Direct current bushing electric field calculation method and device considering charge accumulation effect

Abstract

The invention discloses a direct current bushing electric field calculation method and device considering a charge accumulation effect. The method comprises the following steps: establishing a mathematical model and boundary conditions by considering four current carriers of trap electrons, trap holes, free electrons and free holes and four recombination processes of free electron-free holes, trap electron-free holes, free electron-trap holes and trap electron-trap holes existing in an insulating material of the direct current bushing; and in combination with the boundary conditions, solving the mathematical model by adopting a finite element algorithm to obtain charge distribution and electric field distribution in the direct current bushing under the action of an external electric field. According to the method, the electric field in the sleeve can be accurately calculated, and a basis is provided for accurate evaluation of the equipment operation state.

Description

Technical Field

[0001] The invention belongs to the technical field of direct current transmission systems, and in particular relates to a method and device for numerically calculating internal electric charge and electric field of a direct current bushing with high precision. Background Art

[0002] High-voltage DC bushing is one of the key equipment in AC / DC hybrid power grid. To ensure the normal operation of the power system, it is necessary to accurately calculate the electric field inside the DC bushing in order to evaluate its operating status and avoid equipment failure.

[0003] The current DC bushing electric field calculation is mainly based on traditional electric field theory, such as Gauss's law or Coulomb's law, and is combined with common numerical calculation methods such as finite element, finite difference, and charge simulation for calculation. It is usually assumed that the insulating medium in the bushing is in an ideal state, and then the electric field theory is used for calculation. However, in the process of DC bushing electric field calculation, most of them fail to fully consider the impact of charge accumulation effect in the bushing on the electric field distribution. The few methods that consider charge accumulation only consider the surface charge at the interface based on Poisson's equation, resulting in certain errors in the calculation results, which cannot meet the needs of accurate evaluation of the operating status of DC bushings.

[0004] Therefore, there is an urgent need for a DC bushing electric field calculation method and device that takes into account the charge accumulation effect, so as to achieve accurate calculation of the electric field inside the bushing and provide a basis for accurate evaluation of the equipment operating status. Summary of the invention

[0005] In order to address the problem that the existing technology does not fully consider the influence of the charge accumulation effect inside the bushing on the electric field distribution and the electric field calculation error is large, this method provides a DC bushing electric field calculation method and device taking the charge accumulation effect into consideration, thereby achieving accurate calculation of the electric field inside the bushing and effectively improving the accuracy of equipment status assessment.

[0006] According to a first aspect of the present invention, a method for calculating the electric field of a DC bushing taking into account the charge accumulation effect is provided. The method comprises the following steps:

[0007] By considering the four types of carriers, namely trapped electrons, trapped holes, free electrons and free holes, and the four recombination processes, namely free electron-free hole, trapped electron-free hole, free electron-trapped hole and trapped electron-trapped hole, existing in the insulating material of the DC bushing, a mathematical model and boundary conditions are established; the mathematical model includes: a carrier injection model, a carrier extraction model, a carrier transport model and a recombination reaction model; the boundary conditions include: a carrier injection boundary condition, a carrier extraction boundary condition, a current limiting boundary condition and a multilayer dielectric boundary condition;

[0008] In combination with the boundary conditions, the mathematical model is solved using a finite element algorithm to obtain the charge distribution and electric field distribution inside the DC bushing under the action of an external electric field.

[0009] Furthermore, the establishment of the carrier injection model includes the following steps:

[0010] Set the threshold value of electric field strength at the metal electrode of DC bushing specimen;

[0011] When the electric field strength at the metal electrode does not exceed the threshold, the current density J formed by the carriers injected into the insulating material at the metal electrode is determined according to the Schottky law. in Expression of

[0012] When the electric field strength at the metal electrode exceeds the threshold, J is determined according to the injection barrier constant between the metal electrode and the insulating material. in expression.

[0013] Furthermore, when the electric field strength at the metal electrode does not exceed the threshold, J in The expression is:

[0014]

[0015] When the electric field strength at the metal electrode exceeds the threshold, J in The expression is:

[0016]

[0017] Among them, J in is the current density formed by the carriers injected into the insulation at the metal electrode; A is the de Siemens constant; T is the absolute temperature of the environment; w ei / hi is the potential barrier that carriers need to overcome when entering the insulating material from the electrode metal; K is the Boltzmann constant; E is the external electric field strength at the metal electrode; e is the charge carried by a single electron; ε is the dielectric constant of the sample; A ei / hi , B ei / hi are the constants of the injection barrier between the electrode metal and the insulating material, respectively.

[0018] Furthermore, the establishment of the carrier extraction model includes the following steps:

[0019] According to the experimental data, the expression of carrier extraction coefficient varying with electric field intensity, carrier concentration and temperature is obtained by using multi-dimensional Lagrangian interpolation method.

[0020] The carrier mobility is fitted by integrating the gradient descent method and the Gauss-Newton method, and the mobility expression is obtained;

[0021] Based on the carrier extraction coefficient expression and the mobility expression, the expression of the carrier extraction current density is determined to obtain the carrier extraction model.

[0022] Furthermore, the expression of the carrier extraction current density is:

[0023]

[0024] In the formula, C e / h (E,n e / h ,T) is the expression of carrier extraction coefficient, μ e / h is the mobility expression; f j is the extraction coefficient in the experimental data; E,n e / h , T are the corresponding field intensity, carrier concentration and absolute temperature respectively; E j ,n e / hj ,T j are the corresponding field strength, carrier concentration and absolute temperature in the experimental data respectively; k is the number of samples in the experimental data; e is the charge carried by a single electron; a, b, c are the first, second and third mobility fitting coefficients respectively.

[0025] Furthermore, the establishment of the carrier transport model includes establishing a conduction equation, a Poisson equation and a current continuity equation;

[0026] The conduction equation is:

[0027]

[0028] In the formula, J e and J h are the electron and hole conduction current densities respectively; e is the charge carried by a single electron; E(x,t) is the electric field intensity distribution about position x and time t; n eμ and n hμ are the number of electrons and holes that can migrate per unit volume; D f is the diffusion coefficient; a, b, c are the first, second and third mobility fitting coefficients respectively; T is the absolute temperature;

[0029] The Poisson equation is:

[0030]

[0031] Where V(x) is the electric potential; n ht 、n et They represent the number of trapped holes and trapped electrons per unit volume respectively; ε0 and ε r are the vacuum dielectric constant and relative dielectric constant, respectively;

[0032] The current continuity equation is:

[0033]

[0034] In the formula, s eμ 、s hμ 、s et 、s ht They represent the density changes of free electrons, free holes, trapped electrons, and trapped holes caused by carrier migration behavior; DD eμ , D.D. hμ are the diffusion coefficients of free electrons and free holes, respectively.

[0035] Further, the composite reaction model is expressed as:

[0036]

[0037] Among them, S0, S1, S2, and S3 are the recombination rates of the recombination processes corresponding to free electron-free hole, trapped electron-free hole, free electron-trapped hole, and trapped electron-trapped hole, respectively; D e , D h are the electron detrapping rate and hole detrapping rate respectively; ψ ht , et are the hole barrier height and electron barrier height respectively; n hμ 、n ht 、n eμ 、n et They represent the number of mobile holes, trapped holes, mobile electrons, and trapped electrons per unit volume, respectively.

[0038] Furthermore, the carrier injection boundary condition and the carrier extraction boundary condition are respectively expressed as:

[0039]

[0040]

[0041] in, are the injected electron and hole fluxes respectively; F0 is the Faraday constant; j oe 、j oh are the current densities of electrons and holes calculated by the extraction principle, respectively; represent the extracted electron and hole fluxes, respectively;

[0042] The limiting current boundary condition is expressed as:

[0043]

[0044] Among them, j s The current density is limited by the space charge; is the average electric field strength; d is the material thickness; ε is the dielectric constant of the current medium;

[0045] The multilayer dielectric boundary condition is expressed as:

[0046]

[0047] Among them, E1 and E2 represent the field strength in the two different media on both sides of the interface, ε1 and ε2 are the dielectric constants of the two different media on both sides of the interface, d1 and d2 are the dielectric thicknesses of the two different media on both sides of the interface, δ1 and δ2 are the dielectric conductivity of the two different media on both sides of the interface; ρ is the surface charge density; U is the voltage difference on both sides of the interface.

[0048] According to a second aspect of the present invention, a DC bushing electric field calculation device taking into account the charge accumulation effect using the method described in the first aspect of the present invention is provided. The device comprises:

[0049] A modeling unit is used to establish a mathematical model and boundary conditions by considering four types of carriers, namely trapped electrons, trapped holes, free electrons and free holes, and four types of recombination processes, namely free electron-free hole, trapped electron-free hole, free electron-trapped hole and trapped electron-trapped hole, existing in the insulating material of the DC bushing; the mathematical model includes: a carrier injection model, a carrier extraction model, a carrier transport model and a recombination reaction model; the boundary conditions include: a carrier injection boundary condition, a carrier extraction boundary condition, a limiting current boundary condition and a multilayer dielectric boundary condition;

[0050] A solving unit is used to solve the mathematical model by using a finite element algorithm in combination with the boundary conditions to obtain the charge distribution and electric field distribution inside the DC bushing under the action of an external electric field.

[0051] According to a third aspect of the present invention, a terminal is provided, which includes a processor and a storage medium, wherein the storage medium is used to store instructions, and the processor is used to operate according to the instructions to execute the steps of the method according to the first aspect of the present invention.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] 1. By considering the four carriers of trapped electrons / holes, free electrons / holes, and the four composite processes of free electron-free holes, trapped electron-free holes, free electron-trapped holes, and trapped electron-trapped holes in the insulating material of the DC bushing, a mathematical model and boundary conditions are established. Then, combined with the boundary conditions, the finite element algorithm is used to solve the mathematical model, which can realize the accurate calculation of the charge distribution and electric field in the bushing, and provide support for improving the reliability of the subsequent operation status evaluation of the equipment.

[0054] 2. The extraction coefficient calculated from the experimental data by using the improved Lagrange interpolation method and the corresponding field strength, carrier concentration, temperature and other parameters are fitted to obtain the expression of the extraction coefficient, which can meet the fitting requirements of multidimensional polynomials and improve the accuracy of the extraction coefficient fitting, thereby improving the overall calculation accuracy.

[0055] 3. By considering the influence of temperature and electric field on carrier mobility and integrating the gradient descent method with the Gauss-Newton method to fit the mobility, the accuracy of global and local solutions can be improved while ensuring the convergence speed, avoiding overfitting and underfitting. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a flow chart of the DC bushing electric field calculation method considering the charge accumulation effect in the present invention.

[0057] Figure 2 4 is a geometric model diagram of a DC bushing used in an embodiment of the present invention.

[0058] Figure 3 1 is a diagram of the insulating material structure of a DC bushing in an embodiment of the present invention.

[0059] Figure 4 Schematic diagram of the research part of the DC bushing in the embodiment of the present invention.

[0060] Figure 5 is the calculation result of the charge density inside the DC bushing in the embodiment of the present invention.

[0061] Figure 6 This is a comparison chart of the electric field calculation results with and without considering the charge accumulation effect. DETAILED DESCRIPTION

[0062] In order to make the purpose, technical scheme and advantages of the present invention clearer, the technical scheme of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. The embodiments described in this application are only part of the embodiments of the present invention, not all of them. Based on the spirit of the present invention, other embodiments obtained by ordinary technicians in this field without creative work are all within the scope of protection of the present invention.

[0063] When an external electric field acts on the insulating material, electrons and holes will be injected from the electrode into the insulating material space and move under the action of the electric field. Some free electrons and free holes will be captured by local state traps in the material, and may fall off due to thermal effects. In addition, there is a recombination phenomenon of positive and negative charges during the transport process. All of the above phenomena may cause local electric field distortion inside the bushing, thereby affecting the insulation performance. Therefore, it is necessary to establish a calculation model for the electric field inside the bushing that takes into account the charge accumulation effect.

[0064] To achieve the above purpose, the present invention takes into account the four types of carriers, namely trapped electrons / holes and free electrons / holes, and the four types of recombination processes, namely free electron-free holes, trapped electrons-free holes, free electrons-trapped holes, and trapped electrons-trapped holes, and combines finite element solution with mathematical models such as carrier injection, carrier extraction, carrier transport, and recombination reaction to achieve numerical solution of charge distribution and electric field inside the casing under the action of an external electric field. The present invention is described in detail below through specific embodiments.

[0065] Example 1

[0066] This embodiment provides a method for calculating the electric field of a DC bushing taking into account the charge accumulation effect. Figure 1 , the method comprises the following steps:

[0067] Step 1. By considering the four carriers of trapped electrons, trapped holes, free electrons and free holes existing in the insulating material of the DC bushing and the four recombination processes of free electron-free hole, trapped electron-free hole, free electron-trapped hole and trapped electron-trapped hole, a mathematical model and boundary conditions are established; the mathematical model includes: a carrier injection model, a carrier extraction model, a carrier transport model and a recombination reaction model; the boundary conditions include: a carrier injection boundary condition, a carrier extraction boundary condition, a limiting current boundary condition and a multilayer dielectric boundary condition.

[0068] ①Carrier injection model:

[0069] The establishment of the carrier injection model includes the following steps:

[0070] Step A1, setting a threshold value of the electric field strength applied to the DC bushing sample at the metal electrode;

[0071] Step A2: When the applied electric field strength at the metal electrode does not exceed the threshold, the current density J formed by the carriers injected into the insulating material at the metal electrode is determined according to the Schottky law. in Expression of

[0072] Step A3: When the electric field strength at the metal electrode exceeds the threshold, J is determined based on the injection barrier constant between the metal electrode and the insulating material. in expression.

[0073] As an example, in this embodiment, the electric field strength of 100 kV / mm is used as the threshold. When the electric field strength applied at the metal electrode does not exceed 100 kV / mm, the process of carriers entering the insulating material from the metal electrode follows the Schottky law:

[0074]

[0075] In the formula, J in It is the current density formed by the carriers injected into the insulating material at the metal electrode, in A / m 2 ; A is the de Simen constant (Richardson constant), which is 1.2×10 6 A / (m 2 ·K 2 ), T is the absolute temperature of the environment, in K; w ei / hi It is the potential barrier that carriers (electrons / holes) need to overcome when entering the insulating material from the electrode metal, and the unit is J; K is the Boltzmann constant, and the value is 1.38×10 -23 J / K; E is the electric field strength of the sample near the electrode metal, in V / m; e is the charge carried by a single electron, which is 1.602×10 -19 C; ε is the dielectric constant of the sample, in F / m.

[0076] When the electric field strength applied to the metal electrode is greater than 100kV / mm,

[0077]

[0078] In the formula, A ei / hi , B ei / hi are the constants of the injection barrier between the electrode metal and the insulating material, respectively.

[0079] ②Carrier extraction model:

[0080] The establishment of the carrier extraction model includes the following steps:

[0081] Step B1: Based on the experimental data, the multi-dimensional Lagrangian interpolation method is used to fit the expression of the carrier extraction coefficient that varies with the electric field intensity, carrier concentration and temperature.

[0082] Specifically, the extraction of carriers usually needs to consider overcoming the interface potential barrier. In order to improve the calculation efficiency, the extraction coefficient is often used to reflect the process of overcoming the interface potential barrier during the carrier extraction process. As shown in the following formula:

[0083] J out =C e / h eμ e / h n e / h E (3)

[0084] In the formula, J out is the current density due to the carriers being drawn from the interface between the insulator and the metal electrode, E is the electric field strength, μ e / h is the electron / hole mobility, n e / h is the electron / hole carrier density, C e / h is the extraction coefficient.

[0085] Since the extraction coefficient is related to multiple parameters such as the electric field, carrier concentration, and temperature in the environment, the inherent extraction coefficient will lead to large calculation errors. The extraction coefficient calculated based on the experimental data and the corresponding field strength, carrier concentration, temperature and other parameters are fitted to obtain the expression of the extraction coefficient. The Lagrangian interpolation method is used to fit the coefficient. The conventional Lagrangian interpolation method is only for one-dimensional variables, so it needs to be improved to meet the fitting requirements of multidimensional polynomials.

[0086]

[0087] In the formula, C e / h (E,n e / h ,T) is the expression of carrier extraction coefficient; f j is the extraction coefficient obtained from the test; E,n e / h , T are the corresponding field intensity, carrier concentration and absolute temperature respectively; E j ,n e / hj ,T j are the corresponding field strength, carrier concentration and absolute temperature in the experimental data respectively; k is the number of samples of the experimental data.

[0088] Step B2: Fitting the carrier mobility by integrating the gradient descent method and the Gauss-Newton method to obtain a mobility expression.

[0089] Specifically, considering the influence of temperature and electric field on carrier mobility, to ensure the accuracy of calculation, the carrier mobility μ e / h Formula (5) is used as the objective function.

[0090]

[0091] Where a, b, c are the first, second and third mobility fitting coefficients respectively; T is the absolute temperature.

[0092] The fitting coefficients are calculated. The present invention integrates the gradient descent method and the Gauss-Newton method for fitting, which can improve the accuracy of global and local solutions while ensuring the convergence speed and avoid overfitting and underfitting, as shown in formulas (6) and (7).

[0093]

[0094] In the formula, a k The parameter vector of the kth iteration can be expressed as the vector [a, b, c] of the three parameters to be fitted a, b, c in (5), E is the unit matrix, r k is the residual function, t(p k ) represents the function value obtained by the parameter after the kth iteration, t r represents the observed value, λ is the adjustment parameter, which increases with the increase of the absolute value of the residual value and decreases with the decrease of the absolute value of the residual value. It can maintain a high convergence speed and improve efficiency when the residual is small, and improve stability when the residual is large to avoid oscillation near the local optimal solution. Its initial value is set to 0.02, and R is the Jacobian matrix of the residual function to the residual vector, as shown in formula (7).

[0095] Step B3: Based on the carrier extraction coefficient expression and the mobility expression, determine the expression of the carrier extraction current density to obtain the carrier extraction model.

[0096] Among them, the carrier extraction current density can be rewritten as follows:

[0097]

[0098] ③Carrier transport model:

[0099] The carrier transport process can be expressed by three major equations: conduction equation, current continuity equation and Poisson's equation.

[0100] Take the flat plate sample as an example:

[0101] Conduction equation:

[0102]

[0103] In the formula, J e and J h are the electron and hole conduction current densities respectively; e is the charge carried by a single electron; E(x,t) is the electric field intensity distribution about position x and time t; n eμ and n hμ are the number of electrons and holes that can migrate per unit volume; D f is the diffusion coefficient.

[0104] Poisson's equation:

[0105]

[0106] Where V(x) is the electric potential; n ht 、n et They represent the number of trapped holes and trapped electrons per unit volume respectively; ε0 and ε r are the vacuum dielectric constant and relative dielectric constant respectively. The boundary conditions of Poisson's equation are determined by the grounding electrode and the high voltage electrode, and at the initial moment, the density of all kinds of space charges is 0.

[0107] Current continuity equation:

[0108]

[0109] For different types of carriers, the above equation can be rewritten as:

[0110]

[0111] Where n a is the charge density of the segmentation layer; j a is the current density of electrons and holes, satisfying j a =μ a n a E;s a is the source term, the subscript a represents different carrier types, s eμ 、s hμ 、s et 、s ht Respectively represent the density changes of free electrons, free holes, trapped electrons, and trapped holes caused by carrier migration behavior, and the unit is m -3 ·s -1 ;n hμ 、n ht 、n eμ 、n et Respectively represent the number of mobile holes, trapped holes, mobile electrons, and trapped electrons per unit volume; DD eμ , D.D. hμ are the diffusion coefficients of free electrons and free holes, respectively, in m 2 / s.

[0112] ④Compound reaction model:

[0113] The recombination reaction model is used to describe the four recombination processes of free electron-free hole, trapped electron-free hole, free electron-trapped hole, and trapped electron-trapped hole, which are specifically expressed as follows:

[0114]

[0115] Where S0, S1, S2, and S3 are the recombination rates of the recombination processes corresponding to free electron-free hole, trapped electron-free hole, free electron-trapped hole, and trapped electron-trapped hole, respectively, which can be specified as constants or expressed as a function of charge density and mobility, with the unit of m 3 ·s -1 ;D e , D h are the electron detrapping rate and hole detrapping rate, respectively, in units of 1 / s; ψ ht , et are the hole and electron potential barrier heights, respectively.

[0116] ⑤Boundary conditions:

[0117] As described above, the boundary conditions used in this embodiment include: carrier injection boundary conditions, carrier extraction boundary conditions, current limiting boundary conditions and multi-layer dielectric boundary conditions.

[0118] a. Carrier injection boundary conditions:

[0119] The current density is calculated according to Schottky's theorem, and the charge flux is solved based on it, that is, the charge flux injected into the insulating material is:

[0120]

[0121] In the formula, is the injected electron / hole flux, which indicates the amount of carrier material passing through per unit area, in mol / (m 2 ·s), F0 is Faraday's constant, which is the charge of an electron per unit physical quantity and is 96584C / mol.

[0122] b. Carrier extraction boundary conditions:

[0123] Considering the way the charges near the electrode migrate to the electrode and extract the charges, the outflow rate should be the following, which is similar to the injection equation:

[0124]

[0125] j oe / j oh is the electron / hole current density calculated by the extraction principle, It indicates the amount of carrier material extracted per unit area, in mol / (m 2 ·s).

[0126] c. Limiting current boundary conditions

[0127] When the electric field generated by the space charge reaches equilibrium with the external electric field, the injected current enters a dynamic equilibrium state, and the space charge limited current density approximately satisfies the Mott-Gunet relationship:

[0128]

[0129] j s is the space charge limited current density, in A / m 2 , is the average electric field strength, V / m, and d is the material thickness.

[0130] d. Multilayer dielectric boundary conditions

[0131] Due to the polarization effect, the interface charge of the multilayer dielectric is accumulated. The polarized interface charge can be expressed by the Maxwell-Wagner polarization model, and the interface charge density can be obtained as:

[0132]

[0133] Among them, E1 and E2 represent the field strength in the two different media on both sides of the interface, ε1 and ε2 are the dielectric constants of the two different media on both sides of the interface, d1 and d2 are the dielectric thicknesses of the two different media on both sides of the interface, δ1 and δ2 are the dielectric conductivity of the two different media on both sides of the interface; ρ is the surface charge density; U is the voltage difference on both sides of the interface.

[0134] Step 2: In combination with the boundary conditions, the mathematical model is solved using a finite element algorithm to obtain the charge distribution and electric field inside the DC bushing under the action of an external electric field.

[0135] The principle of the finite element algorithm is to discretize the continuous solution area into a set of finite, interconnected units (or "finite elements") and approximate the solution on each unit to approximately solve the problem of the entire continuum. These units can be of various shapes, such as triangles, quadrilaterals, hexahedrons, etc., depending on the nature of the problem to be solved and the geometry of the solution domain. In each unit, the unknown field function to be solved in the solution domain is represented by an assumed approximate function. This approximate function is usually represented by the numerical interpolation function of the unknown field function and its derivatives at each node of the unit.

[0136] At present, the finite element algorithm can be used with the help of ABQUS, ADINA, ANSYS and other software for auxiliary calculation. The specific calculation process will not be repeated here.

[0137] In this embodiment, as an example, a 800kv DC bushing model is calculated. Figure 2As shown, the voltage is set to 800*sin(0.02*pi*t)kV, the initial temperature is 25℃, and electromagnetic heating is ignored. The calculation results are shown below.

[0138] In such Figure 2 In the bushing geometric model shown in FIG. 1 , the insulating material therein adopts a RIP (Resin Impregnated Paper) structure, which is an insulating structure widely used in electrical equipment and is also a layered structure. The insulating material therein, namely the RIP structure, is as shown in FIG. Figure 3 As shown, it is a hierarchical structure.

[0139] In order to verify the calculation reliability of the model in the insulating material, the middle section of the insulating material is selected for analysis, such as Figure 4 shown.

[0140] right Figure 4 The charge density is calculated at the selected cross section, and the charge density change of the insulating material is obtained as follows: Figure 5 As shown, the height of the area drawn in the figure represents the size of the charge density, which realizes the calculation of the charge distribution in the casing.

[0141] Further, in Figure 4 In the radial direction of the cross section selected in the figure, a radial arc is selected to calculate the electric field of the model with and without considering the charge accumulation effect. The electric field results at a certain moment are as follows: Figure 6 As shown in the figure, the lines connecting the squares correspond to the case where charge accumulation is considered, and the lines connecting the dots correspond to the case where charge accumulation is not considered. It can be seen that due to the charge accumulation effect, obvious electric field distortion occurs in the local area of ​​the casing, which is consistent with the actual situation and proves the reliability of the model.

[0142] It can be seen that in this embodiment, by considering the four carriers of trapped electrons / holes, free electrons / holes and the four composite processes of free electron-free holes, trapped electrons-free holes, free electrons-trapped holes, and trapped electrons-trapped holes in the insulating material of the DC bushing, a mathematical model and boundary conditions are established, and then combined with the boundary conditions, the finite element algorithm is used to solve the mathematical model, which can achieve accurate calculation of the charge distribution and electric field in the bushing, thereby providing support for improving the reliability of subsequent operation status evaluation of the equipment.

[0143] Example 2

[0144] Embodiment 2 of the present invention provides a DC bushing electric field calculation device taking into account the charge accumulation effect using the method described in Embodiment 1. The device comprises:

[0145] A modeling unit is used to establish a mathematical model and boundary conditions by considering four types of carriers, namely trapped electrons, holes, free electrons and free holes, and four types of recombination processes, namely free electron-free hole, trapped electron-free hole, free electron-trapped hole and trapped electron-trapped hole, existing in the insulating material of the DC bushing; the mathematical model includes: a carrier injection model, a carrier extraction model, a carrier transport model and a recombination reaction model; the boundary conditions include: a Poisson equation boundary condition, a carrier injection boundary condition, a carrier extraction boundary condition, a limiting current boundary condition and a multilayer dielectric boundary condition;

[0146] A solving unit is used to solve the mathematical model by using a finite element algorithm in combination with the boundary conditions to obtain the charge distribution and electric field distribution inside the DC bushing under the action of an external electric field.

[0147] Example 3

[0148] Embodiment 3 of the present invention provides a computer-readable storage medium.

[0149] The computer-readable storage medium stores a program thereon, and when the program is executed by a processor, the steps in the DC bushing electric field calculation method considering the charge accumulation effect as described in Embodiment 1 of the present invention are implemented.

[0150] The detailed steps are the same as the DC bushing electric field calculation method considering the charge accumulation effect provided in Example 1, and will not be repeated here.

[0151] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents, and any modifications or equivalent replacements that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A DC bushing electric field calculation method considering charge accumulation effect, characterized in that: The steps include: By considering the four types of carriers, namely trapped electrons, trapped holes, free electrons and free holes, as well as the four recombination processes, namely free electron-free hole, trapped electron-free hole, free electron-trapped hole and trapped electron-trapped hole, the mathematical model and boundary conditions are established. The mathematical model includes: a carrier injection model, a carrier extraction model, a carrier transport model and a composite reaction model; the boundary conditions include: a carrier injection boundary condition, a carrier extraction boundary condition, a limiting current boundary condition and a multilayer dielectric boundary condition; In combination with the boundary conditions, the mathematical model is solved using a finite element algorithm to obtain the charge distribution and electric field distribution inside the DC bushing under the action of an external electric field.

2. The DC bushing electric field calculation method considering charge accumulation effect according to claim 1 is characterized in that: The establishment of the carrier injection model comprises the following steps: Set the threshold value of the electric field strength applied to the metal electrode of the DC bushing sample; When the applied electric field strength at the metal electrode does not exceed the threshold, the current density J formed by the carriers injected into the insulating material at the metal electrode is determined according to the Schottky law. in Expression of When the applied electric field strength at the metal electrode exceeds the threshold, J is determined according to the injection barrier constant between the metal electrode and the insulating material. in expression.

3. The DC bushing electric field calculation method considering charge accumulation effect according to claim 2 is characterized in that: When the electric field strength applied at the metal electrode does not exceed the threshold, J in The expression is: When the electric field strength at the metal electrode exceeds the threshold, J in The expression is: Among them, J in is the current density formed by the carriers injected into the insulation at the metal electrode; A is the de Siemens constant; T is the absolute temperature of the environment; w ei / hi is the potential barrier that carriers need to overcome when entering the insulating material from the electrode metal; K is the Boltzmann constant; E is the external electric field strength at the metal electrode; e is the charge carried by a single electron; ε is the dielectric constant of the sample; A ei / hi , B ei / hi are the constants of the injection barrier between the electrode metal and the insulating material, respectively.

4. The DC bushing electric field calculation method considering charge accumulation effect according to claim 1 is characterized in that: The establishment of the carrier extraction model includes the following steps: According to the experimental data, the multi-dimensional Lagrangian interpolation method is used to fit the expression of carrier extraction coefficient that varies with electric field intensity, carrier concentration and temperature. The carrier mobility is fitted by integrating the gradient descent method and the Gauss-Newton method, and the mobility expression is obtained; Based on the carrier extraction coefficient expression and the mobility expression, the expression of the carrier extraction current density is determined to obtain the carrier extraction model.

5. The DC bushing electric field calculation method considering charge accumulation effect according to claim 4 is characterized in that: The expression of the carrier extraction current density is: In the formula, C e / h (E,n e / h ,T) is the expression of carrier extraction coefficient; f j is the extraction coefficient in the experimental data; E,n e / h , T are the corresponding field intensity, carrier concentration and absolute temperature respectively; E j ,n e / hj ,T j are the corresponding field strength, carrier concentration and absolute temperature in the experimental data respectively; k is the number of samples in the experimental data; e is the charge carried by a single electron; a, b, c are the first, second and third mobility fitting coefficients respectively.

6. The DC bushing electric field calculation method considering charge accumulation effect according to claim 1, characterized in that: The establishment of the carrier transport model includes establishing a conduction equation, a Poisson equation and a current continuity equation; The conduction equation is: In the formula, J e and J h are the electron and hole conduction current densities respectively; e is the charge carried by a single electron; E(x,t) is the electric field intensity distribution about position x and time t; n eμ and n hμ are the number of electrons and holes that can migrate per unit volume, respectively; D f is the diffusion coefficient; a, b, c are the first, second and third mobility fitting coefficients respectively; T is the absolute temperature; The Poisson equation is: Where V(x) is the electric potential; n ht 、n et They represent the number of trapped holes and the number of trapped electrons per unit volume respectively; ε0 and ε r are the vacuum dielectric constant and relative dielectric constant, respectively; The current continuity equation is: In the formula, s eμ 、s hμ 、s et 、s ht They represent the density changes of free electrons, free holes, trapped electrons, and trapped holes caused by carrier migration behavior; DD eμ , D.D. hμ are the diffusion coefficients of free electrons and free holes, respectively.

7. The DC bushing electric field calculation method considering charge accumulation effect according to claim 1 is characterized in that: The composite reaction model is expressed as: Among them, S0, S1, S2, and S3 are the recombination rates of the recombination processes corresponding to free electron-free hole, trapped electron-free hole, free electron-trapped hole, and trapped electron-trapped hole, respectively; D e , D h are the electron detrapping rate and hole detrapping rate respectively; ψ ht , et are the hole barrier height and electron barrier height respectively; n hμ 、n ht 、n eμ 、n et They represent the number of mobile holes, trapped holes, mobile electrons, and trapped electrons per unit volume, respectively.

8. The DC bushing electric field calculation method considering charge accumulation effect according to claim 1, characterized in that: The carrier injection boundary condition and the carrier extraction boundary condition are respectively expressed as: in, are the injected electron and hole fluxes respectively; F0 is the Faraday constant; j oe 、j oh are the current densities of electrons and holes calculated by the extraction principle, respectively; represent the extracted electron and hole fluxes, respectively; The limiting current boundary condition is expressed as: Among them, j s The current density is limited by the space charge; is the average electric field strength; d is the material thickness; ε is the dielectric constant of the current medium; The multilayer dielectric boundary condition is expressed as: Among them, E1 and E2 represent the field strength in the two different media on both sides of the interface, ε1 and ε2 are the dielectric constants of the two different media on both sides of the interface, d1 and d2 are the dielectric thicknesses of the two different media on both sides of the interface, δ1 and δ2 are the dielectric conductivity of the two different media on both sides of the interface; ρ is the surface charge density; U is the voltage difference on both sides of the interface.

9. A DC bushing electric field calculation device taking into account the charge accumulation effect using the method described in any one of claims 1 to 8, characterized in that: include: A modeling unit is used to establish a mathematical model and boundary conditions by considering four types of carriers, namely, trapped electrons, trapped holes, free electrons, and free holes, and four types of recombination processes, namely, free electron-free hole, trapped electron-free hole, free electron-trapped hole, and trapped electron-trapped hole, existing in the insulating material of the DC bushing; The mathematical model includes: a carrier injection model, a carrier extraction model, a carrier transport model and a composite reaction model; the boundary conditions include: a carrier injection boundary condition, a carrier extraction boundary condition, a limiting current boundary condition and a multilayer dielectric boundary condition; A solving unit is used to solve the mathematical model by using a finite element algorithm in combination with the boundary conditions to obtain the charge distribution and electric field distribution inside the DC bushing under the action of an external electric field.

10. A terminal comprising a processor and a storage medium; characterized in that: The storage medium is used to store instructions; The processor is configured to operate according to the instructions to execute the steps of the method according to any one of claims 1-8.

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