CN109030957B - Dielectric loss measuring method - Google Patents

Dielectric loss measuring method Download PDF

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CN109030957B
CN109030957B CN201811015799.6A CN201811015799A CN109030957B CN 109030957 B CN109030957 B CN 109030957B CN 201811015799 A CN201811015799 A CN 201811015799A CN 109030957 B CN109030957 B CN 109030957B
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fundamental wave
dielectric loss
quasi
phase angle
sampling
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CN109030957A (en
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傅中君
王建宇
欧云
陈鉴富
侯雪亚
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Jiangsu University of Technology
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Abstract

The invention relates to a dielectric loss measuring method, which is improved and realized on the basis of quasi-synchronous DFT and comprises the following steps: simultaneously sampling a voltage signal V applied to a tested piece and a current signal I flowing through the tested piece; method for obtaining fundamental wave phase angle of applied voltage by applying quasi-synchronous DFT harmonic phase angle linear correction method
Figure DDA0001786049180000011
Obtaining the initial phase angle of the fundamental wave of the current signal flowing through the tested piece by applying the quasi-synchronous DFT harmonic phase angle linear correction method
Figure DDA0001786049180000012
According to the formula

Description

Dielectric loss measuring method
The application has the following application numbers: 201510258036.4 entitled "a method for measuring dielectric loss", filed as follows: divisional application of the invention patent application on 19/05/2015.
Technical Field
The invention relates to a high-precision dielectric loss measuring method.
Background
The intelligent dielectric loss measuring instrument is an automatic instrument for measuring the dielectric loss tangent and the capacitance value, and can measure the dielectric loss tangent and the capacitance value of various high-voltage equipment such as insulating materials, insulating sleeves, power cables, capacitors, mutual inductors, transformers and the like on site under the condition of power frequency and high voltage. The instrument is also suitable for measuring the dielectric loss tangent and the capacitance value of high-voltage electrical equipment in workshops, laboratories and scientific research units; and the dielectric loss of the insulating oil can be measured by matching the insulating oil cup.
The working principle of the intelligent dielectric loss measuring instrument is as follows: when an alternating voltage is applied to the dielectric medium, the voltage and current in the dielectric medium have a phase angle difference
Figure GDA0002757614260000013
The residual angle of (1) is called the dielectric loss angle, and the tangent tg is called the dielectric loss tangent. the tg value is a parameter used to measure dielectric loss. The measuring circuit of the instrument comprises a standard circuit (Cn) and a tested circuit (Cx). The standard loop consists of a built-in high-stability standard capacitor and a measuring circuit, and the tested loop consists of a tested product and the measuring circuit. The measuring circuit consists of a sampling resistor, a preamplifier and an A/D converter, and because the input resistance of the preamplifier connected in parallel with two ends of the sampling resistor is far greater than the sampling resistor, the loop current can be considered to completely flow through the sampling resistor. The current signal is converted into a digital signal through a measuring circuit, the amplitude and the phase difference of the standard loop current and the tested loop current are respectively measured by a single chip microcomputer through a digital real-time acquisition method, and the capacitance value and the dielectric loss of a test article can be obtained through vector operation.
The harmonic analysis technology is widely applied to the fields of power quality monitoring, electronic product production inspection, electrical equipment monitoring and the like, and is an important technical means for power grid monitoring, quality inspection and equipment monitoring. The most widely used techniques for harmonic analysis are Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) at present. The harmonic analysis technology combining the quasi-synchronous sampling technology and the DFT technology can improve the accuracy of harmonic analysis, and the formula is as follows:
Figure GDA0002757614260000011
in the formula: k is the number of harmonics to be obtained (e.g. fundamental wave k is 1, 3-th harmonic k is 3); sin and cos are sine and cosine functions, respectively; and a iskAnd bkThe real part and the imaginary part of the k harmonic are respectively; n is the number of iterations; w is determined by an integral method, and when a complex trapezoidal integral method is adopted, W is equal to nN; gamma rayiIs a primary weighting coefficient;
Figure GDA0002757614260000012
is the sum of all weighting coefficients; f (i) is the ith sample value of the analysis waveform; and N is the sampling times in the period.
In engineering applications, harmonic analysis always performs finite point sampling and synchronization sampling which is difficult to achieve strictly. Thus, when the quasi-synchronous DFT is applied to harmonic analysis, long-range leakage caused by truncation effect and short-range leakage caused by barrier effect exist, so that the accuracy of the analysis result is not high, even the analysis result is not credible.
Disclosure of Invention
The invention aims to provide a high-precision dielectric loss measurement method, so as to effectively improve the analysis error of the quasi-synchronous DFT harmonic analysis technology and obtain a high-precision harmonic analysis result, thereby improving the reliability of dielectric loss measurement.
The technical scheme for realizing the aim of the invention is to provide a dielectric loss measuring method, which comprises the following steps:
(1) the method comprises the following steps of synchronously sampling W +2 sampling point data of a voltage signal V and a current signal I applied to a tested piece at equal intervals: { fV(i),fI(i),i＝0,1,…,W+1}；
(2) Applying a quasi-synchronous DFT formula starting from a sampling point i of the voltage signal V being 0:
Figure GDA0002757614260000021
analyzing W +1 data to obtain fundamental wave information of the voltage signal V
Figure GDA0002757614260000022
And
Figure GDA0002757614260000023
applying a quasi-synchronous DFT formula from the sampling point i of the voltage signal V to 1:
Figure GDA0002757614260000024
analyzing W +1 data to obtain fundamental wave information of the voltage signal V
Figure GDA0002757614260000025
And
Figure GDA0002757614260000026
applying the formula:
Figure GDA0002757614260000027
calculating a frequency drift mu of the voltage signal Vv；
Using formulas
Figure GDA0002757614260000028
Calculating a fundamental wave initial phase angle of the voltage signal V;
using formulas
Figure GDA0002757614260000029
And linearly correcting the initial phase angle of the fundamental wave of the voltage signal V.
(3) Applying a quasi-synchronous DFT formula starting from a sampling point I of the current signal I being 0:
Figure GDA00027576142600000210
analyzing W +1 data to obtain fundamental wave information of the current signal I
Figure GDA00027576142600000211
And
Figure GDA00027576142600000212
applying a quasi-synchronous DFT formula from the sampling point I of the current signal I to 1:
Figure GDA0002757614260000031
analyzing W +1 data to obtain fundamental wave information of the current signal I
Figure GDA0002757614260000032
And
Figure GDA0002757614260000033
applying the formula:
Figure GDA0002757614260000034
calculating a frequency drift mu of the current signal Il；
Using formulas
Figure GDA0002757614260000035
Calculating a fundamental wave initial phase angle of the current signal I;
using formulas
Figure GDA0002757614260000036
And linearly correcting the initial phase angle of the fundamental wave of the current signal I.
(4) According to the formula
Figure GDA0002757614260000037
The dielectric loss tangent was calculated.
The invention discloses a harmonic phase angle linear correction method capable of effectively inhibiting short-range leakage, so that high-precision harmonic phase angle information and a dielectric loss factor are obtained.
N is the number of sample points in an ideal period. The equal-interval sampling is to sample N points in one period according to the period T and the frequency f (such as the frequency f of a power frequency signal is 50Hz and the period is 20mS) of an ideal signal for harmonic analysis, namely the sampling frequency is fsNf, and N is more than or equal to 64.
The sampling W +2 sampling point data is selected correspondingly according to the selected integration method, and if a complex trapezoidal integration method is adopted, W is equal to nN; if a complex rectangular integral method is adopted, W is N (N-1); if the simpson integration method is adopted, W is N (N-1)/2; then according to the sampling frequency fsObtaining a sampling point data sequence; n is iteration times, and generally n is more than or equal to 3.
Coefficient of one iteration gammaiThe method is determined by an integration method, an ideal period sampling point N and iteration times N, and the specific derivation process is found in the literature [ J]Electrical measuring and instrumentation, 1988, (2):2-7.
Figure GDA0002757614260000041
Is the sum of all weighting coefficients.
Drift mu of signal frequencyvAnd muiThe frequency deviation can be obtained according to the fixed relation between the phase angle difference of the fundamental wave of adjacent sampling points and the number N of the sampling points in an ideal period, and the frequency f of the fundamental wave and the higher harmonic wave can be corrected by the drift of the signal frequency1Frequency f of harmonick。
The invention has the positive effects that: (1) the invention has high-precision dielectric loss measurement results.
(2) The method provided by the invention fundamentally solves the problem of low analysis precision of quasi-synchronous DFT harmonic phase angles, does not need to perform complicated inversion and correction, and is simple in algorithm.
(3) Compared with quasi-synchronous DFT, the harmonic analysis technology of the invention only needs to add one sampling point to solve the problem of large error of quasi-synchronous DFT analysis, and is easy to realize.
(4) The invention is technically feasible for improving the existing instrument and equipment, and the analysis result can be improved to 10 without increasing any hardware expense-8And (4) stages.
(5) The method is also suitable for the harmonic analysis process of carrying out multiple iterations instead of one iteration, and only one iteration needs to be decomposed into multiple iterations to realize the harmonic analysis process. The method is characterized in that the method is used for calculating the coefficient gamma of the iteration coefficient gamma i, and the method is also suitable for the multi-iteration process.
Detailed Description
(example 1)
The dielectric loss measuring method of the embodiment includes the following steps:
(1) the method comprises the following steps of synchronously sampling W +2 sampling point data of a voltage signal V and a current signal I applied to a tested piece at equal intervals: { fV(i),fI(i) I is 0,1, …, W +1 }. W is selected correspondingly according to the selected integration method, and if a complex trapezoidal integration method is adopted, W is equal to nN; if a complex rectangular integral method is adopted, W is N (N-1); if the simpson integration method is adopted, W is N (N-1)/2; then according to the sampling frequency fsObtaining a sampling point data sequence; n is iteration times, and generally n is more than or equal to 3.
(2) Applying a quasi-synchronous DFT formula starting from a sampling point i of the voltage signal V being 0:
Figure GDA0002757614260000042
analyzing W +1 data to obtain fundamental wave information of the voltage signal V
Figure GDA0002757614260000043
And
Figure GDA0002757614260000044
coefficient of one iteration gammaiThe method is determined by an integration method, an ideal period sampling point N and iteration times N;
Figure GDA0002757614260000045
is the sum of all weighting coefficients;
applying a quasi-synchronous DFT formula from the sampling point i of the voltage signal V to 1:
Figure GDA0002757614260000051
analyzing W +1 data to obtain fundamental wave information of the voltage signal V
Figure GDA0002757614260000052
And
Figure GDA0002757614260000053
applying the formula:
Figure GDA0002757614260000054
calculating a frequency drift mu of the voltage signal Vv；
Using formulas
Figure GDA0002757614260000055
Calculating a fundamental wave initial phase angle of the voltage signal V;
using formulas
Figure GDA0002757614260000056
And linearly correcting the initial phase angle of the fundamental wave of the voltage signal V.
(3) Applying a quasi-synchronous DFT formula starting from a sampling point I of the current signal I being 0:
Figure GDA0002757614260000057
analyzing W +1 data to obtain fundamental wave information of the current signal I
Figure GDA0002757614260000058
And
Figure GDA0002757614260000059
applying a quasi-synchronous DFT formula from the sampling point I of the current signal I to 1:
Figure GDA00027576142600000510
analyzing W +1 data to obtain fundamental wave information of the current signal I
Figure GDA00027576142600000511
And
Figure GDA00027576142600000512
applying the formula:
Figure GDA00027576142600000513
calculating a frequency drift mu of the current signal Il；
Using formulas
Figure GDA00027576142600000514
Calculating a fundamental wave initial phase angle of the current signal I;
using formulas
Figure GDA00027576142600000515
And linearly correcting the initial phase angle of the fundamental wave of the current signal I.
(4) According to the formula
Figure GDA00027576142600000516
The dielectric loss tangent was calculated.
It will be appreciated by persons skilled in the art that the above embodiments are only intended to illustrate the present invention, and not to limit the present invention, and that the present invention may be further modified, and that within the spirit and scope of the present invention, changes and modifications to the above described embodiments will fall within the scope of the appended claims.

Claims (2)

1. A dielectric loss measuring method is characterized by comprising the following steps:
(1) the method comprises the following steps of synchronously sampling W +2 sampling point data of a voltage signal V and a current signal I applied to a tested piece at equal intervals: { fV(i),fI(i) I ═ 0,1, …, W +1 }; the W +2 sampling point data are obtained by adopting a complex Simpson integration method, and W is N (N-1)/2;
(2) applying a quasi-synchronous DFT formula starting from a sampling point i of the voltage signal V being 0:
Figure FDA0002757614250000011
analyzing W +1 data to obtain fundamental wave information of the voltage signal V
Figure FDA0002757614250000016
And
Figure FDA0002757614250000017
applying a quasi-synchronous DFT formula from the sampling point i of the voltage signal V to 1:
Figure FDA0002757614250000012
analyzing W +1 data to obtain fundamental wave information of the voltage signal V
Figure FDA0002757614250000018
And
Figure FDA0002757614250000019
applying the formula:
Figure FDA0002757614250000013
calculating a frequency drift mu of the voltage signal Vv；
Using formulas
Figure FDA00027576142500000110
Calculating a fundamental wave initial phase angle of the voltage signal V;
using formulas
Figure FDA00027576142500000111
Linearly correcting the fundamental wave initial phase angle of the voltage signal V;
(3) applying a quasi-synchronous DFT formula starting from a sampling point I of the current signal I being 0:
Figure FDA0002757614250000014
analyzing W +1 data to obtain fundamental wave information of the current signal I
Figure FDA00027576142500000112
And
Figure FDA00027576142500000113
applying a quasi-synchronous DFT formula from the sampling point I of the current signal I to 1:
Figure FDA0002757614250000015
analyzing W +1 data to obtain fundamental wave information of the current signal I
Figure FDA00027576142500000114
And
Figure FDA00027576142500000115
applying the formula:
Figure FDA0002757614250000021
calculating a frequency drift mu of the current signal II；
Using formulas
Figure FDA0002757614250000022
Calculating the currentThe fundamental wave initial phase angle of the signal I;
using formulas
Figure FDA0002757614250000025
Linearly correcting the fundamental wave initial phase angle of the current signal I;
(4) according to the formula
Figure FDA0002757614250000023
Calculating the dielectric loss tangent; in the formula: k is the number of harmonics to be obtained; sin and cos are sine and cosine functions, respectively; and a iskAnd bkThe real part and the imaginary part of the k harmonic are respectively; n is the number of iterations; w is determined by an integration method; gamma rayiIs a primary weighting coefficient;
Figure FDA0002757614250000024
is the sum of all weighting coefficients; f (i) is the ith sample value of the analysis waveform; n is the sampling frequency in the period;
the equal-interval synchronous sampling is to sample N points in one period according to the period T and the frequency f of an ideal signal for harmonic analysis, namely the sampling frequency is fsNf, and N is more than or equal to 64.
2. The dielectric loss measurement method according to claim 1, characterized in that: the W +2 sampling point data are selected according to the selected integration method and then according to the sampling frequency fsObtaining a sampling point data sequence; n is iteration times, and n is more than or equal to 3.
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