CN110795870A - Optimization design method for DC high-voltage generator grading ring - Google Patents

Optimization design method for DC high-voltage generator grading ring Download PDF

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CN110795870A
CN110795870A CN201910912409.3A CN201910912409A CN110795870A CN 110795870 A CN110795870 A CN 110795870A CN 201910912409 A CN201910912409 A CN 201910912409A CN 110795870 A CN110795870 A CN 110795870A
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factor
voltage generator
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李登云
朱凯
岳长喜
李智成
余佶成
李鹤
熊魁
刘洋
邱进
周加斌
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China Electric Power Research Institute Co Ltd CEPRI
Electric Power Research Institute of State Grid Shandong Electric Power Co Ltd
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China Electric Power Research Institute Co Ltd CEPRI
Electric Power Research Institute of State Grid Shandong Electric Power Co Ltd
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Abstract

The invention provides an optimized design method of a DC high-voltage generator grading ring. The invention establishes a simulation model of a direct-current high-voltage generator; listing parameter variables of the main equalizing ring and the auxiliary equalizing ring; selecting a proper orthogonal table according to the number and the horizontal number of the variable factors; constructing a test scheme matrix according to the orthogonal table; calculating the corresponding statistic of each factor according to the test scheme matrix; finding the optimal level of each factor, thereby obtaining a group of optimal parameter combinations; and carrying out significance test according to the deviation square sum and the mean square sum of each factor to obtain the significance level of each factor. The invention greatly reduces the test times, calculates the time and improves the efficiency.

Description

Optimization design method for DC high-voltage generator grading ring
Technical Field
The invention relates to the technical field of direct current transmission, in particular to an optimization design method for a direct current high-voltage generator grading ring.
Background
The primary equipment of the direct current transmission system is influenced by factors such as environment temperature and humidity, hidden insulation defects may exist in local parts of the equipment, and if the equipment is directly put into operation, accidents may occur, and the stable operation of a power grid is influenced. Therefore, before the new equipment is put into operation, a direct-current high-voltage test is required to detect whether the performance of the equipment meets the requirements of technical indexes. The 1100kV direct-current high-voltage generator is used as important primary equipment of a direct-current high-voltage test and is mainly used for insulation tests, performance test tests and the like of part of electric equipment of a direct-current transmission system. The output parameters of the dc high voltage generator and the corona itself are closely related to the reliability of the test results, while the corona of the device is mainly dependent on the field intensity distribution on the surface of the generator. If no voltage grading measures are taken around the generator, the corona current and leakage current of the generator increase with increasing voltage level.
At present, a plurality of equalizing rings are generally installed around the generator, so that the maximum field intensity on the surface of the generator is reduced, the voltage distribution on the surface can be more uniform, and the initial corona field intensity is reduced. The size parameters (main radius, inner ring radius) and the mounting position of the grading ring have an important influence on the surface electric field intensity of the generator. Therefore, the electric field intensity on the surface of the generator can be effectively reduced by optimally designing the grading ring on the surface of the generator.
At present, the finite element method is widely applied to the field of electromagnetic field numerical calculation, and many researchers aim at limiting the maximum field intensity on the surface of a generator, simulate the electric field distribution in the surrounding space of the generator by using the finite element analysis method, and reduce the maximum field intensity by additionally arranging a grading ring at the position with larger field intensity.
Disclosure of Invention
In order to reduce the maximum field intensity of the surface of a generator, the size and the installation position of a grading ring are mostly selected by adopting a trial and error method and experimental verification in the traditional method, the invention provides an optimal design method of a DC high-voltage generator grading ring based on orthogonal experimental design, the method introduces an orthogonal experimental method of multi-objective optimization to carry out optimal design on the size parameters and the installation position of the grading ring, and researches and analyzes the main radius, the inner ring radius and the influence of the ground height of the grading ring on the distribution of a surrounding electric field. The method can effectively reduce the test times, can also obtain more information about each factor than the test result, finds the optimal parameter combination and obtains the influence degree of each factor on the test result.
Specifically, the invention provides an optimized design method of a DC high-voltage generator grading ring, which comprises the following steps:
step 1, establishing a simulation model of a direct-current high-voltage generator;
step 2, listing parameter variables of the main equalizing ring and the auxiliary equalizing ring;
step 3, selecting a proper orthogonal table according to the number and the horizontal number of the variable factors;
step 4, constructing a test scheme matrix according to the orthogonal table;
step 5, calculating the corresponding statistic of each factor according to the test scheme matrix;
step 6, finding the optimal level of each factor so as to obtain a group of optimal parameter combinations;
step 7, carrying out significance test according to the deviation square sum and the mean square sum of each factor to obtain the significance level of each factor;
preferably, the boundary conditions to be satisfied by the simulation model of the dc high voltage generator in step 1 are:
in the formula: r represents the radius of the solution area,
Figure BDA0002215091240000022
representing the potential, and solving a potential function in the region to meet a Laplace equation;the high-voltage end potential of the generator is 1100 kV;
Figure BDA0002215091240000024
the ground potential is 0;
Figure BDA0002215091240000025
the electric potentials of the left side and the right side of the interface of different media are represented, and the electric potentials meet an electric potential continuity equation;
preferably, in step 2, parameter variables of the main equalizing ring and the auxiliary equalizing ring are listed:
setting m variables of parameters of the main equalizing ring and the auxiliary equalizing ring, wherein each variable has r values, constructing an r multiplied by m matrix A to describe the parameter variable, and counting al,jThe value of the l level of the jth variable is represented by the jth column in the l row of the matrix A, l is more than or equal to 1 and less than or equal to r, and j is more than or equal to 1 and less than or equal to m;
preferably, the selection of a suitable orthogonal table in step 3 is: l isn(rm) The method comprises the following steps of representing an orthogonal table, wherein L represents an orthogonal table symbol, n represents the number of times of testing, namely the row number of the orthogonal table, r represents the horizontal number of factors in the orthogonal test, and m represents the maximum number of factors allowed by the test, namely the column number of the orthogonal table;
preferably, the test protocol matrix in step 4 is:
Δ(i,j)
wherein i is more than or equal to 1 and less than or equal to n, j is more than or equal to 1 and less than or equal to m, and delta (i, j) represents the value of the jth element in the ith row of the test scheme table;
step pair according to the test scheme matrix Delta (i, j)1, carrying out simulation model test on the direct-current high-voltage generator by setting parameters of the equalizing ring in the simulation model, and recording the obtained test result as yi，yiRepresents the test results of row i;
preferably, the step 5 of calculating the corresponding statistic of each factor according to the test scheme matrix specifically includes:
step 5.1, calculating the sum K of the test results of the l level on the j columnl,jL is more than or equal to 1 and less than or equal to r, j is more than or equal to 1 and less than or equal to m, and l and j are both positive integers;
since the same level appears t times on each column, it is assumed that the test results are y1、y2···ytThen K isl,j＝y1+y2+···+yt；
Step 5.2, calculating the sum K of the test resultsl,jAverage value of (2) Wherein t is the number of occurrences of the horizontal number l on the jth column;
step 5.3, calculate the sum of squared deviations Sj，
Figure BDA0002215091240000033
Sum of mean square
Figure BDA0002215091240000034
Figure BDA0002215091240000035
Preferably, the optimal level of each factor is found in step 6, so as to obtain a set of optimal parameter combinations, specifically:
comparing different levels in column j
Figure BDA0002215091240000036
Size of (2), definition
Figure BDA0002215091240000037
Then
Figure BDA0002215091240000039
The level l of the column is the optimal level of the factor of the jth column, and is marked as ljmin(ii) a By analogy, the optimal level of each column of factors is found, and the optimal parameter combination is obtained;
preferably, in step 7, the significance test is performed according to the sum of squared deviations and the sum of mean square of each factor, and the significance level of each factor is specifically obtained as follows:
sum of squares of total deviations:
Figure BDA00022150912400000310
wherein, yiThe results of the test in row i are shown,
Figure BDA00022150912400000311
the sum of all test result data is shown, and n represents the test times;
calculating the sum of squared deviations Sj：
Figure BDA00022150912400000312
Wherein t represents the number of occurrences of the horizontal number l on the j-th column,
Figure BDA00022150912400000313
denotes the sum of the test results KljR represents the number of factor levels,the sum of all test result data is shown, and n represents the test times;
computing a sum of mean squares
Figure BDA0002215091240000042
Figure BDA0002215091240000043
Wherein SjRepresenting the sum of squares of deviations, fjDenotes SjThe degree of freedom of (c);
calculating ST、Sj、SeDegree of freedom fT、fjAnd fe：
fT＝n-1
fj＝r-1
fe＝fTSum of degrees of freedom of the factors
Wherein n represents the number of tests, and r represents the number of factor levels;
preferably, whether the jth factor has a significant influence on the test index is checked, and the statistic is calculated as follows:
Figure BDA0002215091240000044
wherein S isjRepresents the sum of squares of deviations, SeRepresents the sum of squared errors, fjDenotes SjDegree of freedom, feDenotes SeThe degree of freedom of (a) is,
Figure BDA0002215091240000045
the sum of the mean square deviations is represented,
Figure BDA0002215091240000046
representing the sum of mean squared error, F (fj, fe) representing the compliance degree of freedom Fj，feF distribution of (3).
If Fj≥F1-α(fj, fe), the j-th factor is considered to have a significant effect on the test results, otherwise no significant effect is considered.
Compared with the prior art, the invention has the following beneficial effects:
by combining a mathematical statistical method, the test times can be greatly reduced, the calculation time can be greatly shortened, and the efficiency can be improved.
Based on an orthogonal test design method, the influence degree of each factor on the electric field distribution can be determined, and the significance level of the factor is obtained.
Drawings
FIG. 1: is a flow chart of the present invention;
FIG. 2: is a simulation model of the direct current high voltage generator.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides an optimized design method of a DC high-voltage generator grading ring, which specifically comprises the following steps:
step 1, establishing a simulation model of the direct-current high-voltage generator, wherein the simulation model is shown in an attached figure 2;
the boundary conditions to be met by the simulation model of the direct-current high-voltage generator in the step 1 are as follows:
in the formula: r represents the radius of the solution area,
Figure BDA0002215091240000052
representing the potential, and solving a potential function in the region to meet a Laplace equation;
Figure BDA0002215091240000053
the high-voltage end potential of the generator is 1100 kV;
Figure BDA0002215091240000054
the ground potential is 0;
Figure BDA0002215091240000055
the electric potentials of the left side and the right side of the interface of different media are represented, and the electric potentials meet an electric potential continuity equation;
step 2, listing parameter variables of the main equalizing ring and the auxiliary equalizing ring;
as can be seen from the simulation model of fig. 2, the main equalizing ring and the auxiliary equalizing ring have six variables: the grading device comprises a main ring radius A of a main grading ring, an inner ring radius B of the main grading ring, a ground height C of the main grading ring, a main ring radius D of an auxiliary grading ring, an inner ring radius E of the auxiliary grading ring and a ground height F of the auxiliary grading ring.
Regardless of the interaction between each factor, 3 levels were chosen for each factor. Constructing a 3X 6 matrix A to describe the parameter variable, number al,j(unit: mm) is positioned in the jth row and jth column of the matrix A and represents the value of the ith level of the jth variable, l is more than or equal to 1 and less than or equal to 3, j is more than or equal to 1 and less than or equal to 6, then
Figure BDA0002215091240000056
Step 3, selecting a proper orthogonal table according to the number and the horizontal number of the variable factors;
the selection of a suitable orthogonal table in step 3 is: l isn(rm) The method comprises the following steps of representing an orthogonal table, wherein L represents an orthogonal table symbol, n represents the number of times of testing, namely the row number of the orthogonal table, r represents the horizontal number of factors in the orthogonal test, and m represents the maximum number of factors allowed by the test, namely the column number of the orthogonal table; the orthogonal table chosen here is L18(21×37) The meaning is 1 factor 2 level, 7 factor 3 levels, for a total of 18 trials.
Step 4, constructing a test scheme matrix according to the orthogonal table;
the test protocol matrix in step 4 is:
Figure BDA0002215091240000061
wherein i is more than or equal to 1 and less than or equal to 18, j is more than or equal to 1 and less than or equal to 7, and delta (i, j) represents the value of the jth element in the ith row of the test scheme table;
setting parameters of the equalizing ring in the simulation model in the step 1 according to the test scheme matrix delta (i, j), performing simulation model test of the direct-current high-voltage generator, and recording the obtained test result as yi，yiRepresents the test results of row i;
the specific test protocol is shown in table 1.
Table 1 test protocol table
Figure BDA0002215091240000071
Step 5, calculating the corresponding statistic of each factor according to the test scheme matrix;
calculating the statistic corresponding to each factor according to the data in the step 4, specifically comprising:
step 5.1, calculating the sum K of the test results of the l level on the j columnl,jL is more than or equal to 1 and less than or equal to r, j is more than or equal to 1 and less than or equal to m, and l and j are both positive integers;
since the same level appears t times on each column, it is assumed that the test results are y1、y2···ytThen K isl,j＝y1+y2+···+yt；
Step 5.2, calculating the sum K of the test resultsl,jAverage value of (2)
Figure BDA0002215091240000072
Figure BDA0002215091240000073
Wherein t is the number of occurrences of the horizontal number l on the jth column;
step 5.3, calculate the sum of squared deviations Sj，
Figure BDA0002215091240000081
Sum of mean square
Figure BDA0002215091240000082
TABLE 2 Experimental factor-related statistic calculation Table
Figure BDA0002215091240000084
The specific data after calculation are shown in Table 2.
Step 6, finding the optimal level of each factor so as to obtain a group of optimal parameter combinations;
comparing different levels in column j
Figure BDA0002215091240000085
Size of (2), definition
Figure BDA0002215091240000086
Figure BDA0002215091240000087
Then
Figure BDA0002215091240000088
The level l of the column is the optimal level of the factor of the jth column, and is marked as ljmin(ii) a By analogy, the optimal level of each column of factors is found, and the optimal parameter combination is obtained;
when j is 1, the factor to be examined is the difference caused by each level of the factor a.
Figure BDA0002215091240000089
Then there are
Figure BDA00022150912400000811
I.e. the optimum level of factor A is A3. Considering the influence of each factor on each level, the optimal parameter combination of the obtained generator grading ring is A3B2C1D3E1F1. This groupThe sum is different from the combination of the minimum values of the orthogonal table test, and therefore, a second test is performed for this new set of parameter combinations. The test result was 3054.6V/mm, which is smaller than 3073.3V/mm, so the optimum parameter combination was A3B2C1D3E1F1。
Step 7, carrying out significance test according to the deviation square sum and the mean square sum of each factor to obtain the significance level of each factor;
calculating the sum of the squares of the total deviations:
Figure BDA00022150912400000812
wherein, yiThe results of the test in row i are shown,
Figure BDA0002215091240000091
the sum of all test result data is shown, and n represents the test times;
calculating the sum of squared deviations Sj：
Figure BDA0002215091240000092
Wherein t represents the number of occurrences of the horizontal number l on the j-th column,
Figure BDA0002215091240000093
denotes the sum of the test results KljR represents the number of factor levels,
Figure BDA0002215091240000094
the sum of all test result data is shown, and n represents the test times;
computing a sum of mean squares
Figure BDA0002215091240000095
Figure BDA0002215091240000096
Wherein SjRepresenting the sum of squares of deviations, fjDenotes SjThe degree of freedom of (c);
calculating ST、Sj、SeDegree of freedom fT、fjAnd fe：
fT＝n-1
fj＝r-1
fe＝fTSum of degrees of freedom of the factors
Wherein n represents the number of tests, and r represents the number of factor levels;
preferably, whether the jth factor has a significant influence on the test index is checked, and the statistic is calculated as follows:
Figure BDA0002215091240000097
wherein S isjRepresents the sum of squares of deviations, SeRepresents the sum of squared errors, fjDenotes SjDegree of freedom, feDenotes SeThe degree of freedom of (a) is,
Figure BDA0002215091240000098
the sum of the mean square deviations is represented,
Figure BDA0002215091240000099
representing the sum of mean squared error, F (fj, fe) representing the compliance degree of freedom Fj，feF distribution of (3).
If Fj≥F1-α(fj,fe) Then the factor in column j is considered to have a significant effect on the test results, otherwise no significant effect is considered.
The significance test was performed according to the data in table 2, and the analysis of variance thereof is shown in table 3.
TABLE 3 analysis of variance factors
Variance source Sum of squares Degree of freedom Sum of mean square F value Significance of
A 1087454.1 2 543727.1 28.8 **
B 147576.1 2 73788.1 3.9 (*)
C 757284.1 2 378642.1 20.1 **
D 936127.0 2 468063.5 24.8 **
E 87540.8 2 43770.4 2.3
F 91113.4 2 45556.7 2.4
e 94338.3 5 18867.7
①F0.99(2,5)＝13.3F0.95(2,5)＝5.79，F0.90(2,5) ≥ 3.78; ② if F ≥ F0.99(fj,fe) The factor is highly significant and is marked as ". star"; ③ if F0.95(fj,fe)≤F＜F0.99(fj,fe) Marked by significant factor, ④ if F0.90(fj,fe)≤F＜F0.95(fj,fe) The factor has a certain influence, marked as "(+"), ⑤ if F < F0.90(fj,fe) This factor had no significant effect.
As can be seen from table 3, the factor A, C, D has a high significance on the test result, that is, the main ring radius of the main grading ring, the ground height, and the main ring radius of the auxiliary grading ring have a significant effect on the maximum field strength. The factor B has certain influence on the test result, and other factors have no obvious influence on the test result.
It should be understood that parts of the specification not set forth in detail are well within the prior art.
It should be understood that the above-mentioned embodiments are described in some detail, and not intended to limit the scope of the invention, and those skilled in the art will be able to make alterations and modifications without departing from the scope of the invention as defined by the appended claims.

Claims (8)

1. An optimal design method for a DC high-voltage generator grading ring is characterized by comprising the following steps:
step 1, establishing a simulation model of a direct-current high-voltage generator;
step 2, listing parameter variables of the main equalizing ring and the auxiliary equalizing ring;
step 3, selecting a proper orthogonal table according to the number and the horizontal number of the variable factors;
step 4, constructing a test scheme matrix according to the orthogonal table;
step 5, calculating the corresponding statistic of each factor according to the test scheme matrix;
step 6, finding the optimal level of each factor so as to obtain a group of optimal parameter combinations;
and 7, performing significance test according to the deviation square sum and the mean square sum of each factor to obtain the significance level of each factor.
2. The method for optimally designing the grading ring of the direct-current high-voltage generator according to claim 1, wherein the method comprises the following steps: the boundary conditions to be met by the simulation model of the direct-current high-voltage generator in the step 1 are as follows:
Figure FDA0002215091230000011
in the formula: r represents the radius of the solution area,
Figure FDA0002215091230000012
representing the potential, and solving a potential function in the region to meet a Laplace equation;
Figure FDA0002215091230000013
the high-voltage end potential of the generator is 1100 kV;
Figure FDA0002215091230000014
the ground potential is 0;
Figure FDA0002215091230000015
and the potentials on the left side and the right side of the interface of different media are represented, and the potential continuity equation is satisfied.
3. The method for optimally designing the grading ring of the direct-current high-voltage generator according to claim 1, wherein the method comprises the following steps: step 2, listing parameter variables of the main equalizing ring and the auxiliary equalizing ring:
setting m variables of parameters of the main equalizing ring and the auxiliary equalizing ring, wherein each variable has r values, constructing an r multiplied by m matrix A to describe the parameter variable, and counting al,jAnd the value of the l level of the jth variable is represented by the jth column in the l row of the matrix A, l is more than or equal to 1 and less than or equal to r, and j is more than or equal to 1 and less than or equal to m.
4. The method for optimally designing the grading ring of the direct-current high-voltage generator according to claim 1, wherein the method comprises the following steps: the selection of a suitable orthogonal table in step 3 is: l isn(rm) The test result is expressed in an orthogonal table, L is an orthogonal table symbol, n is the number of test times, i.e., the number of rows in the orthogonal table, r is the number of levels of factors in the orthogonal test, and m is the number of columns in the orthogonal table, i.e., the maximum number of factors allowed in the test.
5. The method for optimally designing the grading ring of the direct-current high-voltage generator according to claim 1, wherein the method comprises the following steps: the test protocol matrix in step 4 is:
Δ(i,j)
wherein i is more than or equal to 1 and less than or equal to n, j is more than or equal to 1 and less than or equal to m, and delta (i, j) represents the value of the jth element in the ith row of the test scheme table;
setting parameters of the equalizing ring in the simulation model in the step 1 according to the test scheme matrix delta (i, j), performing simulation model test of the direct-current high-voltage generator, and recording the obtained test result as yi，yiThe test results on row i are shown.
6. The method for optimally designing the grading ring of the direct-current high-voltage generator according to claim 1, wherein the method comprises the following steps: the step 5 of calculating the statistics corresponding to each factor according to the test scheme matrix specifically includes:
step 5.1, calculating the sum K of the test results of the l level on the j columnl,jL is more than or equal to 1 and less than or equal to r, j is more than or equal to 1 and less than or equal to m, and l and j are both positive integers;
since the same level appears t times on each column, it is assumed that the test results are y1、y2…ytThen K isl,j＝y1+y2+…+yt；
Step 5.2, calculating the sum K of the test resultsl,jAverage value of (2)
Figure FDA0002215091230000022
Wherein t is the number of occurrences of the horizontal number l on the jth column;
step 5.3, calculate the sum of squared deviations Sj，
Figure FDA0002215091230000023
Sum of mean square
Figure FDA0002215091230000024
Figure FDA0002215091230000025
7. The method for optimally designing the grading ring of the direct-current high-voltage generator according to claim 1, wherein the method comprises the following steps: finding the optimal level of each factor in step 6 to obtain a group of optimal parameter combinations, specifically:
comparing different levels in column jSize of (2), definition
Figure FDA0002215091230000027
j is 1,2, …, m, then
Figure FDA0002215091230000028
The level l of the column is the optimal level of the factor of the jth column, and is marked as ljmin(ii) a By analogy, the optimal level of each column of factors is found, and the optimal parameter combination is obtained.
8. The method for optimally designing the grading ring of the direct-current high-voltage generator according to claim 1, wherein the method comprises the following steps: in step 7, the significance test is performed according to the deviation square sum and the mean square sum of each factor, and the significance level of each factor is specifically obtained as follows:
sum of squares of total deviations:
wherein, yiThe results of the test in row i are shown,presentation instrumentThe sum of test result data exists, and n represents the test times;
calculating the sum of squared deviations Sj：
Figure FDA0002215091230000033
Wherein t represents the number of occurrences of the horizontal number l on the j-th column,
Figure FDA0002215091230000034
denotes the sum of the test results KljR represents the number of factor levels,
Figure FDA0002215091230000035
the sum of all test result data is shown, and n represents the test times;
computing a sum of mean squares
Figure FDA0002215091230000036
Wherein SjRepresenting the sum of squares of deviations, fjDenotes SjThe degree of freedom of (c);
calculating ST、Sj、SeDegree of freedom fT、fjAnd fe：
fT＝n-1
fj＝r-1
fe＝fTSum of degrees of freedom of the factors
Wherein n represents the number of tests, and r represents the number of factor levels;
preferably, whether the jth factor has a significant influence on the test index is checked, and the statistic is calculated as follows:
Figure FDA0002215091230000038
wherein S isjRepresents the sum of squares of deviations, SeRepresents the sum of squared errors, fjDenotes SjDegree of freedom, feDenotes SeThe degree of freedom of (a) is,the sum of the mean square deviations is represented,
Figure FDA00022150912300000310
representing the sum of mean squared error, F (F)j,fe) Representing a degree of freedom of compliance as fj，feF distribution of (a);
if Fj≥F1-α(fj,fe) Then the factor in column j is considered to have a significant effect on the test results, otherwise no significant effect is considered.
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YANZHEN ZHAO等: "Calculation of electric field and voltage distribution along glass insulator string and optimum design of its grading rings for 1000kV a.c. UHV transmission lines", 《2008 WORLD AUTOMATION CONGRESS》 *
王淑娟 等: "基于正交试验设计的电子镇流器参数优化设计方法的研究", 《电子器件》 *

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