CN115578218A - Power quality evaluation method based on variation coefficient and improved TOPSIS - Google Patents
Power quality evaluation method based on variation coefficient and improved TOPSIS Download PDFInfo
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Abstract
The invention discloses a power quality evaluation method based on a coefficient of variation and improved TOPSIS, which is characterized in that an evaluation system is established by dividing 6 evaluation indexes according to the current power quality standard, and the subjective weight of the evaluation indexes is calculated by adopting an improved analytic hierarchy process on the basis of not needing consistency check and reducing the influence of subjective factors; dividing the grade of the power quality evaluation index according to the national standard limit value, and calculating the objective weight of the evaluation index by adopting a CRITIC method; coefficient distribution is carried out on the subjective and objective weighted values by adopting a variable coefficient method, and subjective and objective combination weight is obtained; and obtaining the relative superiority and inferiority and specific grade of the power quality of each evaluation object according to the subjective and objective combination weight and the improved TOPSIS method. According to the invention, the main and objective factors are considered in the weight calculation, so that the calculation result is more scientific and reasonable; the improved TOPSIS method can judge the quality of the electric energy of the monitoring point and determine the level attribution of the monitoring point, and improves the applicability of the TOPSIS method.
Description
Technical Field
The invention relates to the technical field of power quality evaluation, in particular to a TOPSIS (technique for order preference by similarity to zero) improved power quality evaluation method based on a coefficient of variation.
Background
In recent years, with the rapid development of new energy power generation technology, new energy power generation permeates a power grid on a large scale, the operation of a distributed power supply, a nonlinear load and an impact load can affect the power quality of the power grid, and the quality of the power quality is directly related to the quality of alternating current used by the power grid for supply load side industry and resident life, so that the power quality is more and more concerned by both power supply and power utilization, and the comprehensive evaluation of the power quality has very important significance.
In order to reasonably and accurately evaluate the power quality, determining the weight and constructing a proper evaluation model are key. In the evaluation method for determining the weight, a single subjective weighting method is adopted, the importance ranking and the weight of evaluation indexes are completely determined by the experience of experts, and the subjectivity is too strong; the single objective weighting method can effectively transmit data information and difference of evaluation indexes, but only data is considered, the experience of experts is ignored, and when special requirements are required on a certain power quality index under different working conditions, the obtained weight result is inaccurate. The subjective and objective combination weighting method can effectively reflect relevant information among measured data of each index while giving consideration to expert experience, and the subjective and objective methods are unified, so that a weighting result is reasonable and effective. Meanwhile, the traditional TOPSIS evaluation model adopts the Euclidean distance to calculate the closeness between an evaluation object and an ideal solution, the quality of the electric energy of the evaluation object is obtained through the closeness, when the evaluation object is equidistant to the positive ideal solution and the negative ideal solution, an evaluation result cannot be accurately given, and the electric energy quality grade of the evaluation object cannot be measured.
Disclosure of Invention
The invention provides an electric energy quality evaluation method based on a variation coefficient and improved TOPSIS (technique for order preference by similarity to Ideal solution), which is used for carrying out subjective and objective combination weighting by using a variation coefficient method so as to solve the problems that the subjectivity of single subjective weighting is too strong, the single objective weighting result is inaccurate and cannot meet the special requirements of different working conditions on a certain electric energy quality index, and the subjective factors in the subjective and objective combination weighting have larger influence on the evaluation result and need consistency check. A traditional TOPSIS evaluation model is improved by utilizing a subjective and objective combination weight, a gray correlation degree and a variation coefficient method, so that the problems that accurate evaluation cannot be carried out and the power quality grade of an evaluation object cannot be measured when Euclidean distance calculation is adopted are solved.
The invention adopts the following technical scheme to achieve the purpose.
A method for evaluating the quality of electric energy based on the variation coefficient and improved TOPSIS comprises the following steps.
Step 1, selecting 6 evaluation indexes to establish a power quality evaluation system according to the current power quality standard.
Step 2, adopting an improved analytic hierarchy process to establish a judgment matrix to obtain the subjective weight sw of each evaluation index j 。
And 3, grading the 6 evaluation indexes according to the national standard of the power quality, determining the optimal and the worst values of the 6 evaluation indexes, and forming a comprehensive evaluation matrix by the grade range value of each power quality evaluation index, the measured data of the monitoring point and the optimal and the worst values.
Step 4, calculating objective weight ow of each evaluation index in the normalized matrix constructed in the step 3 by adopting a CRITIC method j 。
Step 5, the subjective weight sw obtained in the step 2 is obtained by adopting a variation coefficient method j And step 4, finding out objective weight ow j Coefficient distribution is carried out to obtain the subjective and objective combination weight cw of each evaluation index j 。
Step 6, combining the normalized matrix obtained in the step 4 and the subjective and objective combination weight cw obtained in the step 5 j And (5) obtaining a normalized weighted comprehensive evaluation matrix, and determining the positive and negative ideal solutions of each evaluation index in the normalized weighted comprehensive evaluation matrix.
Step 7, adopting an improved TOPSIS method after introducing the grey correlation degree, and obtaining the subjective and objective combination weight cw according to the step 5 j Calculating weighted Euclidean geometric distance and gray correlation by using the positive and negative ideal solutions obtained in the step 6And fusing the weighted Euclidean geometric distance and the grey correlation degree by adopting a coefficient of variation method to obtain a grey-weighted Euclidean distance measure.
And 8, calculating a relative sticking progress according to the gray-weighted Euclidean distance measure obtained in the step 7, comparing the relative superiority and inferiority of the electric energy quality of each monitoring point according to the relative sticking degree, and determining the attribution of the electric energy quality level of each monitoring point.
Optionally, in step 1, a voltage deviation PI is selected 1 Total voltage harmonic distortion ratio PI 2 And three-phase voltage unbalance PI 3 Frequency deviation PI 4 Voltage fluctuation PI 5 Long time flicker PI 6 As an index set for measuring the quality of the electric energy.
Optionally, in step 2, in order to reduce the influence of the subjective factors of the analytic hierarchy process on the evaluation result, an improved analytic hierarchy process is adopted, a determination matrix is established by using a scale construction method, two evaluation indexes of n items are compared, and the evaluation indexes are sorted according to a non-decreasing importance manner, wherein the established determination matrix is: r = [ R ] ji ] n×n ，n＝6。
Judging whether the matrix R has consistency, and solving the subjective weight sw of each index by using a geometric mean method and column normalization without carrying out consistency test j Comprises the following steps:
optionally, in step 3, according to the national standard of power quality, 6 evaluation indexes are divided into 5 grades of excellent i, good ii, medium iii, qualified iv and unqualified v, the optimal value of the evaluation indexes is determined to be 0, the worst value of the evaluation indexes is determined to be the national standard limit value of each evaluation index, and then the grade range value of each evaluation index, the measured data of the monitoring point, and the optimal and worst values form a comprehensive evaluation matrix as follows: a = [ a ] ij ] m×n 。
In the formula, m represents m evaluation targets, and n represents n evaluation indexes.
Optionally, in step 4, the CRITIC method is adopted to perform min-max normalization on the comprehensive evaluation matrix a obtained in step 3The normalized matrix A is obtained by normalization processing * ：
According to the normalized matrix A * Calculated information quantity IC j Comprises the following steps:
objective weight ow j Comprises the following steps:
in the formula, S j Is the standard deviation of the jth index, p kj And the correlation coefficient of the k index and the j index is obtained.
Optionally, in step 5, the subjective weight sw obtained in step 2 is used j And the objective weight ow found out in step 4 j To obtain the objective and subjective combination weight cw j ：cw j ＝α*sw j +β*ow j ，j＝1,2,…,n。
In the formula, alpha and beta are main and objective weight ratio coefficients determined according to a coefficient of variation method, and alpha and beta are required to be more than or equal to 0, and alpha + beta =1.
Optionally, in step 6, the normalized matrix obtained in step 4 is combined
And the subjective and objective combination weight CW = [ CW ] obtained in step 5 1 ,cw 2 ,…,cw n ]And solving a normalized weighted comprehensive evaluation matrix as follows:
the positive and negative ideal solutions of the evaluation indexes in the normalized weighted comprehensive evaluation matrix B are determined as follows.
In the formula, B + To solve the ideal, B - Is a negative ideal solution.
Optionally, in step 7, an improved TOPSIS method with a gray correlation introduced is adopted, and the subjective and objective combination weight cw obtained in step 5 is used j And calculating the weighted Euclidean geometric distance and the gray correlation degree by the positive ideal solution and the negative ideal solution obtained in the step 6.
In the formula (I), the compound is shown in the specification,
respectively, the weighted euclidean geometrical distance between the solution and the positive and negative ideal solutions.
In the formula (I), the compound is shown in the specification,
is a grey correlation coefficient; rho is a resolution coefficient, and rho belongs to [0,1 ]]And ρ is usually taken to be 0.5.
In the formula (I), the compound is shown in the specification,
grey correlation degrees with positive and negative ideal solutions, respectively.
And fusing the weighted Euclidean geometric distance and the grey correlation degree by adopting a coefficient of variation method to obtain a grey-weighted Euclidean distance measure.
In the formula, gamma and theta are the respective proportion weights of the weighted Euclidean geometric distance and the grey correlation degree, gamma + theta =1 is satisfied, and gamma and theta can be determined by a variation coefficient method; of the object being evaluated
When the numerical values are all larger, the evaluation scheme is closer to the optimal solution,
when the numerical values are all larger, the evaluation scheme is closer to the worst solution, so
The larger the better the evaluation scheme,
the larger the evaluation scheme.
Optionally, in step 8, the gray-weighted euclidean distance measure obtained in step 7 is used
Calculating the relative pasting progress:
in the formula, f i I.e. the calculated relative posting progress. f. of i The larger the value is, the closer the evaluation scheme is to the positive ideal solution, the better the electric energy quality of the monitoring point is, and meanwhile, the electric energy quality can be further determined according to f i And determining the grade of the electric energy quality of the monitoring point according to the value.
The beneficial effects of the invention are as follows: 1) By using an improved analytic hierarchy process, the influence of subjective factors on the empowerment accuracy is reduced on the basis of not needing consistency test; 2) In the weight calculation, the experience of experts and special requirements on certain electric energy quality under different working conditions are considered, the objectivity of the measured data of the electric energy quality is also considered, and the weight calculation result is more scientific and reasonable by the subjective and objective combination; 3) The improved TOPSIS method can judge the quality of the electric energy of the monitoring point, determine the class attribution of the monitoring point and improve the applicability of the TOPSIS evaluation model.
Drawings
Fig. 1 is a flowchart of a method for evaluating power quality based on a variation coefficient and improved toposis according to the present invention.
Fig. 2 shows 6 power quality evaluation indexes in the TOPSIS-improved power quality evaluation method based on the coefficient of variation.
DETAILED DESCRIPTION OF EMBODIMENT (S) OF INVENTION
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings, and it is to be understood that the described embodiments are only a part, and not all, of the embodiments of the present invention. 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.
As shown in fig. 1, a method for evaluating power quality based on the coefficient of variation and improved TOPSIS specifically includes the following steps.
Step 1, selecting a voltage deviation PI according to the current power quality standard 1 Total voltage harmonicsDistortion ratio PI 2 Three-phase voltage unbalance PI 3 Frequency deviation PI 4 Voltage fluctuation PI 5 Long time flicker PI 6 The 6 evaluation indexes establish a power quality evaluation system.
Step 2, in order to reduce the influence of the subjective factors of the analytic hierarchy process on the evaluation result, the improved analytic hierarchy process is adopted, and a scale construction method is utilized to establish a judgment matrix R = [ R ] = ji ] n×n And n =6. The matrix R satisfies the following condition.
1)r ji ＞0；2)r jj ＝1；3)r ji ＝1/r ij ；4)r ji ＝r jl r li ，i、j、l＝1,2,…,n。
Wherein r is ji The scale value of the jth index compared with the ith index is represented, and the specific meaning of the adopted scale construction method is shown in the following table:
by referring to relevant documents and the opinions of experts and users in the field of comprehensive power quality, the relative importance of the evaluation indexes is determined as follows: PI (polyimide) 4 ＞PI 2 ＞PI 6 ＞PI 5 ＞PI 1 ＞PI 3 The corresponding scale values are respectively: 1.4,1.3,1,1.1,1.1. Sequencing according to the mode that the importance of the evaluation index is not reduced by using a scale construction method, and marking the corresponding scale value as x i (x i ≧ 1), the constructed judgment matrix R = [ R ] ji ] n×n As follows.
The judgment matrix R has consistency, consistency check is not needed, and subjective weight sw of each index can be obtained by using a geometric mean method and column normalization j ：
Step 3, according to the national standard of electric energy quality, 10kV voltage grades are selected for analysis, and 6 evaluation indexes are divided into 5 grades of excellence I, good II, medium III, qualified IV and unqualified V:
according to the grade division table, the optimal value is determined to be 0, and the worst value is the national standard limit value of each evaluation index:
then, forming a comprehensive evaluation matrix by the grade range value of each evaluation index, the actually measured data of the monitoring points and the optimal and worst values: a = [ a ] ij ] m×n 。
In the formula, m represents m evaluation targets, and n represents n evaluation indexes.
And 4, performing min-max normalization processing on the comprehensive evaluation matrix A obtained in the step 3 by using a CRITIC method:
1) The forward index (the larger the index value, the better).
2) Inverse type index (the smaller the index value, the better).
After min-max normalization processing, a normalized matrix is obtained
And then according to the normalized matrix A * And (3) calculating:
1) Index variability.
By standard deviation S j (standard deviation of jth index) by the form:
wherein the content of the first and second substances,
2) Index conflict is realized.
Expressed by correlation coefficients:
where ρ is kj For the k index and the j index correlation coefficient,
3) The amount of information.
4) Objective weight.
Step 5, obtaining the subjective weight sw according to the step 2 j And step 4, finding out objective weight ow j Coefficient distribution is performed by using a coefficient of variation method to obtain objective and subjective combination weight cw j ：
cw j ＝α*sw j +β*ow j ，j＝1,2,…,n。
In the formula, alpha and beta are main and objective weight ratio coefficients, and the main and objective weight ratio coefficients satisfy that alpha and beta are more than or equal to 0, alpha + beta =1, alpha, beta,
β can be calculated as follows.
SW＝[sw 1 ,sw 2 ,…,sw n ]。
OW＝[ow 1 ,ow 2 ,…,ow n ]。
Alpha can be calculated according to the SW and OW * 、β * 。
In the formula (I), the compound is shown in the specification,
according to the above-mentioned alpha * 、β * Alpha and beta can be obtained.
α＝α * /(α * +β * )。
β＝β * /(α * +β * )。
Step 6, combining the normalized matrix obtained in the step 4
And the subjective and objective combination weight CW = [ CW ] obtained in step 5 1 ,cw 2 ,…,cw n ]And solving a normalized weighted comprehensive evaluation matrix as follows:
and determining the positive and negative ideal solutions of each evaluation index in the normalized weighted comprehensive evaluation matrix B.
In the formula, B + To solve the ideal, B - Is a negative ideal solution.
Step 7, adopting an improved TOPSIS method after introducing the grey correlation degree, and obtaining the subjective and objective combination weight cw according to the step 5 j And calculating the weighted Euclidean geometric distance and the gray correlation degree by the positive ideal solution and the negative ideal solution obtained in the step 6.
In the formula (I), the compound is shown in the specification,
respectively, the weighted euclidean distance between the solution and the positive and negative ideal solutions.
In the formula (I), the compound is shown in the specification,
is a grey correlation coefficient; rho is a resolution coefficient, and rho belongs to [0,1 ]]And ρ is usually taken to be 0.5.
In the formula (I), the compound is shown in the specification,
gray correlations with positive and negative ideal solutions, respectively.
Fusing the weighted Euclidean geometric distance and the grey correlation degree by adopting a coefficient of variation method to obtain a grey-weighted Euclidean distance measure:
in the formula, gamma and theta are the respective proportion weights of the weighted Euclidean geometric distance and the grey correlation degree, gamma + theta =1 is satisfied, and gamma and theta can be determined by a variation coefficient method; of the object being evaluated
When the numerical values are all larger, the evaluation scheme is closer to the optimal solution,
when the numerical values are all larger, the evaluation scheme is closer to the worst solution, so
The larger the better the evaluation scheme,
the larger the evaluation scheme. The process of determining γ and θ is as follows.
In the formula (I), the compound is shown in the specification,
in the same way, find
Bonding of
The values of γ and θ can be obtained.
Step 8, gray-weighted Euclidean distance measure obtained according to step 7
The relative paste progress can be calculated:
in the formula, f i I.e. the calculated relative posting progress. f. of i The larger the value is, the closer the evaluation scheme is to the positive ideal solution, the better the power quality of the monitoring point is, and meanwhile, the power quality can be further determined according to f i The numerical value determines the grade of the electric energy quality of the monitoring point.
The weight used in the evaluation method is subjective and objective comprehensive weight, so that the influence of subjective factors on weighting accuracy is greatly reduced, and the weight calculation result is more scientific and reasonable; after the TOPSIS method is improved by introducing the grey correlation degree, the electric energy quality superiority and inferiority of the monitoring point can be judged, the electric energy quality class attribution can also be determined, and the applicability of the TOPSIS evaluation model is improved.
It should be noted that the above mentioned embodiments are only preferred embodiments of the present invention, and all other embodiments obtained by those skilled in the art without any inventive work fall within the scope of the present invention.
Claims (9)
1. A method for evaluating the quality of electric energy based on the variation coefficient and improved TOPSIS is characterized by comprising the following steps:
step 1, selecting 6 evaluation indexes to establish a power quality evaluation system according to the current power quality standard;
step 2, adopting an improved analytic hierarchy process to establish a judgment matrix to obtain the subjective weight of each evaluation index
；
Step 3, according to the national standard of the power quality, carrying out grade division on the 6 evaluation indexes, determining the optimal and worst values of the 6 evaluation indexes, and forming a comprehensive evaluation matrix by the grade range value of each power quality evaluation index, the measured data of the monitoring point and the optimal and worst values;
step 4, according to the comprehensive evaluation matrix formed in the step 3, performing min-max normalization processing by adopting a CRITIC method to obtain a normalized matrix, and calculating objective weight of each evaluation index
；
Step 5, adopting a coefficient of variation method to obtain the subjective weight obtained in the step 2
And step 4, finding out objective weight
Coefficient distribution is carried out to obtain the subjective and objective combination weight of each evaluation index
；
Step 6, combining the normalized matrix obtained in the step 4 and the subjective and objective combination weight obtained in the step 5
Obtaining a normalized weighted comprehensive evaluation matrix, and determining positive and negative ideal solutions of each evaluation index in the normalized weighted comprehensive evaluation matrix;
step 7, adopting an improved TOPSIS method after introducing the grey correlation degree, and obtaining the subjective and objective combination weight according to the step 5
Calculating a weighted Euclidean geometric distance and a gray correlation degree by the positive and negative ideal solutions obtained in the step 6, and fusing the weighted Euclidean geometric distance and the gray correlation degree by a coefficient of variation method to obtain a gray-weighted Euclidean distance measure;
and 8, calculating a relative sticking progress according to the gray-weighted Euclidean distance measure obtained in the step 7, comparing the relative superiority and inferiority of the electric energy quality of each monitoring point according to the relative sticking degree, and determining the attribution of the electric energy quality level.
2. The TOPSIS-based power quality assessment method according to claim 1, wherein in step 1, the voltage deviation is selected
Total voltage harmonic distortion
Three-phase voltage unbalance degree
Frequency deviation, frequency deviation
Voltage fluctuation
And flickering for a long time
As an index set for measuring the quality of the electric energy.
3. The method as claimed in claim 1, wherein in step 2, in order to reduce the influence of subjective factors of the analytic hierarchy process on the evaluation result, the improved analytic hierarchy process is used, and a determination matrix is established by a scale construction method, so as to reduce the influence of subjective factors of the analytic hierarchy process on the evaluation result
And comparing every two evaluation indexes, sequencing according to a mode that the importance is not reduced, and constructing a judgment matrix as follows:
judgment matrix
The consistency is achieved, consistency check is not needed, and the subjective weight of each index is obtained by using a geometric mean method and column normalization
Comprises the following steps:
4. the method as claimed in claim 1, wherein in step 3, according to the national standard of power quality, 6 evaluation indexes are divided into 5 grades of excellent I, good II, medium III, qualified IV and unqualified V, the optimal value is determined to be 0, the worst value is determined to be the national standard limit value of each evaluation index, and then the grade range value of each evaluation index, the measured data of the monitoring point and the optimal and worst values form a comprehensive evaluation matrix
:
In the formula (I), the compound is shown in the specification,
is shown as
An object to be evaluated is determined,
is shown as
And (4) evaluating the indexes.
5. The method as claimed in claim 1, wherein in step 4, the CRITIC method is used to evaluate the comprehensive evaluation matrix obtained in step 3
Performing min-max normalization to obtain normalized matrix
：
According to a normalized matrix
Calculated information amount
And objective weight
：
In the formula (I), the compound is shown in the specification,
is a first
The standard deviation of the individual indices is,
is as follows
An index and
individual index correlation coefficient.
6. The TOPSIS-based power quality assessment method according to claim 1, wherein in step 5, the subjective weight obtained from step 2 is used
And step 4, obtaining the objective weight
The subjective and objective combination weight can be obtained
：
In the formula (I), the compound is shown in the specification,
、
the main weight and the objective weight are determined according to a coefficient of variation method
、
，
。
7. The TOPSIS-based power quality assessment method according to claim 1, wherein in step 6, the normalized matrix obtained in step 4 is combined
And the subjective and objective combination weight obtained in step 5
Finding out normalized weighted comprehensive evaluation matrix
：
Determining a normalized weighted composite evaluation matrix
Positive and negative ideal solutions of each evaluation index:
in the formula (I), the compound is shown in the specification,
is just ideal for solving,
Is a negative ideal solution.
8. The TOPSIS-based power quality assessment method according to claim 1, characterized in that in step 7, the TOPSIS method is adopted after the grey correlation degree is introduced, and the main and objective combination weight obtained in step 5 is used
And calculating the weighted Euclidean geometric distance and the gray correlation degree by the positive and negative ideal solutions obtained in the step 6:
in the formula (I), the compound is shown in the specification,
、
respectively, the weighted Euclidean geometric distances between the Euclidean distance and the positive and negative ideal solutions;
in the formula (I), the compound is shown in the specification,
、
is a grey correlation coefficient;
in order to be able to determine the resolution factor,
，
usually taken at 0.5;
in the formula (I), the compound is shown in the specification,
、
grey correlation degrees with positive and negative ideal solutions respectively;
fusing the weighted Euclidean geometric distance and the grey correlation degree by adopting a coefficient of variation method to obtain a grey-weighted Euclidean distance measure:
in the formula (I), the compound is shown in the specification,
、
weighting respective proportion weights of the Euclidean geometric distance and the gray correlation degree to satisfy
，
、
Can be determined by a coefficient of variation method; of the object being evaluated
、
When the numerical values are all larger, the evaluationThe estimation scheme is closer to the optimal solution,
、
when the values are all larger, the evaluation scheme is closer to the worst solution, so that
The larger the size of the evaluation scheme is,
the larger the evaluation scheme.
9. The TOPSIS-improved power quality assessment method according to claim 1, wherein in step 8, the gray-weighted Euclidean distance measure obtained from step 7 is used
、
And calculating the relative pasting progress:
in the formula (I), the compound is shown in the specification,
i.e. the calculated relative posting progress.
The larger the value is, the closer the evaluation scheme is to the positive ideal solution, the better the power quality of the monitoring point is, and meanwhile, the method can also be used according to the
The numerical value determines the grade of the electric energy quality of the monitoring point.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116090800A (en) * | 2023-04-11 | 2023-05-09 | 中国人民解放军海军工程大学 | Equipment stability real-time evaluation method based on monitoring parameters |
| CN116090800B (en) * | 2023-04-11 | 2023-07-18 | 中国人民解放军海军工程大学 | Equipment stability real-time evaluation method based on monitoring parameters |
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