A Calculation Method for the Open-Circuit Voltage of a Vanadium Redox Flow Battery

Abstract

A method for calculating the open circuit voltage of an all-vanadium liquid flow battery is disclosed. In the method, based on the Nernst equation, a relationship between the open circuit voltage and the state of charge of the all-vanadium liquid flow battery is established, and a correction coefficient related to the electrolyte flow rate is added; the electrolyte flow rate is fixed, the battery is charged and discharged, and the relationship curve between the open circuit voltage and the state of charge under the flow rate is obtained experimentally; based on the experimental results, each correction coefficient is identified using a genetic algorithm; the electrolyte flow rate is changed multiple times, and a polynomial is used to fit the relationship between each correction coefficient and the electrolyte flow rate. For a specific liquid flow battery, the above steps are completed in sequence to obtain a complete open circuit voltage calculation method. The correction coefficient of the all-vanadium liquid flow battery open circuit voltage calculation method is related to the electrolyte flow rate, and the influence of the hydrogen ion concentration that is difficult to accurately calculate is taken into account. It is close to the facts of the electrochemical reaction and takes into account the calculation accuracy, which has important basic significance for the modeling of all-vanadium liquid flow batteries.

Description

Technical Field

[0001] The present invention belongs to the technical field of modeling of all-vanadium redox flow batteries, and particularly relates to a method for calculating the open-circuit voltage of an all-vanadium redox flow battery. Background Art

[0002] Among the energy storage systems developed currently, redox flow batteries are highly favored due to their outstanding advantages such as high efficiency, modularity, good stability, long lifespan, and environmental friendliness. At the same time, redox flow battery energy storage systems are large in scale and involve multi-physical field coupling processes such as heat-fluid-electricity. Researchers have established various equivalent models for all-vanadium redox flow battery stacks using different tools. The open-circuit voltage of an all-vanadium redox flow battery, as a very important parameter, plays a crucial role in improving the accuracy and 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 independent variables such as the stack structure, temperature, flow rate, ion concentration, state of charge, etc. The equation describing the equilibrium voltage in electrochemistry is the Nernst equation. Therefore, some researchers usually use the modified Nernst equation for estimation. The traditional method of estimating the modified Nernst equation ignores the influence of hydrogen ion concentration on the open-circuit voltage. At the same time, the ion concentration in the storage tank is used to replace the ion concentration in the monomer. However, the hydrogen ion concentration has a certain influence on the open-circuit voltage, and there are also differences between the ion concentration in the storage tank and the ion concentration in the monomer. For a specific battery, the magnitude of this difference is related to the flow rate. Therefore, the accuracy of the traditional method of estimating the modified Nernst equation is not high. Another part of the researchers only consider the influence of the state of charge on the open-circuit voltage and fit a polynomial with the state of charge as the independent variable and the open-circuit voltage as the dependent variable using experimental data. Although the accuracy of this method increases as the degree of the independent variable increases, it has two inherent defects: one is that it only considers the influence of the battery state of charge and does not consider the influence of other physical quantities such as temperature and flow rate on the open-circuit voltage; the other is that it only uses mathematical methods for fitting, departing from the physical meaning of the open-circuit voltage.

[0003] In summary, starting from the Nernst equation that considers the essence of the physical phenomenon of the open-circuit voltage, the present invention proposes a method for calculating the open-circuit voltage of an all-vanadium redox flow battery that considers the influence of hydrogen ion concentration and electrolyte flow rate.

[0004] The above information disclosed in the background art section is only used to enhance the understanding of the background of the present invention, and thus may include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0005] In view of the problems existing in the prior art, the present invention proposes a method for calculating the open-circuit voltage of a vanadium redox flow battery, which takes into account the influence of hydrogen ion concentration and electrolyte flow rate, and considers the influence of the difficult-to-calculate hydrogen ion concentration on the open-circuit voltage. At the same time, by adding a flow-related correction coefficient to the standard Nernst equation, the difference in ion concentration between the storage tank and the single cell is corrected. In addition, by fitting the relationship between the correction coefficient and the electrolyte flow rate, the calculation of the open-circuit voltage is more accurate for different working states. For a certain vanadium redox flow battery, the present invention can establish an accurate and efficient method for calculating the open-circuit voltage that conforms to the essence of the physical process, which has important fundamental significance for the subsequent establishment of models and the conduct of calculations.

[0006] The object of the present invention is achieved through the following technical solutions. A method for calculating the open-circuit voltage of a vanadium redox flow battery includes:

[0007] Step 1: Establish the relationship between the open-circuit voltage and the state of charge of the vanadium redox flow battery based on the Nernst equation. Among them, a correction coefficient related to the electrolyte flow rate is added. The expression of the open-circuit voltage based on the Nernst equation is:

[0008]

[0009] where E OCV is the open-circuit voltage of the vanadium redox flow battery stack; N cell is the number of single cells included in the vanadium redox flow battery stack; E θ is the electrode electromotive force of a single cell under standard conditions; R is the molar constant; z is the number of electrons transferred in the reaction; F is the Faraday constant; Ts is the reaction temperature; c is the ion concentration; the subscripts V 2+ , V 3+ , V 4+ , V 5+ and H + respectively represent divalent vanadium ions, trivalent vanadium ions, tetravalent vanadium ions, pentavalent vanadium ions and hydrogen ions;

[0010] The open-circuit voltage of the vanadium redox flow battery after adding the correction coefficient related to the electrolyte flow rate is:

[0011]

[0012] where Q is the electrolyte flow rate of the vanadium redox flow battery stack; SOC is the state of charge of the battery stack; k1, k2 and k3 are the correction coefficients respectively; the superscript tk represents the storage tank; for example represents the concentration of SO4 2- in the positive electrolyte storage tank, and the ion concentration in the storage tank is used to replace the real ion concentration in formula (2);

[0013] Step 2: Fix the electrolyte flow rate, charge and discharge the battery, and experimentally obtain the relationship curve between the open-circuit voltage and the state of charge at this flow rate. The state of charge SOC is estimated using the ampere-hour integration method, i.e.:

[0014] During charging:

[0015]

[0016] During discharging:

[0017]

[0018] where t is time; I is the current at a certain moment; V tk is the volume of the liquid storage tank; the superscript 0 represents the initial state when the stack is not charged or discharged, respectively represent the concentrations of V 2+ 、V 3+ 、V 4+ 、V 5+ in the storage tank when the stack is not charged;

[0019] Step 3: Based on the relationship curve between the open-circuit voltage and the state of charge at the flow rate, use the genetic algorithm to identify the correction coefficients k1, k2, and k3. Among them, the electrolyte flow rate of the all-vanadium redox flow battery is Q1, then the identified k1, k2, k3 should be recorded as k1(Q1), k2(Q1), k3(Q1);

[0020] Step 4: Change the electrolyte flow rate multiple times, repeat Steps 2 and 3, and use polynomial fitting to fit the relationship between each correction coefficient and the electrolyte flow rate, i.e.:

[0021]

[0022]

[0023]

[0024] where n is the degree of polynomial fitting; ω1, ω2, ω3 are the coefficients of k1, k2, k3 in polynomial fitting, respectively.

[0025] In the open-circuit voltage calculation method of the all-vanadium redox flow battery, the electrode electromotive force E θ of a single cell under standard conditions is 1.259V.

[0026] In the open-circuit voltage calculation method of the all-vanadium redox flow battery, the number of electrons z transferred in the reaction is 1.

[0027] In the open-circuit voltage calculation method of the all-vanadium redox flow battery, the Faraday constant F is 96487 C / mol.

[0028] In the open-circuit voltage calculation method of the all-vanadium redox flow battery described above, the molar constant R is 8.314 J / (mol·K).

[0029] Compared with the prior art, the present invention has the following advantages: By modifying the standard Nernst equation, the open-circuit voltage calculation method of the all-vanadium redox flow battery described in the present invention takes into account the influence of the hydrogen ion concentration and the difference in ion concentrations between the storage tank and the electrolyte on the calculated value of the open-circuit voltage. Compared with the previous calculation methods for the open-circuit voltage of all-vanadium redox flow batteries, on the one hand, the calculation accuracy is improved, and on the other hand, it is closer to the true physical meaning of the electrochemical reaction. Therefore, the present invention has the characteristics of being scientific and efficient, and has important fundamental significance for the subsequent modeling and parameter identification of the open-circuit voltage of all-vanadium redox flow batteries. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] By reading the following detailed description of the preferred specific embodiments, various other advantages and benefits of the present invention will become clear to those of ordinary skill in the art. The accompanying drawings in the specification are only for the purpose of showing the preferred embodiments, and are not considered to be a limitation of the present invention. Obviously, the following described drawings are only some embodiments of the present invention, and those of ordinary skill in the art can obtain other drawings based on these drawings without creative efforts. Moreover, throughout the drawings, the same reference numerals are used to represent the same components.

[0031] In the drawings:

[0032] Figure 1 is the flowchart of the open-circuit voltage calculation method for the all-vanadium redox flow battery described above;

[0033] Figure 2 is the E OCV -SOC curve graph obtained by selecting all-vanadium redox flow battery stack experiments;

[0034] Figure 3 The curve graph of the calculation method described in the present invention and the experimental data used;

[0035] Figure 4 is the error comparison graph of the simulation results between the traditional Nernst equation correction method and the calculation method of the present invention.

[0036] The following further explains the present invention in conjunction with the drawings and embodiments. SPECIFIC EMBODIMENTS

[0037] The following will refer to the attached Figures 1 to 4Specific embodiments of the present invention will be described in more detail. Although specific embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided so that the present invention can be more thoroughly understood and the scope of the present invention can be fully conveyed to those skilled in the art.

[0038] It should be noted that certain terms are used in the specification and claims to refer to specific components. Those skilled in the art should understand that technicians may use different terms to refer to the same component. The specification and claims of this application do not use the difference in terms as a way to distinguish components, but use the difference in the functions of components as the criterion for distinction. As mentioned throughout the specification and claims, the term "comprising" or "including" is an open-ended term and should be interpreted as "including but not limited to". The following description of the embodiments is for the purpose of implementing the preferred embodiments of the present invention, but the description is for the general principles of the specification and is not intended to limit the scope of the present invention. The protection scope of the present invention shall be determined by the scope defined by the appended claims.

[0039] For the convenience of understanding the embodiments of the present invention, the following will further explain with specific embodiments as examples in conjunction with the drawings, and each drawing does not constitute a limitation on the embodiments of the present invention.

[0040] Since the flow battery energy storage system is large in scale, complex in process, and involves multi-physical field coupling processes such as heat-fluid-electricity, directly using commercial simulation software to simulate the flow battery energy storage system results in a huge amount of calculation and is not easy to converge. With the increasing energy storage demand and the generally increasing lifespan, the number of single cells stacked in the flow battery is gradually increasing, and the electrolyte distribution and electrochemical response between each single cell are also different. The previous electro-thermal model of the flow battery energy storage system did not consider the influence of the uneven distribution of electrolyte flow between single cells over a long time and the transmembrane transport of vanadium ions on the working state of the flow battery energy storage system, and it can no longer accurately estimate the operating characteristics of the flow battery stack.

[0041] In summary, using commercial simulation software to simulate the flow battery energy storage system has a large scale, and there are still many deficiencies in the previous electro-thermal coupling model. Based on the common understanding that the influence of the electrochemical reaction of the flow battery on the flow field is negligible, the present invention proposes a method for predicting the performance of a flow battery considering the uneven flow between single cells.

[0042] For the convenience of understanding the embodiments of the present invention, the following will further explain with specific embodiments as examples in conjunction with the drawings, and each drawing does not constitute a limitation on the embodiments of the present invention.

[0043] The present invention aims to solve the problem that the open-circuit voltage of a vanadium redox flow battery cannot be effectively measured in experiments, and the open-circuit voltage is related to multiple physical quantities, making it impossible to accurately model. A method for calculating the open-circuit voltage of a vanadium redox flow battery stack according to the present invention takes into account the influence of the hydrogen ion concentration in the electrolyte and the ion concentration difference between the storage tank and the stack. In addition, the relationship between the correction coefficient and the electrolyte flow rate is fitted, enabling the more scientific and efficient calculation of the open-circuit voltage of the vanadium redox flow battery. A specific example is described with a 5kW / 3.3kWh vanadium redox flow battery, and the relevant parameters of the vanadium redox flow battery and the electrolyte are shown in Table 1.

[0044] Table 1 Relevant parameters of vanadium redox flow battery and electrolyte

[0045]

[0046] A method for calculating the open-circuit voltage of a vanadium redox flow battery according to the present invention is characterized in that the method comprises the following steps:

[0047] Step 1: Based on the Nernst equation, establish the relationship between the open-circuit voltage of the vanadium redox flow battery and the state of charge, and add a correction coefficient related to the electrolyte flow rate.

[0048] The Nernst equation is used in electrochemistry to calculate the equilibrium voltage of a specified redox pair relative to the standard potential on the electrode. The chemical reaction equation of the vanadium redox flow battery reaction is:

[0049]

[0050] Write its open-circuit voltage expression according to the Nernst equation as:

[0051]

[0052] Among them, E OCV is the open-circuit voltage of the flow battery stack; N cell is the number of single cells included in the vanadium redox flow battery stack; E θ is the electrode electromotive force of a single cell under standard conditions, with a value of 1.259V; R is the molar constant, with a value of 8.314 J / (mol·K); z is the number of electrons transferred in the reaction, with a value of 1; F is the Faraday constant, with a value of 96487 C / mol; Ts is the reaction temperature; c is the ion concentration; the subscripts V 2+ 、V 3+ 、V 4+ 、V 5+ and H + respectively represent divalent vanadium ions, trivalent vanadium ions, tetravalent vanadium ions, pentavalent vanadium ions and hydrogen ions.

[0053] If the transmembrane transport of vanadium ions is not considered, then in the storage tank, V2+ With V 3+ The sum of the concentrations, V 4+ With V 5+ The sum of the concentrations can be regarded as constant and are denoted as And are all known quantities.

[0054] Then the charge state of the flow battery can be expressed as:

[0055]

[0056] For the positive electrolyte, since the volume of the electrolyte in the stack and the volume of the electrolyte in the storage tank can be ignored, from the charge conservation, we have:

[0057]

[0058] That is:

[0059]

[0060] Substitute Equation (2) into Equation (4) and simplify to get:

[0061]

[0062]

[0063] Since the proton exchange membrane theoretically only allows H + To pass through, the values of the positive electrolyte And Can be regarded as constant and are the same as the initial state.

[0064] Substitute Equations (2) and (6) into (1) and simplify to obtain the open-circuit voltage of the modified all-vanadium flow battery as:

[0065]

[0066] Among them, Q is the electrolyte flow rate of the all-vanadium flow battery; SOC is the state of charge of the battery; k1, k2, and k3 are the respective correction coefficients; the superscript tk represents the storage tank; for example Represents the concentration of SO4 2- In the positive electrolyte storage tank. In Equation (7), the ion concentration in the storage tank is used to replace the true ion concentration, and the difference between the two is within the scope of consideration of the correction coefficients k1, k2, and k3.

[0067] Step 2: Fix the electrolyte flow rate, charge and discharge the battery, and experimentally obtain the relationship curve between the open-circuit voltage and the state of charge at this flow rate.

[0068] The state of charge SOC is estimated by the ampere-hour integration method. That is:

[0069] During charging:

[0070]

[0071] During discharging:

[0072]

[0073] where t is time; I is the current at a certain moment; V tk is the volume of the liquid storage tank; the superscript 0 represents the initial state when the stack is not charged or discharged, respectively represent the concentrations of V 2+ 、V 3+ 、V 4+ 、V 5+ in the storage tank when the stack is not charged.

[0074] To reduce the influence of polarization, the small current charge-discharge method is used to test the E OCV -SOC experimental data curve. The SOC is 0.05 at the start of charging, and a small current is used to perform constant current charging on the battery, and the open circuit voltage and SOC values during the charging process are recorded. After the charging is completed, then a small current is used to perform constant current discharging, and the open circuit voltage and SOC values during the discharging process are recorded. The voltage values corresponding to the same SOC during the charging process and the discharging process are averaged to obtain the average E OCV -SOC curve. The E OCV -SOC curve under this working condition is as Figure 2 shown.

[0075] Step 3: According to the experimental results, use the genetic algorithm to identify each correction coefficient in Step 1.

[0076] The genetic algorithm is a computational model that simulates the natural selection of Darwin's theory of biological evolution and the biological evolution process of genetic mechanisms, and is a method for searching for the optimal solution by simulating the natural evolution process. First, binary coding is used to encode k1, k2, and k3, and the initialization population value range is:

[0077] 0 ≤ k1 ≤ 10 (10)

[0078] 0 ≤ k2 ≤ 10 (11)

[0079] 0 ≤ k3 ≤ 10 (12)

[0080] Select the fitness function:

[0081]

[0082] where m is the number of selected data points; E guess is the open circuit voltage predicted by the model; Ereal is the true open-circuit voltage obtained from the experiment.

[0083] Step 4: Change the electrolyte flow rate multiple times, repeat Steps 2 and 3, and use polynomial fitting to establish the relationship between each correction coefficient and the electrolyte flow rate. That is:

[0084]

[0085]

[0086]

[0087] where n is the degree of polynomial fitting, and the value of n is selected according to the prediction accuracy, generally not exceeding 5; ω1, ω2, and ω3 are the coefficients of k1, k2, and k3 in the polynomial fitting, respectively.

[0088] Furthermore, through multiple steps of selection, crossover, mutation, etc., a parameter identification result that meets the operation accuracy is obtained.

[0089] In the first experiment, the electrolyte volume flow rate was set to 0.04 L / s, and the initial values of k1, k2, and k3 were all set to 1. The values of the correction coefficients obtained by using the genetic algorithm for identification under this working condition are:

[0090] k1 = 1.087

[0091] k2 = 1.350

[0092] k3 = 3.779

[0093] The traditional correction method does not consider the influence of hydrogen ion concentration and flow rate. The corrected Nernst equation is:

[0094]

[0095] Using the experimental data in Step 2, under this working condition, parameter identification is also carried out for the traditional Nernst equation. The values of the correction coefficients in Equation (14) are:

[0096] k1 = 0.763

[0097] k2 = 2.305

[0098] The comparison of the prediction effects between this calculation method and the traditional Nernst equation correction method is as Figure 3 shown, and the comparison of the relative errors is as Figure 4 shown. From the identification results, it can be seen that the maximum error of this calculation method is 1%, while the maximum error of the open-circuit voltage calculated by the traditional Nernst equation correction method is about 5%, indicating that this calculation method significantly improves the prediction accuracy. At the same time, from Figure 3 it can be seen that the E predicted by this calculation method OCV- The trend of the SOC curve is closer to the trend of the experimental points, indicating that the proposed correction method is more in line with the actual situation of the reaction.

[0099] Step 4: Change the electrolyte flow rate multiple times, and repeat Steps 2 and 3 to fit the relationship between each correction coefficient and the electrolyte flow rate using polynomial fitting. That is:

[0100]

[0101]

[0102]

[0103] where n is the degree of polynomial fitting, and the value of n is selected according to the prediction accuracy, generally not greater than 5; ω1, ω2, and ω3 are the coefficients of k1, k2, and k3 in polynomial fitting, respectively.

[0104] Compared with the existing open-circuit voltage calculation method for all-vanadium redox flow batteries, the present invention improves the calculation accuracy while being closer to the actual situation of the electrochemical reaction, and can more scientifically and efficiently predict the open-circuit voltage of all-vanadium redox flow batteries, which has important fundamental significance for the subsequent modeling and parameter identification of all-vanadium redox flow batteries.

[0105] Although the embodiments of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the above specific embodiments and application fields. The above specific embodiments are merely illustrative and guiding, rather than restrictive. Those of ordinary skill in the art can also make many forms under the inspiration of this specification and without departing from the scope protected by the claims of the present invention, and all of these are within the scope of protection of the present invention.

Claims

1. A method for calculating the open circuit voltage of an all-vanadium redox flow battery, characterized in that, It includes the following steps, Step 1: Establish the relationship between the open-circuit voltage and the state of charge of the all-vanadium redox flow battery based on the Nernst equation. Among them, a correction coefficient related to the electrolyte flow rate is added. The open-circuit voltage expression based on the Nernst equation is: (1) Among them, is the open-circuit voltage of the all-vanadium redox flow battery stack; is the number of single cells included in the all-vanadium redox flow battery stack; is the electrode electromotive force of a single cell under standard conditions; R is the molar constant; is the number of electrons transferred in the reaction; is the Faraday constant; is the reaction temperature; is the ion concentration; the subscripts , , , and represent divalent vanadium ions, trivalent vanadium ions, tetravalent vanadium ions, pentavalent vanadium ions and hydrogen ions respectively; The open-circuit voltage of the all-vanadium redox flow battery after adding the correction coefficient related to the electrolyte flow rate is: (2) Among them, is the electrolyte flow rate of the all-vanadium redox flow battery stack; is the state of charge of the stack; , and are the correction coefficients respectively; the superscript represents the storage tank; represents in the positive electrolyte storage tank concentration, and the ion concentration in the storage tank is used to replace the true ion concentration in Equation (2); Step 2: Fix the electrolyte flow rate, charge and discharge the battery, and experimentally obtain the relationship curve between the open-circuit voltage and the state of charge at this flow rate. The state of charge is estimated by the ampere-hour integration method, i.e.: During charging: (3) During discharging: (4) Among them, is the time; is the current at a certain moment; is the volume of the liquid storage tank; the superscript represents the initial state where the stack is not charged or discharged, , , respectively represent the concentrations of , , , in the storage tank when the stack is not being charged; Step 3: Identify each correction coefficient using a genetic algorithm based on the relationship curve between the open-circuit voltage and the state of charge under a flow rate , and , where the flow rate of the all-vanadium redox flow battery electrolyte is , then the identified , , should be recorded as , , ; Step 4: Change the electrolyte flow rate multiple times, repeat Steps 2 and 3, and use polynomial fitting to obtain the relationship between each correction coefficient and the electrolyte flow rate, that is: (5) (6) (7) Among them, is the degree of polynomial fitting; , , are respectively , , the coefficients in polynomial fitting.

2. The open-circuit voltage calculation method of the all-vanadium redox flow battery according to claim 1, wherein, Electrode electromotive force of a single cell under standard conditions is 1.259 V.

3. The method for calculating the open-circuit voltage of an all-vanadium redox flow battery according to claim 1, wherein, The number of electrons transferred in the reaction is 1.

4. The open-circuit voltage calculation method of the all-vanadium redox flow battery according to claim 1, wherein, Faraday constant is 96487 C / mol.

5. The open-circuit voltage calculation method of the all-vanadium redox flow battery according to claim 1, wherein, The molar constant R is 8.314 J / (mol·K).

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