CN114678568A - Method for modeling proton exchange membrane fuel cell - Google Patents

Method for modeling proton exchange membrane fuel cell Download PDF

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CN114678568A
CN114678568A CN202210324812.6A CN202210324812A CN114678568A CN 114678568 A CN114678568 A CN 114678568A CN 202210324812 A CN202210324812 A CN 202210324812A CN 114678568 A CN114678568 A CN 114678568A
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fuel cell
cell stack
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temperature
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CN114678568B (en
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肖森林
贺迪华
宁伟
黄超
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Shenzhen Hydrogen Age New Energy Technology Co ltd
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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
    • 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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    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
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    • Y02E60/50—Fuel cells

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Abstract

The embodiment of the invention discloses a method for modeling 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 capacitors connected in parallel; constructing an electrolyzer dynamic model based on the supply of fuel to the fuel cell stack by the electrolyzer and the temperature at which the electrolyzer operates; adjusting the output voltage and frequency of the fuel cell stack to target values by a two-stage converter; and converting the dc voltage of the output fuel cell stack into an ac 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 the proton exchange membrane fuel cell can be applied to power domestic electricity.

Description

Method for modeling proton exchange membrane fuel cell
Technical Field
The invention relates to the field of fuel cells, in particular to a method for modeling a proton exchange membrane fuel cell.
Background
A distributed power source is a power generation source that is directly connected to a power distribution network or consumer, wherein the voltage level of the distributed power source ranges from 400 volts to a maximum of 33 kilowatts, and the capacity thereof ranges from a few watts to a maximum of 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 of electricity to expand the global trend of energy consumption and decentralized production at consumption sites. Among them, a fuel cell is an electrochemical cell for generating electric energy, which is composed of two conductors called electrodes and a conductive film between the electrodes, called an electrolyte. Among them, fuel cells are classified into the following types according to the type 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 commercial use, cogeneration production, and the like. Proton Exchange Membrane (PEM) fuel cells have the advantages of fast start-up, providing part-load availability, etc., compared to other types of fuel cells. Thus, the home load curve can be modified by using PEM fuel cells. However, in the prior art, there is no method for effectively modeling a proton exchange membrane fuel cell.
In summary, how to effectively model the fuel cell and improve the accuracy of the model is a problem to be solved.
Disclosure of Invention
In view of this, the embodiment of the present invention provides a modeling method for a proton exchange membrane fuel cell, which can generate an alternating current, so that the proton exchange membrane fuel cell can be applied to supply electricity for domestic electricity.
In a first aspect, an embodiment of the present invention provides a method for modeling a proton exchange membrane fuel cell, where the method includes:
constructing a dynamic model of the fuel cell stack according to the temperature of the fuel cell and the capacitors connected in parallel;
constructing an electrolyzer dynamic model based on the supply of fuel to the fuel cell stack by the electrolyzer and the temperature at which the electrolyzer operates;
adjusting the output voltage and frequency of the fuel cell stack to target values by a two-stage converter; and converting the dc voltage of the output fuel cell stack into an ac 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 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-υact+ηohmic
wherein E is the open circuit voltage without loss in a single fuel cell, VactIs the activation voltage drop at the anode and cathode in the fuel cell; etaohmicOhmic voltage losses in the fuel cell.
Optionally, the total output voltage V of the fuel cell stack is obtained according to the output voltage V of the single fuel cellstack：
Vstack＝n*V
The fuel cell stack consists of n single fuel cells connected in series, wherein n is a positive integer.
Optionally, E is determined by the following formula:
Figure BDA0003572948370000031
wherein, PH2And PO2Hydrogen partial pressure and oxygen partial pressure, respectively; t is the temperature of the fuel cell;
upsilon is determined by the following formulaact：
Figure BDA0003572948370000032
Figure BDA0003572948370000033
Wherein i is the current of a single fuel cell; zeta1、ζ2、ζ3、ζ4Is a model parameter;
Figure BDA0003572948370000034
is the oxygen concentration at the catalyst surface;
eta is determined by the following formulaohmic：
ηohmic＝-i*Rin
Rin＝0.01605-3.5*10-5*T+8*10-5*i
Wherein i is the current of a single fuel cell; t is the temperature of the fuel cell.
Optionally, the method further includes: determining a thermal balance in the fuel cell stack according to the following equation:
QI＝QS+QL
wherein Q isSFor heat loss from the environment, QLAs internal heat loss.
Optionally, the method further includes: q is determined according to the following formulaI：
Figure BDA0003572948370000035
Q is determined according to the following formulaS：
Figure BDA0003572948370000036
Q is determined according to the following formulaL：
QL＝i2(Ra+Rint)*n
Wherein, CtIs the heat capacity of the fuel cell, T is the temperature of the fuel cell; ta is the ambient temperature; i is a sheetThe current of the fuel cell; raIs a fuel cell resistance; and n is the number of single fuel cells.
Optionally, the cross-sectional area of the electrode used in the capacitor is 500-2000 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:
Figure BDA0003572948370000041
wherein C is 108.75mF millivolts and RcIs a series resistance, RsIs meaningless resistance.
Optionally, the constructing a dynamic model of the electrolyzer based on the supply of fuel to the fuel cell stack by the electrolyzer and the temperature at which the electrolyzer operates comprises:
determining the rate of hydrogen production by the electrolyzer according to Faraday's law
Figure BDA0003572948370000042
Comprises the following steps:
Figure BDA0003572948370000043
wherein ieIs the cell current, nnThe number of the electrolytic cells is equal; etaFFaraday efficiency; f is the Faraday constant.
Optionally, the transfer function G of the controllerr(s) is:
Figure BDA0003572948370000044
wherein, KpIs the proportional amplification factor of the controller; t isiIs the integration time; t is a unit ofdIs 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 including:
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 capacitors connected in parallel;
an electrolyzer modeling module for constructing an electrolyzer dynamic model based on the supply of fuel to the fuel cell stack by the electrolyzer and the temperature at which the electrolyzer is operating;
a converter modeling module for adjusting an output voltage and a frequency of the fuel cell stack to target values by a two-stage converter; and converting the dc voltage of the output fuel cell stack into an ac voltage by a single-phase four-phase inverter;
a controller modeling module to control 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-υact+ηohmic
wherein E is the open circuit voltage without loss in a single fuel cell, VactIs the activation voltage drop at the anode and cathode in the fuel cell; etaohmicOhmic voltage losses 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 cellstack：
Vstack＝n*V
The fuel cell stack consists of n single fuel cells connected in series, wherein n is a positive integer.
Optionally, the fuel cell modeling module is further configured to determine E by the following equation:
Figure BDA0003572948370000051
wherein, PH2And PO2Hydrogen partial pressure and oxygen partial pressure, respectively; t is fuel electricityThe temperature of the cell;
upsilon is determined by the following formulaact：
Figure BDA0003572948370000052
Figure BDA0003572948370000053
Wherein i is the current of a single fuel cell; zeta1、ζ2、ζ3、ζ4Is a model parameter;
Figure BDA0003572948370000054
is the oxygen concentration at the catalyst surface;
eta is determined by the following formulaohmic：
ηohmic＝-i*Rin
Rin＝0.01605-3.5*10-5*T+8*10-5*i
Wherein i is the current of a single fuel cell; t is the temperature of the fuel cell.
Optionally, the fuel cell modeling module is further configured to determine a thermal balance in the fuel cell stack according to the following equation:
QI＝QS+QL
wherein Q issFor heat loss from the environment, QLInternal heat loss.
Optionally, the fuel cell modeling module is further configured to determine Q according to the following equationI：
Figure BDA0003572948370000061
Q is determined according to the following formulaS：
Figure BDA0003572948370000062
Q is determined according to the following formulaL：
QL＝i2(Ra+Rint)*n
Wherein, CtIs the heat capacity of the fuel cell, T is the temperature of the fuel cell; ta is the ambient temperature; i is the current of a single fuel cell; raIs a fuel cell resistance; and n is the number of single fuel cells.
Optionally, the cross-sectional area of the electrode used in the capacitor is 500-2000 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:
Figure BDA0003572948370000063
wherein C is 108.75mF millivolts and RcIs a series resistance, RsIs meaningless resistance.
Optionally, the cell modeling module is further configured to:
determining the rate of hydrogen production by the electrolyzer according to Faraday's law
Figure BDA0003572948370000064
Comprises the following steps:
Figure BDA0003572948370000065
wherein ieIs the cell current, nnThe number of the electrolytic cells is equal; etaFFaraday efficiency; f is the Faraday constant.
Optionally, the transfer function G of the controllerr(s) is:
Figure BDA0003572948370000071
wherein, KpIs the proportional amplification factor of the controller; t isiIs the integration time; t isdIs the differential time.
The method comprises the steps of constructing a dynamic model of a fuel cell stack according to the temperature of a fuel cell and a capacitor connected in parallel, constructing an electrolyzer dynamic model based on the supply of fuel to the fuel cell stack by an electrolyzer and the operating temperature of the electrolyzer, and adjusting the output voltage and the 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 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 the proton exchange membrane fuel cell can be applied to power supply for domestic electricity.
Drawings
The above and other objects, features and advantages of the present invention will become more apparent from the following description of the 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 PEM fuel cell in an embodiment of the invention;
FIG. 3 is a schematic of the output voltage waveform 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 illustration of a filtered load voltage in an embodiment of the present invention;
fig. 6 is a schematic diagram of the 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. It will be apparent to those skilled in the art that the present disclosure may be practiced without these specific details. Well-known methods, procedures, components and circuits have not been described in detail so as not to obscure the present disclosure.
Further, those of ordinary skill in the art will appreciate that the drawings provided herein are for illustrative purposes and are not necessarily drawn to scale.
Unless the context clearly requires otherwise, throughout this specification, the words "comprise", "comprising", and the like are to be construed in an inclusive sense as opposed to an exclusive or exhaustive sense; that is, what is meant is "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. In addition, in the description of the present disclosure, "a plurality" means two or more unless otherwise specified.
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 commercial use, cogeneration production, and the like. Fuel cells have many benefits, including in particular:
A. from the perspective of an energy system, the efficiency is high. For example, PEM fuel cells have efficiencies of 40-60% when generating electricity, with efficiencies of 85% for both electricity and heat.
B. From the point of view of power control, it is easy to adjust. For example, the output power can be controlled by controlling the reactants (hydrogen and oxygen).
C. And the environmental compatibility is strong. If hydrogen is used as the primary fuel, its output is only water, and since there are no mechanical parts, they are free of noise pollution.
D. The fuel has flexibility. Among other things, hydrogen fuel can be obtained from various sources, such as water, natural gas, coal, methanol, hydrocarbon fuels, 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 cell may be classified into 5 types, respectively, according to the type of electrolyte used: solid Oxide Fuel Cells (SOFC), Molten Carbonate Fuel Cells (MCFC), Phosphoric Acid Fuel Cells (PAFC), Alkaline Fuel Cells (AFC), and Proton Exchange Membrane Fuel Cells (PEMFC). Among them, a Solid Oxide Fuel Cell (SOFC) uses an oxygen ion conductor solid oxide as an electrolyte. Molten Carbonate Fuel Cells (MCFCs) use molten lithium-potassium or lithium-sodium carbonate as the electrolyte. A Phosphoric Acid Fuel Cell (PAFC) uses concentrated phosphoric acid as an electrolyte. An Alkaline Fuel Cell (AFC) generally uses an alkaline potassium hydroxide solution as an electrolyte. Proton Exchange Membrane Fuel Cells (PEMFCs) typically use a perfluorinated or partially fluorinated sulfonic acid-type proton exchange membrane as the electrolyte.
PEM fuel cells (PEMFCs) have the advantages of fast start-up, providing availability of part-load, etc., compared to other types of fuel cells. Thus, the home load curve 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 by 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, a simple storage system method is not applicable due to high pressure supply, explosion problems, etc., and 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 electrolyzer. Further, the strategy of the cell may be used during midnight operating periods. Thus, each consumer in the home sector can produce part of their required load during peak hours and remove part of the peak load from the global grid. Further, this strategy will result in 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, and as shown in fig. 1, a polymer electrolyte fuel cell includes: a fuel cell stack 110, a supply pipe part 120, a reformer or a fuel processor 130, and a cooling system 140, wherein the supply pipe part 120 includes a hydrogen supply pipe 121 and an air supply pipe 122. Specifically, 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 in an embodiment of the present invention, and as shown in fig. 2, an embodiment of the present invention provides a method for modeling a proton exchange membrane fuel cell, where the method mainly includes:
s201: constructing a dynamic model of the fuel cell stack according to the temperature of the fuel cell and the capacitors connected in parallel;
s202: constructing an electrolyzer dynamic model based on the supply of fuel to the fuel cell stack by the electrolyzer and the temperature at which the electrolyzer operates;
s203: adjusting the output voltage and frequency of the fuel cell stack to target values by a two-stage converter; and converting the dc voltage of the output fuel cell stack into an ac 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 domestic electricity.
In an alternative embodiment, constructing a dynamic model of the fuel cell stack based on fuel cell temperature and the parallel capacitors comprises:
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-υact+ηohmic
wherein E is the open circuit voltage without loss in a single fuel cell, VactIs the activation voltage drop at the anode and cathode in the fuel cell; etaohmicOhmic voltage losses in the fuel cell.
Specifically, E is the open circuit voltage without loss in a single fuel cell, then
Figure BDA0003572948370000101
Where Δ G explains the change in Gibbs free energy in joules/mole (j/mol) in the above formula and Δ S is the change in entropy in joules/mole (j/mol). F is the Faraday constant and is the value of,
Figure BDA0003572948370000102
and
Figure BDA0003572948370000103
respectively, hydrogen partial pressure and oxygen partial pressure in units of atmospheric air. R is the universal constant for gases; t is the fuel cell temperature, TrefIs a reference temperature (e.g., 25 ℃) in kelvin.
In an alternative embodiment, using standard pressure and temperature Δ S, Δ G values are obtained, E is determined based on the above equation and by the following equation:
Figure BDA0003572948370000111
wherein, PH2And PO2Hydrogen partial pressure and oxygen partial pressure, respectively; t is the temperature of the fuel cell.
Upsilon is determined by the following formulaact：
Figure BDA0003572948370000112
Figure BDA0003572948370000113
Wherein i is the current of a single fuel cell; zeta1、ζ2、ζ3、ζ4Is a model parameter;
Figure BDA0003572948370000114
is the oxygen concentration at the catalyst surface;
eta is determined by the following formulaohmic：
ηohmic＝-i*Rin
Rin＝0.01605-3.5*10-5*T+8*10-5*i
Wherein i is the current of a single fuel cell; t is the temperature of the fuel cell.
In an alternative embodiment, to provide higher voltages, a plurality of individual fuel cells may be combined to form a fuel cell stack. Obtaining the total output voltage V of the fuel cell stack according to the output voltage V of the single fuel cellstαck：
Vstack＝n*V
The fuel cell stack consists of n single fuel cells connected in series, wherein n is a positive integer.
In particular, the concentration of insoluble oxygen in the gas/liquid interface according to Henry's law
Figure BDA0003572948370000115
Comprises the following steps:
Figure BDA0003572948370000116
based on experimental analysis, the parametric equation for determining overvoltage due to activity and internal resistance is:
Figure BDA0003572948370000117
Rin＝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:
Figure BDA0003572948370000121
from the stable 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 by increasing the cell pressure, and the dynamic behavior of the fuel cell voltage can be simulated by adding a capacitor to the stable fuel cell model.
The effect of the double layer charge is simulated with capacitors or resistors in parallel. The differential equation describing the fuel cell voltage is:
Figure BDA0003572948370000122
ohmic voltage loss eta in fuel cellsohmi2Comprises the following steps:
ηohmic＝-i*Rin
the fuel cell stack consists of n single fuel cells connected in series, the total voltage is:
Vstack＝n*V
the rate of hydrogen and oxygen in the fuel cell depends 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 flow rates are specified in moles per second, the gas pressure inside the fuel cell dehumidifier can be obtained using the mole equation. For a fuel cell anode:
Figure BDA0003572948370000123
wherein, VaIs the volume of the anode in liters; UA is the cross-sectional area of the flux;
Figure BDA0003572948370000124
is the molar flux rate; r is a global constant of gas; t is the fuel cell temperature;
Figure BDA0003572948370000125
is the molar density; f is the Faraday constant.
Likewise, for a fuel cell cathode:
Figure BDA0003572948370000131
wherein, VcIs the volume of the anode. For example, the volume of the anode and cathode may be assumed to be 2 liters.
In an alternative embodiment, the balance of total thermal energy in the fuel cell stack:
QI＝QS-QL
wherein Q isIFor internal thermal energy (storage of thermal energy), QSFor heat loss from the environment, QLInternal heat loss.
In particular, internal heat loss QLComprises the following steps:
QL＝i2(Ra+Rint)*n
then the process of the first step is carried out,
Figure BDA0003572948370000132
wherein, CtAs 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.
Figure BDA0003572948370000133
Then the process of the first step is carried out,
Figure BDA0003572948370000134
ta is the ambient temperature, which in this embodiment may be set to 25 ℃.
Further, a 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 with a very porous cross section. In an alternative embodiment, the cross-sectional area of the electrodes used in the capacitor is 500-2000 times greater than the cross-sectional area of the cell electrodes.
If high power is required, large-capacity capacitors can be used for a short time, for example, in an automobile using a fuel cell. In particular, capacitors are considered low voltage devices. Typically, the voltage of the capacitor is about 2.5 volts. But in high voltage capacitor banks, the capacitance of the bulk capacitors 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 milliamps and the leakage current is 10 milliamps, assuming the leakage current of the capacitor is constant. Specifically, a 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 a capacitor module with the characteristics is connected with a fuel cell in parallel to work, so that the voltage fluctuation caused by sudden load change is reduced.
The bulk capacitor is written as a low pass filter:
Figure BDA0003572948370000141
wherein C is 108.75mF millivolts and RcIs a series resistance, RsIs meaningless resistance. For example, C108.75 mF mv, series resistance Rc4 mV, meaningless resistance, Rs0.01W watt.
The decomposition into hydrogen and oxygen can be achieved by using an electric current between two electrodes with separate aqueous electrolytes. The whole electrolysis process can be expressed as:
H2O + electrical power H2(g) +0.5O2(g)
In an implementable embodiment, an electrolysis cell system consists of several electrolysis cells connected in series. The current characteristic of the cell voltage is dependent on the temperature at which it flows and is non-linear and obtained by curve fitting. The rate of hydrogen production in the electrolyzer unit is proportional to the rate of electron transfer at the electrode, according to Faraday's law, determining the hydrogen produced by the electrolyzerRate of change
Figure BDA0003572948370000142
Comprises the following steps:
Figure BDA0003572948370000143
wherein ieIs the cell current, nnThe number of the electrolytic cells is equal; etaFFaraday efficiency; f is the Faraday constant. The faradaic 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 faradaic efficiency is determined as:
Figure BDA0003572948370000151
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 the 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:
Figure BDA0003572948370000152
since the proposed design is a system separate from the mains, the inverter in voltage control mode is the reverse of the current control method normally applied to inverters connected to the 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 frequency of the triangular carrier is 8 khz.
The need for a controller is felt due to the non-linear nature of the system and the long response to load changes and the presence of significant sustained errors. The general transfer function of the controller is as follows:
Figure BDA0003572948370000153
wherein, KpIs the proportional amplification factor of the controller; t isiIs the integration time; t isdIs the differential time.
Further, the mathematical model created by the method for modeling the pem fuel cell described in the above example can be simulated in Simulink of Matlab software by changing the amount of load connected to the system in Matlab software. Wherein the model system consists of 8 main subcomponents: a fuel cell stack, an electrolyzer, a supercapacitor, an inverter, a booster, a hydrogen storage and a hydrogen and oxygen mass flow controller. And the mathematical representations of these sub-components were determined by the proton exchange membrane fuel cell modeling method described in the above example.
FIG. 3 is a schematic of the output voltage waveform 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 illustration of a filtered load voltage in an embodiment of the invention; fig. 6 is a schematic diagram of the load current in an embodiment of the invention.
In one embodiment, to find the response of the fuel cell to the 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 best performance of the controller and the supercapacitor. Two modes of using and not using a supercapacitor are shown in the form of load voltage curves. The voltage drop at the initial moment of the fuel cell output with the supercapacitor is during the period when the initial current enters with the flux, but after a while the voltage across the terminals creates a stable condition.
Then, the response of the fuel cell to the periodic load fluctuations is determined. In this case, a constant load of 10 amps and an oscillating load in the range of 5 amps were applied to the fuel cell for a time interval 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 has fluctuations in the range of 3 volts, and the closing of the supercapacitor reduces the amplitude of these fluctuations by about 0.5 volts.
Since the voltage applied to the load is of an alternating current type, it is necessary to convert the DC output voltage of the fuel cell into alternating current using a single-phase inverter. Therefore, the proton exchange membrane fuel cell of the embodiment of the invention uses the 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 device for modeling a proton exchange membrane fuel cell, 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 capacitors connected in parallel;
an electrolyzer modeling module for constructing an electrolyzer dynamic model based on the supply of fuel to the fuel cell stack by the electrolyzer and the temperature at which the electrolyzer is operating;
a converter modeling module for adjusting an output voltage and a frequency of the fuel cell stack to target values by a two-stage converter; and converting the dc voltage of the output fuel cell stack into an ac voltage by a single-phase four-phase inverter;
a controller modeling module to control the flow of hydrogen and oxygen into the fuel cell stack via a controller.
In an implementable embodiment, the fuel cell modeling module is further configured to determine the output voltage V of the single fuel cell as:
V＝E-υact+ηohmic
wherein E is the open circuit voltage without loss in a single fuel cell, VactIs the activation voltage drop at the anode and cathode in the fuel cell; etaohmicOhmic voltage losses in the fuel cell.
In the same placeIn the present 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 cellstack：
Vsstack＝n*V
The fuel cell stack consists of n single fuel cells connected in series, wherein n is a positive integer.
In an implementable embodiment, the fuel cell modeling module is further configured to determine E by the following equation:
Figure BDA0003572948370000171
wherein, PH2And PO2Hydrogen partial pressure and oxygen partial pressure, respectively; t is the temperature of the fuel cell;
upsilon is determined by the following formulaact：
Figure BDA0003572948370000172
Figure BDA0003572948370000173
Wherein i is the current of a single fuel cell; zeta1、ζ2、ζ3、ζ4Is a model parameter;
Figure BDA0003572948370000174
is the oxygen concentration at the catalyst surface;
eta is determined by the following formulaohmic：
ηohmic＝-i*Rin
Rin＝0.01605-3.5*10-5*T+8*10-5*i
Wherein i is the current of a single fuel cell; t is the temperature of the fuel cell.
In an implementable embodiment, the fuel cell modeling module is further configured to determine a thermal balance in the fuel cell stack according to the following equation:
QI＝QS+QL
wherein QSFor heat loss from the environment, QLInternal heat loss.
Optionally, the fuel cell modeling module is further configured to determine Q according to the following equationI：
Figure BDA0003572948370000181
Q is determined according to the following formulas：
Figure BDA0003572948370000182
Q is determined according to the following formulaL：
QL＝i2(Ra+Rint)*n
Wherein, CtIs the heat capacity of the fuel cell, T is the temperature of the fuel cell; ta is the ambient temperature; i is the current of a single fuel cell; raIs a fuel cell resistance; and n is the number of single fuel cells.
In an implementable 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 an implementable embodiment, the capacitor is a low pass filter and is represented by the following equation:
Figure BDA0003572948370000183
wherein C is 108.75mF millivolts and RcIs a series resistance, RsIs meaningless resistance.
In an implementable embodiment, the electrolyzer modeling module is further to:
determining the rate of hydrogen production by the electrolyzer according to Faraday's law
Figure BDA0003572948370000184
Comprises the following steps:
Figure BDA0003572948370000185
wherein ieIs the cell current, nnThe number of the electrolytic cells is equal; etaFFaraday efficiency; f is the Faraday constant.
In an implementable embodiment, the transfer function G of the controllerr(s) is:
Figure BDA0003572948370000191
wherein, KpIs the proportional amplification factor of the controller; t is a unit ofiIs the integration time; t isdIs the differential time.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (10)

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 capacitors connected in parallel;
constructing an electrolyzer dynamic model based on the supply of fuel to the fuel cell stack by the electrolyzer and the temperature at which the electrolyzer operates;
adjusting the output voltage and frequency of the fuel cell stack to target values by a two-stage converter; and converting the dc voltage of the output fuel cell stack into an ac voltage by a single-phase four-phase inverter;
the flow of hydrogen and oxygen into the fuel cell stack is controlled by a controller.
2. The method of claim 1, wherein constructing a dynamic model of a fuel cell stack based on fuel cell temperature and capacitors connected in parallel comprises:
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-υact+ηohmic
wherein E is the open circuit voltage without loss in a single fuel cell, VactIs the activation voltage drop at the anode and cathode in the fuel cell; etaohmicOhmic voltage losses in the fuel cell.
3. The method of claim 2, further comprising:
obtaining the total output voltage V of the fuel cell stack according to the output voltage V of the single fuel cellstack：
Vstack＝n*V
The fuel cell stack consists of n single fuel cells connected in series, wherein n is a positive integer.
4. The method of claim 2 or 3,
e is determined by the following equation:
Figure FDA0003572948360000021
wherein, PH2And PO2Hydrogen partial pressure and oxygen partial pressure, respectively; t is the temperature of the fuel cell;
upsilon is determined by the following formulaact：
Figure FDA0003572948360000022
Figure FDA0003572948360000023
Wherein i is the current of a single fuel cell; ζ represents a unit1、ζ2、ζ3、ζ4Is a model parameter;
Figure FDA0003572948360000024
is the oxygen concentration at the catalyst surface;
eta is determined by the following formulaohmic：
ηohmic＝-i*Rin
Rin＝0.01605-3.5*10-5*T+8*10-5*i
Wherein i is the current of a single fuel cell; t is the temperature of the fuel cell.
5. The method of claim 1, wherein the method further comprises:
determining a thermal balance in the fuel cell stack according to the following equation:
QI＝QS+QL
wherein Q isIFor internal heat energy, QSFor heat loss from the environment, QLInternal heat loss.
6. The method of claim 5, wherein the method further comprises:
q is determined according to the following formulaL：
Figure FDA0003572948360000025
Q is determined according to the following formulaS：
Figure FDA0003572948360000026
Q is determined according to the following formulaL：
QL＝i2(Ra+Rint)*n
Wherein, CtIs the heat capacity of the fuel cell, T is the temperature of the fuel cell; ta is the ambient temperature; i is the current of a single fuel cell; r isaIs a fuel cell resistance; and n is the number of single fuel cells.
7. The method of claim 3, 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.
8. The method of claim 7, wherein the capacitor is a low pass filter and is represented by the following equation:
Figure FDA0003572948360000031
wherein C is 108.75mF millivolts and RcIs a series resistance, RsIs a meaningless resistance.
9. The method of claim 1, wherein constructing an electrolyzer dynamic model based on the electrolyzer supplying fuel to the fuel cell stack and the temperature at which the electrolyzer is operating comprises:
determining the rate of hydrogen production by the electrolyzer according to Faraday's law
Figure FDA0003572948360000032
Comprises the following steps:
Figure FDA0003572948360000033
wherein ieIs the cell current, nnThe number of the electrolytic cells is equal; etaFFaraday efficiency; f is the Faraday constant.
10. The method of claim 1, wherein the transfer function G of the controllerr(s) is:
Figure FDA0003572948360000041
wherein, KpIs the proportional amplification factor of the controller; t isiIs the integration time; t isdIs the differential time.
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