Design method of multi-dimensional function gradient insulator for direct current gas insulated substation

Abstract

The application discloses a design method of a multi-dimensional function gradient insulator for a direct-current (DC) gas insulated substation, and belongs to the technical field of DC gas insulated substations (DC-GIS). The method is based on COMSOL finite element simulation software, and takes the insulator for a DC-GIS as an optimization model. The method aims to optimize the surface DC electric field distribution and control the surface loss, adopts an enumeration method to select different surface nonlinear conductivity parameters, and finally obtains the optimal distribution of the nonlinear conductivity parameters. The method aims to optimize the surface AC electric field distribution, adopts an iteration method to select different bulk dielectric constant distributions, and finally obtains the optimal distribution of the bulk dielectric constant. The design method of the multi-dimensional function gradient insulator for the DC-GIS realizes the optimization of the surface nonlinear conductivity and the bulk dielectric constant distribution of the multi-dimensional function gradient insulator for the DC-GIS, finally designs a multi-dimensional function gradient (MFGM) insulator, and realizes the synergistic regulation and control of the transient-state and steady-state electric fields of the DC-GIS.

Description

Technical Field

[0001] This invention belongs to the field of high-voltage equipment manufacturing, and more specifically, it relates to a design method for multi-dimensional functional gradient insulators for DC gas-insulated substations. Background Technology

[0002] Gas-insulated switchgear (GIS) is a compact, metal-encapsulated switchgear widely used in power systems due to its high reliability, small footprint, and lack of secondary pollution. Epoxy insulators, widely used in GIS, primarily serve to isolate the gas chamber and support high-voltage conductors. The insulation performance of the insulators largely determines the safety and stability of the GIS. However, research has found that electric field distortion around the insulators can cause flashover, which limits the development and application of DC-GIS equipment. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of the prior art and propose a design method for multi-dimensional functional graded insulators for DC gas-insulated substations. This method optimizes the distribution of nonlinear conductivity and bulk dielectric constant on the surface of multi-dimensional functional graded insulators for DC-GIS, and finally designs multi-dimensional functional graded (MFGM) insulators to achieve coordinated control of the transient-steady-state electric field of DC-GIS.

[0004] The objective of this invention is achieved through the following technical solutions.

[0005] This invention discloses a design method for multidimensional functionally graded insulators used in DC gas-insulated substations. Based on COMSOL finite element simulation software, and using DC-GIS insulators as the optimization model, the method aims to optimize the DC electric field distribution along the surface and control surface losses. It employs an enumeration method to select different surface nonlinear conductivity parameters, ultimately obtaining the optimal distribution of nonlinear conductivity parameters. Similarly, to optimize the AC electric field distribution along the surface, an iterative method is used to select different bulk dielectric constant distributions, ultimately obtaining the optimal distribution of the bulk dielectric constant. The specific design steps include:

[0006] Step 1: Design surface nonlinear conductivity parameters

[0007] The surface portion of the MFGM insulator is made of a surface nonlinear conductive material with a surface nonlinear conductivity γ. s It is dependent on the nonlinearity of the electric field, that is:

[0008]

[0009] In the formula, γ s is the surface nonlinear conductivity; a is the ohmic conductivity of the surface nonlinear material; b is the nonlinear coefficient; E τ d is the tangential electric field along the surface; d is the thickness of the nonlinear conductive coating; the specific optimization steps are as follows:

[0010] A1) Build an insulator model for DC-GIS using COMSOL finite element simulation software, set the expected DC electric field distortion rate f1 along the insulator surface, and the minimum value of the nonlinear parameter a. min Maximum value a max Optimize the step size Δa and the minimum value of the nonlinear parameter b. min Maximum value b max Optimize step size Δb;

[0011] A2) Determine whether a is less than or equal to a max If the condition is met, proceed to step A3); otherwise, proceed to step A7.

[0012] A3) Determine whether b is less than or equal to b max If the condition is met, proceed to step A4); otherwise, proceed to step A6.

[0013] A4) Calculate the DC electric field distribution along the surface using a DC-GIS insulator model to obtain the DC electric field distortion rate f and surface loss Q along the insulator surface. s ;

[0014] f = E av / E DC-max

[0015] In the formula, E av It is the average DC electric field along the surface, E DC-max It is the maximum DC electric field along the surface;

[0016] Q s =∫γ s ·E τ 2 dS

[0017] In the formula, E τ It is the tangential DC electric field along the surface, and S is the surface area of ​​the insulator;

[0018] A5) Let b = b + Δb, and then repeat until step A3);

[0019] A6) Let a = a·Δa, and then repeat until step A2);

[0020] A7) Obtain the distribution maps of the DC electric field distortion rate and surface loss along the surface as a function of nonlinear parameters, and then determine the distribution when f = f1 and Q s At its minimum, the corresponding surface nonlinear material exhibits ohmic conductivity *a*, nonlinear coefficient *b*, and maximum DC electric field *E* along the surface. DC-max Surface loss Q s ;

[0021] Step 2: Design the bulk dielectric constant gradient distribution

[0022] The body of the MFGM insulator is made of a bulk dielectric material. The specific optimization steps are as follows:

[0023] B1) Divide the insulator into n equal layers along the radial direction;

[0024] B2) Set the optimization objective E for the AC electric field along the surface. obj and the initial volume dielectric constant distribution ε r (z)=ε r0 ;

[0025] B3) Calculate the AC electric field distribution along the surface using the bulk dielectric constant, and obtain the maximum AC electric field E along the surface. AC-max ;

[0026] B4) Determine E AC-max If the condition is met, proceed to step B5); otherwise, proceed to step B9.

[0027] B5) Determine if i is less than or equal to n. If it is, proceed to step B6); otherwise, proceed to step B8.

[0028] B6) Calculate the bulk dielectric constant of each layer of the insulator using the following iterative formula:

[0029]

[0030] In the formula, i represents the i-th layer; ε ri ' is the bulk dielectric constant after the i-th layer iteration; ε ri E is the bulk dielectric constant before the i-th layer iteration; i ε is the maximum alternating electric field of the i-th layer; max and ε min These represent the upper and lower limits for the bulk dielectric constant, respectively; C is the iteration coefficient, whose initial value is equal to E. obj Divide by E under the initial conditions AC-max ;

[0031] B7) Let i = i + 1, and then loop to step B5);

[0032] B8) Let i = 1, and loop to step B3);

[0033] B9) Let C = KC, where K is the adjustment coefficient;

[0034] B10) Determine if C is less than or equal to 0.01. If it is, proceed to step B11); otherwise, loop to step B5.

[0035] B11) Obtain the optimized bulk dielectric constant distribution ε r (z) and the distribution of AC electric field along the surface.

[0036] Furthermore, the insulator is a basin-type insulator, a post insulator, or a three-post insulator.

[0037] Furthermore, the thickness d of the nonlinear conductive coating mentioned in the first step is 0.1 to 2 mm.

[0038] Furthermore, the expected DC electric field distortion rate f1 along the insulator surface mentioned in the first step is in the range of 1 to 2; the minimum value of the nonlinear parameter a is a min The range is 10 -20 ~10 -16 S / m, maximum value a max The range is 10 -16 ~10 -12 S / m, the optimization step size Δa ranges from 1 to 10; the minimum value of the nonlinear parameter b is b min The range is 0~2mm / kV, and the maximum value is b. max The range is 3 to 5 mm / kV, and the optimization step size Δb ranges from 0 to 1.

[0039] Furthermore, in the second step, the insulator is divided into n layers radially on average, where n ranges from 4 to 20.

[0040] Furthermore, the upper limit ε of the bulk dielectric constant of the insulator described in the second step is optimized. max The range is 6 to 100, with a lower limit ε. min The range is 2 to 6.

[0041] Furthermore, the adjustment coefficient K mentioned in the second step is 0.01 to 0.1.

[0042] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0043] This invention, based on COMSOL finite element simulation software, uses an insulator for DC-GIS as the optimization model. To optimize the surface DC electric field distribution and control surface losses, it employs an enumeration method to select different surface nonlinear conductivity parameters, ultimately obtaining the optimal distribution of these parameters. Similarly, to optimize the surface AC electric field distribution, it uses an iterative method to select different bulk dielectric constant distributions, ultimately obtaining the optimal bulk dielectric constant distribution. This invention enables the optimization of the surface nonlinear conductivity and bulk dielectric constant distribution of multi-functionally graded (MFGM) insulators for DC-GIS, ultimately designing MFGM insulators and achieving coordinated control of the transient and steady-state electric fields in DC-GIS.

[0044] This invention proposes a parameter design method for multidimensional functionally graded material (MDFM) insulators used in DC gas-insulated substations (DC-GIS), which combines surface nonlinear conductive material coatings (SNCM) and bulk functionally graded dielectric constant materials (ε-FGM). Based on enumeration and iterative methods, this invention designs the surface nonlinear conductivity parameters and bulk dielectric constant gradient distribution of MFGM insulators, achieving coordinated control of the transient and steady-state electric fields of DC-GIS insulators, thereby improving the AC-DC flashover voltage and the operational stability of DC-GIS. By utilizing the bulk dielectric gradient portion of the MFGM insulator to control the AC electric field and the surface nonlinear conductive material portion of the MFGM insulator to control the DC electric field, the synergistic improvement of the AC-DC surface withstand voltage performance of DC-GIS insulators is ultimately achieved. Attached Figure Description

[0045] Figure 1 This is a flowchart illustrating the design process of the surface nonlinear conductivity parameters for this invention.

[0046] Figure 2 This is a flowchart illustrating the design process of the volume dielectric constant gradient distribution of the present invention.

[0047] Figure 3(a) is a schematic diagram showing the variation of the DC electric field distortion rate along the surface of the MFGM insulator of the present invention with nonlinear parameters.

[0048] Figure 3(b) is a schematic diagram of the surface loss of the MFGM insulator of the present invention as a function of nonlinear parameters.

[0049] Figure 4(a) is a schematic diagram of the optimized bulk dielectric constant distribution of the present invention.

[0050] Figure 4(b) is a comparison of the AC electric field distribution along the surface before and after the optimization of the present invention. Detailed Implementation

[0051] The present invention will now be further described with reference to the accompanying drawings.

[0052] This invention relates to a design method for the surface nonlinear conductivity parameters and bulk dielectric constant gradient distribution parameters of multidimensional functionally graded material (MDFM) insulators used in DC gas-insulated substations (DC-GIS). It combines bulk functionally graded dielectric constant material (ε-FGM) and surface nonlinear conductive material coating material (SNCM) to improve the operational stability of DC-GIS equipment and the safety and reliability of the power system.

[0053] This invention discloses a design method for multidimensional functionally graded insulators used in DC gas-insulated substations. Based on COMSOL finite element simulation software, and using DC-GIS insulators as the optimization model, the method aims to optimize the DC electric field distribution along the surface and control surface losses. It employs an enumeration method to select different surface nonlinear conductivity parameters, ultimately obtaining the optimal distribution of nonlinear conductivity parameters. Similarly, to optimize the AC electric field distribution along the surface, an iterative method is used to select different bulk dielectric constant distributions, ultimately obtaining the optimal distribution of the bulk dielectric constant. Specifically, the design steps include:

[0054] Step 1: Design surface nonlinear conductivity parameters

[0055] The surface portion of the MFGM insulator is made of a surface nonlinear conductive material with a surface nonlinear conductivity γ. s It is dependent on the nonlinearity of the electric field, that is:

[0056]

[0057] In the formula, γ s is the surface nonlinear conductivity; a is the ohmic conductivity of the surface nonlinear material, S / m; b is the nonlinear coefficient, mm / kV; E τ is the tangential electric field along the surface, in kV / mm; d is the thickness of the nonlinear conductive coating, with a value ranging from 0.1 to 2 mm, for example, d is set to 0.5 mm. The insulator is a basin-type insulator, a post insulator, or a three-post insulator. Figure 1 As shown, the specific optimization steps are as follows:

[0058] A1) Build an insulator model for DC-GIS using COMSOL finite element simulation software, set the expected DC electric field distortion rate f1 along the insulator surface, and the minimum value of the nonlinear parameter a. min Maximum value a max Optimize the step size Δa and the minimum value of the nonlinear parameter b. min Maximum value b max Optimize the step size Δb.

[0059] The expected DC electric field distortion rate f1 along the insulator surface can range from 1 to 2, for example, f1 = 1.1. The minimum value of the nonlinear parameter a is... min The value range can be 10. -20 ~10 -16 S / m, maximum value a max The value range can be 10. -16 ~10 -12 S / m, the optimization step size Δa can range from 1 to 10, for example, a min =10 -18 S / m, a max =10-14 S / m, Δa=10. The minimum value of the nonlinear parameter b. min The value range can be 0 to 2 mm / kV, with a maximum value of b. max The value range can be 3–5 mm / kV, and the optimization step size Δb can be 0–1, for example, b min =0mm / kV, b max =3mm / kV, Δb=0.1.

[0060] A2) Determine whether a is less than or equal to a max If the condition is met, proceed to step A3; otherwise, proceed to step A7.

[0061] A3) Determine whether b is less than or equal to b max If the condition is met, proceed to step A4; otherwise, proceed to step A6.

[0062] A4) Calculate the DC electric field distribution along the surface using a DC-GIS insulator model to obtain the DC electric field distortion rate f and surface loss Q along the insulator surface. s .

[0063] f = E av / E DC-max (2)

[0064] In the formula, E av It is the average DC electric field along the surface, kV / mm; E DC-max It is the maximum DC electric field along the surface, kV / mm.

[0065] Q s =∫γ s ·E τ 2 dS (3)

[0066] In the formula, E τ It is the tangential DC electric field along the surface, kV / mm; S is the surface area of ​​the insulator.

[0067] A5) Let b = b + Δb, and then repeat until step A3).

[0068] A6) Let a = a·Δa, then loop back to step A2).

[0069] A7) Obtain the distribution diagrams of the DC electric field distortion rate and surface loss along the surface as a function of nonlinear parameters, as shown in Figures 3(a) and 3(b). As can be seen from the figures, with the increase of nonlinear parameters a and b, the DC electric field distortion rate along the surface decreases while the surface loss increases, eventually stabilizing. Finally, it is determined that when f = f1 and Q... s At its minimum, the corresponding surface nonlinear material exhibits ohmic conductivity *a*, nonlinear coefficient *b*, and maximum DC electric field *E* along the surface.DC-max Surface loss Q s .

[0070] Step 2: Design the bulk dielectric constant gradient distribution

[0071] The body of an MFGM insulator is made of a bulk dielectric material, such as... Figure 2 As shown, the specific optimization steps are as follows:

[0072] B1) Divide the insulator into n layers radially, where n can range from 4 to 20, for example, n = 10.

[0073] B2) Set the optimization objective E for the AC electric field along the surface. obj and the initial volume dielectric constant distribution ε r (z)=ε r0 ; where ε r (z) represents the bulk dielectric constant distribution, ε r0 The initial value of the bulk dielectric constant is ε, and the initial value of the bulk dielectric constant for each of the n layers is set to ε. r0 .

[0074] B3) Calculate the AC electric field distribution along the surface using the bulk dielectric constant, and obtain the maximum AC electric field E along the surface. AC-max .

[0075] B4) Determine E AC-max If the condition is met, proceed to step B5; otherwise, proceed to step B9.

[0076] B5) Determine if i is less than or equal to n. If it is, proceed to step B6; otherwise, proceed to step B8.

[0077] B6) Calculate the bulk dielectric constant of each layer of the insulator using the following iterative formula:

[0078]

[0079] In the formula, i represents the i-th layer; ε ri ε' is the bulk dielectric constant after the i-th layer iteration. ri E represents the bulk dielectric constant before the i-th layer iteration. i ε represents the maximum alternating current electric field of the i-th layer. max and ε min These are the upper and lower limits for optimizing the bulk dielectric constant, ε. max The value range can be 6 to 100, ε min The value can range from 2 to 6, for example, ε max =20, ε min =4. C is the iteration coefficient, and its initial value is equal to E. obj Divide by E under the initial conditions AC-max .

[0080] B7) Let i = i + 1, and then loop to step B5).

[0081] B8) Let i = 1, and loop to step B3).

[0082] B9) Let C = KC, where K is the adjustment coefficient, and the value of K can be from 0.01 to 0.1, for example, C = 0.1C.

[0083] B10) Determine if C is less than or equal to 0.01. If so, proceed to step B11; otherwise, loop back to step B5.

[0084] B11) Obtain the optimized bulk dielectric constant distribution ε r (z) and the AC electric field distribution along the surface are shown in Figure 4(a) and Figure 4(b). As can be seen from the figures, the AC electric field along the surface decreases significantly after iterative optimization.

[0085] This invention applies the concepts of functionally graded and nonlinear materials from the field of materials science to the electrical field. To adapt to the transient and steady-state electric field distributions in DC-GIS, this invention proposes the concept of a multidimensional functional material (MFGM) that combines a functionally graded bulk dielectric material (ε-FGM) and a surface nonlinear conductive material (SNCM). Under steady-state DC conditions, the equivalent impedance of the SNCM coating is much smaller than that of the insulator, and the electric field distribution along the insulator is mainly determined by the SNCM coating, which can intelligently optimize DC electric field distortion. However, for transient conditions, because the ε-FGM is much smaller than the SNCM coating, the ε-FGM material controls the transient electric field distribution, and increasing the local dielectric constant can reduce the electric field strength. This invention designs the surface nonlinear conductivity parameters and bulk dielectric constant gradient distribution of the MFGM insulator based on enumeration and iterative methods, realizing the coordinated control of the transient and steady-state electric fields of the DC-GIS insulator, improving the AC-DC flashover voltage of the insulator and the operational stability of the DC-GIS.

[0086] Although the functions and working processes of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the specific functions and working processes described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims, and all of these are within the protection scope of the present invention.

Claims

1. A design method for multidimensional functionally graded insulators for DC gas-insulated substations, characterized in that, Based on COMSOL finite element simulation software, and using DC-GIS insulators as the optimization model, this study aims to optimize the DC electric field distribution along the surface and control surface losses. Different surface nonlinear conductivity parameters are selected using an enumeration method to obtain the optimal distribution of these parameters. Similarly, to optimize the AC electric field distribution along the surface, different bulk dielectric constant distributions are selected using an iterative method to obtain the optimal distribution of the bulk dielectric constant. The specific design steps include: Step 1: Design surface nonlinear conductivity parameters The surface portion of the MFGM insulator is made of a surface nonlinear conductive material with a surface nonlinear conductivity γ. s It is dependent on the nonlinearity of the electric field, that is: In the formula, γ s It is the surface nonlinear conductivity; a is the ohmic conductivity of the surface nonlinear material; b is the nonlinear coefficient; E τ It is a tangential electric field along the surface; d represents the thickness of the nonlinear conductive coating; the specific optimization steps are as follows: A1) Build an insulator model for DC-GIS using COMSOL finite element simulation software, set the expected DC electric field distortion rate f1 along the insulator surface, and the minimum value of the nonlinear parameter a. min Maximum value a max Optimize the step size Δa and the minimum value of the nonlinear parameter b. min Maximum value b max Optimize step size Δb; A2) Determine whether a is less than or equal to a max If the condition is met, proceed to step A3); otherwise, proceed to step A7. A3) Determine whether b is less than or equal to b max If the condition is met, proceed to step A4); otherwise, proceed to step A6. A4) Calculate the DC electric field distribution along the surface using a DC-GIS insulator model to obtain the DC electric field distortion rate f and surface loss Q along the insulator surface. s ; f=E av / AND DC-max In the formula, E av It is the average DC electric field along the surface, E DC-max It is the maximum DC electric field along the surface; Q s =∫γ s ·E τ 2dS In the formula, E τ It is the tangential DC electric field along the surface, and S is the surface area of ​​the insulator; A5) Let b = b + Δb, and then repeat until step A3); A6) Let a = a·Δa, and then repeat until step A2); A7) Obtain the distribution maps of the DC electric field distortion rate and surface loss along the surface as a function of nonlinear parameters, and then determine the distribution when f = f1 and Q s At its minimum, the corresponding surface nonlinear material exhibits ohmic conductivity *a*, nonlinear coefficient *b*, and maximum DC electric field *E* along the surface. DC-max Surface loss Q s ; Step 2: Design the bulk dielectric constant gradient distribution The body of the MFGM insulator is made of a bulk dielectric material. The specific optimization steps are as follows: B1) Divide the insulator into n equal layers along the radial direction; B2) Set the optimization objective E for the AC electric field along the surface. obj and the initial volume dielectric constant distribution ε r (z)=ε r0 ; B3) Calculate the AC electric field distribution along the surface using the bulk dielectric constant, and obtain the maximum AC electric field E along the surface. AC-max ; B4) Determine E AC-max If the condition is met, proceed to step B5); otherwise, proceed to step B9. B5) Determine if i is less than or equal to n. If met, proceed to step B6); otherwise, proceed to step B8. B6) Iteratively calculate the dielectric constant of each layer of the insulator according to the following formula: In the formula, i represents the i-th layer; ε ri ' is the bulk dielectric constant after the i-th layer iteration; ε ri E is the bulk dielectric constant before the i-th layer iteration; i ε represents the maximum alternating electric field of the i-th layer; max and ε min These represent the upper and lower limits for the bulk dielectric constant, respectively; C is the iteration coefficient, whose initial value is equal to E. obj Divide by E under the initial conditions AC-max ; B7) Let i = i + 1, and then loop to step B5); B8) Let i = 1, and loop to step B3); B9) Let C = KC, where K is the adjustment coefficient; B10) Determine if C is less than or equal to 0.

01. If it is, proceed to step B11); otherwise, loop to step B5. B11) Obtain the optimized bulk dielectric constant distribution ε r (z) and the distribution of AC electric field along the surface.

2. The design method for multi-dimensional functionally graded insulators for DC gas-insulated substations according to claim 1, characterized in that, The insulator is a basin-type insulator, a post insulator, or a three-post insulator.

3. The design method for multi-dimensional functionally graded insulators for DC gas-insulated substations according to claim 1, characterized in that, The thickness d of the nonlinear conductive coating mentioned in the first step is 0.1 to 2 mm.

4. The design method for multi-dimensional functionally graded insulators for DC gas-insulated substations according to claim 1, characterized in that, The expected DC electric field distortion rate f1 along the insulator surface mentioned in the first step is in the range of 1 to 2; the minimum value of the nonlinear parameter a is a min The range is 10 -20 ~10 -16 S / m, maximum value a max The range is 10 -16 ~10 -12 S / m, the optimization step size Δa ranges from 1 to 10; the minimum value of the nonlinear parameter b is b min The range is 0~2mm / kV, and the maximum value is b. max The range is 3 to 5 mm / kV, and the optimization step size Δb ranges from 0 to 1.

5. The design method for multi-dimensional functionally graded insulators for DC gas-insulated substations according to claim 1, characterized in that, In the second step, the insulator is divided into n layers radially on average, where n ranges from 4 to 20.

6. The design method for multi-dimensional functionally graded insulators for DC gas-insulated substations according to claim 1, characterized in that, The upper limit of the optimization of the bulk dielectric constant ε of the insulator mentioned in the second step. max The range is 6 to 100, with a lower limit ε. min The range is 2 to 6.

7. The design method for multi-dimensional functionally graded insulators for DC gas-insulated substations according to claim 1, characterized in that, The adjustment coefficient K mentioned in the second step is 0.01 to 0.1.

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