A method for constructing a wideband equivalent circuit model of a ground net based on a vector matching method

Abstract

The application relates to a grounding grid broadband equivalent circuit model construction method based on a vector matching method, which comprises the following steps: firstly, establishing a broadband equivalent circuit model of main equipment of a GIS station suitable for engineering calculation, including building a circuit model of a GIS tubular busbar port voltage and a line current under high frequency, building an actual model of SF6 / Air high-voltage bushing, and building a grounding grid broadband equivalent model composed of actual models of a grounding grid and a grounding pillar; then, according to the established disconnecting switch dynamic arc burning model and the broadband equivalent circuit model of the main equipment of the GIS, finally, simulating and calculating a fast transient overvoltage generated by switch operation in a GIS test loop. The application simulates and calculates the amplitude and frequency of the TEV with the GIS test loop as the basis, compares with existing test results, verifies the effectiveness of the model, and lays a foundation for subsequent theoretical research.

Description

Technical Field

[0001] This invention belongs to the field of electrical engineering, and in particular relates to a method for constructing a broadband equivalent circuit model of a ground grid based on vector matching. Background Technology

[0002] Gas-insulated switchgear (GIS) refers to electrical equipment where all primary electrical equipment between the transformer and overhead line (mainly including circuit breakers, disconnect switches, voltage transformers, current transformers, surge arresters, busbars, and bushings) is sealed within a modular metal casing. It features compact structure, reliable operation, ease of maintenance, immunity to natural conditions, and minimal electromagnetic interference to the surrounding environment. Therefore, it has been widely adopted in many countries, yielding significant economic and social benefits.

[0003] GIS uses SF6 gas as the insulating medium. At normal pressure, SF6 has three times the insulation strength of air, and its arc-quenching ability is far superior to air. However, during GIS equipment switching operations or destructive discharges caused by grounding faults, the contact opening and closing speeds are very low relative to the system frequency, and the disconnecting switches lack sufficient arc-quenching capability. Therefore, multiple breakdowns are prone to occur during the switching of small capacitive currents, resulting in steep-front voltage traveling waves that propagate through the GIS busbars to connected equipment. Compared to traditional air-insulated substations (AIS), the compact structure and shorter internal lines of GIS exacerbate the multiple reflections and refractions of the internal voltage traveling waves at impedance mismatch points, causing waveform distortion and resulting in very fast transient overvoltages (VFTOs). VFTO waveforms have nanosecond-level rise times and frequencies ranging from several kilohertz to several hundred megahertz. Summary of the Invention

[0004] The above-mentioned technical problems of the present invention are mainly solved by the following technical solutions: A method for constructing a broadband equivalent circuit model of a ground network based on vector matching is characterized in that, Establish broadband equivalent circuit models of the main equipment of GIS stations suitable for engineering calculations, including building circuit models of GIS pipe bus port voltage and line current at high frequencies, building actual models of SF6 / Air high voltage bushings, and building broadband equivalent models of grounding grids composed of actual models of grounding grids and grounding supports; Based on the established dynamic arcing model of the disconnecting switch and the broadband equivalent circuit model of the main GIS equipment, the rapid transient overvoltage generated by the switch operation in the GIS test circuit is simulated and calculated.

[0005] In the above-mentioned method for constructing a broadband equivalent circuit model of a grounding grid based on vector matching, the circuit model of the GIS bus port voltage and line current at high frequencies is constructed. The parameters of the GIS bus are divided into two parts: series impedance and parallel admittance. Among them, the series impedance of the two loops can be expressed by two coupled equations: .

[0006] In the aforementioned method for constructing a broadband equivalent circuit model of a ground network based on vector matching, the self-impedance of the inner loop... Z 11 It includes 3 parts:

[0007] in, Z core,out represents the impedance per unit length of the outer surface of the central guide rod. Z Core / enclosure, insulation represents the impedance per unit length of the insulation between the center guide rod and the outer shell. Z enclosure,in represents the impedance per unit length of the inner surface of the enclosure.

[0008]

[0009] like r 1. r 2. R 1. R 2 satisfies the following relationship:

[0010] Simplified to:

[0011]

[0012] Furthermore, the impedance per unit length of the insulation between the center guide rod and the outer casing is: .

[0013] In the aforementioned method for constructing a broadband equivalent circuit model of a ground network based on vector matching, the self-impedance of the external loop is... Z 22 is:

[0014] in, Zenclosure,out represents the impedance per unit length of the outer surface of the enclosure. Z Enclosure / earth insulation refers to the impedance per unit length between the enclosure and the ground. Z Earth represents the return impedance of the earth. The formulas for its calculation are as follows:

[0015]

[0016]

[0017] The Carson formula is used to calculate the ground return impedance:

[0018] r This represents the resistivity of the earth, measured in Ω·m. When 1 / r oh At 0, the displacement current in the ground can be ignored. That is, the upper limit frequency for the Carson formula is... For the calculation of self-impedance, f =0.

[0019] For the variation of current along the GIS busbar, the equations of each loop are independent of each other, that is:

[0020] in, G 11 and C 11 It refers to the parallel conductance and capacitance per unit length of the SF6 insulation layer between the center conductor of the GIS busbar and the outer casing. G 22 and C 22 It refers to the parallel conductance and capacitance per unit length of the air insulation layer between the GIS shell and the ground. The capacitance calculation formula is as follows:

[0021] in, e 1 is the dielectric constant of SF6 gas. e 0 is the dielectric constant of air. For parallel conductance... G The dielectric loss angle can be used. d or dielectric loss coefficient tan d To represent, that is:

[0022] Under alternating current voltage, the energy loss of a dielectric consists of two parts: conductivity loss caused by conductivity and polarization loss caused by periodic polarization. The relative permittivity of the dielectric is written as:

[0023] For gaseous dielectrics, there exists Ignore the parallel conductance of the gaseous dielectric.

[0024] In the above-mentioned method for constructing a broadband equivalent circuit model of a grounding grid based on vector matching, an actual model of the SF6 / Air high-voltage bushing is built, including... The S-parameters are obtained using the finite element method.

[0025] The frequency response curve of its admittance parameter is obtained by parameter transformation.

[0026] The vector matching method and impedance synthesis method are used to restore it to a broadband equivalent circuit.

[0027] A practical model of the SF6 / Air high-voltage bushing is built based on the reconstructed broadband equivalent circuit.

[0028] In the above-mentioned method for constructing a broadband equivalent circuit model of a ground network based on vector matching, the vector matching method is specifically based on the frequency response function:

[0029] Among them, the residue c n and extreme points a n It is either a real number or a pair of conjugate complex numbers. d and h It is a real number. To obtain over a given frequency interval... f ( s The least squares approximation of ) requires calculating all coefficients in the above formula. Specifically, the poles should be located first. a n Furthermore, it is known that the unknown quantities can be calculated using linear least squares equations. c n , d , h .

[0030] In the aforementioned method for constructing a broadband equivalent circuit model of a ground network based on vector matching, the conjugate complex pole part, the real pole part, and the first-order and constant terms are obtained through impedance synthesis; wherein...

[0031]

[0032] .

[0033] In the aforementioned method for constructing a broadband equivalent circuit model of a grounding grid based on vector matching, the actual model of the SF6 / Air high-voltage bushing is built, including... The S-parameters are converted into Y-parameters, and a rational function is fitted using vector matching.

[0034] Fitting Y 1. Y The rational function of 3 contains 4 pairs of conjugate complex poles; fitting Y The rational function of 2 contains 3 pairs of conjugate complex poles.

[0035] In the above-mentioned method for constructing a broadband equivalent circuit model of a grounding grid based on vector matching, an actual model of the grounding grid and grounding posts is built. The response characteristics under different frequency excitations are obtained using the method of moments, and a corresponding broadband equivalent circuit model is established. The equivalent circuits of the grounding posts supporting disconnect switches, the grounding posts supporting bushings, and the grounding posts supporting GIS busbars are the same. Each grounding post in the circuit is equivalent to a closed-loop circuit consisting of a resistor, an inductor, and a parallel resistor and capacitor connected in sequence. The remaining components are equivalent to resistors and inductors connected in sequence. The establishment of the broadband equivalent model of the grounding grid includes: The GIS test circuit grounding grid has 7 grounding points. These 7 grounding points are considered as 7 nodes, and the equivalent circuit of the grounding grid is established using the nodal admittance method. In the... i Current injected at each node I i ( i =1, 2, ..., 7), measure the ground potential rise at each node. U 1i , U 2i ,..., U 7i Then we have:

[0036] Solving this matrix equation yields the nodal admittance matrix of the ground network.

[0037] The admittance of each node in the grounding network to the zero-potential branch is y i0 ,node i With nodes j The branch admittance between them is y ij The relationship between the admittances of each branch and the elements in the admittance matrix of the ground network nodes is as follows: .

[0038] In the above-mentioned method for constructing a broadband equivalent circuit model of a ground network based on vector matching, the simulation calculation specifically includes: The high-frequency characteristics of the GIS busbar are simulated using the relationship between port voltage and current, and the high-voltage bushing is replaced by a broadband equivalent circuit model.

[0039] The transmission line model of the entire test loop is equivalent to a port network to simulate the propagation of traveling waves on the central guide rod and the outer shell, and VFTO and TEV are considered in the same model for calculation.

[0040] Based on the specific grounding arrangement of the test circuit, a broadband equivalent circuit model of 7 grounding pillars and grounding grid was incorporated to obtain the final VFTO-TEV joint simulation model.

[0041] This invention conducts a simulation study on the TEV generated by the operation of a disconnecting switch in a single-phase test circuit of an AC GIS device. A broadband equivalent circuit model of the main GIS equipment is established, and a VFTO-TEV co-simulation model is built. The main components include: (1) The impedance matrix and capacitance matrix reflecting the coupling relationship between the busbar port voltage and the line current under high frequency were calculated. By modeling the geometry of SF6 / Air bushing, grounding post and grounding grid, its frequency-varying admittance matrix was obtained. The frequency-varying admittance matrix was converted into the corresponding broadband equivalent circuit model by vector matching method and impedance synthesis method.

[0042] (2) A VFTO-TEV joint simulation model was established based on the broadband equivalent model of the main GIS equipment. Using the GIS test loop as a basis, the amplitude and frequency of the TEV were simulated and calculated, and compared with existing experimental results to verify the effectiveness of the model. Simultaneously, the calculation results of the joint simulation model were compared with the independent simulation models of VFTO and TEV. It was found that when VFTO and TEV were considered simultaneously, both contained richer high-frequency components, and the amplitude of the TEV in the joint simulation model was lower than the results calculated individually.

[0043] (3) The effects of disconnector operating speed, installation of ferrite cores, and branch bus length on TEV were compared and analyzed. The results showed that when the opening speed was less than 0.8 m / s, the TEV amplitude gradually increased with the increase of the disconnector operating speed; after the opening speed was greater than 0.8 m / s, the amplitudes of both decreased slightly. After installing ferrite cores, the overall TEV amplitude of the simulated circuit decreased, and the high-frequency components were weakened. This trend was particularly obvious at the disconnector operation. Changes in the branch bus length affected the propagation process of transient electromagnetic waves, and the location where the maximum TEV value occurred changed accordingly. In the actual operation of GIS stations, the effects of disconnector operating speed and branch bus length on TEV should be considered comprehensively. Adding ferrite cores and improving the casing layout are both effective ways to suppress TEV.

[0044] Therefore, the present invention has the following advantages: by establishing a broadband equivalent circuit model of the main GIS equipment, the present invention builds a VFTO-TEV joint simulation model, based on the GIS test circuit, simulates and calculates the amplitude and frequency of TEV, and compares it with existing test results to verify the effectiveness of the model, laying the foundation for subsequent theoretical research. Attached Figure Description

[0045] Appendix Figure 1 This is a schematic diagram of the broadband equivalent circuit of the high-voltage bushing of the present invention; Figure 2 is a schematic diagram of the grounding support for the disconnecting switch of the present invention and its broadband equivalent circuit diagram; Figure 3 is a schematic diagram of the grounding post of the supporting bushing and its broadband equivalent circuit; Figure 4 is a schematic diagram of the grounding support post for the GIS busbar and its broadband equivalent circuit diagram; Figure 5 is a circuit diagram of the broadband equivalent model of the grounding grid; Appendix Figure 6 This is a schematic diagram of the VFTO-TEV co-simulation model; Figure 7 shows the TEV waveform and spectrum at the end of the branch bus in the co-simulation model; Figure 8 shows the TEV waveform and spectrum at the end of the branch bus under the traditional simulation model; Appendix Figure 9 These are TEV waveform diagrams at the end of the branch busbar under different tripping speeds; Appendix Figure 10 This is an equivalent model diagram of a ferrite magnetic ring; Appendix Figure 11 This is a TEV waveform diagram at the end of the branch bus after the ferrite core is installed; Appendix Figure 12 This is a TEV spectrum analysis diagram of the branch bus ends before and after the installation of the ferrite core; Detailed Implementation The technical solution of the present invention will be further described in detail below through embodiments and in conjunction with the accompanying drawings.

[0046] Example: This invention comprises two main parts. The first part is the establishment of a broadband equivalent model for GIS equipment, and the second part is the calculation and analysis of transient overvoltage in a 1000kV test circuit based on the established equivalent model. These are described in detail below.

[0047] I. Establishment of a broadband equivalent model for GIS equipment.

[0048] 1. Broadband model of GIS busbar.

[0049] In practical engineering calculations of VFTOs, the circuit models proposed by CIGRE Working Group 33 / 13.09 are mostly used for modeling GIS equipment. These models can usually simulate the calculation results of low-frequency transient fields well. However, VFTOs and TEVs contain rich high-frequency components. Taking TEV as an example, the low-frequency components of several megahertz are generated by electromagnetic transients formed by gap breakdown propagating within the GIS and leaking at high-voltage bushings, etc. The high-frequency components of around tens of megahertz are formed by the development of leaked transient electromagnetic waves between the casing and the ground. The high-frequency components of tens of megahertz are generated by multiple reflections of transient electromagnetic waves on the casing at impedance mismatches (such as between adjacent grounding leads). Therefore, considering the skin effect of GIS busbars under high-frequency conditions and the electromagnetic leakage of high-frequency electromagnetic waves at impedance mismatches in transmission lines, it is necessary to analyze the high-frequency characteristics of GIS equipment. This paper mainly considers establishing broadband response models for the following electrical equipment: (1) GIS busbar: Under the action of low-frequency field, the equivalent resistance and inductance of GIS busbar can be considered as constant values; however, under high-frequency conditions, as the excitation frequency increases, the resistance value will increase and the inductance value will decrease. This will increase the loss of the busbar at high frequencies. Therefore, considering that VFTO and TEV contain high-frequency components, a new model should be established for GIS busbar to replace the original wave impedance model.

[0050] (2) High-voltage bushings: The common explanation for the generation of TEV is that when the traveling voltage wave (VFTO) inside the busbar propagates to the impedance mismatch point, it will be reflected. The voltage wave reflected on the outer casing constitutes the transient ground potential rise of the outer casing, i.e., TEV. Taking SF6 / Air bushings as an example, its lower end is connected to the GIS busbar and its upper end is connected to the overhead line. Due to the impedance mismatch at the port, high-frequency electromagnetic leakage will be generated at the bushing, thus generating TEV. Therefore, it is necessary to establish a broadband equivalent circuit model of high-voltage bushings to simulate the electromagnetic leakage that occurs at the bushing at high frequencies.

[0051] (3) Grounding grid and grounding post: Transient waves reflected from the transmission line cylinder to the outer shell will be reflected at the grounding point of the outer shell. Therefore, the high-frequency transient response of the grounding grid and grounding post is also worth noting. A broadband equivalent circuit model should be established to conduct a more accurate study of TEV and VFTO.

[0052] 1.1 Theoretical calculation basis of GIS busbars.

[0053] The GIS busbar is a key component within a GIS substation, connecting other electrical equipment and serving as the primary propagation path for VFTO and TEV. The GIS busbar structure comprises a central conductor and an outer casing. During the electromagnetic transients generated by switching operations, the transient waveform contains not only the power supply frequency and the first natural frequency, but also abundant higher harmonic components. Because line parameters vary with frequency, the attenuation and distortion of harmonic components at different frequencies differ during propagation. Therefore, calculating the transient using only line parameters at the power supply frequency or the first natural frequency often fails to comprehensively and objectively reflect the transient process. The skin effect varies in degree when electromagnetic waves propagate on the GIS busbar at different frequencies, caused by the different current distributions in the line and the ground. For lossless lines, since the conductor's conductivity approaches infinity, the electric field strength inside the conductor is always zero, thus no electromagnetic waves penetrate the conductor. Therefore, the current at any frequency flows directly between the conductor and the ground surface. When the conductivity of the conductor and the ground is finite, the electric field strength inside them is not zero, and therefore current exists inside them, but the current density distribution is not uniform. This conclusion can be explained by the following theoretical analysis: For a cylindrical conductor, the current density along the radial direction... r The distribution can be approximated as: 1 (2.1) in, I It is the total current in the conductor; c It is electrical conductivity; oh and f These represent angular frequency and frequency, respectively. r 0 is the conductor radius. From the above formula, it can be seen that when... r - r As the current increases from 0, the current density decreases exponentially. At very high frequencies, the current is distributed only near the surface of the conductor.

[0054] Since the GIS busbar consists of a central guide rod and an outer casing, it can be divided into two loops: the central guide rod and the outer casing form the inner loop, and the connection between the outer casing and the ground forms the outer loop. In the GIS busbar structure, r 1. r 2 represents the inner and outer radii of the central guide rod, respectively. R 1. R 2 represents the inner and outer radii of the outer shell, respectively.h This represents the distance from the center of the outer shell to the ground. (Based on existing literature...)

[61] The formulas for calculating the internal impedance of solid and hollow conductors are shown in equations (2.2) and (2.3), respectively: (2.2) (2.3) (2.4) in, a , b These are the outer radius and inner radius of the conductor, respectively. I i and K i The first and second type of modifications are respectively i The order Bessel function. r It is the resistivity of the conductor. m It is the magnetic permeability of the conductor.

[0056] The parameters of a GIS busbar can be divided into two parts: series impedance and parallel admittance. For the series impedance part, the series impedance of the two loops can be expressed by two coupling equations: (2.5) Self-impedance of the inner loop Z 11 It includes 3 parts: (2.6) in, Z core,out represents the impedance per unit length of the outer surface of the central guide rod. Z Core / enclosure, insulation represents the impedance per unit length of the insulation between the center guide rod and the outer shell. Z enclosure,in represents the impedance per unit length of the inner surface of the enclosure. Z core, out and Z The formula for enclosure,in can be derived from equation (3.3): (2.7) (2.8) like r 1. r 2. R 1. R 2 satisfies the following relationship: (2.9) Equations (2.7) to (2.8) can be simplified to: (2.10) (2.11) Furthermore, the impedance per unit length of the insulation between the center guide rod and the outer casing is: (2.12) Similarly, for the external circuit, its self-impedance Z 22 is: (2.13) in, Z enclosure,out represents the impedance per unit length of the outer surface of the enclosure. Z Enclosure / earth insulation refers to the impedance per unit length between the enclosure and the ground. Z Earth represents the return impedance of the earth. The formulas for its calculation are as follows: (2.14) (2.15) (2.16) The Carson formula was used in the calculation of the ground return impedance. (2.17) r This represents the resistivity of the earth, measured in Ω·m. When 1 / r oh At 0, the displacement current in the ground can be ignored. That is, the upper limit frequency for the Carson formula is... For the calculation of self-impedance, f =0.

[0057] For the variation of current along the GIS busbar, the equations of each loop are independent of each other, that is: (2.18) in, G 11 and C 11 It refers to the parallel conductance and capacitance per unit length of the SF6 insulation layer between the center conductor of the GIS busbar and the outer casing. G 22 and C 22 It refers to the parallel conductance and capacitance per unit length of the air insulation layer between the GIS shell and the ground. The capacitance calculation formula is as follows: (2.19) in, e 1 is the dielectric constant of SF6 gas. e 0 is the dielectric constant of air. For parallel conductance... G The dielectric loss angle can be used. d or dielectric loss coefficient tan d To represent, that is: (2.20) Under alternating current voltage, the energy loss of a dielectric consists of two parts: conductivity loss caused by conductivity and polarization loss caused by periodic polarization. The relative permittivity of the dielectric can often be written as: (2.21) Under alternating voltage, the dielectric loss coefficient tg can be used. d Measuring the loss characteristics of dielectrics. The loss of gaseous dielectrics is solely due to conductivity loss, which is extremely small, typically expressed in terms of tg. d <10 -8 Therefore, for GIS busbars, the medium loss coefficients of the SF6 gas medium between the central guide rod and the outer casing, and the air medium between the outer casing and the ground, can be ignored, because: (2.22) Therefore, for gaseous dielectrics, there exists Correspondingly, the parallel conductance of the gaseous dielectric can also be ignored.

[0058] 1.2 Solving for high-frequency parameters of GIS busbars.

[0059] In the ATP-EMTP electromagnetic transient simulation software, the model reflects the relationship between port voltage and line current. The loop voltage and current should be obtained by transforming the relationship.

[0060] The derivation of the conductor surface impedance formula is based on the loop voltage and current representation, while the parameter matrix read from the EMTP .lis file is based on the port voltage and line current representation. The corresponding coupling equations and transformation relationships of the two are as follows: Loop voltage-current coupling equations: (2.23) The transformation relationship is as follows: (2.24) The coupling relationship between the port voltage and line current obtained after conversion is as follows: (2.25) according to Based on the measured and inverted results of soil resistivity at the test site, in the four-layer soil stratification model, the thickness of the first soil layer is 14.25m, corresponding to a soil resistivity of 27Ω·m. The upper limit frequency for the Carson formula is approximately 666MHz. Taking 10MHz as an example, simulation calculations were performed. According to equations (2.6), (2.10) to (2.17), and (2.19), the coupling equations of port voltage and line current can be obtained as shown in equations (2.26) to (2.27).

[0061] (2.26) (2.27) Since parallel conductance is not considered, therefore Y ij = jωC ij Furthermore, the parallel capacitance value does not change with frequency. Based on the above impedance and capacitance matrices, the GIS busbar can be reduced to its corresponding high-frequency equivalent circuit, a process that can be implemented in ATP-EMTP.

[0062] Furthermore, it should be noted that the coupling between the internal and external transmission line systems of the GIS busbar is very weak, almost zero. However, when converted into a circuit model, it reflects the relationship between port voltage and branch current. At this point, the coupling between the two ports (center conductor to ground, outer casing to ground) is very strong, with coupling impedance and coupling capacitive reactance being respectively... Z 12 + Z 22 and Y 12 - Y 11 .

[0063] 2. Wideband model of high-voltage bushing.

[0064] The modeling of the broadband equivalent model of the high-voltage bushing is based on the following approach: First, a geometric model of the high-voltage bushing is established according to its actual dimensions, and its S-parameters are obtained. Then, the S-parameter matrix is ​​converted into the Y-parameter matrix of a two-port network. At this point, the Y-parameter matrix is ​​an admittance vector corresponding to different frequency points. Finally, the rational function expression of the Y-parameter matrix is ​​obtained through the vector matching method, and it is converted into a circuit model through impedance synthesis, which is then implemented in ATP-EMTP.

[0065] 2.1 Finite Element Method The main methods for solving electromagnetic field problems include graphical methods, simulation methods, analytical methods, and numerical analysis methods. In recent years, with the rapid development of computer technology, numerical methods for electromagnetic field calculations have been more widely used. Commonly used methods include the simulated charge method, finite difference method, finite element method, boundary element method, and method of moments. Among these, the finite element method (FEM) solves differential equations within a region, thus requiring the entire field to be discretized, i.e., the entire solution domain is partitioned. The accuracy of numerical calculations can be improved by adjusting the partition density. A key advantage of FEM is that the coefficient matrix of the resulting equation system is positive definite and sparse, making it easy to store and solve, and exhibiting good convergence. Because the interfaces between different media automatically satisfy boundary conditions without separate processing, FEM is suitable for solving complex problems involving multiple media, effectively handling complex geometric structures, and conveniently handling nonlinear media properties. The main disadvantage of FEM is that for complex three-dimensional electromagnetic calculation problems, due to computer memory limitations, it is difficult to meet the requirements of multivariable calculations and high partition accuracy.

[0066] 2.2 Vector Matching Method Vector Fitting (VF) is an effective method for rationally approximating impedance functions. Proposed by B. Gustavsen in 1997, its basic principle is as follows: Suppose the frequency response function can be expressed as: (2.28) Among them, the residue c n and extreme points a n It is either a real number or a pair of conjugate complex numbers. d and h It is a real number. To obtain over a given frequency interval... f ( s The least squares approximation of ) requires calculating all coefficients in the above formula. Since a n Since the unknowns appear in the denominator, the above equation is a nonlinear problem. To solve for the unknowns, our approach is to first locate the poles. a n ,assumed a n If the given information is known, then the above equation represents the unknown quantity. c n , d , h The linear solution problem can be obtained by calculating linear least squares equations. The specific steps are as follows: (1) Specify the initial pole and will f (s ) and an unknown function Multiplication: (2.29) and They have the same poles. At extremely high frequencies, Approaching 1. Multiply the second row of equation (2.29) by... f ( s From this, we can obtain the following expression: (2.30) Or written as: (2.31) This expression is about the unknown. c n , d , h , The linear equation can therefore be written as a linear expression at various frequency points: (2.32) In the formula x Since the unknown quantity is , the above equation is a linear least squares equation problem.

[0067] The sum of the partial fractions in equation (2.31) can be expressed as a product, resulting in: (2.33) (2.34) Therefore, we can conclude that: (2.35) The above derivation process reveals that... and Having the same initial poles Therefore, it can be canceled out during the calculation process. f ( s The extreme point is the same as The zero points are the same, because The zero point is easy to calculate, so we only need to calculate The zero point can be obtained f The poles of (s). In some cases, f ( s Some poles of may be unstable, meaning these poles lie in the right half-plane of s. This problem can be solved by inverting their real parts.

[0068] (2) Determine the residue: In principle, it can be solved directly by equation (2.35). fThe residue of (s), however, by Zero point as f ( s Solving the original problem in (1) by finding the extreme point of ) usually yields a more accurate result. This is still a Linear least squares equations of the form where the unknowns are c n , d , h .because The numerator and denominator correspond one-to-one, which means that if the initial poles If chosen appropriately, the new pole will be equal to the initial pole. =1). In practical applications, if a new pole is used as the initial starting point during the iteration process, the rational function approximation will converge.

[0069] Generally speaking, the closer the initial poles are to the convergent poles, the fewer the number of iterations and the shorter the computation time. Therefore, the initial poles should be chosen as close as possible to the final value. There are two principles for choosing initial poles: when the function contains resonance peaks, the initial poles and zeros include conjugate complex pairs, and the initial poles and zeros are selected according to the following formula: (2.36) in: (2.37) This method calculates a small real part of the poles, which avoids mismatches. When the function does not contain resonance peaks, only real zeros and poles need to be used for fitting.

[0070] 2.3 Impedance Synthesis Method After processing using the vector matching method, a rational function approximation of the impedance can be obtained: (2.38) at this time H ( s All poles lie in the left half-plane of the s-plane. Assume... N Of the 2 poles, there are 2 K The conjugate complex poles and ( N -2 K There are ) real poles. Since two poles that are conjugates of each other are adjacent, there are a total of K A pair of conjugate complex numbers. Assume this... K The conjugate complex poles and their corresponding complex residues are shown in equations (3.39) and (3.40), respectively: (2.39) (2.40) in, n =1, 2, ... , K Remaining ( N -2 K There are ) real poles in the left half-plane of s, i.e. a n <0, the residues corresponding to these real poles are c n ,in n =2 k +1, 2 k +2, ..., N .Will H ( s Decompose into complex pole terms H 1( s Real pole terms H 2( s ), one term H 3( s The term consists of four parts: ) and a constant term. (2.41) in:

[0071] (2.42)

[0072] make:

[0073] (2.43)

[0074] The impedance synthesis method can be used to obtain f 1n ( s ), f 2n ( s )as well as f 3n ( s The corresponding series and parallel equivalent circuits. When dealing with practical problems, the rational function expression obtained by the vector matching method can be represented by different forms of circuits, namely, the impedance series form and the admittance parallel form. The mutual conversion between the two can make the construction of broadband equivalent circuit models more efficient. The principle of the two forms of circuit conversion is explained below.

[0075] (1) Conjugate complex poles f 1n( s ) The branch impedance formula is: (2.44) The branch admittance formula is: (2.45) Comparing equations (2.44) and (2.45), we can obtain: (2.46) Similarly, we can obtain L k , R k , C k , G k The expression, where, L k and C C , R k and G C , C k and L C as well as G k and R C The expressions are identical. The subsequent real poles and the one-time and constant terms are similar. The expressions for inductance, resistance, capacitance, and conductance in the impedance model are the same as those for capacitance, conductance, inductance, and resistance in the admittance model, and will not be repeated in the text.

[0076] (2) Real poles f 2n ( s ) The real poles are transformed into impedance and admittance branches, and defined as follows: (2.47) (2.48) Therefore: (2.49) (3) The linear term and the constant term f 3n ( s ) The impedance and admittance branches are transformed from the linear and constant terms, and defined as follows: (2.50) (2.51) Therefore: (2.52) For the multi-pole case, multiple single-pole equivalent circuits can be connected in series for equivalence. Therefore... H ( s The equivalent circuit of ) is composed of f 1n ( s ), f 2n ( s )as well as f 3n ( s The equivalent circuits are connected in series.

[0077] 2.4 S-parameters.

[0078] S-parameters are parameters used in microwave network methods to process high-frequency networks. In high-frequency networks and microwave systems, the equivalent voltage and current, as well as the associated impedance matrix (Z matrix) or admittance matrix (Y matrix) parameters, are difficult to measure and cannot be analyzed using lumped parameter networks. To characterize the transmission characteristics of port networks at high frequencies, scattering parameters can be used to describe the wave propagation process. For an N-port network, the scattering parameter matrix reflects the relationship between the incident voltage wave and the reflected voltage wave at the port. Taking a two-port network as an example, for the incident signal at port 1... a 1. The portion that is incident and then reflected back through port 1 is S 11 The part transmitted to port 2 is S 21 Similarly, the incident signal at port 2 a The part reflected back from port 2 is S 22 The part transmitted to port 1 is S 12 . b 1. b 2 represents the reflected signals from port 1 and port 2, respectively. Therefore: (2.53) Assumption U 1 and I Let 1 represent the total voltage and total current at port 1, respectively. a 1. b 1 can be viewed as the incident signal and the reflected signal defined by power, that is: (2.54) (2.55) in, R 0 is the reference impedance for port 1.

[0079] Assume port 1 has an internal resistance of R A voltage source of 0 is used as the excitation, that is: (2.56) Substituting into equations (2.54) to (2.55), we get: (2.57) (2.58) That is, the power output by the voltage source is If the load is matched, the entire output power of the voltage source will be absorbed by the load; if the load is mismatched, then... The power of the magnitude is reflected back from port 1, and the actual power absorbed by the load is only a fraction of the total power. .

[0080] Assumption U i1 and U i2 These are the incident voltages at ports 1 and 2, respectively. U r1 and U r2 These are the reflected voltages at ports 1 and 2, respectively. Similarly, the corresponding incident and reflected currents can be defined. Since: (2.59) (2.60) And there are: (2.61) Therefore, the incident voltage and reflected voltage at the two ports can be related using S-parameters, i.e.: (2.62) in:

[0081] Assume the reference impedances of port 1 and port 2 of the two-port network are respectively Z 01 and Z 02 The transformation relationship between the Y parameters and S parameters is shown in equations (2.63) to (2.64). The above Y parameter matrix is ​​converted into a Π-type equivalent circuit of a two-port network.

[0082] (2.63) (2.64) The parameters of the Π-type equivalent circuit are as follows: (2.65) As can be seen from the above analysis, if the scattering parameters of the two-port are known, their impedance matrix can be obtained through transformation.

[0083] 2.5 Establishment of the broadband equivalent model for bushings.

[0084] 1100kV GIS SF6 gas-insulated composite bushings serve to connect GIS equipment to external overhead lines in actual operation. When a high-voltage current-carrying conductor passes through the GIS tank with a different potential, the high-voltage bushing provides insulation and support. In the COMSOL simulation model of the high-voltage bushing, the bushing structure is appropriately simplified, ignoring details such as bolts, the rolled edges of the double-layer metal shielding inside the bushing, and the influence of the equalizing ring is not considered in the model.

[0085] The SF6 gas-insulated bushing for 1100kV GIS adopts a double-layer shielded electrode structure. The inner shield is an aluminum floating potential electrode, and the outer shield is an aluminum grounding electrode. The two ends of the floating potential electrode are connected to the grounding electrode through epoxy resin cast insulating parts. For the sake of model simplification, this paper replaces the more than ten epoxy resin supporting insulating rods in the vertical direction between the two layers of shielding electrodes in the actual bushing structure with epoxy resin cylindrical shells of the same height.

[0086] When obtaining the S-parameters of a bushing in COMSOL, a wide frequency response and a small frequency step size are desired. Therefore, signal conversion between the time and frequency domains can be performed, i.e., simulation calculations are performed in the complementary domain, and then the results are generated in the optimal domain using Fast Fourier Transform (FFT). This paper first conducts a transient study, applying a voltage signal as excitation at the lumped port, then converting this signal from the time domain to the frequency domain, and finally calculating the S-parameters based on the converted frequency domain data. In this paper, a Gaussian function modulated by a sinusoidal function is selected as the excitation voltage, and its expression is: (2.66) in, f 0 is the center frequency of the modulated sine wave signal, which is also the main frequency of the subsequent FFT transformation; σ= 1 / 2 f 0, or f It is the modulation frequency shift ratio. When it takes a smaller value, it can enhance the frequency response near the highest frequency. In this paper, we take... or f =3%. The simulation duration for the time-domain transient study was set to 100 times the periodic function of the modulated sine wave to ensure complete attenuation of the energy input to the high-voltage bushing. To achieve this within the 0~2... fTo generate frequency domain data without significant distortion within a frequency range between 0 and 1, the time step should be set to meet the Nyquist criterion. Since the signal bandwidth B=2... f 0, so the step size can be set to step = 1 / 2B = 1 / 4 f 0. To obtain a finer frequency resolution, the end time of the FFT study was set to three times the duration of the transient study.

[0087] The SF6 insulation interface at the bottom of the bushing is equivalent to a lumped port with voltage excitation applied. The silicone rubber shed is used as the output boundary of the signal. Simulation can obtain the amplitude frequency and phase frequency characteristic curves of each parameter of the high-voltage bushing S-matrix.

[0088] The S-parameters are converted into Y-parameters, and a rational function is fitted using the vector matching method. The selection of the fitting order is crucial during the fitting process. If the fitting order is too low, it cannot accurately reflect the information of the Y-parameters at different frequencies; if the fitting order is too high, the circuit obtained by the subsequent impedance synthesis method becomes complex. Since ATP-EMTP has a truncation bit for digital values, the obtained circuit is prone to error accumulation, leading to inaccurate calculation results. Based on the principle of the vector matching method, after obtaining the admittance matrix from the S-parameters, the... Y 1. Y 2 and Y The original data in step 3 is compared with the results obtained by the vector matching method. Because... Y 1. Y 2 and Y The frequency response curve of 3 contains many resonance peaks, therefore a rational function with many conjugate complex poles is needed to fit it. Specifically, the fitting... Y 1. Y A rational function of 3 contains four pairs of conjugate complex poles and can fit the frequency response curve well; fitting Y The rational function of 2 contains three pairs of conjugate complex poles, thus its fitting effect on individual resonance peaks is poor. However, considering that the higher the order of the reconstructed circuit, the higher the computational complexity, the better the fitting effect is achieved while ensuring computational speed. Y The rational function of 2 can reflect the characteristics of several main resonance peaks well, and taking 3 pairs of conjugate complex poles is acceptable. The comparison results show that the vector matching method has higher accuracy in processing the original data, and the high-voltage bushing broadband circuit model constructed in ATP-EMTP fits the S-parameters obtained from COMSOL simulations well.

[0089] The final schematic diagram of the high-voltage bushing circuit is as follows: Figure 1 As shown: 3. Broadband model of grounding support and grounding grid.

[0090] 3.1 Solution method using the method of moments.

[0091] In 1968, Harlinden published "Method of Moments for Computing Electromagnetic Fields," introducing the method of moments (MoM) into the field of numerical electromagnetic field calculations. The advantage of the MoM lies in its ease of computer-based solution. It divides the conductor into segments, resulting in many conductor unit segments. First, the leakage current and axial current on each conductor unit necessarily obey Kirchhoff's current law. Second, since the potential on the conductor surface is continuous, the voltage across a single conductor unit must equal the voltage across the two outer segments of the conductor. The voltage within a conductor segment can be obtained by multiplying the self-impedance of the segment by the axial current flowing through it. The voltage across the outer segments can be calculated using the leakage current of each conductor unit. Based on these four equations, a system of equations can be established. Solving this system yields the leakage current of each conductor. The principle of the MoM is as follows.

[0092] For general linear eigenvalue equations (2.67) Where L and M are linear operators, we choose basis functions within the domains of L and M. f 1, f 2, f The combination of 3... makes (2.68) In the formula a n If is a constant, then we have (2.69) Assuming a suitable inner product is defined Then, define the test function within the L and M ranges. , , …, for all Taking the inner product according to the above formula, we get: (2.70) in, m =1,2,3... The above formula can be written as: (2.71) In the formula: (2.72) (2.73) (2.74) Then when det| l mn - λm mn When |=0, equation (2.71) has a non-zero solution.

[0093] When solving a system consisting of multiple interconnected conductors, in order to facilitate the application of the method of moments, it is necessary to decompose the entire system into smaller connected parts according to the connection relationship of each conductor. The following assumptions are used in the calculation: (1) The axial current at the end points and midpoint of the conductor segment is constant, and the axial current flows through the conductor along its axis; (2) When solving for the values ​​of axial current and leakage current inside a conductor, it is assumed that the leakage current flows out from the midpoint of the conductor, and when solving for the space potential caused by the leakage current, it is assumed that the leakage current flows out uniformly from the surface of the conductor.

[0094] Based on the above assumptions, in the schematic diagram of a partial conductor of the grounding grid shown in the figure below, let... k - , k + , k They are the first k The two ends and midpoint of the root conductor, obviously, the first k The leakage current on the root conductor is (2.75) in, and They are respectively k - and k + Axial current at the location.

[0095] From the node voltage equation: (2.76) in It is the first k - j The potential at the midpoint of the conductor ( j =1,2,3,…, m ), It is the first k The potential at the midpoint of the conductor is generated by the combined effect of leakage currents in all conductors. Point k - and k - j Self-impedance at the midpoint of the conductor It can be obtained from the following formula: (2.77) in It is the first k The midpoint of the root conductor and the first j The transfer reactance at the midpoint of the root conductor. The same method can be used to calculate... ,but: (2.78) In special circumstances, if the first k Root conductor k + Connect an injection current at the point Then directly set There is no need to solve the nodal voltage equations; for a floating grounded system, it is first divided into segments, and the conductor segments at both ends can be considered to have an injected current connected to their ends. The conductor segments at other locations are solved using the general conductor segment solution method described above. For a single-ended floating grounding system, it is similarly divided into segments, and the conductor segments at the floating end are solved using the floating grounding system calculation method described above. Move it to the right side of the above equation. Moving to the left side of the above equation, we get: (2.79) Rewritten in matrix form, we get: (2.80) The above formula can be used to calculate the leakage current distribution of the system, and then the potential rise at the current injection point. When the applied current is an impulse current, the impulse impedance, step voltage, contact potential, etc., can be calculated.

[0096] 3.2 Establishment of the broadband equivalent model for grounding posts The grounding supports in the test circuit are divided into three types, used to support disconnect switches, bushings, and GIS busbars, respectively. The modeling approach for the grounding supports is as follows: first, a geometric model of the grounding support is constructed, and different frequencies of excitation are applied to obtain the responses at different frequencies. Then, the frequency response characteristics of different types of grounding supports are approximated by rational functions using the vector matching method. Finally, the impedance synthesis method is used to convert the rational function expression into a broadband equivalent circuit model. It is worth noting that although the obtained broadband equivalent circuit model can be used for simulation calculations between 0.1MHz and 100MHz, the resistors, capacitors, and inductors in it do not have actual physical meaning.

[0097] (1) Grounding post supporting the disconnecting switch The parameters of each component in the equivalent circuit are shown in Table 2.1: Table 2.1 Wideband equivalent circuit parameters of the grounding post supporting the disconnecting switch

[0098] The broadband equivalent circuit model is compared with the original data and the results obtained by the vector matching method. The original data (blue solid line) represents the frequency response curve obtained from simulation, the fitted curve (red dashed line) represents the result obtained after approximating the rational function using the vector matching method, the green solid line represents the fitting deviation of the vector matching method, and the blue asterisk represents the amplitude and phase frequency responses of the circuit model obtained by the impedance synthesis method at different frequency points. The comparison results show that the broadband equivalent circuit established by the vector matching method and the impedance synthesis method can well reflect the amplitude and phase frequency response characteristics of the original data between 0.1MHz and 100MHz.

[0099] (2) Grounding post supporting the bushing The broadband equivalent circuit model is compared with the original data and the results obtained by the vector matching method.

[0100] The parameters of each component in the equivalent circuit are shown in Table 2.2. The comparison results show that the frequency response curves of the original data, the results fitted by the vector matching method, and the broadband equivalent circuit model established by the impedance synthesis method are basically consistent, indicating that the final circuit model can well reflect the amplitude-frequency and phase-frequency response characteristics of the original data.

[0101] Table 2.2 Broadband equivalent circuit parameters of the grounding post for the support bushing

[0102] (3) Grounding support post for GIS busbar The schematic diagram of the grounding post supporting the GIS busbar and its broadband equivalent circuit are shown in Figures 4(a) and (b). The parameters of each component in the equivalent circuit are shown in Table 2.3: Table 2.3 Broadband equivalent circuit parameters of grounding posts supporting GIS busbars

[0103] The comparison results above show that the established broadband equivalent circuit model can accurately reflect the amplitude-frequency and phase-frequency response characteristics of the original data. In summary, when establishing the overall circuit connection of a GIS station, the corresponding broadband equivalent circuit model of the grounding post should be connected between the GIS busbar casing and the grounding point of the grounding grid. The grounding post model established in this section more accurately reflects its high-frequency characteristics than the previous method of using only inductors to simulate the grounding down conductor.

[0104] 2.3.3 Establishment of the broadband equivalent model of the grounding grid The GIS test circuit grounding network has 7 grounding points. These 7 grounding points are considered as 7 nodes, and the equivalent circuit of the grounding network is established using the nodal admittance method. Assume that in the first... i Current injected at each node Ii ( i =1, 2, ..., 7), measure the ground potential rise at each node. U 1i , U 2i ,..., U 7i Then we have: (2.81) Solving this matrix equation yields the nodal admittance matrix of the ground network.

[0105] The admittance of each node in the grounding network to the zero-potential branch is y i0 ,node i With nodes j The branch admittance between them is y ij The relationship between the admittances of each branch and the elements in the admittance matrix of the ground network nodes is as follows: (2.82) Establish the geometry of the grounding grid in CDEGS. The large and small grid dimensions are 0.8m × 0.8m and 0.4m × 0.4m, respectively. Both the grounding grid and the grounding rod have a radius of 8mm and a burial depth of 0.8m. The grounding grid is made of steel with a resistivity of 1.75 × 10⁻⁶. -7 The resistivity is 626 Ω·m (relative to 10 for copper). A layered soil model was used. Based on measured and inverted results of soil resistivity at the high-pressure test site, the top layer of soil was 39.91 m thick with a resistivity of 28.43 Ω·m, while the bottom layer had a resistivity of 240302 Ω·m. Furthermore, regarding the branch admittance between grounding points, in the frequency range of 1 MHz to 30 MHz, the branch admittance is 1 to 2 orders of magnitude smaller than the ground-to-ground admittance of each grounding point, and can be treated as an open circuit. For example, at 10 MHz, the ground-to-ground admittance of grounding point 1 is approximately 0.025 S, while the branch admittance between grounding points 1 and 2 is only 0.00023 S, meaning the branch admittance between grounding points 1 and 2 is only about 1% of the ground-to-ground admittance of grounding point 1. Therefore, considering the simplicity and practicality of the overall model, the mutual admittance between grounding points is not considered in the overall modeling.

[0106] A four-pole rational function is used to fit the frequency response characteristics of the ground admittance at the grounding point of the ground grid. Among them, y 10 , y 20 , y 30 , y 50It contains two real poles and a pair of conjugate complex poles. Its wideband equivalent circuit model is shown in Figure 5(a), and the parameters of each component are shown in Table 2.4. y 40 , y 60 , y 70 It contains four real poles, and its wideband equivalent circuit is shown in Figure 5(b). The parameters of each component are shown in Table 2.5.

[0107] respectively y 10 and y 40 For example, the broadband equivalent circuit model is compared with the original data and the results obtained by the vector matching method. The comparison results show that the established broadband equivalent circuit model can well reflect the amplitude-frequency and phase-frequency response characteristics of the original data.

[0108] Table 2.4y 10 y 20 y 30 y 50 Wideband equivalent circuit parameters

[0109] Table 2.5y 40 y 60 y 70 Wideband equivalent circuit parameters

[0110] II. Calculation and analysis of transient overvoltage in a 1000kV test circuit based on the established equivalent model.

[0111] Establishment of VFTO-TEV co-simulation model in 1GIS test loop Previous simulations of TEVs mostly used VFTO as the source and employed Peterson's rule to solve for the wave process in the circuit. However, one of the prerequisites for applying Peterson's rule is that the wave undergoes only one reflection at the node. Since transient waves on the casing undergo multiple reflections at the grounding point, a joint simulation model of VFTO-TEV should be established to calculate a more accurate TEV.

[0112] 1.1 Calculation Results of the Co-simulation Model In the simulation of the dynamic arc model in Chapter 2, the GIS busbar was simulated using a fixed wave impedance, and the high-voltage bushing was simulated using ground capacitance. In the co-simulation model of this chapter, the high-frequency characteristics of the GIS busbar were simulated using port voltage-current relationships; the high-voltage bushing was replaced by a broadband equivalent circuit model. The transmission line model of the entire test circuit was equivalently represented by a port network to simulate the propagation of traveling waves on the central guide rod and the outer shell, and VFTO and TEV were considered in the same model for calculation. In addition, the co-simulation model also considered the broadband equivalent circuit models of the seven grounding posts and the grounding grid according to the specific grounding arrangement of the test circuit. The final schematic diagram of the VFTO-TEV co-simulation model is shown below. Figure 6 As shown: Taking the closing process as an example, the waveform and spectrum of the TEV at the end of the branch bus are obtained by simulation, as shown in Figure 7.

[0113] The TEV amplitude is approximately 131kV; the main frequencies of the TEV waveform are concentrated around 18MHz, 27MHz, 54MHz and 90MHz, with corresponding amplitudes of 2.76kV, 0.95kV, 0.80kV and 1.38kV, respectively.

[0114] 1.2 Consider the differences in TEV simulation results before and after the co-simulation model.

[0115] If we use the traditional method to calculate TEV, that is, first establish a VFTO simulation model, and then use the calculated VFTO as the excitation source for TEV simulation, the specific simulation process is as follows: Apply Peterson's rule to solve for TEV. The circuit should be supplied with a power supply with an amplitude twice that of VFTO as the equivalent power supply of the Peterson equivalent circuit. The formula for calculating the shell ripple impedance is as follows: (3.1) h The height of the center guide rod of the GIS busbar from the ground. R Where is the radius of the tube busbar.

[0116] To more accurately use Peterson's rule to solve for TEV, this section will only consider the combination of the simulation circuit of VFTO and the TEV calculation circuit. The VFTO generated by the disconnecting switch operation is added to the equivalent shell model of GIS using the TACS pointer. The grounding down conductor is equivalent to an inductance of 1.0 μH / m. Based on the above conditions, the waveform and spectrum of the potential of the GIS shell at the end of the branch bus are shown in Figure 8.

[0117] The TEV amplitude is approximately 184kV; the main frequencies of the TEV waveform are concentrated around 3.6MHz, 9MHz, and 19MHz, with corresponding amplitudes of 0.16kV, 0.29kV, and 0.07kV, respectively.

[0118] The above analysis shows that the VFTO-TEV co-simulation model contains richer high-frequency components in the TEV component. Traditional independent simulations of VFTO and TEV do not consider the broadband characteristics of GIS equipment, while the co-simulation model considers the broadband equivalent circuit model of the GIS busbar, high-voltage bushing, grounding grid, and grounding post. Therefore, compared to the independent simulation model, the co-simulation model more accurately reflects the high-frequency characteristics of TEV. Furthermore, the amplitude of TEV in the co-simulation model is smaller than that obtained using Peterson's rule. This is mainly because Peterson's rule only considers the single reflection of transient waves on the outer shell between adjacent grounding leads; while the co-simulation model can more accurately simulate transient waves leaking into the outer shell through impedance mismatches (especially high-voltage bushings) and can simulate multiple reflections of transient waves between grounding points. In calculating the Peterson equivalent circuit of TEV, it is difficult to accurately simulate the shell resistance, and therefore it is impossible to describe the attenuation of TEV during its propagation through the shell. However, the co-simulation model calculates the impedance of the conductor surface in detail when modeling the GIS busbar, thus providing a more accurate description of the shell damping.

[0119] 2. Factors affecting TEV.

[0120] 2.1 The effect of disconnector switch operating speed on TEV.

[0121] The operating speed of the disconnecting switch is an important factor affecting VFTO. There are generally two viewpoints: one viewpoint is that the faster the disconnecting switch operates, the shorter the time for a single opening and closing operation, and the fewer the number of breakdowns, thus reducing the possibility of VFTO; the other viewpoint is that the slower the disconnecting switch operates, the lower the residual voltage on the center conductor of the unloaded bus after opening, which is beneficial to reducing the amplitude of VFTO during closing.

[0122] During the tripping operation, the distance between the moving and stationary contacts of the disconnector gradually increases until the maximum contact gap is reached. Therefore, the maximum VFTO value usually occurs in the later stage of a single tripping operation. During the increase in contact distance, the positive breakdown voltage is still considered to be proportional to time. Once the contact gap reaches its maximum, the breakdown voltage remains constant. Assuming the maximum contact gap of the disconnector is still 50mm, simulations were performed on the VFTO amplitude at the end of the branch busbar within the tripping speed range of 0.1m / s to 1.0m / s. Simultaneously, the relationship between the positive breakdown voltage of the contact gap during the tripping operation and the contact gap formation time was corrected. The total simulation time was taken as 0.08s, and the results are shown in Table 3.2.

[0123] The table shows that when the opening speed is less than 0.8 m / s, the TEV amplitude at the end of the branch busbar generally increases gradually with the increase of the disconnecting switch operating speed. The TEV amplitude reaches its maximum value when the opening speed is equal to 0.8 m / s. Further increasing the opening speed results in a decrease in the TEV amplitude. This conclusion is consistent with the measured results of the test circuit. [6] .

[0124] Table 3.2 TEV amplitude at the end of the branch busbar under different tripping speeds

[0125] Figure 9 (a) and Figure 9 (b) The waveforms of the TEV at the end of the branch bus are given when the disconnecting switch opening speed is 0.4 m / s and 0.7 m / s, respectively. It can be observed that the faster the disconnecting switch opening speed, the fewer breakdowns occur during a single opening process. v The voltage waveform did not break down in the later stage when the speed was 0.7 m / s because the corresponding contact gap had reached its maximum value.

[0126] For the closing process, under the simulation conditions presented in this paper, a VFTO amplitude will appear during the first breakdown. This is because the simulation sets the first breakdown to occur when the power supply voltage is +1.0 pu and the residual voltage on the load side is -1.0 pu, and at this time, the transient voltage wave is superimposed on the peak value of the power frequency voltage. Therefore, the VFTO amplitude of subsequent breakdowns is lower than that of the first breakdown. Since the contact gap breakdown voltage is a constant value during the first breakdown, the operating speed of the disconnecting switch has no effect on the VFTO amplitude generated during the closing process. However, in reality, the residual voltage on the short bus after each opening is random, and the VFTO amplitude may not appear during the first breakdown. Therefore, the VFTO generated during closing is closely related to the residual voltage on the load side after opening.

[0127] 2.2 The impact of installing ferrite rings on TEV.

[0128] Ferrite rings can be classified into two types based on their materials: nickel-zinc ferrite rings and manganese-zinc ferrite rings, used to suppress electromagnetic interference in the high-frequency and low-frequency bands, respectively. Ferrite rings exhibit different impedance characteristics at different frequencies. As the permeability increases, the low-frequency impedance increases, while the high-frequency impedance decreases. Installing ferrite rings on both sides of an operating disconnect switch is equivalent to adding an equivalent impedance between the disconnect switch and the GIS busbar, as illustrated in the simulation diagram below. Figure 9 As shown.

[0129] Where K is the operating disconnect switch, R is the equivalent resistance of the ferrite core (equal to the surge impedance of the busbar), and L is the equivalent inductance of the ferrite core, with a value of 0.05mH. The closing process is taken as an example.

[0130] As shown in the figure, after adding the ferrite core, the TEV amplitude at M5 decreased from 131kV to 103kV, and the amplitudes of TEV in all frequency bands decreased. This indicates that adding the ferrite core has a significant suppression effect on TEV.

[0131] 2.3 The impact of branch bus length on TEV.

[0132] With branch bus lengths of 3m, 6m, and 9m, the TEV amplitude at measurement points M1 to M5 was simulated, and the results are shown in Table 3.3. Table 3.3 TEV amplitude at various observation points under different branch bus lengths

[0133] Based on the table above, the following conclusions can be drawn: The TEV amplitude at each measurement point did not change significantly with the change in branch bus length. The highest TEV amplitude was observed at point M4, and this amplitude remained constant regardless of the branch bus length. This is because point M4 is located at the SF6 / Air bushing, where high-frequency transient waves leak from the cylinder through the high-pressure bushing, forming TEV on the outer shell, hence the highest TEV amplitude at this location. Furthermore, as the branch bus length decreased, the TEV amplitude at its end increased. This is because the distance the TEV leaking from the high-pressure bushing travels along the outer shell to the end of the branch bus decreases, resulting in less TEV attenuation and thus a higher amplitude.

[0134] The presence of a branch busbar affects the propagation path of transient electromagnetic waves inside the GIS equipment and on the outer shell of the cylinder. Changing the length of the branch busbar alters the location where the maximum TEV (transient electromagnetic wave) occurs.

[0135] 3. Measures to suppress TEVs.

[0136] Transient electric vehicles (TEVs) can interfere with secondary equipment, affecting its normal operation. To avoid or mitigate the adverse effects of TEVs on power grid operation, the following limiting measures can be taken: (1) When designing and selecting disconnecting switches, attention should be paid to the impact of the operating speed of the disconnecting switch on the TEV amplitude. For disconnecting switches of different voltage levels and different models, the breakdown voltage per unit length of the contact gap is not the same, and the operating speed corresponding to the inflection point of the TEV amplitude change may be different. In actual operation, the adverse effects of operating speed on the TEV amplitude should be avoided as much as possible.

[0137] (2) Installing a ferrite ring has a significant suppressive effect on TEV. In actual operation, the amplitude of TEV can be reduced and the steepness of TEV can be decreased by adding a ferrite ring.

[0138] (3) The length of the branch busbar has little impact on TEV. In addition, changing the enclosure layout can change the propagation path of transient electromagnetic waves. For example, reducing the number of discontinuities in the enclosure can reduce wave reflection; shortening the distance between the operating mechanism and the grounding point can improve the grounding effect and reduce TEV, etc.

[0139] The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which this invention pertains may make various modifications or additions to the described specific embodiments or use similar methods to substitute them, without departing from the spirit of the invention or exceeding the scope defined by the appended claims.

Claims

1. A method for constructing a broadband equivalent circuit model of a ground network based on vector matching, characterized in that, Establish broadband equivalent circuit models of the main equipment of GIS stations suitable for engineering calculations, including building circuit models of GIS pipe bus port voltage and line current at high frequencies, building actual models of SF6 / Air high voltage bushings, and building broadband equivalent models of grounding grids composed of actual models of grounding grids and grounding supports; Based on the established dynamic arcing model of the disconnecting switch and the broadband equivalent circuit model of the main GIS equipment, the rapid transient overvoltage generated by the switch operation in the GIS test circuit is simulated and calculated. In the circuit model for constructing the GIS busbar port voltage and line current at high frequency, the parameters of the GIS busbar are divided into two parts: series impedance and parallel admittance. The series impedance part can be represented by two coupled equations: Self-impedance of the inner loop Z 11 It includes 3 parts: in, Z core,out represents the impedance per unit length of the outer surface of the central guide rod. Z Core / enclosure, insulation represents the impedance per unit length of the insulation between the center guide rod and the outer shell. Z enclosure,in represents the impedance per unit length of the inner surface of the enclosure; like r 1. r 2. R 1. R 2 satisfies the following relationship: Simplified to: Furthermore, the impedance per unit length of the insulation between the center guide rod and the outer casing is: 。 2. The method for constructing a broadband equivalent circuit model of a ground network based on vector matching as described in claim 1, characterized in that, In the external circuit, its self-impedance Z 22 for: in, Z enclosure,out represents the impedance per unit length of the outer surface of the enclosure. Z Enclosure / earth insulation refers to the impedance per unit length between the enclosure and the ground. Z Earth represents the return impedance of the earth; its calculation formulas are as follows: The Carson formula is used to calculate the ground return impedance: ρ Represents the resistivity of the earth, in Ω·m; when 1 / ρ ωε At 0, the displacement current in the ground is ignored; that is, the upper limit frequency used in the Carson formula is... For the calculation of self-impedance, φ =0; For the variation of current along the GIS busbar, the equations of each loop are independent of each other, that is: in, G 11 and C 11 It refers to the parallel conductance and capacitance per unit length of the SF6 insulation layer between the center conductor of the GIS busbar and the outer casing. G 22 and C 22 It refers to the parallel conductance and capacitance per unit length of the air insulation layer between the GIS shell and the ground; the capacitance calculation formula is as follows: in, ε 1 is the dielectric constant of SF6 gas. ε 0 is the permittivity of air; while for parallel conductance... G The dielectric loss angle can be used. δ or dielectric loss coefficient tan δ To represent, that is: Under alternating current voltage, the energy loss of a dielectric consists of two parts: conductivity loss caused by conductivity and polarization loss caused by periodic polarization. The relative permittivity of the dielectric is written as: For gaseous dielectrics, there exists Ignore the parallel conductance of the gaseous dielectric.

3. The method for constructing a broadband equivalent circuit model of a ground network based on vector matching as described in claim 1, characterized in that, Constructing an actual model of the SF6 / Air high-voltage bushing, including... Its S-parameters are obtained using the finite element method; The frequency response curve of its admittance parameters is obtained by parameter transformation; The vector matching method and impedance synthesis method are used to restore it to a broadband equivalent circuit; A practical model of the SF6 / Air high-voltage bushing is built based on the reconstructed broadband equivalent circuit.

4. The method for constructing a broadband equivalent circuit model of a ground network based on vector matching as described in claim 1, characterized in that, The vector matching method is specifically based on the frequency response function: Among them, the residue c n and extreme points a n It is either a real number or a pair of conjugate complex numbers. d and h It is a real number; it is obtained at a given frequency interval. f ( s The least squares approximation of ) requires calculating all coefficients in the above formula; specifically, the poles should be located first. a n Furthermore, it is known that the unknown quantities can be calculated using linear least squares equations. c n , d , h .

5. The method for constructing a broadband equivalent circuit model of a ground network based on vector matching as described in claim 1, characterized in that, The conjugate complex pole part, real pole part, and linear and constant terms are obtained by impedance synthesis method; in 。 6. A method for constructing a broadband equivalent circuit model of a ground network based on vector matching as described in claim 1, characterized in that, The actual model of SF6 / Air high-voltage bushing is constructed, including The S-parameters are converted into Y-parameters, and a rational function is fitted using the vector matching method. Fitting Y 1. Y The rational function of 3 contains 4 pairs of conjugate complex poles; fitting Y The rational function of 2 contains 3 pairs of conjugate complex poles.

7. The method for constructing a broadband equivalent circuit model of a ground network based on vector matching as described in claim 1, characterized in that, A practical model of the grounding grid and grounding posts is constructed. The response characteristics under different frequency excitations are obtained using the method of moments. The corresponding broadband equivalent circuit model is established. The equivalent circuits of the grounding posts supporting the disconnecting switch, the grounding posts supporting the bushing, and the grounding posts supporting the GIS busbar are the same. Each grounding post in the circuit is equivalent to a closed-loop circuit consisting of a resistor, an inductor, and a parallel resistor and capacitor connected in sequence. The remaining components are equivalent to resistors and inductors connected in sequence. The establishment of the broadband equivalent model of the grounding grid includes: The GIS test circuit grounding grid has 7 grounding points. These 7 grounding points are considered as 7 nodes, and the equivalent circuit of the grounding grid is established using the nodal admittance method; in the first... i Current injected at each node I i ( i =1, 2, ..., 7), measure the ground potential rise at each node. U 1i , U 2i ,..., U 7i Then we have: Solving this matrix equation yields the nodal admittance matrix of the ground network; The admittance of each node in the grounding network to the zero-potential branch is y i0 ,node i With nodes j The branch admittance between them is y ij The relationship between the elements in the admittance matrix of each branch and the admittance matrix of the ground network nodes is as follows: 。 8. The method for constructing a broadband equivalent circuit model of a ground network based on vector matching as described in claim 1, characterized in that, During simulation calculations, specifically including The high-frequency characteristics of the GIS busbar are simulated using the port voltage-current relationship, and the high-voltage bushing is replaced by a broadband equivalent circuit model. The transmission line model of the entire test loop is equivalent to a port network to simulate the propagation of traveling waves on the central guide rod and the outer shell, and VFTO and TEV are considered in the same model for calculation. Based on the specific grounding arrangement of the test circuit, a broadband equivalent circuit model of 7 grounding pillars and grounding grid was incorporated to obtain the final VFTO-TEV joint simulation model.

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