CN113862729A - Photovoltaic hydrogen production system control method based on conductance incremental method - Google Patents

Photovoltaic hydrogen production system control method based on conductance incremental method Download PDF

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CN113862729A
CN113862729A CN202111257305.7A CN202111257305A CN113862729A CN 113862729 A CN113862729 A CN 113862729A CN 202111257305 A CN202111257305 A CN 202111257305A CN 113862729 A CN113862729 A CN 113862729A
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photovoltaic
hydrogen production
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杨立滨
刘庭响
李春来
李志青
李正曦
周万鹏
张海宁
王京阳
董雁楠
马少华
颜宁
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State Grid Qinghai Electric Power Co Clean Energy Development Research Institute
Shenyang University of Technology
State Grid Qinghai Electric Power Co Ltd
Economic and Technological Research Institute of State Grid Qianghai Electric Power Co Ltd
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State Grid Qinghai Electric Power Co Clean Energy Development Research Institute
Shenyang University of Technology
State Grid Qinghai Electric Power Co Ltd
Economic and Technological Research Institute of State Grid Qianghai Electric Power Co Ltd
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Abstract

The invention belongs to the technical field of hydrogen production converter control, and particularly relates to a photovoltaic hydrogen production system control method based on a conductance incremental method. A conductance incremental method control technology is added on the basis of a buck converter to track a photovoltaic maximum power point and is directly coupled with an electrolytic hydrogen production system to improve the hydrogen production efficiency. The method comprises the following steps: step 1, collecting voltage and current information output by a photovoltaic cell under different working environments; step 2, analyzing the photovoltaic buck converter; step 3, designing a conductance increment control method; step 4, respectively sending the measured and collected electric quantity information and the required calculation information to a control module, and sending the calculated information to a buck converter switching device; step 5, designing an electrolytic water system with a hydrogen production function: and 6, directly coupling the step-down converter in the step 4 with the water electrolysis hydrogen production system, sending a voltage and current signal output by the step-down converter into the water electrolysis system, and finally stably producing hydrogen through the water electrolysis system.

Description

Photovoltaic hydrogen production system control method based on conductance incremental method
Technical Field
The invention belongs to the technical field of hydrogen production converter control, and particularly relates to a photovoltaic hydrogen production system control method based on a conductance incremental method.
Background
At present, energy is mainly obtained by burning fossil resources, so that the environmental pollution problem and the waste of resources are aggravated. At present, the world energy situation is severe, and in view of the increase of energy demand and the current situation of climate change, the trend of using renewable energy which is rich in reserves, free of pollution and capable of being continuously developed and utilized is inevitable for dealing with energy problems. Compared with renewable energy sources such as geothermal energy and wind energy, the photovoltaic panel has the largest power generation capacity with low environmental cost by collecting solar power, but the photovoltaic panel has the defects of very obvious intermittence and difficulty in continuous and reliable power supply, and under the normal condition, the illumination dense area and the power consumption area are usually far away from each other, so that the supply and the demand are often mismatched, the safety and the stability of a power grid are hindered, and the fluctuation of generated energy brings problems to the consumption of clean energy. Therefore, the energy storage device is particularly important as an efficient and clean energy carrier for storing the residual renewable energy bridge. Hydrogen energy is considered to be the best material to serve as an energy carrier in the future due to its advantages of cleanliness, high energy density and efficiency, can replace fossil fuels, and reduces carbon dioxide emissions, thereby mitigating the impact on global warming. Therefore, after the fossil fuel age, the use of photovoltaic electrolysis of water to produce hydrogen is a powerful driving force to sustain energy development.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a photovoltaic hydrogen production system control method based on a conductance incremental method. The photovoltaic power generation system can quickly track the maximum power point aiming at the power fluctuation generated by the photovoltaic power generation caused by the change of illumination temperature, can well adapt to an electrolysis system requiring a high-current low-voltage working environment and can well adapt to the power fluctuation, improves the hydrogen production efficiency and reduces the hydrogen production energy consumption while ensuring the stable operation of the system, and has a certain engineering application value.
In order to achieve the purpose, the invention adopts the following technical scheme that a conductance incremental method control technology is added on the basis of a buck converter to track the maximum photovoltaic power point and is directly coupled with an electrolytic hydrogen production system to improve the hydrogen production efficiency, and discloses a photovoltaic hydrogen production system control method based on the conductance incremental method.
According to a photovoltaic system output model, a maximum power tracking control method based on a conductance incremental method is researched from the analysis of working states of a photovoltaic system in different environments; secondly, a hydrogen production system is constructed according to an electrolytic hydrogen production mechanism, and a buck converter control model meeting the working conditions of low voltage and high current of the photovoltaic hydrogen production system is researched; and finally, coupling the photovoltaic buck converter based on the conductance incremental method with a water electrolysis hydrogen production system model, wherein the control method can provide a required low-voltage high-current working environment for the electrolyzer, and can also adapt to power fluctuation of the system, thereby reducing the energy consumption of the system.
The method comprises the following steps:
step 1, collecting voltage and current information output by a photovoltaic cell under different working environments;
step 2, analyzing the photovoltaic buck converter;
step 3, designing a conductance increment control method for realizing maximum power point tracking;
step 4, respectively sending the measured and collected electric quantity information and the required calculation information into a control module with a conductance incremental method, and sending the calculated information into a buck converter switching device directly connected with the photovoltaic module;
step 5, designing an electrolytic water system with a hydrogen production function:
and 6, directly coupling the step-down converter in the step 4 with the water electrolysis hydrogen production system, sending a voltage and current signal output by the step-down converter into the water electrolysis system, and finally stably producing hydrogen through the water electrolysis system.
Further, in step 2, analyzing the photovoltaic buck converter includes: the principle of the photovoltaic buck converter is that when the PWM wave is at a high level, the switching element is turned on to magnetize the energy storage inductor, and the current passing through the inductor is linearly increased to charge the capacitor and provide energy to the load; when the PWM waveform is at low level, the switch element is turned off, the inductor and capacitor elements release energy to maintain the output voltage, and when the circuit works stably, the average value U of the load voltageoIs composed of
Figure BDA0003324294570000031
Wherein, tonFor the on-time of the switching element, toffThe switching-off time of the switching element is T, a switching period is T, alpha is the turn-on duty ratio of the switching period, and E is the direct-current power supply voltage;
the average value U of the voltage output by the converter is derived from equation (1)oMaximum E, however, when the duty cycle α is reduced, UoIt is reduced accordingly, so it is called a buck converter.
Further, in step 3, the designing of the conductance increment control method with maximum power point tracking includes:
the instantaneous output power of the photovoltaic cell is expressed as:
P＝VI (2)
where V is the photovoltaic system output voltage and I is the photovoltaic system output current.
Meanwhile, whether the maximum power point is tracked is judged, and if yes, disturbance tracking is stopped; if not, continuing disturbance tracking;
calculating a difference dV between V and V (n-1), calculating a difference dI between I and I (n-1), and calculating dI/dV by adopting an increment electric conduction method; v (n-1) is the output voltage of the photovoltaic cell in the previous control period, I (n-1) is the output current of the photovoltaic cell in the previous control period, and n is the control period;
judging whether dV is 0, if dV is 0, judging whether dI is 0; if not, judging whether the dI/dV is equal to-I/V or not;
if dI is equal to 0, then I (n-1) is equal to I; v (n-1) ═ V; if dI is not equal to 0, judging whether dI is greater than 0, if so, increasing the output voltage of the photovoltaic cell so that I (n-1) is equal to I; v (n-1) ═ V; if not, reducing the output voltage of the photovoltaic cell so that I (n-1) is I; v (n-1) ═ V;
if dI/dV is true, I (n-1) is I; v (n-1) ═ V; if the dI/dV is not established, judging whether the dI/dV is larger than the I/V or not, and if so, increasing the output voltage of the photovoltaic cell so that I (n-1) is I; v (n-1) ═ V; if not, reducing the output voltage of the photovoltaic cell so that I (n-1) is I; v (n-1) ═ V.
Further, in step 5, the water electrolysis system with hydrogen production function is designed to comprise:
the electrolytic water system mainly comprises two electrodes and a polymer film, wherein hydrogen is generated at a cathode, oxygen is generated at an anode, and the electrode reaction formula is as follows:
anode:
Figure BDA0003324294570000041
cathode:
2H++2e-→H2 (4)
the general reaction formula is as follows:
Figure BDA0003324294570000042
step 5-1, designing an electrolytic water anode system:
the anode of the electrolytic water system loses electrons to generate oxidation reaction, and the molar flow relation of water and oxygen before and after the reaction is as follows:
Figure BDA0003324294570000043
Figure BDA0003324294570000044
in the formula,
Figure BDA0003324294570000045
respectively, the molar flow rates of oxygen and water into and out of the anode. Since there is no oxygen inflow to the system, therefore
Figure BDA0003324294570000046
Is zero.
Figure BDA0003324294570000047
Is the electromigration and diffusion flow rate of water from the anode through the membrane. O is2sFlow rate for oxygen generated at anodeThe expression is as follows:
Figure BDA0003324294570000048
wherein the number of the electrolyzers is m, the current of an electrolysis system is I, the Faraday constant is F, and the efficiency of the electrolysis system is eta.
Step 5-2, designing an electrolytic water cathode system:
the cathode of the electrolytic water system obtains electrons to perform reduction reaction, and the molar flow relation of water and hydrogen before and after the reaction is as follows:
Figure BDA0003324294570000051
Figure BDA0003324294570000052
wherein,
Figure BDA0003324294570000053
is the molar flow rate of hydrogen into the cathode,
Figure BDA0003324294570000054
is the molar flow rate of water into the cathode.
Figure BDA0003324294570000055
Figure BDA0003324294570000056
Is the molar flow rate of hydrogen and water out of the cathode. H2sIs the flow rate of hydrogen generated at the cathode, and the expression is as follows:
Figure BDA0003324294570000057
step 5-3, designing an electrolytic water film system model:
membrane systems are important components of water electrolysis systems, and the role of the membrane in the water transport process is very important. Two modes of water transport within the membrane are expressed as:
Figure BDA0003324294570000058
Figure BDA0003324294570000059
wherein,
Figure BDA00033242945700000510
is the electromigration flow rate and,
Figure BDA00033242945700000511
is the rate of the electrical diffusion flow,
Figure BDA00033242945700000512
is the molar mass of water, m is the number of electrolyzers, A is the area of the cell,
Figure BDA00033242945700000513
is the coefficient of water diffusion;
Figure BDA00033242945700000514
is the concentration of cathode water,
Figure BDA00033242945700000515
Is the concentration of the anode water; t is tmThickness of electrolytic system film, ndIs the electric traction coefficient;
step 5-4, designing an electrolyzed water voltage system model:
voltage V of electrolysis systemelThe effects of Nernst equation, systematic activation polarization, and ohmic polarization can be expressed as:
Vel-Vact-Vohm＝En (14)
wherein E isnFor open circuit voltage of electrolytic system, meterThe expression is as follows:
Figure BDA0003324294570000061
Vactfor the system to activate the polarization voltage, the expression is as follows:
Figure BDA0003324294570000062
Vohmfor the system ohmic polarization voltage, the expression is as follows:
Vohm＝iRohm (17)
in the formula, E0Standard electromotive force for electrolytic systems, RgasIs the gas universal constant, TelIn order to obtain the temperature of the electrolysis system,
Figure BDA0003324294570000063
is the water activity between the anode and the membrane is 1, alpha is the membrane transfer coefficient, i is the current density of the electrolysis system, i is0Exchange of current density, Ro, for electrolytic systemshmIs the membrane resistance of the electrolytic system.
Compared with the prior art, the invention has the beneficial effects.
(1) The control method can quickly and stably enable the photovoltaic to track to the maximum power point, so that the photovoltaic hydrogen production system can meet the working conditions of low voltage and high current of the photovoltaic hydrogen production system, and provide the required low voltage and high current for the electrolyzer, thereby improving the overall working efficiency and reducing the hydrogen production energy consumption.
(2) The control method of the electrolytic hydrogen production system designed by the invention can well adapt to power fluctuation and improve the stability of the system.
Drawings
The invention is further described with reference to the following figures and detailed description. The scope of the invention is not limited to the following expressions.
Fig. 1 is a flow chart of the invention.
Fig. 2 is a flowchart of maximum power point tracking based on the conductance delta method.
FIG. 3 is a schematic diagram of the electrolytic hydrogen production system.
FIG. 4 is a block diagram of an electrolytic hydrogen production system including a buck converter control.
Detailed Description
The specific flow is shown in the attached figure 1, and the invention provides a photovoltaic hydrogen production system control method based on a conductance incremental method, which is based on the control of a buck converter, can quickly track the maximum power point aiming at the power fluctuation problem generated by photovoltaic caused by illumination temperature change, can well adapt to an electrolysis system requiring high-current low-voltage working environment, can well adapt to the power fluctuation, and can improve the hydrogen production efficiency while ensuring the stable operation of the system.
A photovoltaic hydrogen production system control method based on a conductance incremental method comprises the following steps:
step 1, collecting voltage and current information output by a photovoltaic cell under different working environments;
step 2, analyzing the photovoltaic buck converter, and briefly describing the principle of the photovoltaic buck converter:
the principle of the photovoltaic buck converter is that when the PWM wave is at a high level, the switching element is turned on to magnetize the energy storage inductor, and the current passing through the inductor is linearly increased to charge the capacitor and provide energy to the load; when the PWM waveform is at low level, the switch element is turned off, the inductor and capacitor elements release energy to maintain the output voltage, and when the circuit works stably, the average value U of the load voltageoIs composed of
Figure BDA0003324294570000071
Wherein, tonFor the on-time of the switching element, toffT is the turn-off time of the switching element, a switching period, alpha is the turn-on duty ratio of the switching period, and E is the DC power supply voltage.
The average value U of the voltage output by the converter is derived from equation (1)oMaximum E, however, when the duty cycle isWhen alpha is lowered, UoIt is reduced accordingly, so it is called a buck converter.
Step 3, designing a conductance increment control method for realizing maximum power point tracking;
the instantaneous output power of the photovoltaic cell is expressed as:
P＝VI (2)
where V is the photovoltaic system output voltage and I is the photovoltaic system output current.
Meanwhile, whether the maximum power point is tracked is judged, and if yes, disturbance tracking is stopped; if not, continuing disturbance tracking.
Calculating a difference dV between V and V (n-1), calculating a difference dI between I and I (n-1), and calculating dI/dV by adopting an increment electric conduction method; v (n-1) is the output voltage of the photovoltaic cell in the previous control period, I (n-1) is the output current of the photovoltaic cell in the previous control period, and n is the control period;
judging whether dV is 0, if dV is 0, judging whether dI is 0; if not, judging whether the dI/dV is equal to-I/V or not;
if dI is equal to 0, then I (n-1) is equal to I; v (n-1) ═ V; if dI is not equal to 0, judging whether dI is greater than 0, if so, increasing the output voltage of the photovoltaic cell so that I (n-1) is equal to I; v (n-1) ═ V; if not, reducing the output voltage of the photovoltaic cell so that I (n-1) is I; v (n-1) ═ V;
if dI/dV is true, I (n-1) is I; v (n-1) ═ V; if the dI/dV is not established, judging whether the dI/dV is larger than the I/V or not, and if so, increasing the output voltage of the photovoltaic cell so that I (n-1) is I; v (n-1) ═ V; if not, reducing the output voltage of the photovoltaic cell so that I (n-1) is I; v (n-1) ═ V.
Step 4, respectively sending the measured and collected electric quantity information and the required calculation information into a control module with a conductance incremental method, and sending the calculated information into a buck converter switching device directly connected with the photovoltaic module;
step 5, designing an electrolytic water system with a hydrogen production function:
the electrolytic water system mainly comprises two electrodes and a polymer film, wherein hydrogen is generated at a cathode, oxygen is generated at an anode, and the electrode reaction formula is as follows:
anode:
Figure BDA0003324294570000081
cathode:
2H++2e-→H2 (4)
the general reaction formula is as follows:
Figure BDA0003324294570000091
step 5-1, designing an electrolytic water anode system:
the anode of the electrolytic water system loses electrons to generate oxidation reaction, and the molar flow relation of water and oxygen before and after the reaction is as follows:
Figure BDA0003324294570000092
Figure BDA0003324294570000093
in the formula,
Figure BDA0003324294570000094
respectively, the molar flow rates of oxygen and water into and out of the anode. Since there is no oxygen inflow to the system, therefore
Figure BDA0003324294570000095
Is zero.
Figure BDA0003324294570000096
Is the electromigration and diffusion flow rate of water from the anode through the membrane. O is2sThe flow rate of oxygen generated at the anode is expressed as follows:
Figure BDA0003324294570000097
wherein the number of the electrolyzers is m, the current of an electrolysis system is I, the Faraday constant is F, and the efficiency of the electrolysis system is eta.
Step 5-2, designing an electrolytic water cathode system:
the cathode of the electrolytic water system obtains electrons to perform reduction reaction, and the molar flow relation of water and hydrogen before and after the reaction is as follows:
Figure BDA0003324294570000098
Figure BDA0003324294570000099
wherein,
Figure BDA00033242945700000910
is the molar flow rate of hydrogen into the cathode,
Figure BDA00033242945700000911
is the molar flow rate of water into the cathode.
Figure BDA00033242945700000912
Figure BDA00033242945700000913
Is the molar flow rate of hydrogen and water out of the cathode. H2sIs the flow rate of hydrogen generated at the cathode, and the expression is as follows:
Figure BDA00033242945700000914
step 5-3, designing an electrolytic water film system model:
membrane systems are important components of water electrolysis systems, and the role of the membrane in the water transport process is very important. Two modes of water transport within the membrane are expressed as:
Figure BDA0003324294570000101
Figure BDA0003324294570000102
wherein,
Figure BDA0003324294570000103
is the electromigration flow rate and,
Figure BDA0003324294570000104
is the rate of the electrical diffusion flow,
Figure BDA0003324294570000105
is the molar mass of water, m is the number of electrolyzers, A is the area of the cell,
Figure BDA0003324294570000106
is the coefficient of water diffusion;
Figure BDA0003324294570000107
is the concentration of cathode water,
Figure BDA0003324294570000108
Is the concentration of the anode water; t is tmThickness of electrolytic system film, ndIs the electric traction coefficient.
Step 5-4, designing an electrolyzed water voltage system model:
voltage V of electrolysis systemelThe effects of Nernst equation, systematic activation polarization, and ohmic polarization can be expressed as:
Vel-Vact-Vohm＝En (14)
wherein E isnFor the open circuit voltage of the electrolysis system, the expression is as follows:
Figure BDA0003324294570000109
Vactfor the system to activate the polarization voltage, the expression is as follows:
Figure BDA00033242945700001010
Vohmfor the system ohmic polarization voltage, the expression is as follows:
Vohm＝iRohm (17)
in the formula, E0Standard electromotive force for electrolytic systems, RgasIs the gas universal constant, TelIn order to obtain the temperature of the electrolysis system,
Figure BDA00033242945700001011
is the water activity between the anode and the membrane is 1, alpha is the membrane transfer coefficient, i is the current density of the electrolysis system, i is0Exchange of current density, Ro, for electrolytic systemshmIs the membrane resistance of the electrolytic system.
And 6, directly coupling the step-down converter in the step 4 with the water electrolysis hydrogen production system, sending a voltage and current signal output by the step-down converter into the water electrolysis system, and finally performing stable hydrogen production through the water electrolysis system.
It should be understood that the detailed description of the present invention is only for illustrating the present invention and is not limited by the technical solutions described in the embodiments of the present invention, and those skilled in the art should understand that the present invention can be modified or substituted equally to achieve the same technical effects; as long as the use requirements are met, the method is within the protection scope of the invention.

Claims (4)

1. A photovoltaic hydrogen production system control method based on a conductance incremental method is characterized by comprising the following steps: the method comprises the following steps:
step 1, collecting voltage and current information output by a photovoltaic cell under different working environments;
step 2, analyzing the photovoltaic buck converter;
step 3, designing a conductance increment control method for realizing maximum power point tracking;
step 4, respectively sending the measured and collected electric quantity information and the required calculation information into a control module with a conductance incremental method, and sending the calculated information into a buck converter switching device directly connected with the photovoltaic module;
step 5, designing an electrolytic water system with a hydrogen production function:
and 6, directly coupling the step-down converter in the step 4 with the water electrolysis hydrogen production system, sending a voltage and current signal output by the step-down converter into the water electrolysis system, and finally stably producing hydrogen through the water electrolysis system.
2. The method for controlling the photovoltaic hydrogen production system based on the conductance-increasing method according to claim 1, wherein the method comprises the following steps: in the step 2, analyzing the photovoltaic buck converter comprises: the principle of the photovoltaic buck converter is that when the PWM wave is at a high level, the switching element is turned on to magnetize the energy storage inductor, and the current passing through the inductor is linearly increased to charge the capacitor and provide energy to the load; when the PWM waveform is at low level, the switch element is turned off, the inductor and capacitor elements release energy to maintain the output voltage, and when the circuit works stably, the average value U of the load voltageoIs composed of
Figure FDA0003324294560000011
Wherein, tonFor the on-time of the switching element, toffThe switching-off time of the switching element is T, a switching period is T, alpha is the turn-on duty ratio of the switching period, and E is the direct-current power supply voltage;
the average value U of the voltage output by the converter is derived from equation (1)oMaximum E, however, when the duty cycle α is reduced, UoIt is reduced accordingly, so it is called a buck converter.
3. The method for controlling the photovoltaic hydrogen production system based on the conductance-increasing method according to claim 1, wherein the method comprises the following steps: in step 3, the method for designing conductance increment control with maximum power point tracking function includes:
the instantaneous output power of the photovoltaic cell is expressed as:
P＝VI (2)
where V is the photovoltaic system output voltage and I is the photovoltaic system output current.
Meanwhile, whether the maximum power point is tracked is judged, and if yes, disturbance tracking is stopped; if not, continuing disturbance tracking;
calculating a difference dV between V and V (n-1), calculating a difference dI between I and I (n-1), and calculating dI/dV by adopting an increment electric conduction method; v (n-1) is the output voltage of the photovoltaic cell in the previous control period, I (n-1) is the output current of the photovoltaic cell in the previous control period, and n is the control period;
judging whether dV is 0, if dV is 0, judging whether dI is 0; if not, judging whether the dI/dV is equal to-I/V or not;
if dI is equal to 0, then I (n-1) is equal to I; v (n-1) ═ V; if dI is not equal to 0, judging whether dI is greater than 0, if so, increasing the output voltage of the photovoltaic cell so that I (n-1) is equal to I; v (n-1) ═ V; if not, reducing the output voltage of the photovoltaic cell so that I (n-1) is I; v (n-1) ═ V;
if dI/dV is true, I (n-1) is I; v (n-1) ═ V; if the dI/dV is not established, judging whether the dI/dV is larger than the I/V or not, and if so, increasing the output voltage of the photovoltaic cell so that I (n-1) is I; v (n-1) ═ V; if not, reducing the output voltage of the photovoltaic cell so that I (n-1) is I; v (n-1) ═ V.
4. The method for controlling the photovoltaic hydrogen production system based on the conductance-increasing method according to claim 1, wherein the method comprises the following steps: in step 5, the design of the electrolytic water system with hydrogen production function comprises:
the electrolytic water system mainly comprises two electrodes and a polymer film, wherein hydrogen is generated at a cathode, oxygen is generated at an anode, and the electrode reaction formula is as follows:
anode:
Figure FDA0003324294560000031
cathode:
2H++2e-→H2 (4)
the general reaction formula is as follows:
Figure FDA0003324294560000032
step 5-1, designing an electrolytic water anode system:
the anode of the electrolytic water system loses electrons to generate oxidation reaction, and the molar flow relation of water and oxygen before and after the reaction is as follows:
Figure FDA0003324294560000033
Figure FDA0003324294560000034
in the formula,
Figure FDA0003324294560000035
the molar flow rates of oxygen and water, respectively, into and out of the anode; since there is no oxygen inflow to the system, therefore
Figure FDA0003324294560000036
Is zero.
Figure FDA0003324294560000037
Is the electromigration and diffusion flow rate of water from the anode through the membrane; o is2sThe flow rate of oxygen generated at the anode is expressed as follows:
Figure FDA0003324294560000038
wherein the number of the electrolyzers is m, the current of an electrolysis system is I, the Faraday constant is F, and the efficiency of the electrolysis system is eta;
step 5-2, designing an electrolytic water cathode system:
the cathode of the electrolytic water system obtains electrons to perform reduction reaction, and the molar flow relation of water and hydrogen before and after the reaction is as follows:
Figure FDA0003324294560000039
Figure FDA00033242945600000310
wherein,
Figure FDA0003324294560000041
is the molar flow rate of hydrogen into the cathode,
Figure FDA0003324294560000042
is the molar flow rate of water into the cathode.
Figure FDA0003324294560000043
Figure FDA0003324294560000044
Is the molar flow rate of hydrogen and water out of the cathode.
Figure FDA0003324294560000045
Is the flow rate of hydrogen generated at the cathode, and the expression is as follows:
Figure FDA0003324294560000046
step 5-3, designing an electrolytic water film system model:
membrane systems are important components of water electrolysis systems, and the role of the membrane in the water transport process is very important. Two modes of water transport within the membrane are expressed as:
Figure FDA0003324294560000047
Figure FDA0003324294560000048
wherein,
Figure FDA0003324294560000049
is the electromigration flow rate and,
Figure FDA00033242945600000410
is the rate of the electrical diffusion flow,
Figure FDA00033242945600000411
is the molar mass of water, m is the number of electrolyzers, A is the area of the cell,
Figure FDA00033242945600000412
is the coefficient of water diffusion;
Figure FDA00033242945600000413
is the concentration of cathode water,
Figure FDA00033242945600000414
Is the concentration of the anode water; t is tmThickness of electrolytic system film, ndIs the electric traction coefficient;
step 5-4, designing an electrolyzed water voltage system model:
voltage V of electrolysis systemelPassing NernsThe effect of the equation, the system activation polarization, and the ohmic polarization can be expressed as:
Vel-Vact-Vohm＝En (14)
wherein E isnFor the open circuit voltage of the electrolysis system, the expression is as follows:
Figure FDA00033242945600000415
Vactfor the system to activate the polarization voltage, the expression is as follows:
Figure FDA0003324294560000051
Vohmfor the system ohmic polarization voltage, the expression is as follows:
Vohm＝iRohm (17)
in the formula, E0Standard electromotive force for electrolytic systems, RgasIs the gas universal constant, TelIn order to obtain the temperature of the electrolysis system,
Figure FDA0003324294560000052
is the water activity between the anode and the membrane is 1, alpha is the membrane transfer coefficient, i is the current density of the electrolysis system, i is0Exchange of current density, R, for electrolytic systemsohmIs the membrane resistance of the electrolytic system.
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