CN107505536B - Transformer substation grounding grid earth surface potential distribution calculation method considering multiple metal pipelines - Google Patents

Transformer substation grounding grid earth surface potential distribution calculation method considering multiple metal pipelines Download PDF

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CN107505536B
CN107505536B CN201710665777.3A CN201710665777A CN107505536B CN 107505536 B CN107505536 B CN 107505536B CN 201710665777 A CN201710665777 A CN 201710665777A CN 107505536 B CN107505536 B CN 107505536B
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matrix
metal
grounding grid
potential
transformer substation
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CN107505536A (en
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施会
王丰华
盛连军
茅晓亮
周超杰
朱李超
黄建勇
孟琦斌
吕佩佩
吴顺超
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Shanghai Jiaotong University
State Grid Shanghai Electric Power Co Ltd
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State Grid Shanghai Electric Power Co Ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/08—Locating faults in cables, transmission lines, or networks
    • G01R31/081—Locating faults in cables, transmission lines, or networks according to type of conductors
    • G01R31/086—Locating faults in cables, transmission lines, or networks according to type of conductors in power transmission or distribution networks, i.e. with interconnected conductors
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation

Abstract

The invention relates to a method for calculating the distribution of earth surface potential of a transformer substation grounding grid considering a plurality of metal pipelines. Compared with the prior art, the method has the advantages of improving the accuracy of the earth surface potential distribution calculation of the transformer substation grounding grid, reducing the calculation amount and the like.

Description

Transformer substation grounding grid earth surface potential distribution calculation method considering multiple metal pipelines
Technical Field
The invention relates to the technical field of transformer substation grounding networks, in particular to a method for calculating the distribution of earth surface potentials of a transformer substation grounding network by considering a plurality of metal pipelines.
Background
The grounding grid is an important component of a transformer substation, and the reliability of the grounding grid has great significance for safe and stable operation of a power system. In order to ensure the safe and reliable operation of the grounding grid, how to accurately and effectively find the potential fault of the grounding grid and then take protective measures in a targeted manner becomes the most prominent problem in the operation and maintenance work of the power industry. A grounding grid fault diagnosis method based on earth surface potential distribution is one of the more applied means at present. However, the field environment of the transformer substation is complex, and the existence of the underground metal pipeline can affect the earth surface potential of the grounding grid and the accuracy of a fault diagnosis result thereof. Therefore, it is necessary to analyze and research the influence of the underground metal pipeline on the ground potential distribution of the transformer substation grounding grid, so as to provide a basis for effective diagnosis of the grounding grid fault.
The study of scholars at home and abroad on the distribution of the earth surface potential of the grounding grid of the transformer substation is mainly divided into two types: and (4) numerical calculation and field test. The numerical calculation is mainly to calculate and analyze the earth surface potential distribution according to the grounding grid structure, and commonly used methods are a finite difference method, a finite element method, an analog charge method, a boundary element method and the like. The field test is mainly used for researching more accurate test on the distribution of the surface potential of the actual grounding grid of the transformer substation.
However, the earth surface potential of the grounding grid of the transformer substation is mostly calculated according to a design drawing of the grounding grid at present. In addition, when the field test result of the grounding grid of the transformer substation is analyzed, the test result is only related to the state of the grounding grid and the soil structure, and the influence of the underground metal pipeline of the transformer substation on the surface potential is ignored, so that the obtained related test result is difficult to reflect the actual condition of the surface potential distribution of the grounding grid of the transformer substation.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a method for calculating the earth surface potential distribution of a grounding grid of a transformer substation, which takes a plurality of metal pipelines into account.
The purpose of the invention can be realized by the following technical scheme:
a method for calculating the distribution of earth surface potentials of a transformer substation grounding network considering a plurality of metal pipelines comprises the following steps:
1) obtaining the injection current i of the grounding gridset；
2) Establishing a potential relation expression of the grounding grid and the plurality of pipelines:
Figure GDA0002210078840000021
in the formula: r00The resistance coefficient matrix of the grounding grid is self; u shape0,UA,UB,…,UKThe potentials of the grounding grid and the metal pipelines are set; i is0,I1,…,IKThe distributed current is distributed for the grounding grid and a plurality of metal pipelines; t isA,TB,…,TKThe equivalent circuit matrix is an equivalent circuit matrix of a plurality of metal pipelines; rIJThe resistance coefficient matrix is a resistance coefficient matrix which is influenced by a grounding grid and a plurality of metal pipeline pairs and each other, and I, J is A, B, …, K; k is the total number of the metal pipelines;
writing the potential relation expression into a matrix form as follows:
Figure GDA0002210078840000022
in the formula: rT＝[RA0TARB0TB…RK0TK]；
Figure GDA0002210078840000023
Figure GDA0002210078840000024
EmIs a unit matrix of m orders; m is the total number of subdivision sections of all metal pipelines; i is the ground net current distribution; i isA＝[I1I2…IK]The stray current distribution of K metal pipelines; u shapeAT＝[UAUB…UK]Is K metal pipeline potentials; u shape0To earth gridsAnd (4) electric potential.
3) Solving the potential relation matrix equation by applying an antisymmetric iterative algorithm to obtain I, IA、UATAnd U0；
4) And 3) calculating to obtain the potential of any point above the transformer substation grounding grid according to the step 3), wherein the potential of any point above the transformer substation grounding grid is defined as the sum of the potential generated at the point by the stray current of the grounding grid and the stray current of the metal pipeline.
And the equivalent circuit matrix of the metal pipeline is obtained by calculation by adopting a infinitesimal method.
The equivalent circuit matrix expression of the ith metal pipeline is as follows:
Figure GDA0002210078840000031
wherein, i is 1, …, K, ZL(j-1)The longitudinal resistance of the j section of the ith metal pipeline, wherein j is 1,2, …, a-1; a is the number of sections of the ith metal pipe.
In the step 3), the step of solving the potential relation matrix equation by applying an antisymmetric iterative algorithm comprises the following steps:
3a) given an arbitrary matrix X1With both the number of rows and the number of columns equal to the matrix [ I I ]AU0UAT]TThe number of columns of (a), let i equal to 1, and superscript T denote the transpose of the matrix;
3b) w is calculated according to the following equation1、P1And Q1The calculation formula is
Figure GDA0002210078840000032
Figure GDA0002210078840000033
Figure GDA0002210078840000034
3c) If W 10, or W1Not equal to 0 and Q1If the value is 0, stopping the calculation, and going to step 3f), otherwise, if the value is i +1, going to step 3 d);
3d) w is calculated according to the following equationi+1、Pi+1And Qi+1The calculation formula is
Figure GDA0002210078840000035
Figure GDA0002210078840000041
Figure GDA0002210078840000042
Figure GDA0002210078840000043
Wherein, | | WiI represents the matrix WiNorm of (d); < - > represents the inner product of the matrix;
3e) if W i+10, or W1Not equal to 0 and Q1If the value is 0, stopping calculation, and going to step 3f), otherwise, going to step 3 d);
3f) let Xi+1＝[I IAU0UAT]TI, I is obtainedA、UATAnd U0。
In the step 2), the grounding grid is taken as an equivalent body when the relation matrix equation is established.
The total number K of the metal pipelines is more than or equal to 1.
When the total number K of the metal pipelines is equal to 0, replacing the established relation matrix equation with a relation matrix equation
Figure GDA0002210078840000044
In the formula u0Is the ground net potential;
and solving the relational matrix equation to obtain the potential of the grounding grid and the distribution vector of the scattered current when the metal pipeline is not contained.
Compared with the prior art, the method provided by the invention considers the influence of the underground metal pipeline of the transformer substation on the grounding grid, can reflect the ground surface potential distribution condition of the grounding grid of the transformer substation as truly as possible, can provide important basis for the grounding grid fault diagnosis method based on ground surface potential distribution, and has the following beneficial effects:
(1) the earth surface potential distribution of the transformer substation grounding grid can be accurately and comprehensively calculated.
(2) The mutual influence between the longitudinal resistance of the metal pipeline and the stray current of the grounding grid is considered, and the accuracy of the ground surface potential distribution calculation of the grounding grid of the transformer substation is improved.
(3) The equivalent circuit matrix of the metal pipeline is obtained by adopting a infinitesimal method, so that the accuracy of the earth surface potential distribution calculation of the grounding network of the transformer substation is improved.
(4) And the grounding grid is taken as an equivalent body, and an antisymmetric iterative algorithm is applied to solve a potential relation matrix equation, so that the calculated amount is reduced.
(5) The method can be suitable for the condition that a plurality of metal pipelines exist near the grounding grid, and the comprehensiveness of the distribution calculation of the earth surface potential of the grounding grid of the transformer substation is improved.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a calculated earth surface potential distribution of the grounding grid in the absence of metal pipes;
FIG. 3 is a calculated earth surface potential distribution of the grounding grid in the presence of metal pipes;
FIG. 4 is the measured ground potential distribution of the grounding grid;
fig. 5 shows the calculation and measurement results of the surface potential of the conductor through which the metal pipe passes.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.
As shown in fig. 1, the present embodiment provides a method for calculating a distribution of a ground potential of a transformer substation grounding grid in consideration of a plurality of metal pipelines, including the following steps:
1) obtaining the injection current i of the grounding gridset；
2) Taking the grounding grid as an equivalent body, establishing a potential relation expression of the grounding grid and the plurality of pipelines:
Figure GDA0002210078840000051
in the formula: r00The resistance coefficient matrix of the grounding grid is self; u shape0,UA,UB,…,UKThe potentials of the grounding grid and the metal pipelines are set; i is0,I1,…,IKThe distributed current is distributed for the grounding grid and a plurality of metal pipelines; t isA,TB,…,TKThe equivalent circuit matrix is an equivalent circuit matrix of a plurality of metal pipelines; rIJThe resistance coefficient matrix is a resistance coefficient matrix which is influenced by a grounding grid and a plurality of metal pipeline pairs and each other, and I, J is A, B, …, K; k is the total number of the metal pipelines.
Writing the potential relation expression into a matrix form as follows:
Figure GDA0002210078840000061
in the formula: rT＝[RA0TARB0TB... RK0TK]；
Figure GDA0002210078840000062
Figure GDA0002210078840000063
EmIs a unit matrix of m orders; m is the total number of subdivision sections of all metal pipelines; i is the ground net current distribution; i isA＝[I1I2…IK]The stray current distribution of K metal pipelines; u shapeAT＝[UAUB…UK]The potential distribution of the metal pipeline is adopted; u shape0Is the ground net potential.
3) Solving the potential relation matrix equation by applying an antisymmetric iterative algorithm to obtain I, IA、UATAnd U0. The basic steps are as follows:
3a) given an arbitrary matrix X1With both the number of rows and the number of columns equal to the matrix [ I I ]AU0UAT]TI is 1. Here, superscript T represents the transpose of the matrix;
3b) w is calculated according to the following equation1、P1And Q1The calculation formula is
Figure GDA0002210078840000064
Figure GDA0002210078840000065
Figure GDA0002210078840000066
3c) If W 10, or W1≠0，Q1If the value is 0, stopping the calculation, and turning to 3f), otherwise, if the value is i +1, turning to 3 d);
3d) w is calculated according to the following equationi+1、Pi+1And Qi+1The calculation formula is
Figure GDA0002210078840000071
Figure GDA0002210078840000072
Figure GDA0002210078840000073
Figure GDA0002210078840000074
Wherein, | | WiI represents the matrix WiNorm of (d); < - > represents the inner product of the matrix.
3e) If W isi+10, or W1≠0，Q1If the value is 0, stopping the calculation, and turning to 3f), otherwise, turning to 3 d);
3f) let Xi+1＝[I IAU0UAT]TI, I is obtainedA、UATAnd U0。
4) And 3) calculating to obtain the potential of any point in the space according to the step 3), wherein the potential of any point in the space is defined as the sum of the potential generated by the stray current of the grounding grid and the stray current of the metal pipeline at the point.
The equivalent circuit matrix of the metal pipeline is obtained by adopting a infinitesimal method for calculation, and the equivalent circuit matrix expression of the ith metal pipeline is as follows:
Figure GDA0002210078840000075
wherein, i is 1, …, K, ZL(j-1)The longitudinal resistance of the j-th segment of the ith metal pipeline is j equal to 1,2, …, a-1, and a is the number of the segments of the ith metal pipeline.
The distribution calculation method is suitable for the condition that the total number K of the metal pipelines is more than or equal to 1.
When the total number K of the metal pipelines is 0, replacing the established relation matrix equation with that of the metal pipelines
Figure GDA0002210078840000081
In the formula u0Is the ground net conductor potential;
and solving the relational matrix equation to obtain the potential of the grounding grid and the distribution vector of the scattered current when the metal pipeline is not contained.
Referring to fig. 1, in order to verify the accuracy of the method for calculating the distribution of the earth surface potential of the transformer substation grounding grid based on the field coupling, the field earth surface potential distribution of the actual 35kV transformer substation grounding grid is measured.
Fig. 2 to 3 show the calculated ground potential distribution of the 35kV substation grounding grid, fig. 2 shows the ground potential distribution in the actual case (i.e., the substation has underground metal pipes), and fig. 3 shows the ground potential when the substation is assumed to have no metal pipes. Here, the 2 pipes are each 2m in length and 4cm in radius. As can be seen from fig. 2-3, when there is no underground metal pipeline in the substation, the ground potential distribution curve of the grounding grid is smoother, the ground potential above the conductor is significantly higher than that above the mesh, the potentials at the two end nodes of the conductor are slightly higher than the potential at the middle section of the conductor, and meanwhile, the potentials are higher as the current injection point is closer; the maximum value of the earth surface potential is 1.513V and appears at a current injection point; the potential minimum was 0.693V, appearing in the center of the lower left mesh. When the transformer substation has metal pipelines, the general rule of the earth surface potential distribution, the maximum value and the minimum value of the earth surface potential are consistent with the condition when no pipelines exist; but the surface potential curve above the pipe is not very smooth.
Fig. 4 shows the measured ground potential distribution of the grounding grid. As can be seen from the figure, the earth surface potential distribution rule obtained by field measurement is consistent with the calculation result. The maximum value of the earth surface potential is also present at a current injection point, the magnitude is 1.484V, and the error with the calculation result is only 1.94%; the surface potential minimum also appears in the center of the lower left mesh, 0.710V, with an error of only 2.50% from the calculated results. The consistency of the surface potential distribution measurement and the calculation result verifies the accuracy of the calculation result obtained by the method.
In order to more intuitively embody the accuracy of the method for calculating the earth surface potential value of the transformer substation grounding grid based on the field coupling, fig. 5 compares the earth surface potential calculation and measurement results of conductors in the OB section (i.e. conductors through which metal pipelines pass). As can be seen from the figure, the approximate change rules of the 3 surface potential curves are consistent, and only certain differences exist in the areas where the metal pipelines pass through. Comparing the 2 calculated curves, it can be seen that the surface potential in this region with the metal pipe is reduced by at most about 6.66% compared to the case without the pipe. In the region, the measurement result and the corresponding calculation result have higher coincidence degree, only because of the influence of factors such as measurement error, field interference and the like, part of the measurement result and the calculation result have little difference, but the difference degree is smaller and is in an acceptable range. The potential of the surface potential measurement decreased by up to about 8.29% compared to the calculation without the pipe. Therefore, the substation grounding grid earth surface potential numerical calculation method based on the field coupling can accurately and comprehensively calculate the distribution of the substation grounding grid earth surface potential. Meanwhile, the influence of the underground metal pipeline of the transformer substation on the grounding grid is considered, the ground potential distribution condition of the grounding grid of the transformer substation can be reflected as truly as possible, and an important basis can be provided for the grounding grid fault diagnosis method based on the ground potential distribution.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.

Claims (6)

1. A method for calculating the distribution of earth surface potentials of a transformer substation grounding network considering a plurality of metal pipelines is characterized by comprising the following steps:
1) obtaining the injection current i of the grounding gridset；
2) Establishing a potential relation expression of the grounding grid and the plurality of pipelines:
Figure FDA0002210078830000011
in the formula: r00The resistance coefficient matrix of the grounding grid is self; u shape0,UA,UB,…,UKThe potentials of the grounding grid and the metal pipelines are set; i is0,I1,…,IKThe distributed current is distributed for the grounding grid and a plurality of metal pipelines; t isA,TB,…,TKThe equivalent circuit matrix is an equivalent circuit matrix of a plurality of metal pipelines; rIJFor grounding net and multiple metal pipesFor the resistivity matrices, I, J ═ a, B, …, K, which affect themselves and each other; k is the total number of the metal pipelines;
writing the potential relation expression into a matrix form as follows:
Figure FDA0002210078830000012
in the formula: rT＝[RA0TARB0TB… RK0TK]；RP＝[R0AR0B… R0K]；
Figure FDA0002210078830000013
Figure FDA0002210078830000014
EmIs a unit matrix of m orders; m is the total number of subdivision sections of all metal pipelines; i is the ground net current distribution; i isA＝[I1I2… IK]The stray current distribution of K metal pipelines; u shapeAT＝[UAUB… UK]Is K metal pipeline potentials; u shape0Is the ground net potential.
3) Solving the potential relation matrix equation by applying an antisymmetric iterative algorithm to obtain I, IA、UATAnd U0；
4) Calculating to obtain the potential of any point above the transformer substation grounding grid according to the step 3), wherein the potential of any point above the transformer substation grounding grid is defined as the sum of the potential generated at the point by the grounding grid stray current and the metal pipeline stray current;
in the step 3), the step of solving the potential relation matrix equation by applying an antisymmetric iterative algorithm comprises the following steps:
3a) given an arbitrary matrix X1With both the number of rows and the number of columns equal to the matrix [ I I ]AU0UAT]TThe number of columns of (a), let i equal to 1, and superscript T denote the transpose of the matrix;
3b) w is calculated according to the following equation1、P1And Q1The calculation formula is
Figure FDA0002210078830000021
Figure FDA0002210078830000022
Figure FDA0002210078830000023
3c) If W10, or W1Not equal to 0 and Q1If the value is 0, stopping the calculation, and going to step 3f), otherwise, if the value is i +1, going to step 3 d);
3d) w is calculated according to the following equationi+1、Pi+1And Qi+1The calculation formula is
Figure FDA0002210078830000024
Figure FDA0002210078830000025
Figure FDA0002210078830000026
Figure FDA0002210078830000027
Wherein, | | WiI represents the matrix WiNorm of (d); < - > represents the inner product of the matrix;
3e) if Wi+10, or W1Not equal to 0 and Q1If the value is 0, stopping calculation, and going to step 3f), otherwise, going to step 3 d);
3f) let Xi+1＝[I IAU0UAT]TI, I is obtainedA、UATAnd U0。
2. The method for calculating the earth surface potential distribution of the transformer substation grounding network considering the plurality of metal pipelines according to claim 1, wherein the equivalent circuit matrix of the metal pipelines is obtained by calculation through a infinitesimal method.
3. The method for calculating the earth surface potential distribution of the transformer substation grounding network considering the plurality of metal pipelines according to claim 2, wherein the equivalent circuit matrix expression of the ith metal pipeline is as follows:
Figure FDA0002210078830000031
wherein, i is 1, …, K, ZL(j-1)The longitudinal resistance of the j section of the ith metal pipeline, wherein j is 1,2, …, a-1; a is the number of sections of the ith metal pipe.
4. The method for calculating the earth surface potential distribution of the transformer substation grounding network considering the plurality of metal pipes according to claim 1, wherein in the step 2), the grounding network is regarded as an equivalent body when the relational matrix equation is established.
5. The method for calculating the earth surface potential distribution of the transformer substation grounding network considering the plurality of metal pipelines according to claim 1, wherein the total number K of the metal pipelines is more than or equal to 1.
6. The method for calculating the earth surface potential distribution of the transformer substation grounding network considering a plurality of metal pipelines according to claim 1, wherein when the total number K of the metal pipelines is 0, the established relation matrix equation is replaced by
Figure FDA0002210078830000032
In the formula u0Is the ground net potential;
and solving the relational matrix equation to obtain the potential of the grounding grid and the distribution vector of the scattered current when the metal pipeline is not contained.
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