Method for predicting performance of flow battery based on flow rate non-uniformity between monomers

Abstract

A method for predicting the performance of a flow battery based on the flow rate non-uniformity between monomers is disclosed. In the method, the internal flow field of the stack is numerically calculated to obtain the flow rate distribution of each monomer; each monomer is respectively equivalent to an independent circuit and connected in series to form a stack equivalent circuit; isothermal sample experiments are carried out to obtain the response curves of each monomer, and a genetic algorithm is used to identify the parameters of each monomer equivalent circuit; a temperature field model of the flow battery system is established based on the law of conservation of energy; the stack equivalent circuit model is coupled with the temperature field model based on the modified Nernst equation; non-isothermal sample experiments are carried out and the parameters of the temperature field model are identified; the obtained complete coupled model is used to predict the performance response of the flow battery under different working conditions. The present invention comprehensively considers the flow rate non-uniformity between monomers of the flow battery, the transmembrane transport of vanadium ions and the influence of heat generation on the battery operation state, and accurately and efficiently calculates the output voltage, operating temperature and state of charge to guide the safe operation of the flow battery.

Description

Technical Field

[0001] The present invention belongs to the technical field of modeling technology for energy storage systems, and particularly relates to a method for predicting the performance of a flow battery based on the flow unevenness between monomers. Background Art

[0002] In recent years, renewable energy sources represented by solar energy, wind energy, etc. have received extensive attention in the energy field. However, due to problems such as randomness, volatility, unpredictability, and discontinuity of such energy sources, developing an efficient and stable energy storage system remains one of the major challenges in the energy field.

[0003] Among the currently developed energy storage systems, flow batteries are highly favored due to their outstanding advantages such as high efficiency, modularity, good stability, long lifespan, and environmental friendliness. However, due to the large scale of the flow battery energy storage system and the complex coupling process involving multiple physical fields such as heat - flow - electricity, directly using commercial multi - physical field simulation software to simulate the flow battery energy storage system results in a huge amount of calculation and is not easy to converge. In addition, with the increasing energy storage demand and the generally growing lifespan, the number of stacked flow battery monomers is gradually increasing, and the electrolyte distribution and electrochemical response between each monomer are also different. The previous electrothermal model of the flow battery energy storage system did not consider the influence of the uneven distribution of electrolyte flow between monomers and the long - term transmembrane transport of vanadium ions on the operating state of the flow battery energy storage system, and thus could not accurately estimate the operating characteristics of the flow battery stack.

[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] Aiming at the problems existing in the prior art, the present invention proposes a method for predicting the performance of a flow battery based on the flow unevenness between monomers, which considers the influence of the uneven distribution of electrolyte flow, transmembrane transport of vanadium ions, self - discharge phenomenon, and temperature on the operating state of the flow battery, and dynamically models the temperature field of the flow battery and couples it with the flow and circuit model processes. This method can not only accurately and comprehensively reflect the characteristics of the thermal - flow - electricity system of the flow battery stack, but also observe and predict the capacity attenuation phenomenon of the flow battery.

[0006] The object of the present invention is achieved through the following technical solutions. A method for predicting the performance of a flow battery based on the flow unevenness between monomers includes:

[0007] Step 1: According to the internal structure of the stack of the flow battery, use the finite element method to numerically calculate the internal flow field of the stack to obtain the flow distribution of each monomer when the total flow is constant, where

[0008]

[0009] Equation (1) represents the relationship between the total volume flow rate and the individual volume flow rate. The superscript s represents the stack, and the superscript av represents the individual cell. Q s is the total electrolyte flow rate through the stack; N cell is the number of individual cells in the stack; i represents the number of the individual cell, taking values from 1 to N cell ; is the electrolyte flow rate through the i-th individual cell,

[0010] Step 2: Perform equivalent circuit modeling for each individual cell of the all-vanadium redox flow battery, and represent it using Equations (2)–(7):

[0011] U c = E ocv + I s R1 (2)

[0012] U d = Uc + IR2 (3)

[0013] I d = I3 + I (4)

[0014]

[0015] I = I s + I c (6)

[0016]

[0017] where, U d is the output voltage of the individual cell; I d is the charge and discharge current of the individual cell; E OCV is the open-circuit voltage of the individual cell of the flow battery; R1 is the internal resistance loss caused by reaction kinetics; R2 is the sum of the mass transfer impedance, diaphragm impedance, solution impedance, electrode impedance, and bipolar plate impedance; R3 is the parasitic loss; C1 is the electrode capacitance of the individual cell, used to simulate the dynamic process of the battery; I s , I, I3, and I c are the currents passing through R1, R2, R3, and C1, respectively; U c is the voltage of the electrode capacitance C1;

[0018] Connect the equivalent circuits of N cell individual cells in series to form the equivalent circuit of the stack;

[0019] Step 3: At a constant temperature T s , the total electrolyte flow rate Q s through the stack, the charge and discharge current , and the initial state of charge SOC of the electrolyte 0When the response data of the flow battery stack is obtained, the stack terminal voltage is measured as , and the terminal voltage of each single cell . Since the stack is formed by connecting each single cell in series, each physical quantity satisfies equations (8)–(9):

[0020]

[0021]

[0022] Substitute and into the equivalent circuit of each single cell, and use the genetic algorithm to identify R1, R2, R3, and C1 of each single cell, so as to obtain the complete equivalent circuit of the flow battery stack based on the flow unevenness between single cells;

[0023] Step 4: Analyze the heat generation and heat dissipation during the operation of the stack, and establish a temperature field model among the storage tank, the electrolyte flow channel, and the stack in the flow battery system based on the law of conservation of energy, which is expressed by equations (10)–(13):

[0024] For the stack:

[0025]

[0026]

[0027] For the storage tank:

[0028]

[0029] For the pipeline:

[0030]

[0031]

[0032] Among them, T is the temperature; V is the volume; t is the time; the superscript in represents the pipeline through which the electrolyte flows from the storage tank into the stack; the superscript out represents the pipeline through which the electrolyte flows out of the stack and returns to the storage tank; the superscript tk represents the storage tank; the superscript pipe represents the pipeline; the superscript air represents the air in the environment; T s is the stack temperature; T in is the temperature of the electrolyte in the pipeline flowing into the stack; T air is the ambient air temperature; T out is the temperature of the electrolyte in the pipeline flowing out of the stack; T tk is the temperature of the electrolyte in the storage tank; V pipe is the pipeline volume; V tk is the storage tank volume; represents the product of the equivalent heat capacity, equivalent density, and equivalent volume of the stack; (HA) sRepresents the product of the equivalent heat transfer coefficient and the equivalent heat transfer area between the stack and the environment; (HA) tk Represents the product of the equivalent heat transfer coefficient and the equivalent heat transfer area between the storage tank and the environment; (HA) pipe Represents the product of the equivalent heat transfer coefficient and the equivalent heat transfer area between the pipeline and the environment; Q s Is the total flow rate of the positive / negative electrolyte; C p Is the specific heat capacity of the electrolyte; ρ is the density of the electrolyte; p is the total heat generated during the operation of the stack, including the heat generated by obstruction P r 、The heat generated by flow friction P flow And the reaction heat P entro , Expressed by equations (14)–(17):

[0033] p = p r +P flow +P entro (14)

[0034]

[0035] P flow =2(P fri +P part +P ele ) (16)

[0036]

[0037] Among them, z is the number of electrons transferred in the reaction; F is the Faraday constant; The molar reaction entropy change under standard conditions; R is the molar constant; And Respectively represent V in the i-th monomer 2+ 、V 3+ 、V 4+ And V 5+ Concentration; P fri 、P part And P ele Are the heat generated by the frictional resistance loss, local resistance loss and the loss through the electrodes during the flow of the electrolyte, respectively, expressed by equations (18)–(20):

[0038]

[0039]

[0040]

[0041] Among them, f D Is the Darcy friction coefficient; L is the pipeline length; D is the wetted perimeter of the pipeline; f Lis the local loss coefficient; μ is the dynamic viscosity of the electrolyte; l is the electrode thickness; A is the electrode area; κ is the electrode permeability, calculated by Equation (21):

[0042]

[0043] where d f is the fiber diameter of the electrode porous medium; ε is the electrode porosity; K ck is the Kozeny–Carman constant;

[0044] Step 5: Based on the Nernst equation, couple the temperature field model with the equivalent circuit of the flow battery stack. The parameters to be identified are (HA) s 、(HA) tk and (HA) pipe ;

[0045] Step 6: According to the non-isothermal sample experimental data, use the genetic algorithm to identify the parameters to be identified (HA) s 、(HA) tk and (HA) pipe , and obtain the equivalent model of the flow battery stack based on the flow unevenness between monomers;

[0046] Step 7: Use the equivalent model of the flow battery stack based on the flow unevenness between monomers to predict the performance response of the flow battery under different working conditions. Given the total volume flow rate Q s 、initial SOC 0 、ambient temperature T air and charge-discharge current I d , calculate the output voltage of the stack the output voltage of each monomer the working temperature T of the stack s .

[0047] In the above-mentioned flow battery performance prediction method based on the flow unevenness between monomers, the open-circuit voltage E of the flow battery monomer OCV is calculated using Equation (22):

[0048]

[0049] where E θ is the electrode electromotive force of a single cell under standard conditions; and are the V in the i-th monomer 2+ 、V 3+ 、V 4+ and V 5+Concentration, the flow distribution of each monomer is uniform, and the electrolyte concentration at the inlet and outlet of the single cell is equal to the average concentration in the single cell. The V in the liquid storage tank and the monomer 2+ 、V 3+ 、V 4+ and V 5+ The dynamic differential equations of concentration are as shown in Eqs. (23)–(30):

[0050] Liquid storage tank:

[0051]

[0052]

[0053]

[0054]

[0055] Stack:

[0056]

[0057]

[0058]

[0059]

[0060] Among them, V av is the volume of the positive / negative half-cell monomer; k2, k3, k4, and k5 are the transmembrane diffusion coefficients of V 2+ 、V 3+ 、V 4+ and V 5+ respectively; d is the thickness of the proton exchange membrane; S is the membrane area of the proton exchange membrane; the symbols ± and The upper symbol indicates charging, the lower symbol indicates discharging, the positive sign indicates increase, and the negative sign indicates decrease.

[0061] In the performance prediction method of the flow battery based on the flow non-uniformity between monomers, the electrode electromotive force E θ of the single cell under standard conditions is 1.259V.

[0062] In the performance prediction method of the flow battery based on the flow non-uniformity between monomers, the temperature model of the flow battery energy storage system satisfies the following constraint conditions:

[0063] Constraint condition 1: The temperature is uniform inside the stack, inside the storage tank, and inside the electrolyte flow pipeline;

[0064] Constraint condition 2: The physical properties of components such as the end plates, electrodes, flow channels, and proton exchange membranes inside the stack do not change with temperature;

[0065] Constraint 3: Physical properties such as the viscosity and density of the electrolyte do not change with the ionic valence state or the state of charge of the electrolyte.

[0066] In the method for predicting the performance of a flow battery based on the uneven flow rate between monomers, the number of electrons transferred z in the reaction is 1.

[0067] In the method for predicting the performance of a flow battery based on the uneven flow rate between monomers, the Faraday constant F is 96487 C / mol.

[0068] In the method for predicting the performance of a flow battery based on the uneven flow rate between monomers, the molar reaction entropy change under standard conditions is -121.7 J / (mol·K) during charging and 121.7 J / (mol·K) during discharging.

[0069] In the method for predicting the performance of a flow battery based on the uneven flow rate between monomers, the molar constant R is 8.314 J / (mol·K).

[0070] In the method for predicting the performance of a flow battery based on the uneven flow rate between monomers, the flow battery is a all-vanadium redox flow battery.

[0071] Compared with the prior art, the present invention has the following advantages: The method for predicting the performance of a flow battery based on the uneven flow rate between monomers according to the present invention takes into account the uneven distribution of the electrolyte flow rate between the monomers of the flow battery stack, and can more accurately and efficiently estimate the response differences of each monomer of the flow battery under certain working conditions, thereby better guiding the design of the flow channels of the flow battery stack and the optimization of the operation strategy. It takes into account the influence of the transmembrane transport of vanadium ions on the life and maintenance time of the flow battery stack, and has practical significance for the actual engineering application of all-vanadium redox flow battery stacks. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] By reading the following detailed description of the preferred 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 drawings described below are only some embodiments of the present invention, and those of ordinary skill in the art can obtain other drawings without creative efforts based on these drawings. Moreover, throughout the drawings, the same reference numerals are used to denote the same components.

[0073] In the drawings:

[0074] Figure 1 is a flowchart of the method for predicting the performance of a flow battery stack considering the uneven flow rate between monomers proposed by the present invention;

[0075] Figure 2 is the equivalent circuit diagram of a single cell of a vanadium redox flow battery stack;

[0076] Figure 3 is the equivalent temperature model diagram of a vanadium redox flow battery energy storage system;

[0077] Figure 4 is the coupled equivalent circuit and equivalent temperature model diagram of a vanadium redox flow battery energy storage system;

[0078] Figure 5 is between each single cell during the charge and discharge process of a vanadium redox flow battery simulation result diagram of differences;

[0079] Figure 6 is the simulation result diagram of the voltage differences between each single cell during the charge and discharge process of a vanadium redox flow battery.

[0080] The present invention will be further explained below in conjunction with the accompanying drawings and embodiments. Detailed implementation manners

[0081] The following will refer to the attached Figures 1 to 6 The specific embodiments of the present invention will be described in more detail. Although the 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.

[0082] 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 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 used 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 subsequent description of the specification is for the purpose of describing the preferred embodiments of implementing the present invention, but the description is for the general purpose of the specification and is not intended to limit the scope of the present invention. The protection scope of the present invention shall be defined by the appended claims.

[0083] 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 accompanying drawings, and each drawing does not constitute a limitation on the embodiments of the present invention.

[0084] Due to the large scale, complex process, and multi - physical - field coupling processes such as heat - flow - electricity involved in the flow - battery energy storage system, directly simulating the flow - battery energy storage system using commercial simulation software results in a huge computational amount and is not easy to converge. With the increasing energy storage demand and generally longer lifespan, the number of single - cell stacks in the flow battery gradually increases, and the electrolyte distribution and electrochemical response among the single cells are also different. The previous electro - thermal model of the flow - battery energy storage system did not consider the long - term uneven distribution of electrolyte flow rate among single cells and the influence of vanadium ion transmembrane transport on the working state of the flow - battery energy storage system, and thus can no longer accurately estimate the operating characteristics of the flow - battery stack.

[0085] 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 electrochemical reaction of the flow battery has a negligible influence on the flow field, the present invention proposes a method for predicting the performance of the flow battery considering the uneven flow rate among single cells.

[0086] To facilitate the understanding of the embodiments of the present invention, the following will further explain and illustrate with specific embodiments in conjunction with the attached drawings, and the attached drawings do not limit the embodiments of the present invention.

[0087] In a specific example, a vanadium redox flow battery with a power of 1.54 kW and an energy capacity of 6.15 kW·h is taken as an example for description, and its parameters are shown in Table 1:

[0088] Table 1 Related parameters of the vanadium redox flow battery

[0089]

[0090] A method for establishing an unevenness model and parameter identification among single cells of a vanadium redox flow - battery stack, the steps including:

[0091] Step 1: According to the internal structure of the stack, use the finite - element method to numerically calculate the internal flow field of the stack, so as to obtain the flow - rate distribution of each single cell when the total flow rate is constant.

[0092]

[0093] Equation (1) represents the relationship between the total volume flow rate and the volume flow rate of a single cell. Among them, the superscript s represents the stack, the superscript av represents the single cell, Q s is the total volume flow rate of the electrolyte passing through the stack; N cell is the number of single cells in the stack; i represents the number of the single cell, taking values from 1 to N cell ; is the volume flow rate of the electrolyte passing through the i - th single cell.

[0094] Regarding the electrolyte flow as the flow of a viscous incompressible fluid, with the physical properties of the fluid being constant, the flow control equation is:

[0095] Continuity equation:

[0096]

[0097] Navier - Stokes equations:

[0098]

[0099] where \(t\) is time, the density \(\rho\) and the dynamic viscosity coefficient \(\mu\) are known quantities. In addition, the body force per unit mass \(f\) acting on the fluid is a known quantity, and the unknowns are the three components of the electrolyte velocity vector \(\mathbf{u}\) and the pressure \(p\). The four scalar - form equations contain four unknowns, and the system of equations is closed.

[0100] For viscous flow, the velocity satisfies the no - slip boundary condition. At the solid boundary, the fluid adjacent to the boundary adheres to the solid boundary, and there is no relative motion between them. Since the flow battery stack is stationary, the no - slip boundary condition of the electrolyte is expressed as:

[0101] \(\mathbf{u} = 0\) (4)

[0102] For the all - vanadium redox flow battery stack, when the volume flow rate \(Q\) s is independent of time and is \(0.04\ L / s\), the flow rate distribution of each single cell is calculated as follows:

[0103]

[0104]

[0105]

[0106]

[0107] Step 2: Perform equivalent - circuit modeling for each single cell of the all - vanadium redox flow battery. As Figure 2 shown in the equivalent - circuit model of a single cell, the relationships between the physical quantities in the circuit are described by Equations (5) - (10):

[0108] \(U\) c \(= E\) OCV \(+ I\) s \(R_1\) (5)

[0109] \(U\) d \(= U\) c \(+ IR_2\) (6)

[0110] \(I\) d \(= I_3+I\) (7)

[0111]

[0112] \(I = I\)s +I c (9)

[0113]

[0114] Among them, U d is the output voltage of the monomer; I d is the charge and discharge current of the all-vanadium redox flow battery monomer; R1 is the internal resistance of loss caused by reaction kinetics; R2 is the sum of mass transfer impedance, diaphragm impedance, solution impedance, electrode impedance and bipolar plate impedance; R3 is the parasitic loss; C1 is the electrode capacitance of the monomer, mainly used to simulate the dynamic process of the battery and is related to the vanadium ion concentration; I s , I, I3 and I c are the currents passing through R1, R2, R3 and C1 respectively; U c is the voltage of C1; E OCV is the open-circuit voltage of the all-vanadium redox flow battery monomer, which is calculated by Equation (11) (ignoring the influence of hydrogen ion concentration):

[0115]

[0116] θ Among them, E and are the concentrations of V 2+ , V 3+ , V 4+ and V 5+ in the i-th monomer respectively. According to the law of conservation of mass, considering the self-discharge cross-reaction caused by the transmembrane transport of vanadium ions in various valence states, assuming that the flow distribution in each monomer is uniform and the electrolyte concentration at the inlet and outlet of the single cell is equal to the average concentration in the single cell, the dynamic differential equations of the concentrations of V 2+ , V 3+ , V 4+ and V 5+ in the storage tank and the monomer are as shown in Equations (12)–(19):

[0117] Storage tank:

[0118]

[0119]

[0120]

[0121]

[0122] Stack:

[0123]

[0124] ​

[0125]

[0126]

[0127] Among them, V av is the volume of the positive / negative half-cell monomer; k2, k3, k4, and k5 are the ion transmembrane diffusion coefficients of V 2+ , V 3+ , V 4+ , and V 5+ respectively; d is the thickness of the proton exchange membrane; S is the membrane area of the proton exchange membrane; the symbols and , the upper symbol indicates charging, the lower symbol indicates discharging, the positive sign indicates an increase, and the negative sign indicates a decrease.

[0128] Connect N cell monomer equivalent circuits in series to form a stack equivalent circuit.

[0129] Step 3: At a constant temperature T s , the volume flow rate Q s of the positive / negative electrode electrolytes, the charge / discharge current , and the initial state of charge SOC 0 of the electrolyte, obtain the stack response data of the flow battery. The measured stack terminal voltage is the terminal voltage of each monomer Since the stack is connected in series by each monomer, each physical quantity should satisfy Equations (20)–(21):

[0130]

[0131]

[0132] Substitute into the equivalent circuit of each monomer established in Step 2, and use the genetic algorithm to identify R1, R2, R3, and C1 of each monomer. Then the complete electrical equivalent circuit of the flow battery considering the flow unevenness between monomers can be obtained.

[0133] Step 4: Analyze the heat generation and heat dissipation during the operation of the stack, and establish the temperature relationship among the storage tank, the electrolyte flow channel, and the stack in the flow battery system based on the law of conservation of energy. The temperature model of the all-vanadium flow battery energy storage system satisfies the following constraints:

[0134] Constraint 1: The temperature inside the stack, inside the storage tank, and inside the electrolyte flow pipeline is uniform;

[0135] Constraint 2: The physical properties of components such as the end plates, electrodes, flow channels, and proton exchange membranes inside the stack do not change with temperature;

[0136] Constraint 3: Physical properties such as the viscosity and density of the electrolyte do not change with the ionic valence state or the state of charge of the electrolyte.

[0137] The temperature model constrained by the above conditions is as Figure 3 shown, and the temperature relationships of the liquid storage tank, flow channel, and stack are expressed by equations (22)–(25):

[0138] For the stack:

[0139]

[0140]

[0141] For the storage tank:

[0142]

[0143] For the pipeline:

[0144]

[0145]

[0146] where T is the temperature; V is the volume; t is the time; the superscript in represents the pipeline through which the electrolyte flows from the storage tank into the stack; the superscript out represents the pipeline through which the electrolyte flows out of the stack and returns to the storage tank; the superscript tk represents the storage tank; the superscript pipe represents the pipeline; the superscript air represents the air in the environment; T s is the stack temperature; T in is the temperature of the electrolyte in the pipeline flowing into the stack; T air is the ambient air temperature; T out is the temperature of the electrolyte in the pipeline flowing out of the stack; T tk is the temperature of the electrolyte in the storage tank; V pipe is the pipeline volume; V tk is the storage tank volume; represents the product of the equivalent heat capacity, equivalent density, and equivalent volume of the stack; (HA) s represents the product of the equivalent heat transfer coefficient and equivalent heat transfer area between the stack and the environment; (HA) tk represents the product of the equivalent heat transfer coefficient and equivalent heat transfer area between the storage tank and the environment; (HA) pipe represents the product of the equivalent heat transfer coefficient and equivalent heat transfer area between the pipeline and the environment; Q s is the total flow rate of positive / negative electrolytes; C p is the specific heat capacity of the electrolyte; ρ is the density of the electrolyte; p is the total heat generation during the operation of the stack, including the heat generated by obstruction P r 、the heat generated by flow friction P flow and the heat of reaction P entro, which is expressed by formulas (26) - (29):

[0147] P = P r + P flow + P entro (26)

[0148]

[0149] P flow = 2(P fri + P part + P ele ) (28)

[0150]

[0151] Among them, 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; The molar reaction entropy change under standard conditions is -121.7 J / (mol·K) during charging and 121.7 J / (mol·K) during discharging; R is the molar constant, with a value of 8.314 J / (mol·K); and respectively represent the concentrations of V 2+ , V 3+ , V 4+ and V 5+ in the i-th monomer; P fri , P part and P ele are the heat generation due to the frictional resistance loss, local resistance loss, and the loss through the electrode during the flow of the electrolyte, respectively, and are expressed by formulas (30) - (32):

[0152]

[0153]

[0154]

[0155] Among them, f D is the Darcy friction coefficient; L is the pipe length; D is the wetted perimeter of the pipe; f L is the local loss coefficient; μ is the dynamic viscosity of the electrolyte; l is the electrode thickness; A is the electrode area; κ is the electrode permeability, which is calculated by the following formula:

[0156]

[0157] Among them, d f is the fiber diameter of the electrode porous medium; ε is the electrode porosity; K ckis the Kozeny-Carman constant, which is an empirical parameter characterizing the structure and fiber distribution of fiber materials.

[0158] Step 5: As Figure 4 shown, based on the Nernst equation, couple the temperature field model with the equivalent circuit model. At this time, the parameters to be identified are (HA) s 、(HA) tk and (HA) pipe .

[0159] Step 6: According to the non-isothermal sample experimental data, use the genetic algorithm to identify the 4 parameters to be identified in Step 5. Then an equivalent model of the flow battery considering the flow unevenness between monomers is obtained.

[0160] Step 7: Use the obtained complete coupling model to predict the performance response of the flow battery under different working conditions. Given the total volume flow rate Q s 、the initial SOC, the ambient temperature T air and the charge and discharge current I d , this method can calculate the output voltage of the stack, the output voltage of each monomer, the working temperature T of the stack s and other parameters more accurately and efficiently, which has guiding significance for optimizing the operating conditions of the all-vanadium flow battery stack.

[0161] As Figure 5 shown, in order to clearly observe the working state of each monomer during the charge and discharge process, draw the change curve of the concentration of each monomer V 3+ with time. It can be observed that the of the four monomers in the flow battery stack shows obvious differences, and the greater the electrolyte flow rate inside the monomer, the slower the change. This is because the monomers are connected in series, and the number of charges transferred by the electrochemical reaction of each monomer per unit time is equal, which means that the amount of reactants consumed by each monomer per unit time is equal. The greater the electrolyte flow rate, the more sufficient the reactant supply, and the slower the concentration change. As Figure 6 shown, the output voltages of each monomer also show obvious differences. Combining Figure 5 it can be known that the higher, the lower the output voltage of the monomer, which is determined by the Nernst equation. Figure 5 and Figure 6 clearly show the influence of the flow unevenness between the monomers of the flow battery stack on its working state, indicating that the consideration of the present invention has scientific value.

[0162] 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 fall within the scope of protection of the present invention.

Claims

1. A method for predicting the performance of a flow battery based on the flow rate non-uniformity between monomers, characterized in that, It includes the following steps: Step 1: According to the internal structure of the stack of the flow battery, use the finite element method to perform numerical calculations on the internal flow field of the stack to obtain the monomer flow distribution when the total flow is constant. Among them, （1）； Equation (1) represents the relationship between the total volume flow rate and the individual volume flow rate. The superscript represents the stack, and the superscript represents the single cell. is the total flow rate of the electrolyte passing through the stack; is the number of single cells in the stack; represents the serial number of the single cell, with values ranging from 1 to ; is the flow rate of the electrolyte passing through the th single cell; Step 2: Perform equivalent circuit modeling on each monomer of the all-vanadium flow battery, and express it with Equations (2)–(7): （2）； （3）； （4）； （5）； （6）； （7）； Among them, is the single-cell output voltage; is the single-cell charge and discharge current; is the open-circuit voltage of the flow battery single cell; is the internal resistance of loss caused by reaction kinetics; is the sum of mass transfer impedance, diaphragm impedance, solution impedance, electrode impedance and bipolar plate impedance; is the parasitic loss; is the electrode capacitance of the single cell, used to simulate the dynamic process of the battery; , , and are respectively the currents passing through , , and ; is the voltage of the electrode capacitance . Connect individual equivalent circuits in series to form a stack equivalent circuit; Step 3: At a constant temperature 、the total flow rate of the electrolyte passing through the stack 、the charge-discharge current and the initial state of charge of the electrolyte When, the response data of the flow battery stack are obtained, and the stack terminal voltage is measured to be and the terminal voltage of each single cell Since the stack is connected in series by each single cell, each physical quantity satisfies Equations (8)–(9): （8）； （9）； Substitute and into the equivalent circuits of each single cell, and use the genetic algorithm to identify , , and , so as to obtain a complete equivalent circuit of the flow battery stack based on the flow unevenness between single cells; Step 4: Analyze the heat generation and heat dissipation during the operation of the stack, and establish a temperature field model among the storage tank, the electrolyte flow channel, and the stack in the flow battery system based on energy conservation, and express it with Equations (10)–(13): For the stack: （10）； For the storage tank: （11）； For the pipeline: （12）； （13）； Wherein, is temperature; is volume; is time; The superscript represents the pipeline through which the electrolyte flows from the storage tank into the stack; The superscript represents the pipeline through which the electrolyte flows out of the stack and returns to the storage tank; The superscript represents the storage tank; The superscript represents the pipeline; The superscript represents the air in the environment; is the stack temperature; is the temperature of the electrolyte in the pipeline flowing into the stack; is the temperature of the ambient air; is the temperature of the electrolyte in the pipeline flowing out of the stack; The temperature of the electrolyte in the storage tank; is the pipeline volume; is the storage tank volume; represents the product of the equivalent heat capacity, equivalent density and equivalent volume of the stack; represents the product of the equivalent heat transfer coefficient and equivalent heat transfer area between the stack and the environment; represents the product of the equivalent heat transfer coefficient and equivalent heat transfer area between the storage tank and the environment; represents the product of the equivalent heat transfer coefficient and equivalent heat transfer area between the pipeline and the environment; is the total flow rate of positive / negative electrolyte; is the specific heat capacity of the electrolyte; is the density of the electrolyte; is the total heat generation during the operation of the stack, including heat generated by obstruction and heat generated by flow friction and reaction heat , which is expressed by equations (14)–(17): （14）； （15）； （16）； （17）； Among them, is the number of electrons transferred in the reaction; is the Faraday constant; is the molar reaction entropy change under standard conditions; R is the molar constant; , , and respectively represent the th monomer , , and concentrations; , and are respectively the heat generation due to the frictional resistance loss, local resistance loss and electrode loss during the electrolyte flow process, which are expressed by equations (18)–(20): （18）； （19）； （20）； Among them, is the Darcy friction coefficient; is the pipe length; is the wetted perimeter of the pipe; is the local loss coefficient; is the dynamic viscosity of the electrolyte; is the electrode thickness; is the electrode area; is the electrode permeability, calculated by Equation (21): （21）； Among them, is the diameter of the porous medium fiber of the electrode; is the porosity of the electrode; is the Kozeny–Carman constant; Step 5: Based on the Nernst equation, couple the temperature field model with the equivalent circuit of the flow battery stack. The parameters to be identified are , , and ; Step 6: According to the non-isothermal sample experimental data, use the genetic algorithm to identify the parameters to be identified , , and , and obtain an equivalent model of the flow battery stack based on the flow unevenness between monomers Step 7: Use the equivalent model of the flow battery stack based on the flow unevenness between monomers to predict the performance response of the flow battery under different working conditions, and given the total volume flow rate , initial , ambient temperature and charge-discharge current , the output voltage of the stack, the output voltage of each monomer, and the working temperature of the stack are calculated by the equivalent model of the flow battery stack based on the flow unevenness between monomers.

2. The method for predicting the performance of a flow battery based on the flow rate non-uniformity between monomers according to claim 1, wherein, Open-circuit voltage of a single flow battery It is calculated using Equation (22): （22）； Among them, is the electromotive force of the single cell under standard conditions; , , and are respectively the th monomer , , and concentrations. The flow rate distribution in each monomer is uniform, and the electrolyte concentration at the inlet and outlet of the single cell is equal to the average concentration in the single cell. The dynamic differential equations of , , and in the storage tank and the monomer are as shown in Equations (23)–(30): Liquid storage tank: （23）； （24）； （25）； （26）； Stack: （27）； （28）； （29）； （30）； Among them, is the volume of the positive / negative half-cell monomer; , , and are respectively , , and the ion transmembrane diffusion coefficients; is the thickness of the proton exchange membrane; is the membrane area of the proton exchange membrane; The symbols and , the upper symbol represents charging, the lower symbol represents discharging, the plus sign represents an increase, and the minus sign represents a decrease.

3. The method for predicting the performance of a flow battery based on the flow rate non-uniformity between monomers according to claim 2, wherein, Electrode electromotive force of a single battery under standard conditions is 1.259 V.

4. The method for predicting the performance of a flow battery based on the flow unevenness between monomers according to claim 1, wherein, The temperature model of the flow battery energy storage system satisfies the following constraint conditions: Constraint condition 1: The temperature inside the stack, inside the storage tank, and inside the electrolyte flow pipeline is uniform; Constraint condition 2: The physical properties of the end plates, electrodes, flow channels, and proton exchange membranes inside the stack do not change with temperature; Constraint condition 3: The viscosity and density of the electrolyte do not change with the ionic valence state and the charged state of the electrolyte.

5. The method for predicting the performance of a flow battery based on the flow unevenness between monomers according to claim 1, wherein, The number of electrons transferred in the reaction is 1.

6. The method for predicting the performance of a flow battery based on the flow rate non-uniformity between monomers according to claim 1, wherein, Faraday constant is 96487 C / mol.

7. The method for predicting the performance of a flow battery based on the flow rate non-uniformity between monomers according to claim 1, wherein, Molar reaction entropy change under standard conditions It takes the value of –121.7 J / (mol·K) during charging and 121.7 J / (mol·K) during discharging.

8. The method for predicting the performance of a flow battery based on the flow unevenness between monomers according to claim 1, wherein, The molar constant R is 8.314 J / (mol·K).

9. The method for predicting the performance of a flow battery based on the flow rate non-uniformity between monomers according to claim 1, wherein, The flow battery is an all-vanadium flow battery.

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