CN116125286A - Open-circuit voltage calculation method of all-vanadium redox flow battery - Google Patents

Open-circuit voltage calculation method of all-vanadium redox flow battery Download PDF

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CN116125286A
CN116125286A CN202310027647.2A CN202310027647A CN116125286A CN 116125286 A CN116125286 A CN 116125286A CN 202310027647 A CN202310027647 A CN 202310027647A CN 116125286 A CN116125286 A CN 116125286A
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吴若冰
胡宇
田地
屈治国
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Abstract

The method comprises the steps of establishing a relation between open-circuit voltage and state of charge of the all-vanadium redox flow battery based on a Nernst equation, and adding a correction coefficient related to electrolyte flow; fixing the flow of electrolyte, charging and discharging the battery, and obtaining a relation curve of open-circuit voltage and state of charge under the flow through experiments; identifying each correction coefficient by utilizing a genetic algorithm according to the experimental result; and changing the flow rate of the electrolyte for a plurality of times, and fitting the relation between each correction coefficient and the flow rate of the electrolyte by using a polynomial. And (3) sequentially completing the steps aiming at a specific flow battery to obtain a complete open-circuit voltage calculation method. The correction coefficient of the open-circuit voltage calculation method of the all-vanadium redox flow battery is related to electrolyte flow, meanwhile, the influence of the hydrogen ion concentration which is difficult to calculate accurately is taken into consideration, the calculation accuracy is considered in the approach to the electrochemical reaction fact, and the method has important basic significance for modeling of the all-vanadium redox flow battery.

Description

Open-circuit voltage calculation method of all-vanadium redox flow battery
Technical Field
The invention belongs to the technical field of modeling of all-vanadium redox flow batteries, and particularly relates to a method for calculating open-circuit voltage of an all-vanadium redox flow battery.
Background
Among currently developed energy storage systems, flow batteries are favored because of their outstanding advantages of high efficiency, modularity, good stability, long life, and environmental friendliness. Meanwhile, the energy storage system of the flow battery has large scale and relates to a multi-physical field coupling process such as heat-flow-electricity and the like. Researchers build a variety of equivalent models with different tools for all-vanadium redox flow battery stacks. The open-circuit voltage of the all-vanadium redox flow battery is taken as a very important parameter, and plays a vital role in improving the accuracy and the calculation efficiency of the equivalent model. However, in experiments, the open circuit voltage is often difficult to measure, and has a very complex relationship with the independent variables such as the stack structure, temperature, flow, ion concentration, state of charge, and the like. The equation describing the equilibrium voltage in electrochemistry is the Nernst equation. Thus, some researchers typically use a modified Nernst equation for estimation. The conventional modified nernst equation estimation method ignores the effect of the hydrogen ion concentration on the open circuit voltage, and simultaneously replaces the ion concentration in the monomer with the ion concentration in the storage tank. However, the hydrogen ion concentration has an effect on the open circuit voltage, and the ion concentration in the reservoir is also different from the ion concentration in the cell, the magnitude of this difference being related to the flow rate for a particular cell. Therefore, the accuracy of the conventional modified Nernst equation estimation method is not high. Another part of researchers only consider the influence of the state of charge on the open-circuit voltage, the state of charge is fitted to an independent variable by using experimental data, the open-circuit voltage is a polynomial of a dependent variable, and the precision of the method is naturally increased along with the increase of the number of independent variables, but the method has two natural defects: firstly, only the influence of the charge state of the battery is considered, and the influence of other physical quantities such as temperature, flow and the like on the open-circuit voltage is not considered; and secondly, fitting is carried out only by using a mathematical method, so that the physical meaning of open-circuit voltage is separated.
In summary, the invention provides an open-circuit voltage calculation method of an all-vanadium redox flow battery considering the influence of the concentration of hydrogen ions and the flow of electrolyte, starting from a Nernst equation considering the nature of the physical phenomenon of the open-circuit voltage.
The above information disclosed in the background section is only for enhancement of understanding of the background of the invention and therefore may contain information that does not form the prior art that is already known to a person of ordinary skill in the art.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a method for calculating the open-circuit voltage of an all-vanadium redox flow battery, which considers the influence of the concentration of hydrogen ions and the flow of electrolyte, considers the influence of the concentration of hydrogen ions on the open-circuit voltage which is difficult to calculate, and simultaneously corrects the difference of the concentration of ions in a storage tank and a monomer by adding a correction coefficient related to the flow into a standard Nernst equation. In addition, the relation between the correction coefficient and the electrolyte flow is fitted, and the open-circuit voltage is calculated more accurately according to different working states. Aiming at a certain all-vanadium redox flow battery, the invention can establish an accurate and efficient open-circuit voltage calculation method conforming to the essence of a physical process, and has important basic significance for the establishment of a subsequent model and the development of calculation.
The invention aims to realize the following technical scheme, and the open-circuit voltage calculation method of the all-vanadium redox flow battery comprises the following steps of:
step 1: establishing a relation between open-circuit voltage and state of charge of the all-vanadium redox flow battery based on a Nernst equation, wherein a correction coefficient related to electrolyte flow is added, and the open-circuit voltage expression based on the Nernst equation is as follows:
Figure BDA0004044818110000031
wherein E is OCV The open circuit voltage of the electric pile of the all-vanadium redox flow battery is set; n (N) cell The number of monomers contained in the all-vanadium redox flow battery pile is the number of monomers contained in the all-vanadium redox flow battery pile; e (E) θ Is the electrode electromotive force of a single cell in a standard state; r is a molar constant; z is the number of electrons transferred in the reaction; f is Faraday constant; ts is the reaction temperature; c is the ion concentration; subscript V 2+ 、V 3+ 、V 4+ 、V 5+ And H + Respectively represent divalent vanadium ion, trivalent vanadium ion, tetravalent vanadium ion, pentavalent vanadium ion and hydrogen ion;
the open circuit voltage of the all-vanadium redox flow battery with the correction coefficient related to the electrolyte flow rate added is as follows:
Figure BDA0004044818110000032
wherein Q is the electrolyte flow rate of the all-vanadium redox flow battery stack; SOC is the state of charge of the stack; k (k) 1 、k 2 And k 3 Respectively correcting coefficients; superscript tk denotes a tank; for example
Figure BDA0004044818110000033
Representing SO in the positive electrolyte storage tank 4 2- In formula (2) replacing the true ion concentration with the ion concentration in the tank;
step 2: and (3) fixing the flow of the electrolyte, charging and discharging the battery, and obtaining a relation curve of open-circuit voltage and state of charge under the flow through experiments, wherein the state of charge SOC is estimated by adopting an ampere-hour integration method, namely:
when in charging:
Figure BDA0004044818110000034
when discharging, the following steps are carried out:
Figure BDA0004044818110000041
wherein t is time; i is current at a certain moment; v (V) tk The volume of the liquid storage tank is; the superscript 0 indicates an initial state in which the cell stack is not charged and discharged,
Figure BDA0004044818110000042
respectively indicate V in the storage tank when the galvanic pile is not charged 2+ 、V 3+ 、V 4+ 、V 5+ Is a concentration of (2);
step 3: based on the relation curve of open-circuit voltage and state of charge under the flow, each correction coefficient k is identified by utilizing a genetic algorithm 1 、k 2 And k 3 Wherein the flow rate of electrolyte of the all-vanadium redox flow battery is Q 1 Then identify k 1 、k 2 、k 3 Should be noted as k 1 (Q 1 )、k 2 (Q 1 )、k 3 (Q 1 )；
Step 4: repeatedly changing the flow rate of the electrolyte, repeating the step 2 and the step 3, and fitting the relation between each correction coefficient and the flow rate of the electrolyte by using a polynomial, namely:
Figure BDA0004044818110000043
Figure BDA0004044818110000044
Figure BDA0004044818110000045
wherein n is the degree of polynomial fitting; omega 1 、ω 2 、ω 3 Respectively k 1 、k 2 、k 3 Coefficients in polynomial fitting.
In the method for calculating the open-circuit voltage of the all-vanadium redox flow battery, the electrode electromotive force E of the single cell under the standard state θ 1.259V.
In the method for calculating the open-circuit voltage of the all-vanadium redox flow battery, the number z of electrons transferred in the reaction is 1.
In the method for calculating the open circuit voltage of the all-vanadium redox flow battery, the Faraday constant F is 96487C/mol.
In the method for calculating the open circuit voltage of the all-vanadium redox flow battery, the molar constant R is 8.314J/(mol.K).
Compared with the prior art, the invention has the following advantages: according to the method for calculating the open-circuit voltage of the all-vanadium redox flow battery, disclosed by the invention, the influence of the difference of the concentration of hydrogen ions and the concentration of the storage tank and the concentration of the electrolyte on the calculated value of the open-circuit voltage is taken into consideration by correcting the standard Nernst equation, and compared with the previous method for calculating the open-circuit voltage of the all-vanadium redox flow battery, the calculation accuracy is improved, and the method is more close to the actual physical meaning of an electrochemical reaction. Therefore, the method has the characteristics of science, high efficiency and the like, and has important fundamental significance for the subsequent modeling and parameter identification of the open-circuit voltage of the all-vanadium redox flow battery.
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Various other advantages and benefits of the present invention will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. It is evident that the figures described below are only some embodiments of the invention, from which other figures can be obtained without inventive effort for a person skilled in the art. Also, like reference numerals are used to designate like parts throughout the figures.
In the drawings:
FIG. 1 is a flow chart of a method for calculating open circuit voltage of an all-vanadium redox flow battery;
FIG. 2 is a schematic illustration of E obtained by selecting an all vanadium redox flow battery stack OCV -SOC graph;
FIG. 3 is a graph of the calculation method according to the present invention and experimental data used;
FIG. 4 is a diagram showing the comparison of simulation result errors of the conventional Nernst equation correction method and the calculation method of the present invention.
The invention is further explained below with reference to the drawings and examples.
Detailed Description
Specific embodiments of the present invention will be described in more detail below with reference to fig. 1 to 4. While specific embodiments of the invention are shown in the drawings, it should be understood that the invention may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
It should be noted that certain terms are used throughout the description and claims to refer to particular components. Those of skill in the art will understand that a person may refer to the same component by different names. The description and claims do not identify differences in terms of components, but rather differences in terms of the functionality of the components. As used throughout the specification and claims, the terms "include" and "comprise" are used in an open-ended fashion, and thus should be interpreted to mean "include, but not limited to. The description hereinafter sets forth a preferred embodiment for practicing the invention, but is not intended to limit the scope of the invention, as the description proceeds with reference to the general principles of the description. The scope of the invention is defined by the appended claims.
For the purpose of facilitating an understanding of the embodiments of the present invention, reference will now be made to the drawings, by way of example, and specific examples of which are illustrated in the accompanying drawings.
Because the flow battery energy storage system has large scale and complex flow, and relates to a multi-physical field coupling process such as heat-flow-electricity, the flow battery energy storage system is directly simulated by adopting commercial simulation software, and the calculated amount is huge and is not easy to converge. Along with the increase of energy storage requirements, the service life is generally prolonged, the stacking number of the flow battery monomers is also increased gradually, and the electrolyte distribution and electrochemical response conditions among the monomers are different. The traditional electric heating model of the flow battery energy storage system does not consider the influence of electrolyte flow distribution nonuniformity and vanadium ion transmembrane transport among long-time monomers on the working state of the flow battery energy storage system, and the operation characteristics of the flow battery stack cannot be accurately estimated.
In summary, the simulation calculation of the flow battery energy storage system by using the commercial simulation software has a large scale, and the previous electrothermal coupling model has many disadvantages. Based on the consensus that the electrochemical reaction of the flow battery has little influence on the flow field, the invention provides a flow battery performance prediction method considering flow non-uniformity among monomers.
For the purpose of facilitating an understanding of the embodiments of the present invention, reference will now be made to the drawings, by way of example, and specific examples of which are illustrated in the accompanying drawings.
The method aims to solve the problems that the open-circuit voltage of the all-vanadium redox flow battery cannot be effectively measured in experiments and is related to various physical quantities, so that accurate modeling cannot be performed. According to the method for calculating the open-circuit voltage of the all-vanadium redox flow battery pile, provided by the invention, the influences of the concentration of hydrogen ions in the electrolyte and the difference between the storage tank and the pile ion concentration are considered, in addition, the relation between the correction coefficient and the flow of the electrolyte is fitted, and the open-circuit voltage of the all-vanadium redox flow battery can be calculated more scientifically and efficiently. Specific examples are described with respect to an all-vanadium redox flow battery of 5kW/3.3kWh, with all-vanadium redox flow batteries and electrolyte related parameters as shown in Table 1.
TABLE 1 all vanadium redox flow battery and electrolyte related parameters
Figure BDA0004044818110000081
The invention relates to a method for calculating open-circuit voltage of an all-vanadium redox flow battery, which is characterized by comprising the following steps:
step 1: based on the Nernst equation, a relation between the open-circuit voltage and the state of charge of the all-vanadium redox flow battery is established, and a correction coefficient related to electrolyte flow is added.
The Nernst equation is used in electrochemistry to calculate the equilibrium voltage of a given redox pair on an electrode relative to a standard potential. The chemical reaction equation of the all-vanadium redox flow battery reaction is as follows:
Figure BDA0004044818110000098
the open circuit voltage expression is written according to the Nernst equation:
Figure BDA0004044818110000091
wherein E is OCV Open circuit voltage for flow cell stack; n (N) cell The number of monomers contained in the all-vanadium redox flow battery pile is the number of monomers contained in the all-vanadium redox flow battery pile; e (E) θ The electrode electromotive force of the single cell in the standard state is 1.259V; r is a mole constant, and the value is 8.314J/(mol.K); z is the number of electrons transferred in the reaction, and the value is 1; f is Faraday constant and takes the value of 96487C/mol; ts is the reaction temperature; c is the ion concentration; subscript V 2+ 、V 3+ 、V 4+ 、V 5+ And H + Respectively represent divalent vanadium ion, trivalent vanadium ion, tetravalent vanadium ion, pentavalent vanadium ion and hydrogen ion.
If the trans-membrane transport of vanadium ions is not considered, V in the liquid storage tank 2+ And V is equal to 3+ Concentration sum, V 4+ And V is equal to 5+ The sum of the concentrations can be regarded as unchanged and is respectively denoted as
Figure BDA0004044818110000092
And are all known amounts.
The flow battery state of charge can be expressed as:
Figure BDA0004044818110000093
for the positive electrolyte, the volume of the electrolyte in the galvanic pile and the volume of the electrolyte in the storage tank are negligible, and the volume is obtained by conservation of charge:
Figure BDA0004044818110000094
namely:
Figure BDA0004044818110000095
bringing formula (2) into formula (4) to simplify:
Figure BDA0004044818110000096
Figure BDA0004044818110000097
since proton exchange membranes theoretically only allow H + Through, positive electrode electrolyte
Figure BDA0004044818110000101
And->
Figure BDA0004044818110000102
The values of (2) may be regarded as unchanged, as in the initial state.
And (3) bringing the formulas (2) and (6) into the formula (1) for simplification, and obtaining the corrected open-circuit voltage of the all-vanadium redox flow battery as follows:
Figure BDA0004044818110000103
wherein Q is the electrolyte flow rate of the all-vanadium redox flow battery; SOC is the state of charge of the battery; k (k) 1 、k 2 And k 3 Respectively correcting coefficients; superscript tk denotes a tank; for example
Figure BDA0004044818110000104
Representing SO in the positive electrolyte storage tank 4 2- Is a concentration of (3). In the formula (7), the ion concentration in the storage tank is used for replacing the real ion concentration, and the difference between the real ion concentration and the storage tank is the correction coefficient k 1 、k 2 、k 3 Is contemplated.
Step 2: and fixing the flow of the electrolyte, charging and discharging the battery, and obtaining a relation curve of open-circuit voltage and state of charge under the flow through experiments.
The state of charge SOC is estimated using an ampere-hour integration method. Namely:
when in charging:
Figure BDA0004044818110000105
when discharging, the following steps are carried out:
Figure BDA0004044818110000106
wherein t is time; i is current at a certain moment; v (V) tk The volume of the liquid storage tank is; the upper mark 0 indicates an initial state in which the cell stack is not charged and discharged,
Figure BDA0004044818110000111
respectively indicate V in the storage tank when the galvanic pile is not charged 2+ 、V 3+ 、V 4+ 、V 5+ Is a concentration of (3).
To reduce the effect of polarization, test E was performed by low current charge-discharge OCV -SOC experimental data curve. SOC at initial charge of 0.05 to
Figure BDA0004044818110000112
And (3) carrying out constant current charging on the battery, and recording the values of open-circuit voltage and SOC in the charging process. After the charging is finished, then add +.>
Figure BDA0004044818110000113
Constant current discharge is carried out by the small current of the battery, and the values of open circuit voltage and SOC in the discharging process are recorded. Averaging the corresponding voltage values in the same SOC during the charging process and the discharging process to obtain an average E OCV -SOC curve. Under the working condition E OCV The SOC curve is shown in fig. 2.
Step 3: and (3) identifying each correction coefficient in the step (1) by utilizing a genetic algorithm according to an experimental result.
The genetic algorithm is a calculation model of the biological evolution process simulating the natural selection and genetic mechanism of the Darwin biological evolution theory, and is a method for searching the optimal solution by simulating the natural evolution process. First, a binary coding method is adopted for k 1 、k 2 、k 3 Coding, and initializing a population value range as follows:
0≤k 1 ≤10 (10)
0≤k 2 ≤10 (11)
0≤k 3 ≤10 (12)
selecting a fitness function:
Figure BDA0004044818110000114
wherein m is the number of data points selected; e (E) guess Predicting open circuit voltage for the model; e (E) real The experimental result shows that the open circuit voltage is true.
Step 4: and (3) changing the flow rate of the electrolyte for a plurality of times, repeating the steps (2) and (3), and fitting the relation between each correction coefficient and the flow rate of the electrolyte by using a polynomial. Namely:
Figure BDA0004044818110000121
Figure BDA0004044818110000122
Figure BDA0004044818110000123
wherein n is the number of times of polynomial fitting, and the value of n is selected according to the prediction precision and is generally not more than 5; omega 1 、ω 2 、ω 3 Respectively k 1 、k 2 、k 3 Coefficients in polynomial fitting.
Further, the steps of multiple selection, crossing, variation and the like are carried out, and a parameter identification result conforming to the operation precision is obtained.
The volume flow of the electrolyte in the first experiment is set to be 0.04L/s, k 1 、k 2 、k 3 The initial values are all set to be 1, and the values of the correction coefficients under the working condition are respectively obtained by utilizing the identification of a genetic algorithm:
k 1 ＝1.087
k 2 ＝1.350
k 3 ＝3.779
the traditional correction method does not consider the influence of the concentration and flow of hydrogen ions, and the corrected Nernst equation is as follows:
Figure BDA0004044818110000124
using the experimental data in step 2, under the working condition, the parameter identification is also performed on the traditional nernst equation, and the values of the correction coefficients in the formula (14) are respectively as follows:
k 1 ＝0.763
k 2 ＝2.305
the prediction effect pair of the calculation method and the traditional Nernst equation correction method is shown in figure 3, and the relative error pair is shown in figure 4. As shown by the identification result, the maximum error of the calculation method is 1%, and the maximum error of the open-circuit voltage calculated by the traditional Nernst equation correction method is about 5%, which proves that the calculation method remarkably improves the prediction accuracy. Meanwhile, as can be seen from FIG. 3, E predicted by the present calculation method OCV And the SOC curve trend is closer to the side drawing trend of the experimental point, so that the correction method is closer to the real reaction condition.
Step 4: and (3) changing the flow rate of the electrolyte for a plurality of times, repeating the steps (2) and (3), and fitting the relation between each correction coefficient and the flow rate of the electrolyte by using a polynomial. Namely:
Figure BDA0004044818110000131
Figure BDA0004044818110000132
Figure BDA0004044818110000133
wherein n is the number of times of polynomial fitting, and the value of n is selected according to the prediction precision and is generally not more than 5; omega 1 、ω 2 、ω 3 Respectively k 1 、k 2 、k 3 Coefficients in polynomial fitting.
Compared with the open-circuit voltage calculation method of the all-vanadium redox flow battery in the prior art, the method has the advantages that the calculation accuracy is improved while the method is close to the real situation of electrochemical reaction, the open-circuit voltage of the all-vanadium redox flow battery can be predicted more scientifically and efficiently, and the method has important basic significance for the follow-up modeling and parameter identification of the all-vanadium redox flow battery.
Although the embodiments of the present invention have been described above with reference to the accompanying drawings, the present invention is not limited to the above-described specific embodiments and application fields, and the above-described specific embodiments are merely illustrative, and not restrictive. Those skilled in the art, having the benefit of this disclosure, may effect numerous forms of the invention without departing from the scope of the invention as claimed.

Claims (5)

1. The method for calculating the open-circuit voltage of the all-vanadium redox flow battery is characterized by comprising the following steps of,
step 1: establishing a relation between open-circuit voltage and state of charge of the all-vanadium redox flow battery based on a Nernst equation, wherein a correction coefficient related to electrolyte flow is added, and the open-circuit voltage expression based on the Nernst equation is as follows:
Figure FDA0004044818100000011
wherein E is ocv The open circuit voltage of the electric pile of the all-vanadium redox flow battery is set; n (N) cell The number of monomers contained in the all-vanadium redox flow battery pile is the number of monomers contained in the all-vanadium redox flow battery pile; e (E) θ Is the electrode electromotive force of a single cell in a standard state; r is a molar constant; z is the number of electrons transferred in the reaction; f is Faraday constant; t (T) s Is the reaction temperature; c is the ion concentration; subscript V 2+ 、V 3+ 、V 4+ 、V 5+ And H + Respectively represent divalent vanadium ion, trivalent vanadium ion and tetravalent vanadium ionVanadium ions, pentavalent vanadium ions, and hydrogen ions;
the open circuit voltage of the all-vanadium redox flow battery with the correction coefficient related to the electrolyte flow rate added is as follows:
Figure FDA0004044818100000012
wherein Q is the electrolyte flow rate of the all-vanadium redox flow battery stack; SOC is the state of charge of the stack; k (k) 1 、k 2 And k 3 Respectively correcting coefficients; superscript tk denotes a tank; for example
Figure FDA0004044818100000013
Representing SO in the positive electrolyte storage tank 4 2- In formula (2) replacing the true ion concentration with the ion concentration in the tank;
step 2: and (3) fixing the flow of the electrolyte, charging and discharging the battery, and obtaining a relation curve of open-circuit voltage and state of charge under the flow through experiments, wherein the state of charge SOC is estimated by adopting an ampere-hour integration method, namely:
when in charging:
Figure FDA0004044818100000021
when discharging, the following steps are carried out:
Figure FDA0004044818100000022
wherein t is time; i is current at a certain moment; v (V) tk The volume of the liquid storage tank is; the superscript 0 indicates an initial state in which the cell stack is not charged and discharged,
Figure FDA0004044818100000023
respectively indicate V in the storage tank when the galvanic pile is not charged 2+ 、V 3+ 、V 4+ 、V 5+ Is a concentration of (2);
step 3: based on the relation curve of open-circuit voltage and state of charge under the flow, each correction coefficient k is identified by utilizing a genetic algorithm 1 、k 2 And k 3 Wherein the flow rate of electrolyte of the all-vanadium redox flow battery is Q 1 Then identify k 1 、k 2 、 k 3 should be noted as k 1 (Q 1 )、k 2 (Q 1 )、k 3 (Q 1 )；
Step 4: repeatedly changing the flow rate of the electrolyte, repeating the step 2 and the step 3, and fitting the relation between each correction coefficient and the flow rate of the electrolyte by using a polynomial, namely:
Figure FDA0004044818100000024
Figure FDA0004044818100000025
Figure FDA0004044818100000026
/>
wherein n is the degree of polynomial fitting; omega 1 、ω 2 、ω 3 Respectively k 1 、k 2 、k 3 Coefficients in polynomial fitting.
2. The method for calculating an open circuit voltage of an all-vanadium redox flow battery according to claim 1, wherein preferably, an electrode electromotive force E of the single cell in a standard state θ 1.259V.
3. The method for calculating the open circuit voltage of the all-vanadium redox flow battery according to claim 1, wherein the number z of electrons transferred in the reaction is 1.
4. The all-vanadium redox flow battery open circuit voltage calculation method of claim 1, wherein faraday constant F is 96487C/mol.
5. The all-vanadium redox flow battery open circuit voltage calculation method according to claim 1, wherein the molar constant R is 8.314J/(mol-K).
CN202310027647.2A 2023-01-09 2023-01-09 Open-circuit voltage calculation method of all-vanadium redox flow battery Pending CN116125286A (en)

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