynamic model of the fuel cell stack according to the temperature of the fuel cell and the parallel capacitor;
constructing an electrolytic cell dynamic model based on the fuel supplied by the electrolytic cell to the fuel cell stack and the operating temperature of the electrolytic cell;
adjusting the output voltage and frequency of the fuel cell stack to target values by a two-stage converter; and converting the direct current voltage of the fuel cell stack into an alternating current voltage by a single-phase four-phase inverter;
controlling the flow of hydrogen and oxygen into the fuel cell stack by a controller;
wherein, the constructing a dynamic model of the fuel cell stack according to the temperature of the fuel cell and the parallel capacitor comprises:
determining the output voltage of a single fuel cell based on the parameters of the fuel cell stack and the electrochemical thermodynamic principlesThe method comprises the following steps:
wherein,is the lossless open-circuit voltage in a single fuel cell, ">An active pressure drop at an anode and a cathode in the fuel cell; />Ohmic voltage loss in the fuel cell;
wherein, according to the output voltage of the single fuel cellObtaining the total output voltage of the fuel cell stack +.>：
The fuel cell group consists of n single fuel cells which are connected in series, wherein n is a positive integer;
wherein, is determined by the following formula：
Wherein P is H2 And P O 2 Respectively hydrogen partial pressure and oxygen partial pressure; t is the temperature of the fuel cell;
is determined by the following formula：
Wherein i is the current of the single fuel cell;、/>is a model parameter; />Oxygen concentration at the catalyst surface;
is determined by the following formula：
Wherein i is the current of the single fuel cell; t is the temperature of the fuel cell;
wherein the constructing an electrolyzer dynamic model based on the electrolyzer supplying fuel to the fuel cell stack and the temperature at which the electrolyzer operates comprises:
determining the rate of hydrogen produced by the electrolyzer according to Faraday's lawThe method comprises the following steps:
wherein,for the cell current>The number of the electrolytic cells; />Is Faraday efficiency; f is Faraday constant, wherein +.>In moles per second, is the chemical reaction rate unit;
wherein the transfer function of the controllerThe method comprises the following steps:
wherein,the proportional magnification of the controller; />Is the integration time; />Is the differential time.
2. The method of claim 1, wherein the method further comprises:
the heat balance in the fuel cell stack is determined according to the following equation:
wherein,is internal heat energy->For the heat loss of the environment>Is internal heat loss.
3. The method of claim 2, wherein the method further comprises:
according to the following formula：
According to the following formula：
According to the following formula：
Wherein,is the heat capacity of the fuel cell,Tis the temperature of the fuel cell;T a is ambient temperature;icurrent for a single fuel cell; />Is the fuel cell resistance;nin the number of single fuel cells,R t in the case of an environmental resistance value,R int is an internal resistance.
4. The method of claim 1, wherein the cross-sectional area of the electrode used in the capacitor is 500-2000 times the cross-sectional area of the fuel cell electrode.
5. The method of claim 4, wherein the capacitor is a low pass filter and is expressed by the following formula:
wherein,108.75mF millivolts, +.>Is a series resistor>Is nonsensical resistance.
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| CN109657348A (en) * | 2018-12-18 | 2019-04-19 | 安徽江淮汽车集团股份有限公司 | One proton exchanging film fuel battery modeling method |
| CN113346111A (en) * | 2021-05-08 | 2021-09-03 | 中汽研汽车检验中心（天津）有限公司 | Modeling method of proton exchange membrane fuel cell system |
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| CN109657348A (en) * | 2018-12-18 | 2019-04-19 | 安徽江淮汽车集团股份有限公司 | One proton exchanging film fuel battery modeling method |
| CN113346111A (en) * | 2021-05-08 | 2021-09-03 | 中汽研汽车检验中心（天津）有限公司 | Modeling method of proton exchange membrane fuel cell system |
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