CN109408868B - Transformer winding space electric field calculation method - Google Patents
Transformer winding space electric field calculation method Download PDFInfo
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- 230000005684 electric field Effects 0.000 title claims abstract description 70
- 238000004804 winding Methods 0.000 title claims abstract description 57
- 238000004364 calculation method Methods 0.000 title claims abstract description 12
- 239000004020 conductor Substances 0.000 claims abstract description 46
- 238000000034 method Methods 0.000 claims abstract description 27
- 238000009826 distribution Methods 0.000 claims abstract description 14
- 238000009827 uniform distribution Methods 0.000 claims abstract description 4
- 238000011438 discrete method Methods 0.000 claims description 3
- 230000005686 electrostatic field Effects 0.000 claims description 3
- 238000010586 diagram Methods 0.000 description 2
- 239000000463 material Substances 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
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Abstract
The invention relates to a method for calculating a space electric field of a transformer winding, which comprises the steps of constructing a two-dimensional model by taking a winding conductor section, dividing the conductor section model by a finite element, simplifying winding voltage into uniform distribution from a high-voltage end to a low-voltage end, and obtaining voltage distribution on each conductor. And obtaining a point electric field by the superposition integral of the electric fields of all parts of the conductor acting on one point in the space, and obtaining the electric field distribution around the winding conductor by the method. The invention can obtain the space electric field distribution of the transformer winding through simple calculation.
Description
Technical Field
The invention relates to the field of electric field calculation of transformer windings, in particular to a method for calculating a space electric field of a transformer winding.
Background
In recent years, the capacity of the transformer is increased along with the technical development, the internal insulation of the transformer is closely related to the internal electric field of the transformer, the research on the winding electric field has important significance for the safe and stable operation of the transformer, and no calculation method for the transformer winding space electric field which is easy to calculate exists at present.
Disclosure of Invention
In view of this, the present invention provides a method for calculating a space electric field of a transformer winding, which is simple in calculation.
The invention is realized by adopting the following scheme: a transformer winding space electric field calculation method comprises the following steps:
step S1: taking the section of a winding conductor to construct a two-dimensional model;
step S2: dividing a conductor section model through finite elements, simplifying winding voltage into uniform distribution from a high-voltage end to a low-voltage end, and further obtaining voltage distribution on each conductor;
step S3: the electric field of a point in space is obtained by the superposition integral of the electric fields of all parts of the conductor acting on the point in space, and then the electric field distribution around the winding conductor is obtained by the method.
Further, in step S1, the two-dimensional model of the winding conductor cross section is a regularly arranged circle.
Further, step S2 specifically includes the following steps:
step S21: subtracting the voltage of the low-voltage end from the voltage of the high-voltage end, and dividing the voltage by the number of turns of the winding to obtain a voltage level difference;
step S22: and obtaining the voltage difference of each turn according to the voltage level difference.
Further, in step S3, the step of obtaining the electric field at a point in space by the superposition and integration of the electric fields acting on the point in space by the respective portions of the conductor is specifically as follows: the finite element idea is applied, the integral area is divided into a plurality of subunits by a discrete method, then the discrete subunits are used for calculating a multivariate extreme value, and finally, the electric field of each point is obtained by a corresponding algebraic method according to the characteristics of an equation set.
Further, the step S3 of obtaining the electric field at a point in space by the superposition integral of the electric fields acting on the point in space by the respective portions of the conductor specifically includes the following steps:
step S31: one point P (x, y, z) in the computation space 0 ) In which z is 0 The position of the cross section is symmetrical in the front and back direction, and the position of the cross section does not influence the size of the electric field, so that the electric field of the P (x, y) point is only needed to be calculated, the electric fields of all elements of the cross section at the point are superposed, and the obtained superposed electric field is a three-dimensional electric field;
step S32: memory element (x) i ，y j ) To a point in space electric field of
The electric field at that point is the sum of the infinitesimal values at that point,
wherein n represents the total number of the longitudinal coordinate points of the winding number; m represents the total number of the abscissa of the winding number;
wherein,
the method specifically comprises the following steps:
step S33: the potential of the point P (x, y) for each small winding conductor section is calculated using the following formula
In the formula, σ (x) i ,y i ) The electric charge density of the winding conductor section infinitesimal at the moment, R is the distance from a point P (x, y) to a certain infinitesimal, S represents the infinitesimal area of the conductor section, and epsilon 0 Represents the vacuum dielectric constant;
step S34: solving the potential of the space electrostatic field by adopting a finite element method, and utilizing a Laplace equation:
wherein ε represents a dielectric constant of air,
is the potential of a certain point in space, gamma is the boundary of a field region,
in order to set the electrical potential value at the boundary,
represents the laplacian operator; and solving the Laplace partial differential equation by adopting a finite element method to obtain the electric field distribution of one point P (x, y) in the winding conductor space.
Compared with the prior art, the invention has the following beneficial effects: the method of the invention can be used for simply calculating the space electric field distribution of the transformer winding.
Drawings
Fig. 1 is a schematic diagram of a winding cross-section model according to an embodiment of the present invention.
FIG. 2 is a schematic diagram of an electric field calculation method according to an embodiment of the present invention.
FIG. 3 is a flow chart of a method according to an embodiment of the present invention.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an", and/or "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of the features, steps, operations, devices, components, and/or combinations thereof.
As shown in fig. 1, fig. 2 and fig. 3, the present embodiment provides a method for calculating a space electric field of a transformer winding, including the following steps:
step S1: taking the section of a winding conductor to construct a two-dimensional model;
step S2: dividing a conductor section model through finite elements, simplifying winding voltage into uniform distribution from a high-voltage end to a low-voltage end, and further obtaining voltage distribution on each conductor;
step S3: the electric field of a point in space is obtained by the superposition integral of the electric fields of all parts of the conductor acting on the point in space, and then the electric field distribution around the winding conductor is obtained by the method.
As shown in fig. 1, in the present embodiment, in step S1, the two-dimensional model of the winding conductor cross section is a circle with regular arrangement.
In this embodiment, to determine the applied boundary condition, the winding conductor is required to be powered up, and the step S2 specifically includes the following steps:
step S21: subtracting the voltage of the low-voltage end from the voltage of the high-voltage end, and dividing the voltage by the number of turns of the winding to obtain a voltage level difference;
step S22: and obtaining the voltage difference of each turn according to the voltage level difference.
For example, if the difference between the high voltage terminal and the low voltage terminal is 38.5KV and the total number of turns is 2292, the voltage difference is 16.8V, and the voltage difference of each turn is subtracted from the voltage of the next turn from the high voltage terminal to the low voltage terminal to obtain the voltage of each turn, which is calculated from U (x) 1 ，y 1 ) Can obtain U (x) 2 ，y 1 )，With U (x) 2 ，y 1 ) Find U (x) 3 ,y 1 ) And the same reasoning can be used to obtain the end U (x) of the first column n ，y 1 ) The next following can determine the first row U (x) of the second column 1 ，y 2 ) Finally, the end voltage U (x) is determined n ，y n )。
In this embodiment, in step S3, the step of obtaining the electric field at one point in space from the superposition integral of the electric fields acting on the one point in space by the respective portions of the conductor is specifically as follows: the integral area is divided into a plurality of subunits by a discrete method by using the finite element thought, then a plurality of extreme values are calculated by using the discrete subunits, and finally the electric field of each point is obtained by using a corresponding algebraic method according to the characteristics of an equation set.
In this embodiment, the step S3 of obtaining the electric field at a point in space from the superposition integral of the electric fields acting on the point in space by the respective portions of the conductor specifically includes the following steps:
step S31: one point P (x, y, z) in the computation space 0 ) In which z is 0 The position of the cross section is symmetrical in the front and back direction, and the position of the cross section does not influence the size of the electric field, so that the electric field of the P (x, y) point is only needed to be calculated, the electric fields of all elements of the cross section at the point are superposed, and the obtained superposed electric field is a three-dimensional electric field;
step S32: memory element (x) i ，y j ) To a point in space electric field of
The electric field at that point is the summation of the infinitesimal elements at that point,
wherein n represents the total number of the longitudinal coordinate points of the winding number; m represents the total number of the abscissa of the winding number;
in which, as shown in figure 2,
the method specifically comprises the following steps:
step S33: the potential of the point P (x, y) for each small winding conductor section is calculated using the following formula
In the formula, σ (x) i ,y i ) The electric charge density of the winding conductor section infinitesimal at the moment, R is the distance from a point P (x, y) to a certain infinitesimal, S represents the infinitesimal area of the conductor section, epsilon 0 Represents a vacuum dielectric constant;
step S34: solving the potential of the space electrostatic field by adopting a finite element method, and utilizing a Laplace equation:
wherein ε represents a dielectric constant of air,
is the potential of a certain point in space, gamma is the field boundary,
in order to set the electrical potential value at the boundary,
represents the laplacian operator; and solving the Laplace partial differential equation by adopting a finite element method to obtain the electric field distribution of one point P (x, y) in the winding conductor space.
Because the cross sections of the winding conductors are uniformly distributed, the calculation precision can be effectively improved by using the calculation of the two-dimensional mode under the condition of meeting the requirements and conditions.
In this embodiment, a discretization iterative operation may be performed by using a finite element method, and the specific steps of calculating the electric field by using the calculation programming are as follows:
firstly, analyzing a specific model and a problem to be solved, making a reasonable assumption, and drawing a winding conductor model by using drawing software.
And secondly, adding material properties, respectively setting physical parameters of the material, and looking up and setting the relative dielectric constant of the winding conductor.
And thirdly, carrying out grid division and discretization on the imported model, applying boundary conditions according to winding voltage and solving.
And fourthly, taking the sectional area of each winding as a unit, and performing iterative operation on a plurality of windings and accumulating and summing to obtain the electric field distribution.
The above description is only a preferred embodiment of the present invention, and all equivalent changes and modifications made in accordance with the claims of the present invention should be covered by the present invention.
Claims (3)
1. A transformer winding space electric field calculation method is characterized by comprising the following steps: the method comprises the following steps:
step S1: taking the section of a winding conductor to construct a two-dimensional model;
step S2: dividing a conductor section model through finite elements, simplifying winding voltage into uniform distribution from a high-voltage end to a low-voltage end, and further obtaining voltage distribution on each conductor;
step S3: the electric field superposition integral of each part of the conductor acting on one point of the space is used for obtaining the electric field of the point of the space, and then the electric field distribution around the winding conductor is obtained by the method;
in step S3, the step of obtaining the electric field at a point in space by the superposition integral of the electric fields acting on the point in space by the respective portions of the conductor is specifically: by using the finite element thought, the integral area is divided into a plurality of subunits by a discrete method, then the discrete subunits are used for calculating a multivariate extreme value, and finally, according to the characteristics of an equation set, the electric field of each point is obtained by a corresponding algebraic method;
in step S3, the step of obtaining the electric field at a point in space by the superposition integral of the electric fields applied to the point in space by the respective portions of the conductor specifically includes the following steps:
step S31: one point P (x, y, z) in the computation space 0 ) In which z is 0 The position of the cross section is the position of the winding conductor, and the position of the cross section does not influence the size of the electric field, so that the size of the electric field of the P (x, y) point is only needed to be calculated, the electric fields of all elements of the cross section at the point are superposed, and the obtained superposed electric field is a three-dimensional electric field;
step S32: memory element (x) i ，y j ) To a point in space electric field of
The electric field at that point being the sum of the infinitesimal elements at that point, i.e.
Wherein n represents the total number of the ordinate of the winding number, and m represents the total number of the abscissa of the winding number;
step S33: the potential of the point P (x, y) for each small winding conductor cross section is calculated using the following formula
In the formula, σ (x) i ,y i ) The electric charge density of the winding conductor section infinitesimal at the moment, R is the distance from a point P (x, y) to a certain infinitesimal, S represents the infinitesimal area of the conductor section, epsilon 0 Represents the vacuum dielectric constant;
step S34: solving the potential of the space electrostatic field by adopting a finite element method, and utilizing a Laplace partial differential equation:
wherein ε represents a dielectric constant of air,
is the potential of a certain point in space, gamma is the field boundary,
in order to set the electrical potential value at the boundary,
represents the laplacian operator; and solving the Laplace partial differential equation by adopting a finite element method to obtain the electric field distribution of one point P (x, y) in the winding conductor space.
2. The method for calculating the space electric field of the transformer winding according to claim 1, wherein the method comprises the following steps: in step S1, the two-dimensional model constructed on the cross section of the winding conductor is a circle arranged regularly.
3. The method for calculating the space electric field of the transformer winding according to claim 1, wherein the method comprises the following steps: the step S2 specifically includes the following steps:
step S21: subtracting the voltage of the low-voltage end from the voltage of the high-voltage end, and dividing the voltage by the number of turns of the winding to obtain a voltage level difference;
step S22: and obtaining the voltage difference of each turn according to the voltage level difference.
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