Bipolar carrier model-based charge density estimation method in direct current bushing

Abstract

The invention discloses a method for estimating the density of charges in a direct current bushing based on a bipolar carrier model, and the method comprises the following steps: S1, carrying out the calculation to obtain the simulation parameters of the direct current bushing, the simulation parameters comprise hole injection current density, electron injection current density, hole electron extraction current density, free electron density, sunken electron density, free hole density and sunken hole density; s2, obtaining a direct-current bushing simulation model by utilizing bushing high-voltage simulation software according to the simulation parameters; and S3, calculating the space charge density CU, T of the direct current bushing by using the data in the direct current bushing simulation model. The method for estimating the charge density in the direct current bushing based on the bipolar carrier model solves the problem that simulation parameter calculation cannot be realized in the prior art.

Description

Technical Field

[0001] The invention relates to the field of charge density estimation, and in particular to a method for estimating charge density in a DC bushing based on a bipolar carrier model. Background Art

[0002] The Chinese patent discloses a method and related device for calculating the transient electric field and charge distribution at the gas-solid interface of the bushing with application number CN202311111693.7. The method comprises: applying a DC voltage to the high-voltage conductor in the two-dimensional axisymmetric model of the bushing to calculate the steady-state AC electric field distribution at the initial moment; then drawing the electric lines at the gas-solid interface of the bushing; calculating the effective volume enclosed by every two electric lines and the surface area of ​​the corresponding gas-solid interface obtained by dividing the corresponding two electric lines; determining the position of the gas-side current density corresponding to each surface according to the position of the two electric lines that determine the size of each surface area on the surface of the insulator, and calculating the current density flowing into the gas side of all surfaces; then establishing the interface charge density equation on the dielectric interface; combining the electrostatic field equations to iteratively calculate the transient electric field and charge distribution at the gas-solid interface of the bushing.

[0003] Although the above-mentioned method for calculating the transient electric field and charge distribution at the gas-solid interface of the bushing of the present invention can solve the problem of the difficulty in convergence of the interface charge simulation calculation of the large bushing gas-solid insulation composite system, the method for calculating the transient electric field and charge distribution at the gas-solid interface of the bushing and the related device still have the disadvantage that it is not possible to first calculate the simulation parameters and then calculate the simulation model of the DC bushing based on the calculated simulation parameters. Summary of the invention

[0004] The present invention aims to provide a method for estimating the charge density in a DC bushing based on a bipolar carrier model, so as to solve the problem that simulation parameter calculation cannot be realized in the prior art.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] The present invention discloses a method for estimating charge density in a DC bushing based on a bipolar carrier model. The object of the method for estimating charge density in a DC bushing based on a bipolar carrier model is a DC bushing. The DC bushing comprises: an annular shell and a cylindrical core, the annular shell is a cathode, the cylindrical core is an anode, the annular shell surrounds the cylindrical core, a filling cavity is formed between the annular shell and the cylindrical core, and the filling cavity is filled with SF6 gas;

[0007] The method for estimating the charge density in a DC bushing based on a bipolar carrier model comprises the following steps:

[0008] S1. Calculate and obtain the simulation parameters of the DC bushing, including: hole injection current density j h (x=d,t), electron injection current density j e (x=0,t), hole-electron extraction current density j ext , free electron density s1, trapped electron density s2, free hole density s3 and trapped hole density s4;

[0009] S2. Using bushing high voltage simulation software according to simulation parameters, obtain a DC bushing simulation model;

[0010] S3. Calculate the space charge density C of the DC bushing using the data in the DC bushing simulation model U,T .

[0011] Preferably, step S1 comprises the following steps:

[0012] S11. Based on the bipolar carrier model, the hole injection current density j of the DC bushing is calculated according to the Schottky theorem. h (x=d,t) and the electron injection current density j e (x=0,t),j h (x=d,t) and j e The unit of (x=0,t) is A / m 2 ;j h (x=d,t) and j e (x=0,t) The calculation formula is:

[0013]

[0014] In the above formula, A is the Richardson constant, which is related to the properties of the cathode and anode materials; E(x=0,t) is the electric field strength at the anode interface, in V / m; E(x=d,t) is the electric field strength at the cathode interface, in V / m, where d represents the inner radius from the cathode to the anode; e=1.6×10 -19 C, and e is the charge of the electron; w h is the hole injection barrier, w e Electron injection barrier, w h and w e The unit is eV; k is the Boltzmann constant, and the unit of k is eV / K; T is the temperature, and the unit of T is K; ε is the dielectric constant.

[0015] Preferably, step S1 further comprises the following steps:

[0016] S12. Assuming that the carrier extraction current is proportional to the carrier mobility, the hole-electron extraction current density j ext The calculation formula is as follows:

[0017] j ext =C ext neμE

[0018] In the above formula, μ is the carrier mobility, and the unit of μ is m 2 / (V·s); n is the carrier number density, and the unit of n is m -3 ; C ext is the extraction coefficient, C ext The value range is from 0 to 1, where 0 means that no carrier extraction occurs and 1 means that there is no extraction barrier at the electrode; E is the electric field strength.

[0019] Preferably, step S1 further comprises the following steps:

[0020] S13, calculate the free electron density s1, trapped electron density s2, free hole density s3 and trapped hole density s4, the formula is as follows:

[0021]

[0022]

[0023] In the above formula, n eμ is the electron number density in the migration state, n hμ is the hole number density in the migration state; n et is the hole number density in the trap, n ht is the hole number density in the trap; n et,0 is the electron trap number density, n ht,0 is the hole trap number density; B e is the free electron trapping coefficient, B h is the free hole trapping coefficient; D e is the trapped electron detrapping coefficient, D h is the trapped hole detrapping coefficient.

[0024] Preferably, step S3 comprises the following steps:

[0025] S31, let the temperature translation factor be α T , temperature shift factor α T Represents the relationship between space charge density and temperature T; let the voltage shift factor be β U , voltage shift factor β U It represents the relationship between space charge density and injection voltage U;

[0026] S32. Establish and calculate the temperature translation factor α T The formula is:

[0027]

[0028] In the above formula, temperature T has M temperature values, t i-1 represents the i-1th temperature value, t i Indicates the i-th temperature value; C peek(i-1) represents the maximum value of space charge density at the i-1th temperature value; C peek(i) represents the maximum value of space charge density at the i-th temperature value;

[0029] S33, establish and calculate voltage translation factor β U The formula is:

[0030]

[0031] In the above formula, the injected voltage U has N voltage values, u j-1 represents the j-1th voltage value, u j represents the jth voltage value; C peek(j-1) represents the maximum value of space charge density at the j-1th voltage value; C peek(j) Indicates the maximum value of space charge density at the jth temperature value;

[0032] S34, using M known temperature values ​​and M known C peek(i) Fitting formula 1, we get α T ; Using N known temperature values ​​and N known C peek(j) Fitting formula 2, we get β U ;

[0033] S35. Establish the space charge density C under the combined action of temperature and voltage U,T Estimation formula, the estimation formula is:

[0034] C U,T =α T β T C peek(ij)

[0035] In the above formula, C peek(ij) Indicates the maximum value of space charge density at the i-th temperature value and the j-th voltage value.

[0036] Compared with the prior art, the present invention has the following beneficial effects:

[0037] In the present application, firstly, by establishing a simulation parameter calculation formula, the simulation parameters of the DC bushing are calculated; then, according to the calculated simulation parameters, the DC bushing high voltage simulation software is simulated to obtain a DC bushing simulation model; through the DC bushing simulation model, the maximum value C of the space charge density under the conditions of M known temperature values ​​and N known temperature values ​​can be obtained through the bushing high voltage simulation software. peek(ij) , so as to establish the space charge density C under the combined action of temperature and voltage.U,T The estimation formula is ready. Finally, in this application, the relationship between temperature and the maximum value of space charge density is analyzed through the simulation model, and the temperature translation factor α is calculated. T The relationship between the injection voltage and the maximum space charge density was analyzed, and the voltage shift factor β was calculated. U , and finally established the temperature translation factor α T and the temperature shift factor β U The associated space charge density C U,T The estimation formula lays a foundation for the charge analysis of DC bushings.

[0038] Other advantages, objectives and features of the present invention will be embodied in part through the following description, and in part will be understood by those skilled in the art through study and practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is a schematic diagram of the structure of the DC bushing.

[0040] Figure 2 This is a cross-sectional view of the DC bushing. DETAILED DESCRIPTION

[0041] In order to make the technical means, creative features, objectives and functions of the present invention clearer and easier to understand, the present invention is further described below in conjunction with the accompanying drawings and specific embodiments:

[0042] like Figure 1 as well as Figure 2 As shown, the present invention discloses a method for estimating charge density in a DC bushing based on a bipolar carrier model. The object of the method for estimating charge density in a DC bushing based on a bipolar carrier model is a DC bushing. The DC bushing comprises: an annular shell and a cylindrical core, the annular shell is a cathode, the cylindrical core is an anode, the annular shell surrounds the cylindrical core, a filling cavity is formed between the annular shell and the cylindrical core, and the filling cavity is filled with SF6 gas;

[0043] The method for estimating the charge density in a DC bushing based on a bipolar carrier model comprises the following steps:

[0044] S1. Calculate and obtain the simulation parameters of the DC bushing, including: hole injection current density j h (x=d,t), electron injection current density j e (x=0,t), hole-electron extraction current density j ext , free electron density s1, trapped electron density s2, free hole density s3 and trapped hole density s4;

[0045] S2. Using bushing high voltage simulation software according to simulation parameters, obtain a DC bushing simulation model;

[0046] S3. Calculate the space charge density C of the DC bushing using the data in the DC bushing simulation model U,T .

[0047] Step S1 includes the following steps:

[0048] S11. Based on the bipolar carrier model, the hole injection current density j of the DC bushing is calculated according to the Schottky theorem. h (x=d,t) and the electron injection current density j e (x=0,t),j h (x=d,t) and j e The unit of (x=0,t) is A / m 2 ;j h (x=d,t) and j e (x=0,t) The calculation formula is:

[0049]

[0050] In the above formula, A is the Richardson constant, which is related to the properties of the cathode and anode materials; E(x=0,t) is the electric field strength at the anode interface, in V / m; E(x=d,t) is the electric field strength at the cathode interface, in V / m, where d represents the inner radius from the cathode to the anode; e=1.6×10 -19 C, and e is the charge of the electron; w h is the hole injection barrier, w e Electron injection barrier, w h and w e The unit is eV; k is the Boltzmann constant, and the unit of k is eV / K; T is the temperature, and the unit of T is K; ε is the dielectric constant.

[0051] Step S1 also includes the following steps:

[0052] S12. Assuming that the carrier extraction current is proportional to the carrier mobility, the hole-electron extraction current density j ext The calculation formula is as follows:

[0053] j ext =C ext neμE

[0054] In the above formula, μ is the carrier mobility, and the unit of μ is m 2 / (V·s); n is the carrier number density, and the unit of n is m -3 ; C ext is the extraction coefficient, C extThe value range is from 0 to 1, where 0 means that no carrier extraction occurs and 1 means that there is no extraction barrier at the electrode; E is the electric field strength.

[0055] Step S1 also includes the following steps:

[0056] S13, calculate the free electron density s1, trapped electron density s2, free hole density s3 and trapped hole density s4, the formula is as follows:

[0057]

[0058] In the above formula, n eμ is the electron number density in the migration state, n hμ is the hole number density in the migration state; n et is the hole number density in the trap, n ht is the hole number density in the trap; n et,0 is the electron trap number density, n ht,0 is the hole trap number density; B e is the free electron trapping coefficient, B h is the free hole trapping coefficient; D e is the trapped electron detrapping coefficient, D h is the trapped hole detrapping coefficient.

[0059] Step S3 includes the following steps:

[0060] S31, let the temperature translation factor be α T , temperature shift factor α T Represents the relationship between space charge density and temperature T; let the voltage shift factor be β U , voltage shift factor β U It represents the relationship between space charge density and injection voltage U;

[0061] S32. Establish and calculate the temperature translation factor α T The formula is:

[0062]

[0063] In the above formula, temperature T has M temperature values, t i-1 represents the i-1th temperature value, t i Indicates the i-th temperature value; C peek(i-1) represents the maximum value of space charge density at the i-1th temperature value; C peek(i) represents the maximum value of space charge density at the i-th temperature value;

[0064] S33, establish and calculate voltage translation factor β U The formula is:

[0065]

[0066] In the above formula, the injected voltage U has N voltage values, u j-1 represents the j-1th voltage value, u j represents the jth voltage value; C peek(j-1) represents the maximum value of space charge density at the j-1th voltage value; C peek(j) Indicates the maximum value of space charge density at the jth temperature value;

[0067] S34, using M known temperature values ​​and M known C peek(i) Fitting formula 1, we get α T ; Using N known temperature values ​​and N known C peek(j) Fitting formula 2, we get β U ;

[0068] S35. Establish the space charge density C under the combined action of temperature and voltage U,T Estimation formula, the estimation formula is:

[0069] C U,T =α T β T C peek(ij)

[0070] In the above formula, C peek(ij) Indicates the maximum value of space charge density at the i-th temperature value and the j-th voltage value.

[0071] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution of the present invention, which should be included in the scope of the claims of the present invention.

Claims

1. A method for estimating charge density in a DC bushing based on a bipolar carrier model, characterized in that: The object of the charge density estimation method in a DC bushing based on a bipolar carrier model is a DC bushing, which includes: an annular shell and a cylindrical core, the annular shell is a cathode, the cylindrical core is an anode, the annular shell surrounds the cylindrical core, a filling cavity is formed between the annular shell and the cylindrical core, and the filling cavity is filled with SF6 gas; The method for estimating the charge density in a DC bushing based on a bipolar carrier model comprises the following steps: S1. Calculate and obtain the simulation parameters of the DC bushing, including: hole injection current density j h (x=d,t), electron injection current density j e (x=0,t), hole-electron extraction current density j ext , free electron density s1, trapped electron density s2, free hole density s3 and trapped hole density s4; S2. Using bushing high voltage simulation software according to simulation parameters, obtain a DC bushing simulation model; S3. Calculate the space charge density C of the DC bushing using the data in the DC bushing simulation model U,T .

2. The method for estimating charge density in a DC bushing based on a bipolar carrier model according to claim 1, characterized in that: Step S1 includes the following steps: S11. Based on the bipolar carrier model, the hole injection current density j of the DC bushing is calculated according to the Schottky theorem. h (x=d,t) and the electron injection current density j e (x=0,t),j h (x=d,t) and j e The unit of (x=0,t) is A / m 2 ;j h (x=d,t) and j e (x=0,t) The calculation formula is: In the above formula, A is the Richardson constant, which is related to the properties of the cathode and anode materials; E(x=0,t) is the electric field strength at the anode interface, in V / m; E(x=d,t) is the electric field strength at the cathode interface, in V / m, where d represents the inner radius from the cathode to the anode; e=1.6×10 -19 C, and e is the charge of the electron; w h is the hole injection barrier, w e Electron injection barrier, w h and w e The unit is eV; k is the Boltzmann constant, and the unit of k is eV / K; T is the temperature, and the unit of T is K; ε is the dielectric constant.

3. The method for estimating charge density in a DC bushing based on a bipolar carrier model according to claim 2, characterized in that: Step S1 also includes the following steps: S12. Assuming that the carrier extraction current is proportional to the carrier mobility, the hole-electron extraction current density j ext The calculation formula is as follows: I ext =C ext neμE In the above formula, μ is the carrier mobility, and the unit of μ is m 2 / (V·s); n is the carrier number density, and the unit of n is m -3 ; C ext is the extraction coefficient, C ext The value range is from 0 to 1, where 0 means that no carrier extraction occurs and 1 means that there is no extraction barrier at the electrode; E is the electric field strength.

4. The method for estimating charge density in a DC bushing based on a bipolar carrier model according to claim 3, characterized in that: Step S1 also includes the following steps: S13, calculate the free electron density s1, trapped electron density s2, free hole density s3 and trapped hole density s4, the formula is as follows: In the above formula, n eμ is the electron number density in the migration state, n hμ is the hole number density in the migration state; n et is the hole number density in the trap, n ht is the hole number density in the trap; n et, 0 is the electron trap number density, n ht, 0 is the hole trap number density; B e is the free electron trapping coefficient, B h is the free hole trapping coefficient; D e is the trapped electron detrapping coefficient, D h is the trapped hole detrapping coefficient.

5. The method for estimating charge density in a DC bushing based on a bipolar carrier model according to claim 4, characterized in that: Step S3 includes the following steps: S31, let the temperature translation factor be α T , temperature shift factor α T Represents the relationship between space charge density and temperature T; let the voltage shift factor be β U , voltage shift factor β U It represents the relationship between space charge density and injection voltage U; S32. Establish and calculate the temperature translation factor α T The formula is: In the above formula, temperature T has M temperature values, t i-1 represents the i-1th temperature value, t i Indicates the i-th temperature value; C peek(i-1) represents the maximum value of space charge density at the i-1th temperature value; C peek(i) represents the maximum value of space charge density at the i-th temperature value; S33, establish and calculate voltage translation factor β U The formula is: In the above formula, the injected voltage U has N voltage values, u j-1 represents the j-1th voltage value, u j represents the jth voltage value; C peek(j-1) represents the maximum value of space charge density at the j-1th voltage value; C peek(j) Indicates the maximum value of space charge density at the jth temperature value; S34, using M known temperature values ​​and M known C peek(i) Fitting formula 1, we get α T ; Using N known temperature values ​​and N known C peek(j) Fitting formula 2, we get β U ; S35. Establish the space charge density C under the combined action of temperature and voltage U,T Estimation formula, the estimation formula is: C U,T =a T b T C peek(ij) In the above formula, C peek(ij) Indicates the maximum value of space charge density at the i-th temperature value and the j-th voltage value.

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