A method for calculating the lithium concentration of active material particles in a lithium-ion battery based on a lithium concentration-stress coupling model

Abstract

This application provides a method for calculating the lithium concentration of lithium-ion battery active material particles based on a lithium concentration-stress coupling model. This method includes four steps: determining the lithium concentration-stress coupling model parameters required for the calculation, calculating the lithium flux on the surface of the lithium-ion battery active material particles, calculating the lithium concentration at the center of the lithium-ion battery active material particles, and calculating the lithium concentration off the center of the lithium-ion battery active material particles. Using this method, the lithium concentration of lithium-ion battery active material particles can be calculated quickly and accurately, making it suitable for lithium-ion battery simulation and lithium-ion battery state of charge estimation in electronic devices, electric vehicles, and energy storage power stations.

Description

Technical Field

[0001] The present invention relates to the field of lithium-ion battery simulation, and in particular to a method for calculating the lithium concentration of active material particles in lithium-ion batteries based on a lithium concentration-stress coupling model. Background Art

[0002] Lithium-ion batteries have the advantages of high energy density, high power density, and long cycle life. Since their commercialization in 1991, lithium-ion batteries have been widely used in the field of energy storage. Obtaining the lithium concentration of lithium-ion battery active material particles can not only help lithium-ion battery engineers understand the working mechanism of lithium-ion batteries, but also help lithium-ion battery users understand the working status of lithium-ion batteries. Since the lithium concentration of lithium-ion battery active material particles is difficult to measure, the lithium concentration of lithium-ion battery active material particles is obtained by calculation. At present, the calculation speed and accuracy of the lithium concentration of lithium-ion battery active material particles still cannot meet the application requirements, which limits its application in lithium-ion battery simulation and lithium-ion battery state of charge estimation in electronic devices, electric vehicles, and energy storage power stations. Summary of the Invention

[0003] The purpose of the present invention is to be able to calculate the lithium concentration of lithium ion battery active material particles at high speed and precision, so that it can be used for lithium ion battery simulation and charge state estimation of lithium ion batteries in electronic devices, electric vehicles, and energy storage power stations.

[0004] In order to achieve this object, the present invention adopts the following technical solutions:

[0005] A method for calculating the lithium concentration of active material particles in lithium-ion batteries based on a lithium concentration-stress coupling model. This method includes the following four steps:

[0006] S1. Determine the lithium concentration-stress coupling model parameters required for calculation;

[0007] S2. Calculate the lithium flux on the surface of active material particles in lithium-ion batteries;

[0008] S3. Calculate the lithium concentration at the center of the active material particles of the lithium ion battery;

[0009] S4. Calculate the non-central lithium concentration of the active material particles in lithium-ion batteries.

[0010] The methods for determining the lithium concentration-stress coupling model parameters required for calculation in S1 are literature review, instrument measurement, and parameter identification.

[0011] In S2, the lithium flux on the surface of active material particles of lithium-ion batteries is calculated using the following formula:

[0012] (1)

[0013] (2)

[0014] in: a is the specific surface area of lithium-ion battery electrodes; F is the Faraday constant; I L is the lithium-ion battery load current; is the lithium flux on the surface of active material particles in lithium-ion batteries; L is the thickness of lithium-ion battery electrodes; n + is the lithium ion charge; S is the electrode area of the lithium-ion battery; n It is the negative electrode of lithium-ion battery; p It is the positive electrode of lithium-ion battery; I L The reference direction is given by n to p .

[0015] In S3 and S4, the lithium concentration of active material particles in lithium-ion batteries is calculated using the following formula:

[0016] (3)

[0017] (4)

[0018] (5)

[0019] (6)

[0020] (7)

[0021] in: C s is the lithium concentration of active material particles in lithium-ion batteries; D s is the lithium diffusion coefficient of the active material particles in lithium-ion batteries; E is the Young's modulus of the active material particles of lithium-ion batteries; R is the gas constant; T is the thermodynamic temperature of the lithium-ion battery; is the Poisson's ratio of the active material particles in lithium-ion batteries; is the partial molar volume of lithium in lithium-ion battery active material particles; For spatial interval; is the time interval; i is the spatial ordinal number, i = 0 is the center of the lithium-ion battery active material particle; j is the time sequence number, j= 0 is the starting point of time; initial is the initial value; max is the maximum value; Equations 3 to 7 are obtained based on the lithium concentration-stress coupling model.

[0022] In S3 C s,i, j-1 is a known quantity, C s,0, j is the independent variable. From Equation 3 and Equation 5, we can know that C s,i, j For C s,0, j As a function of the independent variable, the left side of Equation 6 is C s,0,j is a function of the independent variable, let it be f ( C s,0, j ), f ( C s,0, j ) = 0 is C s,0,j value.

[0023] S3 includes the following eight steps:

[0024] S31, Order C s,0, j = C s,0, j-1 ;

[0025] S32, Solution C s,i, j ;

[0026] S33, Solution f ( C s,0, j );

[0027] S34, f ( C s,0, j )<0: C s,0, j As the starting point, let C s,0, j Arithmetic increment until C s,0, j satisfy f ( C s,0, j )>0, then the last one that satisfies f ( C s,0, j )<0 C s,0, j As the starting point, reduce the incremental difference, and repeat this step until C s,0, j Meet the accuracy requirements;

[0028] S35, f ( C s,0, j )>0, f ' ( C s,0, j )>0: C s,0, j As the starting point, let C s,0, j Arithmetic decrease until C s,0,j satisfy f ( C s,0, j )<0 or f ( C s,0, j ) is an imaginary number, then the last one that satisfies f ( C s,0, j )>0, f ' ( C s,0, j )>0 C s,0, j As the starting point, reduce the decreasing difference, and repeat this step until C s,0, j Meet the accuracy requirements;

[0029] S36, f ( C s,0, j )>0, f ' ( C s,0, j )<0: C s,0, j = C s,0, j + C add Make C s,0, j satisfy f ( C s,0, j )>0, f ' ( C s,0, j )>0, jump back to step S35;

[0030] S37, f ( C s,0, j ) is an imaginary number: C s,0, j = C s,0, j + C add Make C s,0, j satisfy f (C s,0, j )>0, f ' ( C s,0, j )>0, jump back to step S35;

[0031] S38, f ( C s,0, j ) = 0: C s,0, j = C s,0, j-1 Established.

[0032] In S4, equations 3 and 5 are used to solve the non-central lithium concentration of the active material particles of the lithium ion battery.

[0033] S2-S4 are executed by a computing device.

[0034] Using this method, the lithium concentration of active material particles in lithium-ion batteries can be calculated quickly and accurately. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 These are the method steps in the embodiment.

[0036] Figure 2 This is the mapping relationship in the embodiment.

[0037] Figure 3 is the load current of the lithium-ion battery in the embodiment.

[0038] Figure 4 is the lithium concentration of the negative electrode active material particles of the lithium ion battery in the embodiment.

[0039] Figure 5 is the lithium concentration of the positive electrode active material particles of the lithium ion battery in the embodiment. DETAILED DESCRIPTION

[0040] The following examples illustrate the embodiments of the present invention. The examples are provided to illustrate the embodiments of the present invention, but are not intended to limit the scope of application of the present invention.

[0041] In an embodiment, a method for calculating the lithium concentration of active material particles in a lithium ion battery based on a lithium concentration-stress coupling model includes the following four steps:

[0042] S1. Determine the lithium concentration-stress coupling model parameters required for calculation;

[0043] S2. Calculate the lithium flux on the surface of active material particles in lithium-ion batteries;

[0044] S3. Calculate the lithium concentration at the center of the active material particles of the lithium ion battery;

[0045] S4. Calculate the non-central lithium concentration of the active material particles in lithium-ion batteries.

[0046] The methods for determining the lithium concentration-stress coupling model parameters required for calculation in S1 are literature review, instrument measurement, and parameter identification.

[0047] Table 1. Lithium concentration-stress coupling model parameters required for calculation.

[0048]

[0049]

[0050] Table 2. Initial lithium concentration of active material particles in lithium-ion batteries and thermodynamic temperature of lithium-ion batteries.

[0051]

[0052] In S2, the lithium flux on the surface of active material particles of lithium-ion batteries is calculated using the following formula:

[0053] (1)

[0054] (2)

[0055] in: a is the specific surface area of lithium-ion battery electrodes; F is the Faraday constant; I L is the lithium-ion battery load current; is the lithium flux on the surface of active material particles in lithium-ion batteries; L is the thickness of lithium-ion battery electrodes; n + is the lithium ion charge; S is the electrode area of the lithium-ion battery; n It is the negative electrode of lithium-ion battery; p It is the positive electrode of lithium-ion battery; I L The reference direction is given by n to p .

[0056] In S3 and S4, the lithium concentration of active material particles in lithium-ion batteries is calculated using the following formula:

[0057] (3)

[0058] (4)

[0059] (5)

[0060] (6)

[0061] (7)

[0062] in: C s is the lithium concentration of active material particles in lithium-ion batteries; D s is the lithium diffusion coefficient of the active material particles in lithium-ion batteries; E is the Young's modulus of the active material particles of lithium-ion batteries; R is the gas constant; T is the thermodynamic temperature of the lithium-ion battery; is the Poisson's ratio of the active material particles in lithium-ion batteries; is the partial molar volume of lithium in lithium-ion battery active material particles; For spatial interval; is the time interval; i is the spatial ordinal number, i = 0 is the center of the lithium-ion battery active material particle; j is the time sequence number, j = 0 is the starting point of time; initial is the initial value; max is the maximum value; Equations 3 to 7 are obtained based on the lithium concentration-stress coupling model.

[0063] In S3 C s,i, j-1 is a known quantity, C s,0, j is the independent variable. From formula 3 and formula 5, we can know that C s,i, j For C s,0, j As a function of the independent variable, the left side of Equation 6 is C s,0,j is a function of the independent variable, let it be f ( C s,0, j ), f ( C s,0, j ) = 0 is C s,0,j The value of .

[0064] S3 includes the following eight steps:

[0065] S31, Order C s,0, j = C s,0, j-1 ;

[0066] S32, SolutionC s,i, j ;

[0067] S33, Solution f ( C s,0, j );

[0068] S34, f ( C s,0, j )<0: C s,0, j As the starting point, let C s,0, j Arithmetic increment until C s,0, j satisfy f ( C s,0, j )>0, then the last one that satisfies f ( C s,0, j )<0 C s,0, j As the starting point, reduce the incremental difference, and repeat this step until C s,0, j Meet the accuracy requirements;

[0069] S35, f ( C s,0, j )>0, f ' ( C s,0, j )>0: C s,0, j As the starting point, let C s,0, j Arithmetic decrease until C s,0,j satisfy f ( C s,0, j )<0 or f ( C s,0, j ) is an imaginary number, and the last one that satisfies f ( C s,0, j )>0, f ' ( C s,0, j )>0 C s,0, j As the starting point, reduce the decreasing difference, and repeat this step until C s,0, j Meet the accuracy requirements;

[0070] S36, f ( C s,0, j )>0, f '( C s,0, j )<0: C s,0, j = C s,0, j + C add Make C s,0, j satisfy f ( C s,0, j )>0, f ' ( C s,0, j )>0, jump back to step S35;

[0071] S37, f ( C s,0, j ) is an imaginary number: C s,0, j = C s,0, j + C add Make C s,0,j satisfy f ( C s,0, j )>0, f ' ( C s,0, j )>0, jump back to step S35;

[0072] S38, f ( C s,0, j ) = 0: C s,0, j = C s,0, j-1 Established.

[0073] In S4, equations 3 and 5 are used to solve the non-central lithium concentration of the active material particles of the lithium ion battery.

[0074] S2-S4 are executed by a computing device, which is a computer (CPU = Intel Core i7-10750H, RAM = 16GB).

[0075] The embodiments are only intended to illustrate the technical concept of the present invention and are not intended to limit the scope of protection of the present invention. Any modification to the technical concept of the present invention shall fall within the scope of protection of the present invention.

Claims

1. A method for calculating the lithium concentration of active material particles in a lithium ion battery based on a lithium concentration-stress coupling model, characterized in that: It includes the following four steps: S1. Determine the parameters of the lithium concentration-stress coupling model required for calculation. The method for determining the parameters of the lithium concentration-stress coupling model required for calculation in S1 is to consult literature, perform instrument measurement, and perform parameter identification. S2. Calculate the lithium flux on the surface of the active material particles of the lithium ion battery. In S2, the lithium flux on the surface of the active material particles of the lithium ion battery is calculated using the following formula: Formula 1 Formula 2 in: a is the specific surface area of lithium-ion battery electrodes; F is the Faraday constant; I L is the lithium-ion battery load current; is the lithium flux on the surface of active material particles in lithium-ion batteries; L is the thickness of lithium-ion battery electrodes; n + is the lithium ion charge; S is the electrode area of the lithium-ion battery; n It is the negative electrode of lithium-ion battery; p It is the positive electrode of lithium-ion battery; I L The reference direction is given by n to p ; S3. Calculate the lithium concentration at the center of the active material particles of the lithium ion battery; S4. Calculate the non-central lithium concentration of active material particles in lithium-ion batteries; In S3 and S4, the lithium concentration of active material particles in lithium-ion batteries is calculated using the following formula: Formula 3 Formula 4 Formula 5 Formula 6 Formula 7 in: C s is the lithium concentration of active material particles in lithium-ion batteries; D s is the lithium diffusion coefficient of the active material particles in lithium-ion batteries; E is the Young's modulus of the active material particles of lithium-ion batteries; R is the gas constant; T is the thermodynamic temperature of the lithium-ion battery; is the Poisson's ratio of the active material particles in lithium-ion batteries; is the partial molar volume of lithium in lithium-ion battery active material particles; For spatial interval; is the time interval; i is the spatial ordinal number, i = 0 is the center of the lithium-ion battery active material particle; j is the time sequence number, j = 0 is the starting point of time; initial is the initial value; max is the maximum value; Equations 3 to 7 are obtained based on the lithium concentration-stress coupling model.

2. The method for calculating lithium concentration of active material particles in lithium ion batteries based on a lithium concentration-stress coupling model according to claim 1, wherein: In S3 C s,i, j-1 is a known quantity, C s,0, j is the independent variable, and from Equation 3 and Equation 5, we can know that C s,i,j For C s,0,j is a function of the independent variable, and the left side of Equation 6 is C s,0, j is a function of the independent variable, let it be f ( C s,0, j ), f ( C s,0, j The largest real number solution for ) = 0 is C s,0,j value.

3. The method for calculating the lithium concentration of active material particles in a lithium ion battery based on a lithium concentration-stress coupling model according to claim 2, characterized in that: S3 includes the following eight steps: S31, Order C s,0, j = C s,0, j-1 ; S32, Solution C s,i, j ; S33, Solution f ( C s,0, j ); S34, f ( C s,0, j ) < 0: C s,0, j As the starting point, let C s,0, j Arithmetic increment until C s,0, j satisfy f ( C s,0, j )> 0, then the last one that satisfies f ( C s,0, j ) < 0 C s,0, j As the starting point, reduce the incremental difference, and repeat this step until C s,0, j Meet the accuracy requirements; S35, f ( C s,0, j ) > 0, f ' ( C s,0, j ) > 0: C s,0, j As the starting point, let C s,0, j Arithmetic decrease until C s,0,j satisfy f ( C s,0, j ) < 0 or f ( C s,0, j ) is an imaginary number, and the last one that satisfies f ( C s,0,j ) > 0, f ' ( C s,0, j ) > 0 C s,0, j As the starting point, reduce the decreasing difference, and repeat this step until C s,0, j Meet the accuracy requirements; S36, f ( C s,0, j ) > 0, f ' ( C s,0, j ) < 0: set C s,0, j = C s,0, j + C add Make C s,0, j satisfy f ( C s,0, j ) > 0, f ' ( C s,0, j ) > 0, jump back to step S35; S37, f ( C s,0, j ) is an imaginary number: C s,0, j = C s,0, j + C add Make C s,0, j satisfy f ( C s,0, j ) > 0, f ' ( C s,0, j ) > 0, jump back to step S35; S38, f ( C s,0, j ) = 0: C s,0, j = C s,0, j-1 Established.

4. The method for calculating lithium concentration of active material particles in lithium ion batteries based on a lithium concentration-stress coupling model according to claim 1, characterized in that: In S4, equations 3 and 5 are used to solve the non-central lithium concentration of the active material particles of the lithium ion battery.

5. The method for calculating lithium concentration of active material particles in lithium ion batteries based on a lithium concentration-stress coupling model according to claim 1, characterized in that: S2-S4 are executed by a computing device.

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