CN116859187A - Transformer oil paper insulation state evaluation method based on fractional Poynting-Thomson model and gray entropy weight - Google Patents
Transformer oil paper insulation state evaluation method based on fractional Poynting-Thomson model and gray entropy weight Download PDFInfo
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Abstract
The transformer oil paper insulation state evaluation method based on the fractional poyning-Thomson model and gray entropy weight comprises the steps of firstly, deducing a relational expression between the fractional poyning-Thomson model and actual measured complex dielectric modulus by using fractional calculus theory; after the parameter identification, the aging characteristic parameter is obtainedα、β、ε a 、τThe dielectric characteristic parameters are proposed by researching the spectrum of the actually measured complex dielectric modulusA DP 、ΔA DP . And establishing evaluation indexes of insulation aging and moisture of transformer oil paper according to DL/T984-2018 'insulation aging judgment guide rule of oil-immersed transformer'. Based on an entropy weight method and a gray system theory, a new method for evaluating the insulation aging and damp state of the oil paper is provided, and a plurality of evaluation aging characteristic parameter indexes are combined to realize accurate evaluation of the insulation state of the oil paper of the transformer.
Description
Technical Field
The invention relates to the field of transformer oil paper insulation state evaluation, in particular to a transformer oil paper insulation state evaluation method based on a fractional Poynting-Thomson model and gray entropy weights.
Background
The power transformer is important power transmission and transformation equipment matched with the generator set to perform energy exchange and energy transmission, and safe and stable operation of the power transformer is a foundation for guaranteeing reliable power supply of a large power grid. An oil immersed transformer is a typical oiled paper insulation device, and its internal main insulation is a composite insulation structure composed of insulation paper, insulation paper board and insulation oil. Because the transformer runs under a complex environment for a long time, the insulation performance of the main insulation of the transformer is reduced due to factors such as temperature, moisture, mechanical stress, chemical corrosion and the like, and insulation faults are easy to cause. Therefore, the aging state of the oil paper insulation is rapidly and accurately evaluated, a reasonable operation and maintenance strategy is formulated, the service life of the power equipment can be effectively prolonged, and the failure occurrence rate is reduced.
Grey system theory is a new method suitable for researching the problem of uncertainty of less data and poor information. During long-term operation, the power transformer is susceptible to various uncertain factors such as moisture, aging, temperature and the like, so that the internal oilpaper insulation system can be regarded as a typical gray system.
The traditional evaluation method of the insulation state of the oil paper often adopts a single evaluation index, such as a chemical evaluation index and an electrical evaluation index, to judge the insulation state of the oil paper of the transformer, but the evaluation method of the single aging evaluation index often cannot truly reflect the insulation aging condition inside the oil paper of the transformer.
Disclosure of Invention
In order to solve the technical problems, the invention provides a transformer oil paper insulation state evaluation method based on a fractional poyning-Thomson model and gray entropy weight, which selects ageing characteristic parameters alpha, beta and epsilon after the parameters of the fractional poyning-Thomson model are identified a τ and dielectric characteristic parameter A DP 、ΔA DP As an electrical evaluation index; selecting acid value A of insulating oil v As chemical evaluation indexes, an improved gray correlation method is applied, so that the insulation state of the transformer oil paper system is accurately evaluated based on a plurality of evaluation indexes.
The technical scheme adopted by the invention is as follows:
the transformer oil paper insulation state evaluation method based on the fractional Poynting-Thomson model and gray entropy weight comprises the following steps:
step 1: preparing multiple groups of insulating oil paper samples with different ageing and wetting degrees, performing FDS measurement on the prepared insulating oil paper samples, and measuring the DP value of the polymerization degree of the insulating paper board and the acid value A of the insulating oil v ；
Step 2: extracting characteristic parameters alpha, beta and epsilon in fractional Poynting-Thomson model a τ is used as an aging characteristic parameter for characterizing the transformer, and a dielectric characteristic parameter A is provided based on a measured dielectric modulus spectrum DP 、ΔA DP As a dielectric aging characteristic parameter for characterizing the transformer;
step 3: expected DP from transformer oil impregnated paper v The insulation state of the insulation oil paper is divided by combining 3 damp evaluation grades and 3 aging evaluation grades to obtain X 1 ～X 9 Totally 9 transformer oil paper insulating states;
step 4: measuring and calculating aging characteristic parameters of the insulating oil paper in the step 1 to the step 3, and establishing a comparison sequence and a reference sequence;
step 5: eliminating the influence of units and orders on gray correlation analysis, carrying out dimensionless treatment on each reference sequence by adopting a averaging operator, and calculating a difference vector;
step 6: calculating to obtain entropy weight-gray correlation degree R of insulating oilpaper i Based on the influence degree of the evaluation index on the tested insulating oil paper sample, R is calculated as 1 ～R 7 Sequencing from large to small to obtain an insulation state evaluation result of the insulation oilpaper.
The step 1 comprises the following steps:
s1.1: first, groups of oiled paper insulation samples of different ageing and moisture degrees were prepared:
placing the insulating oil paper sample at 130 ℃ for accelerated heat aging treatment to prepare different insulating oil paper aging samples;
s1.2: respectively taking out a group of insulating oilpaper aging samples at 0 day, 21 day and 42 day of heat aging, placing the insulating oilpaper samples at room temperature for natural wetting in order to prepare oilpaper insulating samples with different wetting degrees, and weighing the single insulating oilpaper to the target water content by using a high-precision electronic scale: 1%, 2%, 4%;
s1.3: FDS measurement is carried out at 30 ℃ by using IDAX-300, the measurement voltage is set to 140V, the measurement frequency is 0.1 mHz-1 kHz, and the average value of 3 FDS measurement results is taken as the final measurement result;
s1.4: after the FDS measurement is completed, the DP value of the polymerization degree of the insulating paper board and the acid value A of the insulating oil are measured again v 。
In the step 2, a weighted least square method is adopted to perform parameter fitting on a fractional Poynting-Thomson model, and the objective constraint function is as follows:
wherein: r is an optimization target; m's' fi And M fi Fitting values of real parts and imaginary parts of complex dielectric modulus under the ith measuring frequency respectively; m's' mi And M mi Respectively measuring the real part and the imaginary part of the complex dielectric modulus at the ith measuring frequency;
i means the ith frequency measurement point, 23 is the common point in dielectric oil paper frequency domain dielectric measurement23 frequency points were measured, and the measured frequency domain range was (10 -4 ～10 3 Hz)。
After parameter fitting, alpha, beta, epsilon are obtained a The T and the DP of the insulating paper board have a higher fitting degree functional relation, so alpha, beta and epsilon are selected a τ is an aging characteristic parameter for evaluating the oiled paper insulation.
In the step 2, a frequency-domain dielectric spectrum is obtained when the frequency-domain dielectric measurement is performed on the oilpaper insulation, and a dielectric constant (epsilon) * ) Dielectric constant and dielectric modulus (M * (ω)) is:
the dielectric constant of each frequency point obtained through actual measurement is converted into a dielectric modulus form, and a dielectric modulus spectrum can be obtained.
Dielectric characteristic parameter A DP 、ΔA DP The calculation formula is as follows:
indicated at 10 3 The real part of the dielectric modulus at the Hz frequency point; />Indicated at 10 -4 The real part of the dielectric modulus at the Hz frequency point.
Dielectric characteristic parameter A DP 、ΔA DP Has higher fitting degree function relation with the polymerization degree DP of the insulating paper board, so the dielectric characteristic parameter A DP 、ΔA DP The aging state of the oiled paper insulation can also be characterized.
In the step 3, in DL/T984-2018 "oil immersed transformer insulation aging judgment guide", the aggregation of mineral oil transformer insulation oil paper is specified, three grades are defined as 500,250,150, and the state of the transformer is diagnosed: degree of polymerization DP of insulating oilpaper v When the oil paper is more than 500, the insulating state is good, and when the insulating oil paper has the polymerization degree DP v Between 250 and 150, the oilpaper is less insulating and needs attention. Degree of polymerization DP of the insulating oil paper v If the oil paper insulation state is less than 150, the oil paper insulation state is seriously aged, and the oil paper insulation state is not suitable for continuous use.
Combining and dividing the insulation states of the insulating oil paper to obtain X 1 ～X 9 Totally 9 transformer oil paper insulating states;
the combination division is limited by the degree of polymerization DP of the insulating paper board being 1200, 1000 and 650, the moisture content of the insulating oiled paper being 1.5 percent and the moisture content of the insulating oiled paper being 2.5 percent.
DL/T596-2021, electrical Equipment preventive test procedure, states that the moisture content of the insulating paper (insulating paper board) should not exceed 1%, 2% and 3% for oil-immersed power transformers at 500kV, 330kV and 220kV voltage levels, respectively. On the basis, the invention takes the water content m.c. as 1.5% and 2.5% as the limit, and the wet state of the vegetable oil paper insulation system is classified into 3 evaluation grades of dryness, wetness and severity from low to high. When m.c. is less than or equal to 1.5%, judging that the moisture state of the vegetable oil paper insulation system is dry; when the m.c. is less than or equal to 1.5 percent and less than or equal to 2.5 percent, judging that the moisture state of the vegetable oil paper insulation system is moist; when m.c. > 2.5%, the wet state of the vegetable oil paper insulation system is judged to be serious.
In DL/T984-2018 'oil immersed transformer insulation aging judgment guide rule', the aggregation of mineral oil transformer insulation oilpaper is regulated, three grades are defined as 500,250,150, and the invention takes the aggregation degree DP of an insulation paperboard as 1000 and 650 as a limit, and the aging state of a plant oilpaper insulation system is classified into 3 excellent, medium and serious evaluation grades from good to bad. When DP is more than 1000 and less than or equal to 1200, judging that the aging state of the vegetable oil paper insulation system is excellent; when DP is more than 650 and less than or equal to 1000, judging that the aging state of the vegetable oil paper insulation system is medium; and when the DP is less than or equal to 650, judging that the aging state of the vegetable oil paper insulation system is serious.
In the step 4, a comparison sequence and a reference sequence are determined:
setting the insulation state of the insulation oil paper sample to be diagnosed as a comparison sequence X 0 ：
X 0 ＝[X 0 (1),X 0 (2),…,X 0 (7)]
Wherein: x is X 0 (1)、X 0 (2)、X 0 (3)、X 0 (4) Characteristic parameters alpha, beta and epsilon extracted after the identification of the parameters of the fractional Poynting-Thomson model a 、τ；X 0 (5) Integral value A being imaginary part of complex dielectric modulus DP ；X 0 (6) Amplitude difference ΔA, which is the real part of complex dielectric modulus DP ；X 0 (7) Acid value A of insulating oil v 。
Establishing the insulation states of the insulation oilpaper with different ageing degrees and humidity degrees as a reference sequence X i ，i＝1，2，…，9：
X i ＝[X i (1),X i (2),…,X i (7)]
Wherein: x is X i (1),X i (2),…,X i (7) The insulation states of the vegetable oilpaper insulation systems with different ageing degrees and humidity degrees in the (i=1, 2, …, 9) are reference sequences;
said step 5 comprises the steps of:
s5.1: carrying out dimensionless treatment on each reference sequence by adopting a averaging operator, wherein the averaging operator is defined as follows:
wherein: i represents the number of rows of the sequence, i=1, 2, …,9; j represents the number of columns of the sequence, j=1, 2, …,7. Corresponding values of each evaluation index in the reference sequence:
s5.2: find the minimum and maximum differences, compare sequence X 0 (j) Each of which is respectively associated with a reference sequence X i (j) Each term in the two-dimensional image is subjected to difference and takes absolute value to obtain a difference vector delta i (j)：
In the above formula: x is X 0 (1)、X 0 (2)、X 0 (3)、X 0 (4) Characteristic parameters alpha, beta and epsilon extracted after the identification of the parameters of the fractional Poynting-Thomson model a 、τ；X 0 (5) Integral value A being imaginary part of complex dielectric modulus DP ；X 0 (6) Amplitude difference ΔA, which is the real part of complex dielectric modulus DP ；X 0 (7) Acid value A of insulating oil v 。
Carrying out dimensionless treatment on each reference sequence by adopting a averaging operator, wherein the averaging operator is defined as follows:
wherein: i represents the number of rows of the sequence, i=1, 2, …,9; j represents the number of columns of the sequence, j=1, 2, …,7.
X 1 ′(1)X 2 ′(1)X 9 ′(1)X 1 ′(2)X 2 ′(2)X 9 ′(2)X 1 ′(7)X 2 ′(7)……X 9 And (7) respectively representing the average operators of the reference sequences after dimensionless treatment.
S5.3: from the difference vector delta i (j) The maximum and minimum values are respectively marked as M and M:
in the step 6, xi is recorded as a resolution systemA number of the gray correlation coefficients r, wherein the physical meaning of the number is the degree of correlation between the jth evaluation index and the evaluation object in the ith state ij The definition is as follows:
the j (j=1, 2, …, 7) index specific gravity P for the i (i=1, 2, …, 9) th state ij ：
Index specific gravity P calculated from the above ij Obtaining an index entropy value E j ：
ln(P ij ) Is to index specific gravity P ij Taking the logarithm to obtain the final product.
Entropy weight W of each evaluation index j ：
Correlating the grey with the coefficient R ij Entropy weight W with each evaluation index j Multiplying to obtain entropy weight-gray correlation degree R of insulating oilpaper i ：
R is calculated 1 ～R 7 Sequencing from large to small to obtain an insulation state evaluation result of the insulation oiled paper.
The invention discloses a method for detecting damage of an overhead transmission line based on electromagnetic ultrasound, which has the following beneficial effects:
1) Aiming at the problem that the traditional single index evaluation cannot truly reflect the oil paper insulation state of the transformer, the invention applies the fractional order theory to the relaxation process of the oil paper insulation, obtains the dielectric evaluation index of the oil paper insulation of more transformers from a fractional Poynting-Thomson model, and the dielectric evaluation index can represent the oil paper insulation state of the transformer.
2) According to the invention, an oil paper insulation system in the transformer can be regarded as a typical gray system, a series of model aging characteristic parameters, dielectric characteristic parameters and physicochemical characteristic parameters are combined based on an entropy weight method and a gray system theory, and a novel method for evaluating the insulation state of the oil paper is provided, so that the insulation state of the oil paper system of the transformer can be accurately evaluated.
Drawings
FIG. 1 is a schematic flow chart of the present invention.
Fig. 2 is a schematic structural diagram of a test piece measurement test platform insulated by oilpaper.
FIG. 3 (a) is a graph showing the fit of the aging characteristic parameter α to the degree of polymerization DP of the insulating board;
FIG. 3 (b) is a graph showing the fit of the aging characteristic parameter β to the degree of polymerization DP of the insulating board;
FIG. 3 (c) shows the ageing characteristic parameter ε a A graph of fit relationship with the degree of polymerization DP of the insulating paperboard;
fig. 3 (d) is a graph showing the fit of the aging characteristic parameter τ to the degree of polymerization DP of the insulating board.
FIG. 4 (a) shows dielectric characteristic A DP A graph fitted with the degree of polymerization DP of the insulating board;
FIG. 4 (b) shows the dielectric characteristic quantity ΔA DP Fitting graph with degree of polymerization DP of the insulation board.
Detailed Description
A transformer oil paper insulation state evaluation method based on a fraction Poynting-Thomson model and gray entropy weight,
1) In terms of the evaluation feature quantity of the transformer: more effective information in the frequency domain dielectric spectrum is expanded by utilizing a parameter identification method, and characteristic parameters alpha, beta, epsilon a and tau in a fractional Poynting-Thomson model are extracted to serve as characteristic indexes for representing the aging of the transformer; based on the measured dielectric modulus spectrum, dielectric characteristic parameters ADP and delta ADP are provided as dielectric ageing characteristic indexes for characterizing the transformer. According to the invention, the evaluation indexes of a plurality of oilpaper states are combined to evaluate the insulating state of the oilpaper of the transformer instead of directly evaluating the single dielectric value in the dielectric modulus spectrum.
2) Parameter identification: and carrying out parameter identification on the fraction Poynting-Thomson model by adopting a weighted least square method, fitting the parameter identified by the parameter with the polymerization degree DP of the oil-immersed insulating paper board, and verifying that the aging characteristic parameter of the model can represent the insulating state of the transformer oil paper.
3) In terms of transformer insulation state evaluation criteria: according to DL/T984-2018 'oil immersed transformer insulation aging judgment guide rules', the insulation states of an oil paper insulation system are divided by combining 3 damp evaluation grades and 3 aging evaluation grades, and 9 transformer oil paper insulation states in total are obtained, wherein the method is different from the traditional method for evaluating the transformer insulation oil paper state, and is only a single index in the oil paper insulation: aging or wetting, and evaluating.
4) In terms of transformer state evaluation: regarding the transformer oil paper insulation system as a gray system, adopting a gray correlation analysis method to process a plurality of aging characteristic parameters, eliminating the influence of units and orders of magnitude on gray correlation analysis, and adopting a averaging operator to carry out dimensionless treatment on each reference sequence; and the entropy weight-gray association Ri evaluation index is provided for evaluating the insulating state of the oil paper, so that the insulating state of the transformer is accurately evaluated.
As shown in fig. 1, the method comprises the following steps:
step one: firstly, preparing various groups of oil paper insulation test samples with different ageing degrees and moisture degrees, performing FDS measurement on the prepared sample samples by using IDAX-300, and measuring the polymerization degree DP of the oil-immersed insulation paper board and the acid value A in the insulation oil v The specific operation steps are as follows:
to simulate the thermal aging process of the main insulation inside an actual transformer, a DHG-9425A forced air drying oven was used to insulate the sample at 130 from the oilpaperAnd (3) performing accelerated heat aging treatment at the temperature. A set of oiled paper insulation samples were taken at each of 0 day, 21 day, and 42 day of heat aging. In order to prepare oil paper insulating samples with different wetting degrees, firstly, wiping insulating oil on the surface of an oil-immersed insulating paperboard by petroleum ether at a ventilation place, then, naturally wetting the insulating oil at room temperature, and periodically weighing single insulating paper to a target water content (1%, 2% and 4%) by using a high-precision electronic scale (with the precision of 0.001 g), wherein the weight of the insulating paper is M 0 Target weight is M 1 The water content m.c. is defined as:
FDS measurement was performed at (30.+ -.1) ℃using IDAX-300, the measurement voltage was set to 140V, and the measurement frequency was 0.1 mHz-1 kHz. After the FDS measurement is completed.
Step two: the measured frequency domain dielectric modulus spectrum is identified by parameters to obtain aging characteristic parameters alpha, beta and epsilon a And τ, and calculating the dielectric characteristic A of each aging group DP 、ΔA DP ；
(1) Deriving from the fractional dielectric model, and establishing a relation between complex dielectric modulus and an insulation system:
wherein: alpha, beta, gamma, epsilon a 、ε b And τ is a parameter of six independent fractional Poynting-Thomson models. Wherein, the alpha parameter is a shape parameter describing the symmetric distribution of the relaxation process, and the beta and gamma parameters are shape parameters describing the asymmetric distribution of the relaxation process, so that 0 < beta < gamma < alpha < 1; the tau parameter represents relaxation time and is closely related to the polarization class and the position of the relaxation peak; epsilon a Is a dielectric parameter reflecting the low-frequency relaxation process and is closely related to the peak value (maximum value) of the relaxation peak; epsilon b Is a dielectric parameter reflecting the high frequency relaxation process, and is closely related to the peak value (minimum value) of the relaxation peak.
(2) In the invention, a weighted least square method is adopted to carry out parameter fitting on a fractional number Poynting-Thomson model, and the objective constraint function is as follows:
wherein: r is an optimization target; m's' fi And M fi Fitting a value for the real part and the imaginary part of the complex dielectric modulus at the ith measurement frequency; m's' mi And M mi Is a measurement of the real part and the imaginary part of the complex dielectric modulus at the ith measurement frequency. After the parameter identification, alpha, beta and epsilon are obtained a τ is closely related to the insulating oil insulating aging state, and the four model parameters are used as characteristic parameters for evaluating the insulating oil aging state.
(3) Calculation of dielectric characteristic parameter A DP 、ΔA DP Value:
at the selection of the imaginary part frequency spectrum of the complex dielectric modulus at 10 -4 Hz～10 3 Integral area within Hz "A DP "As dielectric characteristic parameter for characterizing insulating ageing state of oiled paper", research shows that A DP The better power function relation exists between the polymer and the polymerization degree DP of the insulating paper board; selecting the real part spectrum of complex dielectric modulus to be f=10 3 Hz and f=10 -4 Amplitude difference "delta A" of Hz DP "as a dielectric characteristic parameter for characterizing the insulating aging state of oilpaper, the dielectric characteristic parameter is shown in a formula. Studies have shown that Δa DP The polymer has a better exponential function relation with the polymerization degree DP of the insulating paper board;
step three: according to DL/T984-2018 (oil immersed transformer insulation aging judgment guide) about mineral oil immersed paper expected DP v The insulation state of the oilpaper insulation system is divided by combining 3 damp evaluation grades and 3 aging evaluation grades to obtain X 1 、X 2 、…、X 9 Totally 9 insulating states.
The invention takes the polymerization degree DP of the insulating paper board as the limit of 1000 and 650, and classifies the aging state of the oilpaper insulating system from good to bad into 3 kinds of excellent, medium and serious evaluation grades.
When DP is more than 1000 and less than or equal to 1200, judging that the aging state of the oilpaper insulation system is excellent; when the DP is more than 650 and less than or equal to 1000, judging that the aging state of the oilpaper insulation system is medium; and when the DP is less than or equal to 650, judging that the aging state of the oilpaper insulation system is serious. When m.c. is less than or equal to 1.5%, judging that the aging state of the oilpaper insulation system is dry; when the m.c. is less than or equal to 1.5 percent and less than or equal to 2.5 percent, judging that the aging state of the oilpaper insulation system is moist; when m.c. > 2.5%, the aging state of the oilpaper insulation system is judged to be serious. The insulation states of the oil paper insulation system are divided by combining the 3 damp evaluation grades and the 3 aging evaluation grades to obtain X 1 、X 2 、…、X 9 Totally 9 insulating states. As shown in table 1.
TABLE 1 insulation State partitioning for oiled paper insulation systems
Let X (1) to X (7) respectively represent reference characteristic parameters alpha, beta and epsilon a 、τ、A DP 、ΔA DP And A v Wherein the first six characteristic parameters are unit-free dimensions, characteristic parameter A v In mg KOH/g. Nine aged, humidified samples closest to the expected targets were selected as reference samples, and dielectric modulus spectrum measurement and insulated oleic acid value measurement were performed according to the measurement procedure shown in the present invention, respectively, to obtain reference state vectors of the samples as shown in table 2.
TABLE 2 reference State vector for oiled paper insulation samples
Step four: measuring and calculating aging characteristic parameters of the oilpaper insulation system in the first to third steps, and establishing a comparison sequence and a reference sequence;
determining the comparison sequence and the reference sequence, and setting the insulation state of the sample to be diagnosed as the comparison sequence X 0 ：
X 0 ＝[X 0 (1),X 0 (2),…,X 0 (7)]
Wherein: x is X 0 (1)、X 0 (2)、X 0 (3)、X 0 (4) Characteristic parameters alpha, beta and epsilon extracted for fractional P-T model a 、τ；X 0 (5) Integral value A being imaginary part of complex dielectric modulus DP ；X 0 (6) Amplitude difference ΔA, which is the real part of complex dielectric modulus DP ；X 0 (7) Acid value A of insulating oil v . The insulation states of the oil paper insulation systems with different ageing degrees and humidity degrees are the reference sequence X i (i＝1，2，…，9)：
X i ＝[X i (1),X i (2),…,X i (7)]
Step five: the influence of units and orders on gray correlation analysis is eliminated, the dimensionless treatment is carried out on each reference sequence by adopting a averaging operator, the dimensionless treatment is carried out on each evaluation index in the table 1 by utilizing the following formula, and the result is shown in the table 3. And calculates a difference vector. The insulation states of the oil paper insulation systems with different ageing degrees and humidity degrees are the reference sequence X i (i＝1，2，…，9)：
X i ＝[X i (1),X i (2),…,X i (7)]
In order to eliminate the influence of units and orders on gray correlation analysis, a averaging operator is adopted to carry out dimensionless treatment on each reference sequence. The averaging operator is defined as:
table 3 dimensionless treatment of reference vectors
Step six: calculating to obtain entropy weight-gray correlation degree R of oil paper insulation system i Based on the influence degree of the evaluation index on the tested sample, R is calculated 1 ～R 7 Sequencing from large to small to obtain an insulation state evaluation result of the oilpaper insulation system. According to the formula (calculate specific gravity P of each evaluation index ij And entropy weight W j As shown in tables 4 and 5. The j (j=1, 2, …, 7) index specific gravity P for the i (i=1, 2, …, 9) th state ij ：
According to the calculation of P ij Calculating index entropy value E j ：
Entropy weight W of each evaluation index j ：
Table 4 specific gravity P of each evaluation index ij
Table 5 entropy weight Wj of each evaluation index
As can be seen from Table 4, index τ, A DP 、ΔA DP And A v The entropy weight of the evaluation index is smaller, which indicates that the dispersion degree of the evaluation index is larger and the influence on the evaluation result of the insulation state of the oil paper is larger. Wherein: r is R i R is the gray correlation degree between the ith evaluation index and the tested sample i A larger value indicates a larger degree of association, and conversely, a smaller degree of association.
R is R 1 ～R 7 Sequencing from large to small, wherein the sequence reflects the influence degree of each evaluation index on the tested sample, and the standard state corresponding to the maximum value is the nearest insulating state of the sample. The entropy weight-gray correlation degree can be objectively assigned according to the change degree of each evaluation index, so that large differences between quantitative evaluation results and qualitative analysis results are avoided, and a guarantee is provided for accurately evaluating the insulation state of the oil paper insulation system.
Examples:
in order to verify the feasibility of the fractional poyning-Thomson model and gray entropy weight evaluation method for oil paper insulation state evaluation, two groups of oil paper insulation samples are prepared again according to the sample pretreatment method and the accelerated thermal ageing test in the first step, FDS measurement is carried out at (30+/-1) ℃ by using an IDAX-300 instrument, and a dielectric modulus spectrum image of the samples is obtained.
Sample 1,2, insulation board polymerization degree DP and moisture content m using the measurement method in step one c The measurement results are as follows:
1) Sample 1: dp=999, m.c. =3.21%.
2) Sample 2: dp=735, m.c. =3.15%.
The measured complex dielectric modulus imaginary frequency spectrum is subjected to parameter identification, and the identification result is shown in table 6.
TABLE 6 results of sample 1 and sample 2 parameter identification
And according to the second stepA of samples 1 and 2 of the sample are calculated respectively DP And delta A DP The calculation results are shown in table 7. Acid value measurement is carried out on the insulating oil of the samples 1 and 2 according to the acid value measurement flow in the first step, and the measurement results are A respectively v ＝0.09mg KOH/g、A v ＝0.38mg KOH/g。
TABLE 7 calculation of dielectric characteristics for samples 1 and 2
From the above calculation measurement results, the comparison vectors of the configuration samples 1 and 2 in the fourth step and the fifth step are shown in table 8.
Table 8 comparison vectors for samples 1 and 2
The gray entropy weight evaluation calculation method in the fifth step and the sixth step is applied, and S is calculated from the table 3 and the table 7 1 And S is 2 The entropy weight-gray correlation of the samples is shown in table 8.
Table 9 entropy weight-gray correlation of laboratory samples 1 and 2 with reference state
As can be seen from Table 9, the maximum gray correlation of samples 1 and 2 is 0.773 and 0.830, respectively, indicating that the insulating states of samples 1 and 2 are respectively equal to the reference state X 3 、X 6 Closest to each other.
The evaluation results and actual measurement results in comparison with the present invention are shown in Table 10.
Table 10 comparison of evaluation results with actual measurement results
As can be seen from Table 10, when the method provided by the invention is used for carrying out state evaluation on the laboratory oilpaper insulation sample, the ageing and moisture state evaluation results of the transformer insulation oilpaper are accurately judged, and the feasibility of the method for evaluating the insulation state of the oilpaper system by using the fractional Poynting-Thomson model and the gray entropy weight evaluation method is verified.
FIG. 3 (a) is a graph showing the fit of the aging characteristic parameter α to the degree of polymerization DP of the insulating board;
FIG. 3 (b) is a graph showing the fit of the aging characteristic parameter β to the degree of polymerization DP of the insulating board;
FIG. 3 (c) shows the ageing characteristic parameter ε a A graph of fit relationship with the degree of polymerization DP of the insulating paperboard;
fig. 3 (d) is a graph showing the fit of the aging characteristic parameter τ to the degree of polymerization DP of the insulating board.
From 3 (a) to 3 (d), the aging characteristics α, β, ε can be obtained a The four model parameters and the degree of polymerization DP of the insulating paper board show good function fitting relation, and the degree of polymerization DP of the insulating paper board is a characteristic index for representing the insulating state of the insulating oil paper, thereby explaining the four model parameters alpha, beta and epsilon a τ can characterize the insulation state of the insulating oilpaper.
FIG. 4 (a) shows dielectric characteristic A DP A graph fitted with the degree of polymerization DP of the insulating board;
FIG. 4 (b) shows the dielectric characteristic quantity ΔA DP Fitting graph with degree of polymerization DP of the insulation board.
From fig. 4 (a) and 4 (b), the dielectric characteristic parameter a can be obtained DP 、ΔA DP The four model parameters and the degree of polymerization DP of the insulating paper board show good function fitting relation, and the degree of polymerization DP of the insulating paper board is a characteristic index for representing the insulating state of the insulating oil paper, thereby illustrating the dielectric characteristic parameter A DP 、ΔA DP The insulation state of the insulating oilpaper can be characterized.
The invention applies fractional order theory to the relaxation process of dielectric medium, and expands more dielectric information in the dielectric modulus of frequency domain. The gray correlation degree of each index is obtained by regarding the inside of the whole transformer as a gray system through a series of calculation, the aim of evaluating the insulation state of the transformer oil paper by applying a plurality of evaluation indexes (dielectric and physicochemical indexes) is fulfilled, and the accurate evaluation of the insulation state of the transformer oil paper can be realized through verification.
Claims (8)
1. The transformer oil paper insulation state evaluation method based on the fractional Poynting-Thomson model and gray entropy weight is characterized by comprising the following steps of:
step 1: preparing multiple groups of insulating oil paper samples with different ageing and wetting degrees, performing FDS measurement on the prepared insulating oil paper samples, and measuring the DP value of the polymerization degree of the insulating paper board and the acid value A of the insulating oil v ；
Step 2: extracting characteristic parameters alpha, beta and epsilon in fractional Poynting-Thomson model a τ is used as an aging characteristic parameter for characterizing the transformer, and a dielectric characteristic parameter A is provided based on a measured dielectric modulus spectrum DP 、ΔA DP As a dielectric aging characteristic parameter for characterizing the transformer;
step 3: expected DP from transformer oil impregnated paper v The insulation state of the insulation oil paper is divided by combining 3 damp evaluation grades and 3 aging evaluation grades to obtain X 1 ～X 9 Totally 9 transformer oil paper insulating states;
step 4: measuring and calculating aging characteristic parameters of the insulating oil paper in the step 1 to the step 3, and establishing a comparison sequence and a reference sequence;
step 5: eliminating the influence of units and orders on gray correlation analysis, carrying out dimensionless treatment on each reference sequence by adopting a averaging operator, and calculating a difference vector;
step 6: calculating to obtain entropy weight-gray correlation degree R of insulating oilpaper i Based on the influence degree of the evaluation index on the tested insulating oil paper sample, R is calculated as 1 ～R 7 Sequencing from large to small to obtain an insulation state evaluation result of the insulation oilpaper.
2. The transformer oil paper insulation state evaluation method based on the fractional Poynting-Thomson model and gray entropy weight according to claim 1 is characterized by comprising the following steps: the step 1 comprises the following steps:
s1.1: carrying out accelerated heat aging treatment on the insulating oil paper samples to prepare different insulating oil paper aging samples;
s1.2: taking out a group of insulating oil paper aging samples respectively at 0 day, 21 day and 42 day of heat aging, placing the insulating oil paper aging samples at room temperature for natural wetting, and weighing the single insulating oil paper until the target water content is reached: 1%, 2%, 4%;
s1.3: FDS measurement is carried out at 30 ℃, the measurement voltage is set to 140V, the measurement frequency is 0.1 mHz-1 kHz, and the average value of 3 FDS measurement results is taken as the final measurement result;
s1.4: after the FDS measurement is completed, the DP value of the polymerization degree of the insulating paper board and the acid value A of the insulating oil are measured again v 。
3. The transformer oil paper insulation state evaluation method based on the fractional Poynting-Thomson model and gray entropy weight according to claim 1 is characterized by comprising the following steps: in the step 2, a weighted least square method is adopted to perform parameter fitting on a fractional Poynting-Thomson model, and the objective constraint function is as follows:
wherein: r is an optimization target; m's' fi And M fi Fitting values of real parts and imaginary parts of complex dielectric modulus under the ith measuring frequency respectively; m's' mi And M mi Respectively measuring the real part and the imaginary part of the complex dielectric modulus at the ith measuring frequency; i represents the meaning of the ith frequency measurement point;
after parameter fitting, alpha, beta, epsilon are obtained a The T and the DP of the insulating paper board have a higher fitting degree functional relation, so alpha, beta and epsilon are selected a τ is an aging characteristic parameter for evaluating the oiled paper insulation.
4. The transformer oil paper insulation state evaluation method based on the fractional Poynting-Thomson model and gray entropy weight according to claim 1 is characterized by comprising the following steps: in the step 2, a frequency-domain dielectric spectrum is obtained when the frequency-domain dielectric measurement is performed on the oilpaper insulation, and a dielectric constant (epsilon) * ) Dielectric constant and dielectric modulus (M * (ω)) is:
converting the dielectric constant of each frequency point obtained through actual measurement into a dielectric modulus form, and obtaining a dielectric modulus spectrum;
dielectric characteristic parameter A DP 、ΔA DP The calculation formula is as follows:
indicated at 10 3 The real part of the dielectric modulus at the Hz frequency point; />Indicated at 10 -4 The real part of the dielectric modulus at the Hz frequency point;
dielectric characteristic parameter A DP 、ΔA DP Has higher fitting degree function relation with the polymerization degree DP of the insulating paper board, so the dielectric characteristic parameter A DP 、ΔA DP The aging state of the oiled paper insulation can also be characterized.
5. The transformer oil paper insulation state evaluation method based on the fractional Poynting-Thomson model and gray entropy weight according to claim 1 is characterized by comprising the following steps: in the step (3) of the above-mentioned process,
combining and dividing the insulation states of the insulating oil paper to obtain X 1 ～X 9 Totally 9 transformer oil paper insulating states;
the wet state of the vegetable oil paper insulation system is classified into 3 evaluation grades of dryness, wetness and severity from low to high by taking the water content m.c. as a limit of 1.5 percent and 2.5 percent; when m.c. is less than or equal to 1.5%, judging that the moisture state of the vegetable oil paper insulation system is dry; when the m.c. is less than or equal to 1.5 percent and less than or equal to 2.5 percent, judging that the moisture state of the vegetable oil paper insulation system is moist; when m.c. is more than 2.5%, judging that the moisture state of the vegetable oil paper insulation system is serious;
the aging state of the vegetable oil paper insulation system is classified into 3 kinds of excellent, medium and serious evaluation grades from good to bad by taking the polymerization degree DP of the insulation paper board as the limit of 1000 and 650; when DP is more than 1000 and less than or equal to 1200, judging that the aging state of the vegetable oil paper insulation system is excellent; when DP is more than 650 and less than or equal to 1000, judging that the aging state of the vegetable oil paper insulation system is medium; and when the DP is less than or equal to 650, judging that the aging state of the vegetable oil paper insulation system is serious.
6. The transformer oil paper insulation state evaluation method based on the fractional Poynting-Thomson model and gray entropy weight according to claim 1 is characterized by comprising the following steps: in the step 4, a comparison sequence and a reference sequence are determined:
setting the insulation state of the insulation oil paper sample to be diagnosed as a comparison sequence X 0 ：
X 0 ＝[X 0 (1),X 0 (2),…,X 0 (7)]
Wherein: x is X 0 (1)、X 0 (2)、X 0 (3)、X 0 (4) Characteristic parameters alpha, beta and epsilon extracted after the identification of the parameters of the fractional Poynting-Thomson model a 、τ；
X 0 (5) Integral value A being imaginary part of complex dielectric modulus DP ；X 0 (6) Amplitude difference ΔA, which is the real part of complex dielectric modulus DP ；X 0 (7) Acid value A of insulating oil v ；
Establishing the insulation states of the insulation oilpaper with different ageing degrees and humidity degrees as a reference sequence X i ，i＝1，2，…，9：
X i ＝[X i (1),X i (2),…,X i (7)]
Wherein: x is X i (1),X i (2),…,X i (7) The insulation states of the vegetable oilpaper insulation systems for different ageing and humidity degrees in (i=1, 2, …, 9) are the reference sequences.
7. The transformer oil paper insulation state evaluation method based on the fractional Poynting-Thomson model and gray entropy weight according to claim 1 is characterized by comprising the following steps: said step 5 comprises the steps of:
s5.1: carrying out dimensionless treatment on each reference sequence by adopting a averaging operator, wherein the averaging operator is defined as follows:
wherein: i represents the number of rows of the sequence, i=1, 2, …,9; j represents the number of columns of the sequence, j=1, 2, …,7; corresponding values of each evaluation index in the reference sequence:
s5.2: find the minimum and maximum differences, compare sequence X 0 (j) Each of which is respectively associated with a reference sequence X i (j) Each term in the two-dimensional image is subjected to difference and takes absolute value to obtain a difference vector delta i (j)：
In the above formula: x is X 0 (1)、X 0 (2)、X 0 (3)、X 0 (4) Characteristic parameters alpha, beta and epsilon extracted after the identification of the parameters of the fractional Poynting-Thomson model a 、τ；X 0 (5) Integral value A being imaginary part of complex dielectric modulus DP ；X 0 (6) Amplitude difference ΔA, which is the real part of complex dielectric modulus DP ；X 0 (7) Acid value A of insulating oil v ；
Carrying out dimensionless treatment on each reference sequence by adopting a averaging operator, wherein the averaging operator is defined as follows:
wherein: i represents the number of rows of the sequence, i=1, 2, …,9; j represents the number of columns of the sequence, j=1, 2, …,7;
X 1 ′(1)X 2 ′(1)X 9 ′(1)X 1 ′(2)X 2 ′(2)X 9 ′(2)X 1 ′(7)X 2 ′(7)……X 9 (7) respectively representing the average operators of the reference sequences after dimensionless treatment;
s5.3: from the difference vector delta i (j) The maximum and minimum values are respectively marked as M and M:
8. the transformer oil paper insulation state evaluation method based on the fractional Poynting-Thomson model and gray entropy weight according to claim 1 is characterized by comprising the following steps: in the step 6, xi is a resolution coefficient, the physical meaning of xi is the association degree between the j-th evaluation index and the evaluation object in the i-th state, and the gray association coefficient r ij The definition is as follows:
the j (j=1, 2, …, 7) index specific gravity P for the i (i=1, 2, …, 9) th state ij ：
Index specific gravity P calculated from the above ij Obtaining an index entropy value E j ：
ln(P ij ) Is to index specific gravity P ij Taking logarithm to obtain;
entropy weight W of each evaluation index j ：
Correlating the grey with the coefficient R ij Entropy weight W with each evaluation index j Multiplying to obtain entropy weight-gray correlation degree R of insulating oilpaper i ：
R is calculated 1 ～R 7 Sequencing from large to small to obtain an insulation state evaluation result of the insulation oiled paper.
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