CN118645651B - Hydrogen supply system based on concentration battery and control method thereof - Google Patents
Hydrogen supply system based on concentration battery and control method thereof Download PDFInfo
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- CN118645651B CN118645651B CN202411119618.XA CN202411119618A CN118645651B CN 118645651 B CN118645651 B CN 118645651B CN 202411119618 A CN202411119618 A CN 202411119618A CN 118645651 B CN118645651 B CN 118645651B
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- 239000001257 hydrogen Substances 0.000 title claims abstract description 112
- 229910052739 hydrogen Inorganic materials 0.000 title claims abstract description 112
- UFHFLCQGNIYNRP-UHFFFAOYSA-N Hydrogen Chemical compound [H][H] UFHFLCQGNIYNRP-UHFFFAOYSA-N 0.000 title claims abstract description 105
- 238000000034 method Methods 0.000 title claims abstract description 16
- 239000012528 membrane Substances 0.000 claims description 19
- 238000012544 monitoring process Methods 0.000 claims description 17
- 239000003054 catalyst Substances 0.000 claims description 16
- 150000002431 hydrogen Chemical class 0.000 claims description 9
- 239000007809 chemical reaction catalyst Substances 0.000 claims description 8
- 238000007254 oxidation reaction Methods 0.000 claims description 6
- 238000004364 calculation method Methods 0.000 claims description 4
- 239000012530 fluid Substances 0.000 claims description 3
- UQSQSQZYBQSBJZ-UHFFFAOYSA-N fluorosulfonic acid Chemical compound OS(F)(=O)=O UQSQSQZYBQSBJZ-UHFFFAOYSA-N 0.000 claims description 3
- 230000000087 stabilizing effect Effects 0.000 claims description 2
- 239000000446 fuel Substances 0.000 abstract description 9
- 239000000126 substance Substances 0.000 abstract description 7
- 230000010354 integration Effects 0.000 abstract description 4
- 238000005381 potential energy Methods 0.000 abstract description 3
- 230000001276 controlling effect Effects 0.000 description 8
- BASFCYQUMIYNBI-UHFFFAOYSA-N platinum Chemical group [Pt] BASFCYQUMIYNBI-UHFFFAOYSA-N 0.000 description 8
- 230000000694 effects Effects 0.000 description 5
- 238000010586 diagram Methods 0.000 description 4
- 229910052697 platinum Inorganic materials 0.000 description 4
- KJTLSVCANCCWHF-UHFFFAOYSA-N Ruthenium Chemical compound [Ru] KJTLSVCANCCWHF-UHFFFAOYSA-N 0.000 description 2
- 239000008151 electrolyte solution Substances 0.000 description 2
- 238000005516 engineering process Methods 0.000 description 2
- GPRLSGONYQIRFK-UHFFFAOYSA-N hydron Chemical compound [H+] GPRLSGONYQIRFK-UHFFFAOYSA-N 0.000 description 2
- 230000003647 oxidation Effects 0.000 description 2
- 238000001556 precipitation Methods 0.000 description 2
- 229910052707 ruthenium Inorganic materials 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 238000003411 electrode reaction Methods 0.000 description 1
- 239000003792 electrolyte Substances 0.000 description 1
- 239000007789 gas Substances 0.000 description 1
- 239000007788 liquid Substances 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000006479 redox reaction Methods 0.000 description 1
- 230000001105 regulatory effect Effects 0.000 description 1
Classifications
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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
- H01M8/04082—Arrangements for control of reactant parameters, e.g. pressure or concentration
- H01M8/04201—Reactant storage and supply, e.g. means for feeding, pipes
-
- 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
- H01M8/04082—Arrangements for control of reactant parameters, e.g. pressure or concentration
- H01M8/04089—Arrangements for control of reactant parameters, e.g. pressure or concentration of gaseous reactants
-
- 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
- H01M8/04746—Pressure; Flow
- H01M8/04753—Pressure; Flow of fuel cell reactants
-
- 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
- H01M8/04895—Current
- H01M8/0491—Current of fuel cell stacks
-
- 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
-
- 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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- Engineering & Computer Science (AREA)
- Life Sciences & Earth Sciences (AREA)
- General Chemical & Material Sciences (AREA)
- Electrochemistry (AREA)
- Chemical Kinetics & Catalysis (AREA)
- Chemical & Material Sciences (AREA)
- Sustainable Energy (AREA)
- Sustainable Development (AREA)
- Manufacturing & Machinery (AREA)
- Computing Systems (AREA)
- Theoretical Computer Science (AREA)
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- Medical Informatics (AREA)
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- Automation & Control Theory (AREA)
- Artificial Intelligence (AREA)
- Fuel Cell (AREA)
Abstract
The application discloses a hydrogen supply system based on a concentration battery and a control method thereof, belonging to the field of fuel cells, wherein the system comprises the concentration battery and a current-voltage control module, and the output current of the concentration battery is controlled by the current-voltage control module by utilizing the chemical potential energy of high-pressure hydrogen of the concentration battery so as to realize the accurate regulation of the hydrogen flow. The application solves the technical problems of complex mechanical structure and high integration difficulty of the traditional functional system.
Description
Technical Field
The application relates to a hydrogen supply system and a control method thereof, belonging to the field of fuel cells.
Background
The fuel cell is a device for directly converting chemical energy into electric energy, and generates electric power through oxidation-reduction reaction, and has the technical characteristics of high energy conversion efficiency, low noise, zero emission and the like, and is regarded as one of important development directions of clean energy technologies in the future.
The hydrogen supply system of the fuel cell system is an important component of the overall fuel cell power system and is responsible for supplying hydrogen gas at an appropriate pressure, flow rate, temperature and humidity to the fuel cell. In view of the operating characteristics of the fuel cell, the hydrogen supply system needs to precisely control the pressure and flow rate of hydrogen gas to meet the requirements of the fuel cell under different load conditions. Meanwhile, the hydrogen supply system is generally required to be highly integrated, and the total volume of the fuel cell system is reduced to meet the application of the hydrogen supply system in narrow spaces such as vehicles.
The hydrogen supply system based on the high-pressure hydrogen storage tank has the problem of complex structure. Therefore, the prior art is mainly directed to the integration problem of the hydrogen supply system, for example, CN216389454U provides a high-integration hydrogen supply system based on a multi-stage pressure reducing valve, and CN103180645B provides a valve body structure with pressure regulation and flow control. However, the traditional mechanical valve body generally has the problems of single function, high integration difficulty and the like.
Disclosure of Invention
According to one aspect of the application, a hydrogen supply system based on a concentration battery is provided, the system eliminates a traditional complex mechanical valve body, reduces the difficulty of system integration, fully utilizes the chemical potential energy of high-pressure hydrogen, and realizes the accurate regulation of hydrogen supply.
The concentration cell-based hydrogen supply system comprises:
The concentration battery is formed by stacking one or more single cells, wherein the anode of the concentration battery is connected with a high-pressure hydrogen storage container, and a hydrogen stop valve is arranged between the anode and the high-pressure hydrogen storage container;
and the current-voltage control module is used for controlling the output current of the concentration battery so as to accurately control the hydrogen flow.
Optionally, the single cell is formed by stacking two polar plates and a membrane electrode, and the membrane electrode is positioned between the two polar plates.
Optionally, the membrane electrode mainly comprises a cathode electrode, a proton exchange membrane and an anode electrode stack.
Optionally, the catalyst of the cathode electrode is a hydrogen precipitation reaction catalyst, the proton exchange membrane is a perfluorosulfonic acid membrane, and the catalyst of the anode electrode is a hydrogen oxidation reaction catalyst.
Preferably, the hydrogen evolution reaction catalyst is a platinum-based catalyst or a ruthenium-based catalyst.
Preferably, the hydrogen oxidation catalyst is a platinum-based catalyst. The catalyst provided by the application is the most efficient catalyst type for hydrogen precipitation and hydrogen oxidation reaction, and has high commercialization degree.
Optionally, a first-stage pressure reducing valve and a safety valve are arranged at the outlet of the high-pressure hydrogen storage container, so that the pressure of the high-pressure hydrogen storage container is reduced, and the fluid pressure is regulated and stabilized when the pressure of the high-pressure hydrogen storage container is far higher than the bearable pressure of the concentration battery.
Optionally, the current-voltage control module comprises:
the monitoring submodule is used for monitoring actual voltage data V of the concentration battery;
the calculation sub-module is used for obtaining the set voltage minimum threshold V L of the concentration battery and the hydrogen flow Q required by the hydrogen supply system, calculating the current I 0 of the concentration battery corresponding to the Q, and taking the current I 0 as the set current value of the concentration battery;
The current adjusting sub-module is used for controlling the actual output current I of the concentration battery to reach I 0 so that the system is in steady-state operation;
If I > I 0, readjusting the actual output current of the concentration cell;
If I < I 0, judging whether the actual voltage data V is greater than or equal to the voltage minimum threshold V L, if so, re-monitoring and adjusting the actual output current I of the concentration battery, otherwise, continuously applying a positive voltage V 1 to the anode of the concentration battery, improving the hydrogen output flow of the cathode of the concentration battery until the monitored actual voltage data of the concentration battery reaches V L or above, and re-monitoring and adjusting the actual output current I of the concentration battery.
Optionally, the output current of the concentration battery is also used for feeding back to the system battery module for other power consumption components.
Optionally, the pressure range of the high-pressure hydrogen storage container is 1-75 MPa.
Preferably, the pressure of the high-pressure hydrogen storage container or the outlet pressure of the primary pressure reducing valve ranges from 1 to 35 MPa, and the opening pressure of the safety valve ranges from 35 to 40 MPa.
According to still another aspect of the present application, there is provided a control method of a hydrogen supply system based on the concentration cell described above, the method comprising the steps of:
Opening a hydrogen stop valve;
Setting a voltage minimum threshold V L of the concentration battery and a hydrogen flow Q required by a hydrogen supply system;
Calculating the current I 0 of the concentration battery corresponding to the hydrogen flow Q required by the hydrogen supply system;
Starting a current-voltage control module, and setting a current value as I 0;
The current-voltage control module automatically adjusts the actual output current I of the concentration battery to the set current value I 0 of the concentration battery, and the output current of the current-voltage control module charges the system battery module.
Optionally, the method further comprises the steps of:
real-time monitoring actual voltage data V of the concentration battery during system operation;
When the actual voltage monitoring data V of the concentration battery cannot reach the voltage minimum threshold V L of the concentration battery, the control current-voltage control module applies a positive voltage V 1 to the anode of the concentration battery until the actual output current I of the concentration battery is a set current value I 0.
The hydrogen supply system based on the concentration battery and the control method thereof provided by the application have the beneficial effects that the system discards the traditional complex mechanical valve body, fully utilizes the chemical potential energy of high-pressure hydrogen, and realizes the accurate regulation of hydrogen supply by controlling the output current of the concentration battery.
Drawings
FIG. 1 is a schematic diagram of a concentration cell according to the present application;
FIG. 2 is a schematic diagram of a concentration cell-based hydrogen supply system according to the present application;
Fig. 3 is a logic diagram of a control method of a concentration cell-based hydrogen supply system according to an embodiment of the present application.
Detailed Description
The present application is described in detail below with reference to examples, but the present application is not limited to these examples.
The application provides a hydrogen supply system based on a concentration battery, which comprises the concentration battery 201.
The concentration cell is a device for generating potential difference by utilizing the concentration difference of substances, and at a certain temperature, the electromotive force of the single-liquid concentration cell is irrelevant to the activity of electrolyte and the standard electrode potential and is only relevant to the activity of two electrode substances. For pure hydrogen concentration cells, the hydrogen activity can be converted to hydrogen pressure for calculation.
A schematic diagram of the concentration cell is shown in fig. 1, which shows the equilibrium electrode potential difference expression of the hydrogen concentration cell based on the nernst equation, as shown in the following formula:
Wherein, Is the cathode and anode of the hydrogen concentration battery extremely balancing the potential difference of the electrodes; is a gas constant; Is Faraday constant; is the electrode reaction temperature; hydrogen pressure for anode (high pressure); is the cathodic (low pressure) hydrogen pressure; Hydrogen ion activity for the anode (high pressure) electrolyte solution; hydrogen ion activity for the cathodic (low pressure) electrolyte solution.
By utilizing the chemical potential difference of high-pressure hydrogen and low-pressure hydrogen, a concentration difference voltage is formed at the two ends of the cathode and anode of the concentration battery 201, and then the accurate control of the hydrogen flow is realized by controlling the output current of the concentration battery 201.
As shown in fig. 2, the concentration cell 201 is composed of one or more single cells stacked, an anode of the concentration cell is connected with a high-pressure hydrogen source 101, a hydrogen stop valve 102 is arranged between the anode and the high-pressure hydrogen source, and a cathode of the concentration cell is connected with a low-pressure hydrogen pipeline 303.
In one embodiment, concentration cell 201 employs a 6-cell concentration cell stack.
The hydrogen supply system further comprises a current-voltage control module for controlling the output current of the concentration cell 201, thereby precisely controlling the flow of hydrogen.
In one embodiment, the single cell is formed by stacking two electrode plates and a membrane electrode, wherein the membrane electrode is positioned between the two electrode plates.
In one embodiment, the membrane electrode consists essentially of a cathode electrode, a proton exchange membrane, and an anode electrode stack.
In one embodiment, the catalyst of the cathode electrode is a hydrogen evolution reaction catalyst, the proton exchange membrane is a perfluorosulfonic acid membrane, and the anode catalyst is a hydrogen oxidation reaction catalyst.
In one embodiment, the hydrogen evolution reaction catalyst is a platinum-based catalyst or a ruthenium-based catalyst.
In one embodiment, the hydrogen oxidation catalyst is a platinum-based catalyst.
The outlet of the high-pressure hydrogen source 101 is provided with a first-stage pressure reducing valve and a safety valve 301 for reducing pressure, adjusting and stabilizing fluid pressure when the pressure of the high-pressure hydrogen source 101 is far higher than the bearable pressure of the concentration cell 201.
In one embodiment, a current-voltage control module includes:
A monitoring sub-module for monitoring the actual voltage data V 0 of the concentration battery 201;
The calculation sub-module is used for obtaining the set lowest voltage threshold V L of the concentration battery 201 and the hydrogen flow Q required by the hydrogen supply system, calculating the current I 0 of the concentration battery 201 corresponding to the Q, and taking the current I 0 as the set current value of the concentration battery 201;
The current adjustment sub-module is used for controlling the actual output current I of the concentration battery 201 to reach I 0 so that the system is in steady-state operation;
If I > I 0, readjusting the actual output current of concentration cell 201;
If I < I 0, judging whether the actual voltage data V is greater than or equal to the voltage minimum threshold V L, if so, re-monitoring and adjusting the actual output current I of the concentration battery 201, otherwise, continuously applying a positive voltage V 1 to the anode of the concentration battery 201 to improve the hydrogen output flow of the cathode of the concentration battery 201 until the monitored actual voltage data of the concentration battery reaches V L or above, and re-monitoring and adjusting the actual output current I of the concentration battery.
In one embodiment, the output current of the concentration battery 201 is also used for feeding back to the system battery module for other power components.
In one embodiment, the pressure of the high-pressure hydrogen source 101 ranges from 1 to 75 MPa.
In one embodiment, the pressure of the high-pressure hydrogen source 101 or the outlet pressure of the primary pressure reducing valve ranges from 1 to 35 MPa, and the opening pressure of the safety valve ranges from 35 to 40 MPa.
Both 35MPa and 75MPa are standard pressures of current commercial hydrogen tanks, and from the practical standpoint, the hydrogen supply system should meet the pressure range of the commercial hydrogen tanks, where 35MPa is the upper limit of use (in terms of current technology) of the proton exchange membrane of the concentration cell selected, and when hydrogen tanks exceeding 35MPa are used, safety concerns are considered to increase the pressure relief valve and the safety valve to avoid over-pressure rupture of the concentration cell and damage to the backend system stack.
As a preferred embodiment, the high pressure hydrogen source 101 has a pressure of 35 MPa.
As a preferred embodiment, the opening pressure of the relief valve 301 is 40MPa.
The application also provides a control method of the hydrogen supply system based on the concentration battery, the flow of which is shown in figure 3, and the method comprises the following steps:
s1, opening a hydrogen stop valve 102;
S2, setting a voltage minimum threshold V L of the concentration battery 201 and a hydrogen flow Q required by a hydrogen supply system;
s3, calculating the current I 0 of the concentration battery corresponding to the hydrogen flow Q required by the hydrogen supply system;
S4, starting a current-voltage control module 202, and setting a current value as I 0;
S5, the current-voltage control module 202 automatically adjusts the actual output current I of the concentration battery to the set current value I 0 of the concentration battery, and the output current of the current-voltage control module 202 charges the system battery module 203.
In one embodiment, the method further comprises the steps of:
s6, real-time monitoring actual voltage data V of the concentration battery 201 during system operation;
And S7, when the actual voltage data V of the concentration battery 201 cannot reach the voltage minimum threshold V L of the concentration battery 201, controlling the current-voltage control module to apply a positive voltage V 1 to the anode of the concentration battery 201 until the actual output current I of the concentration battery is the set current value I 0.
While the application has been described in terms of preferred embodiments, it will be understood by those skilled in the art that various changes and modifications can be made without departing from the scope of the application, and it is intended that the application is not limited to the specific embodiments disclosed.
Claims (9)
1. A concentration cell-based hydrogen supply system, the system comprising:
The concentration battery is formed by stacking one or more single cells, wherein the anode of the concentration battery is connected with a high-pressure hydrogen storage container, and a hydrogen stop valve is arranged between the anode and the high-pressure hydrogen storage container;
the current-voltage control module is used for controlling the output current of the concentration battery so as to accurately control the hydrogen flow;
The current-voltage control module includes:
the monitoring submodule is used for monitoring actual voltage data V of the concentration battery;
the calculation sub-module is used for obtaining the set voltage minimum threshold V L of the concentration battery and the hydrogen flow Q required by the hydrogen supply system, calculating the current I 0 of the concentration battery corresponding to the Q, and taking the current I 0 as the set current value of the concentration battery;
The current adjusting sub-module is used for controlling the actual output current I of the concentration battery to reach I 0 so that the system is in steady-state operation;
If I > I 0, readjusting the actual output current of the concentration cell;
If I < I 0, judging whether the actual voltage data V is greater than or equal to the voltage minimum threshold V L, if so, re-monitoring and adjusting the actual output current I of the concentration battery, otherwise, continuously applying a positive voltage V 1 to the anode of the concentration battery, improving the hydrogen output flow of the cathode of the concentration battery until the monitored actual voltage data of the concentration battery reaches V L or above, and re-monitoring and adjusting the actual output current I of the concentration battery.
2. The concentration cell-based hydrogen supply system of claim 1 wherein said single cell is formed by stacking two plates with a membrane electrode, said membrane electrode being located between the two plates.
3. The concentration cell-based hydrogen supply system of claim 2, wherein the membrane electrode comprises a stacked cathode electrode, a proton exchange membrane, and an anode electrode, wherein the catalyst of the cathode electrode is a hydrogen evolution reaction catalyst, the proton exchange membrane is a perfluorosulfonic acid membrane, and the catalyst of the anode electrode is a hydrogen oxidation reaction catalyst.
4. The concentration cell-based hydrogen supply system according to claim 1, wherein a primary pressure reducing valve and a safety valve are provided at the outlet of the high-pressure hydrogen storage container for reducing pressure, adjusting and stabilizing fluid pressure when the pressure of the high-pressure hydrogen storage container is far higher than the bearable pressure of the concentration cell.
5. The concentration cell-based hydrogen supply system of claim 1 wherein the output current of the concentration cell is also used to feed back to the system battery module for use by other electrical components.
6. The concentration cell-based hydrogen supply system of claim 1 wherein the high pressure hydrogen storage vessel has a pressure in the range of 1 to 75 MPa.
7. The concentration cell-based hydrogen supply system according to claim 4, wherein the pressure of the high-pressure hydrogen storage container or the outlet pressure of the primary pressure reducing valve ranges from 1 to 35 MPa, and the opening pressure of the safety valve ranges from 35 to 40 MPa.
8. A control method based on the concentration cell-based hydrogen supply system according to any one of claims 1 to 7, characterized in that the method comprises the steps of:
Opening a hydrogen stop valve;
Setting a voltage minimum threshold V L of the concentration battery and a hydrogen flow Q required by a hydrogen supply system;
Calculating the current I 0 of the concentration battery corresponding to the hydrogen flow Q required by the hydrogen supply system;
Starting a current-voltage control module, and setting a current value as I 0;
The current-voltage control module automatically adjusts the actual output current I of the concentration battery to the set current value I 0 of the concentration battery, and the output current of the current-voltage control module charges the system battery module.
9. The control method according to claim 8, characterized in that the method further comprises the steps of:
real-time monitoring actual voltage data V of the concentration battery during system operation;
When the actual voltage monitoring data V of the concentration battery cannot reach the voltage minimum threshold V L of the concentration battery, the control current-voltage control module applies a positive voltage V 1 to the anode of the concentration battery until the actual output current I of the concentration battery is a set current value I 0.
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