Flow battery stack thermal management system and method

Through the liquid flow battery stack thermal management system, the temperature acquisition and control module is used to keep the stack temperature in the appropriate range, solving the problem of side reactions of the liquid flow battery at abnormal temperatures, improving the efficiency and availability of the battery, and reducing costs .

CN119297337APending Publication Date: 2025-01-10BEI JING HONG TONG WEI HE KE JI YOU XIAN GONG SI
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Patent Information

Application Number
CN202411429872.X
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-10-14
Publication Date
2025-01-10

AI Technical Summary

Technical Problem

Flow batteries will experience side reactions at abnormal temperatures, resulting in reduced efficiency and increased cost of the battery system.

Method used

A liquid flow battery stack thermal management system is designed, including ambient temperature acquisition module, stack temperature acquisition module, heating device, heat dissipation device and temperature control module. By collecting temperature data, the heating and heat dissipation device work is controlled to maintain electricity. The stack temperature is within the set threshold range to ensure that the electrolyte reaction is carried out in a high-efficiency and low-side reaction state.

Benefits of technology

Effectively maintain the reaction temperature of the flow battery electrolyte, improve the capacity efficiency and availability of the battery, and reduce the cost of the battery system.

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Abstract

The invention provides a flow battery stack thermal management system and method. The flow battery stack thermal management system comprises an ambient temperature acquisition module for acquiring ambient temperatures T1 and T2 inside and outside a stack container cabin, a stack temperature acquisition module for acquiring a stack temperature T3, a heating device and a heat dissipation device, and a temperature control module. The temperature control module is electrically connected with the environment temperature acquisition module, the multiple electric pile temperature acquisition modules, the heating device and the heat dissipation device, when one of the acquired temperatures T1, T2 and T3 exceeds threshold high limit values Tah, Tbh and Tch, the heat dissipation device is controlled to work until the electric pile temperature is reduced to a threshold interval, and when one of the acquired temperatures T1, T2 and T3 is lower than threshold low limit values Tal, Tbl and Tcl, the heat dissipation device is controlled to work until the electric pile temperature is reduced to a threshold interval. And controlling the heating device to work until the temperature of the galvanic pile rises to the threshold interval. According to the system in the scheme, the electrolyte reaction temperature of the flow battery can be kept, the side reaction condition is reduced, the electrolyte reacts in a high-efficiency and low-side-reaction state all the time, and the capacity efficiency of the battery is improved.
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Description

Technical Field

[0001] The present invention belongs to the technical field of thermal management of liquid flow battery stacks, and in particular relates to a thermal management system and method for a liquid flow battery stack. Background Art

[0002] In the flow battery industry, there are electrolytes with various chemical compositions. Different chemical compositions require different temperatures for redox reactions. Even for the same electrolyte, the reaction rates are different at different temperatures. Some electrolytes even have serious side reactions at inappropriate temperatures. Therefore, temperature management of the battery system is an indispensable part. Summary of the invention

[0003] The main purpose of the present invention is to propose a liquid flow battery stack thermal management system and method, aiming to solve the technical problem that the electrolyte of the liquid flow battery will have side reactions under abnormal temperatures.

[0004] To achieve the above object, the present invention proposes a liquid flow battery stack thermal management system, comprising: Ambient temperature collection module, used to collect the ambient temperatures T1 and T2 inside and outside the stack container cabin; The stack temperature acquisition module is used to collect the stack temperature T3; A heating device, used to heat the battery stack; A heat dissipation device, used to cool the battery stack; and The temperature control module is electrically connected to the ambient temperature acquisition module, the stack temperature acquisition module, the heating device and the heat dissipation device respectively. When one of the acquired temperatures T1, T2 and T3 exceeds the corresponding upper threshold value T ah , T bh , T ch When the temperature control module controls the heat dissipation device to work, the stack temperature is kept within the threshold range. When one of the collected temperatures T1, T2, and T3 is lower than the corresponding threshold lower limit value T al , T bl , T cl When the temperature control module controls the heating device to work, the temperature of the battery stack is kept within the threshold range; Among them, when multiple of the collected temperatures T1, T2, and T3 jump out of the threshold range, the temperature control module controls the operation of the heat dissipation device and the heating device in a manner in which the priorities of T3, T2, and T1 decrease in sequence.

[0005] Optionally, there are a plurality of the battery stacks, and each of the battery stacks has a plurality of electrolytes; Among them, one of the battery stacks is an all-vanadium liquid flow battery, and the operating temperature of its electrolyte is selected to be 33±5°C, that is, Tch 38℃, T cl The ambient temperature is 28℃; the ambient temperature is 25±10℃, that is, T ah , T bh At 35°C, T al , T bl is 15℃.

[0006] Optionally, the heat dissipation device is a liquid heat exchange system, and the transmission fluid thereof is a mixture of water and ethylene glycol in a volume ratio of 1:1.

[0007] Optionally, the liquid heat exchange system includes a plurality of heat conducting plates having microchannels, each of the heat conducting plates is arranged corresponding to each of the fuel cell stacks, and the transmission fluid flows in the microchannels.

[0008] Optionally, the liquid heat exchange system includes a plurality of solenoid valves, each used to control the circulation of the transmission fluid in the heat conducting plate of each of the fuel cell stacks.

[0009] Optionally, the temperature control module and each of the solenoid valves are interlocked and controlled so that when one of the fuel cell stacks needs to dissipate heat, the corresponding solenoid valve is opened.

[0010] Optionally, the liquid heat exchange system further includes a liquid storage tank and a heat exchanger connected to the liquid storage tank, and each of the heat conducting plates is connected to the liquid storage tank to dissipate heat from the circulating transmission fluid.

[0011] The present invention also provides a flow battery stack thermal management method, which comprises the following steps: S10, collecting the ambient temperatures T1 and T2 inside and outside the stack container cabin and the temperature T3 of the stack; S20: One of the collected temperatures T1, T2, T3 exceeds the upper threshold value T ah , T bh , T ch When the temperature of the battery stack drops to the threshold range, the heat dissipation device is controlled to work until the temperature of the battery stack drops to the threshold range. When one of the collected temperatures T1, T2, and T3 is lower than the lower threshold value T al , T bl , T cl When the temperature of the battery stack rises to a threshold value, the heating device is controlled to work; S30. Repeat steps S10 and S20.

[0012] Optionally, in step S10, there are multiple battery stacks in the battery stack container compartment, and there are multiple types of electrolytes in the battery stacks.

[0013] Optionally, in step S20, different threshold intervals are set according to different electrolytes in the battery stack.

[0014] Optionally, in step S20, when multiple of the collected temperatures T1, T2, and T3 jump out of the threshold range, the temperature control module controls the operation of the heat dissipation device and the heating device in a manner in which the priorities of T3, T2, and T1 decrease in sequence.

[0015] In the technical solution of the present invention, by collecting the temperature of the battery stack module and the ambient temperature inside and outside the battery stack container cabin, several temperature data work in coordination, and thresholds are set separately for the battery stack temperature and the temperature inside and outside the cabin, and the three temperatures need to be within the threshold range. This system can maintain the reaction temperature of the flow battery electrolyte, allowing the electrolyte to react at high efficiency and low side reaction state to improve the capacity efficiency of the battery; low side reaction conditions reduce the reduction cost of the battery system; and improve the availability of the battery system in different environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying creative work.

[0017] Figure 1 This is a schematic structural diagram of an embodiment of a thermal management system for a liquid flow battery stack proposed by the present invention.

[0018] Figure 2 for Figure 1 Three-dimensional structural diagram of the middle part structure.

[0019] Figure 3 The figure is a flow chart of an embodiment of the thermal management method for a flow battery stack proposed by the present invention.

[0020] In the figure: 1-liquid flow battery stack, 2-liquid heat exchange system, 21-heat conduction plate, 22-liquid storage tank, 23-heat exchanger, 24-fan.

[0021] The realization of the purpose, functional features and advantages of the present invention will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0022] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0023] In order to better describe and illustrate the embodiments of the present application, reference may be made to one or more drawings, but the additional details or examples used to describe the drawings should not be considered as limiting the scope of the invention of the present application, any of the currently described embodiments or preferred methods.

[0024] In the description of the present invention, it should be noted that the directions or positional relationships indicated by terms such as "length", "width", "up", "down", "front", "back", "left", "right", "top", "bottom", "inside" and "outside" are based on the positional relationships shown in the accompanying drawings and are only for the convenience of describing the present invention. They do not indicate that the device referred to must have a specific direction or operate in a specific direction, and therefore cannot be understood as a limitation on the present invention.

[0025] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art to which this application belongs. The terms used herein in the specification of this application are only for the purpose of describing specific embodiments and are not intended to limit this application.

[0026] In the flow battery industry, there are electrolytes with various chemical compositions. Different chemical compositions require different temperatures for redox reactions. Even for the same electrolyte, the reaction rates are different at different temperatures. Some electrolytes even have serious side reactions at inappropriate temperatures. Therefore, temperature management of the battery system is an indispensable part.

[0027] In view of this, the present invention proposes a liquid flow battery stack thermal management system. Figure 1 and Figure 2 See the schematic diagram of the structure of an embodiment of the proposed thermal management system for a flow battery stack. Figure 1 and Figure 2 The thermal management system of the flow battery stack includes an ambient temperature acquisition module, a stack temperature acquisition module, a heating device, a heat dissipation device and a temperature control module.

[0028] Specifically, the flow battery stack is generally placed in the stack container cabin. The ambient temperature acquisition module can collect the ambient temperatures T1 and T2 inside and outside the stack container cabin. The stack temperature acquisition module is located at the stack and can collect the stack temperature T3. The heating device can heat up the stack and the heat dissipation device can cool down the stack. The temperature control module is electrically connected to the ambient temperature acquisition module, multiple stack temperature acquisition modules, the heating device and the heat dissipation device respectively. When one of the collected temperatures T1, T2 and T3 exceeds the corresponding threshold high limit T ah , T bh , T chWhen the temperature of the battery stack drops to the threshold range, the heat sink is controlled to work until the temperature of the battery stack drops to the threshold range. When one of the collected temperatures T1, T2, and T3 is lower than the corresponding threshold lower limit T al , T bl , T cl When the heating device is controlled to work, the stack temperature is kept within the threshold range. It should be noted that the upper threshold value T ah , T bh , T ch and the lower threshold value T al , T bl , T cl All are interval values. The collected temperatures T1, T2, and T3 use different threshold upper limits T a and the lower threshold value T b By comparison, fine-tuning of the stack temperature can be achieved; in this way, even if the stack temperature T3 is within the threshold range, the temperature inside and outside the cabin can be sensed to coordinate the temperature inside the stack container cabin and the stack temperature, so that the reaction temperature of the flow battery is always in a better state.

[0029] Due to the large temperature difference between the inside and outside of the cabin and the stack, such as when both the inside and outside of the cabin are in a cold environment and the collected temperatures T1 and T2 are lower than the lower threshold value T al , T bl , and the stack temperature is too high and exceeds the upper threshold value T ch Similarly, when the stack temperature T3 is within the threshold range, if the temperature difference between the cabin and the outside is too large, such as the cabin is in a cold environment, the collected temperature T1 is lower than the threshold lower limit T al , and the cabin temperature is too high, the collected temperature T2 is higher than the upper threshold value T bh , the control module gives priority to turning on the heat dissipation device, and does not turn on the heating device. Therefore, when more than one of the collected temperatures T1, T2, and T3 jumps out of the threshold range, the temperature control module controls the operation of the heat dissipation device and the heating device in a descending order of priority of T3, T2, and T1.

[0030] Among them, the ambient temperature acquisition module and the battery stack temperature acquisition module can use temperature sensors, such as infrared sensors and other devices; the heating device can use electric heating to heat up the container cabin and the battery stack; the heat dissipation device can use water cooling or air cooling to cool down the container cabin and the battery stack.

[0031] In the technical solution of the present invention, by collecting the temperature of the battery stack module and the ambient temperature inside and outside the battery stack container cabin, several temperature data work in coordination, and thresholds are set separately for the battery stack temperature and the temperature inside and outside the cabin, and the three temperatures need to be within the threshold range. This system can maintain the reaction temperature of the flow battery electrolyte, allowing the electrolyte to react at high efficiency and low side reaction state to improve the capacity efficiency of the battery; low side reaction conditions reduce the reduction cost of the battery system; and improve the availability of the battery system in different environments.

[0032] Since the liquid flow battery has electrolytes with various chemical compositions, in order to reasonably optimize the liquid flow battery stack, in one embodiment of the present invention, the liquid flow battery stack 1 has multiple small stacks, and each small stack has multiple electrolytes. Therefore, the upper limit value T of each small stack is ch and the lower threshold value T cl Not the same either.

[0033] As a preferred embodiment, the small battery stack is an all-vanadium liquid flow battery, and the electrolyte is vanadium ions of different valence states. At present, the operating temperature range of the all-vanadium liquid flow battery at the international advanced level is 5~45℃, and it needs to be adjusted if it is too high or too low. In this embodiment, the operating temperature of the vanadium electrolyte is selected at 33±5℃, that is, T ch 38℃, T cl The ambient temperature is 28℃; the ambient temperature is 25±10℃, that is, T ah , T bh At 35°C, T al , T bl The working temperature of the vanadium electrolyte is reduced to a smaller range by coordinating several temperature data. The electrolyte has high reactivity at the positive and negative electrodes, and the charging and discharging performance is faster, which better improves the energy efficiency of the battery stack.

[0034] In addition, the active substances of all-vanadium batteries exist in liquids, and the electrolyte ions are only vanadium ions. Therefore, there are no phase changes common in other batteries during charging and discharging, and the battery has a long service life. The vanadium battery has a large degree of freedom in site selection, and the system can be operated in a fully automatic closed manner. The energy efficiency is high, reaching 75%~80%, and the cost performance is very high.

[0035] To better regulate the temperature of the flow battery stack 1, please refer to Figure 2 In one embodiment of the present invention, both the heating device and the heat dissipation device use a liquid heat exchange system 2, and the liquid heat exchange system 2 heats or dissipates heat to an object by circulating a transmission fluid (i.e., a cooling medium). The transmission fluid is a mixture of water and ethylene glycol in a volume ratio of 1:1. Of course, a more efficient heat transfer medium can also be used, but for a large battery stack 1, a mixture of water and ethylene glycol has better stability and lower cost.

[0036] For further information, see Figure 2 In one embodiment of the present invention, the liquid heat exchange system 2 includes a plurality of heat conducting plates 21 with microchannels, the microchannels in each heat conducting plate 21 are interconnected, and each heat conducting plate 21 is arranged corresponding to each small battery stack. In this embodiment, the all-vanadium battery can be operated in a fully automatic closed manner, and the heat conducting plate 21 can be used to completely wrap the small battery stack. Among them, each small battery stack includes a plurality of liquid flow batteries connected in series, and the heat conducting plate 21 is in contact with the surface of the liquid flow battery. When the transmission fluid flows in the microchannels in the heat conducting plate 21, it can take away the heat generated in the liquid flow battery or transfer heat to the liquid flow battery.

[0037] It should be understood that due to the high threshold value T used by each small stack ch and the lower threshold value T cl Therefore, in one embodiment of the present invention, the liquid heat exchange system 2 includes a plurality of solenoid valves, which are respectively used to control the circulation of the transmission fluid in the heat conduction plates 21 of each small stack.

[0038] In order to achieve a rapid response of the solenoid valve, in one embodiment of the present invention, the temperature control module and each solenoid valve are interlocked and controlled. When the temperature of one of the small stacks exceeds the upper threshold value T ch Or below the lower threshold value T cl The temperature control module determines that the small battery stack needs to be cooled or heated, and at the same time opens the solenoid valve corresponding to the small battery stack, so that the transmission fluid circulates in the microchannel of the heat conducting plate 21.

[0039] To achieve circulating heat dissipation, in one embodiment of the present invention, the liquid heat exchange system 2 also includes a pump, a liquid storage tank 22, a heat exchanger 23 connected to the liquid storage tank 22, and a fan II 24. Among them, the heat conducting plates 21 of each small battery stack are connected in parallel with the liquid storage tank 22, respectively. When the pump draws the transmission fluid of the heat conducting plate 21 into the liquid storage tank 22, it is sent to the heat exchanger 23 for circulation, and the transmission fluid in the liquid storage tank 22 is dissipated by the fan II 24, or the transmission fluid in the liquid storage tank 22 is heated by the heater. It should be noted that in order to facilitate the transfer of heat, the battery stack container is provided with a plurality of vents, and the fans I and II 24 are both arranged at the vents to discharge the heat in the cabin or the heat of the heat exchanger 23 to the outside.

[0040] It should be understood that, in order to facilitate auxiliary heat dissipation and heating, the heat dissipation device also includes a fan I arranged in the container cabin. When one of the collected temperatures T1 and T2 exceeds the upper threshold value T ah , T bh The heating device also includes an electric auxiliary heater. When one of the collected temperatures T1 and T2 is lower than the lower threshold value T al , Tbl When the temperature is high, the hot air generated by the electric auxiliary heater can be blown into the container cabin by the fan I to increase the temperature. This is to cooperate with the liquid heat exchange system 2 to keep the electrolyte reaction temperature of the flow battery at the optimal state.

[0041] The present invention also proposes a liquid flow battery stack thermal management method, combining Figure 3 A schematic flow chart of an embodiment of a proposed method for thermal management of a flow battery stack, the method for thermal management of a flow battery stack comprising the following steps: Step S10, collecting the ambient temperatures T1 and T2 inside and outside the stack container cabin and the temperature T3 of the stack.

[0042] During specific implementation, in step S10, there are multiple battery stacks in the battery stack container compartment, and there are multiple types of electrolytes in the battery stacks.

[0043] Step S20: One of the collected temperatures T1, T2, T3 exceeds the upper threshold value T ah , T bh , T ch When the temperature of the battery stack drops to the threshold range, the heat dissipation device is controlled to work until the temperature of the battery stack drops to the threshold range. When one of the collected temperatures T1, T2, and T3 is lower than the lower threshold value T al , T bl , T cl When the heating device is controlled to work, the temperature of the battery stack rises to the threshold range.

[0044] In specific implementation, in step S20, different threshold intervals are set according to different electrolytes in the battery stack. When multiple of the collected temperatures T1, T2, and T3 jump out of the threshold interval, the temperature control module controls the operation of the heat dissipation device and the heating device in a manner of decreasing priority of T3, T2, and T1.

[0045] Due to the large temperature difference between the inside and outside of the cabin and the stack, such as when both the inside and outside of the cabin are in a cold environment and the collected temperatures T1 and T2 are lower than the lower threshold value T al , T bl , and the stack temperature is too high and exceeds the upper threshold value T ch Similarly, when the stack temperature T3 is within the threshold range, if the temperature difference between the cabin and the outside is too large, such as the cabin is in a cold environment, the collected temperature T1 is lower than the threshold lower limit T al , and the cabin temperature is too high, the collected temperature T2 is higher than the upper threshold value T bh, the control module gives priority to turning on the heat dissipation device, and does not turn on the heating device. Therefore, when more than one of the collected temperatures T1, T2, and T3 jumps out of the threshold range, the temperature control module controls the operation of the heat dissipation device and the heating device in a descending order of priority of T3, T2, and T1.

[0046] Step S30: repeat step S10 and step S20.

[0047] In specific implementation, the reaction temperature of the flow battery is kept at an optimal state at all times by continuously collecting the temperature inside and outside the battery stack and the cabin.

[0048] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0049] The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.

Claims

1. A liquid flow battery stack thermal management system, characterized in that: include: Ambient temperature collection module, used to collect the ambient temperatures T1 and T2 inside and outside the stack container cabin; The stack temperature acquisition module is used to collect the stack temperature T3; A heating device, used to heat the battery stack; A heat dissipation device, used to cool the battery stack; and The temperature control module is electrically connected to the ambient temperature acquisition module, the stack temperature acquisition module, the heating device and the heat dissipation device respectively. When one of the acquired temperatures T1, T2 and T3 exceeds the corresponding upper threshold value T ah , T bh , T ch When the temperature control module controls the heat dissipation device to work, the stack temperature is kept within the threshold range. When one of the collected temperatures T1, T2, and T3 is lower than the corresponding threshold lower limit value T al , T bl , T cl When the temperature control module controls the heating device to work, the temperature of the battery stack is kept within the threshold range; Among them, when multiple of the collected temperatures T1, T2, and T3 jump out of the threshold range, the temperature control module controls the operation of the heat dissipation device and the heating device in a manner in which the priorities of T3, T2, and T1 decrease in sequence.

2. The liquid flow battery stack thermal management system according to claim 1, characterized in that: There are a plurality of battery stacks, and each of the battery stacks has a plurality of electrolytes; Among them, one of the battery stacks is an all-vanadium liquid flow battery, and the operating temperature of its electrolyte is selected to be 33±5°C, that is, T ch 38℃, T cl The ambient temperature is 28℃; the ambient temperature is 25±10℃, that is, T ah 、T bh At 35°C, T al 、T bl is 15℃.

3. The liquid flow battery stack thermal management system according to claim 2, characterized in that: The heat dissipation device is a liquid heat exchange system, and its transmission fluid is a mixture of water and ethylene glycol in a volume ratio of 1:

1.

4. The liquid flow battery stack thermal management system according to claim 3, characterized in that: The liquid heat exchange system includes a plurality of heat conducting plates with microchannels, each of the heat conducting plates is arranged corresponding to each of the battery stacks, and the transmission fluid flows in the microchannels.

5. The liquid flow battery stack thermal management system according to claim 4, characterized in that: The liquid heat exchange system includes a plurality of solenoid valves, which are respectively used to control the circulation of the transmission fluid in the heat conduction plates of each of the fuel cell stacks.

6. The liquid flow battery stack thermal management system according to claim 5, characterized in that: The temperature control module and each of the solenoid valves are interlocked and controlled so that when one of the fuel cells needs to dissipate heat, the corresponding solenoid valve is opened.

7. The liquid flow battery stack thermal management system according to claim 5, characterized in that: The liquid heat exchange system further includes a liquid storage tank and a heat exchanger connected to the liquid storage tank. Each of the heat conducting plates is connected to the liquid storage tank to circulate and dissipate heat for the transmission fluid.

8. A method for thermal management of a flow battery stack, characterized in that: The following steps are involved: S10, collecting the ambient temperatures T1 and T2 inside and outside the stack container cabin and the temperature T3 of the stack; S20: One of the collected temperatures T1, T2, T3 exceeds the upper threshold value T ah 、T bh 、T ch When the temperature of the battery stack drops to the threshold range, the heat dissipation device is controlled to work until the temperature of the battery stack drops to the threshold range. When one of the collected temperatures T1, T2, and T3 is lower than the lower threshold value T al 、T bl 、T cl When the temperature of the battery stack rises to a threshold value, the heating device is controlled to work; S30. Repeat steps S10 and S20.

9. The method for thermal management of a flow battery stack according to claim 8, characterized in that: In the step S20, there are multiple battery stacks in the battery stack container compartment, and there are multiple electrolytes in the battery stacks. Different threshold ranges are set according to different electrolytes in the battery stacks.

10. The method for thermal management of a flow battery stack according to claim 8, characterized in that: In the step S20, when more than one of the collected temperatures T1, T2, and T3 jumps out of the threshold range, the operation of the heat dissipation device and the heating device is controlled in a manner in which the priorities of T3, T2, and T1 decrease in sequence.

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