CN109239463B - Dielectric loss measurement method based on linear correction algorithm - Google Patents

Dielectric loss measurement method based on linear correction algorithm Download PDF

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CN109239463B
CN109239463B CN201811014756.6A CN201811014756A CN109239463B CN 109239463 B CN109239463 B CN 109239463B CN 201811014756 A CN201811014756 A CN 201811014756A CN 109239463 B CN109239463 B CN 109239463B
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fundamental wave
dielectric loss
current signal
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phase angle
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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 based on a linear correction algorithm, 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 DDA0001785861300000011
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 DDA0001785861300000012
According to the formula

Description

Dielectric loss measurement method based on linear correction algorithm
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 GDA0002490267390000011
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 GDA0002490267390000021
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 GDA0002490267390000022
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 based on a linear correction algorithm, so as to effectively improve the analysis error of a 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 based on a linear correction algorithm, 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 GDA0002490267390000023
analyzing W +1 data to obtain fundamental wave information of the voltage signal V
Figure GDA0002490267390000024
And
Figure GDA0002490267390000025
applying a quasi-synchronous DFT formula from the sampling point i of the voltage signal V to 1:
Figure GDA0002490267390000031
analyzing W +1 data to obtain fundamental wave information of the voltage signal V
Figure GDA0002490267390000032
And
Figure GDA0002490267390000033
applying the formula:
Figure GDA0002490267390000034
calculating a frequency drift mu of the voltage signal VV；
Using formulas
Figure GDA0002490267390000035
Calculating a fundamental wave initial phase angle of the voltage signal V;
using formulas
Figure GDA0002490267390000036
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 GDA0002490267390000037
analyzing W +1 data to obtain fundamental wave information of the current signal I
Figure GDA0002490267390000038
And
Figure GDA0002490267390000039
applying a quasi-synchronous DFT formula from the sampling point I of the current signal I to 1:
Figure GDA00024902673900000310
analyzing W +1 data to obtain fundamental wave information of the current signal I
Figure GDA00024902673900000311
And
Figure GDA00024902673900000312
applying the formula:
Figure GDA0002490267390000041
calculating a frequency drift mu of the current signal II；
Using formulas
Figure GDA0002490267390000042
Calculating a fundamental wave initial phase angle of the current signal I;
using formulas
Figure GDA0002490267390000043
And linearly correcting the initial phase angle of the fundamental wave of the current signal I.
(4) According to the formula
Figure GDA0002490267390000044
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 measurement and instrumentation, 1988, (2): 2-7.
Figure GDA0002490267390000045
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 applied to improve the existing instruments and equipmentIs technically feasible and can improve the analysis result to 10 without increasing any hardware overhead-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. One iteration and multiple iterations are essentially the same, only multiple iterations are carried out step by step in the calculation, and one iteration is to combine the process of multiple iterations into an iteration coefficient gammaiThe calculation is completed in one time, so the method is also suitable for a plurality of iterative processes.
Detailed Description
(example 1)
The dielectric loss measuring method based on the linear correction algorithm in the embodiment 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 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 GDA0002490267390000051
analyzing W +1 data to obtain fundamental wave information of the voltage signal V
Figure GDA0002490267390000052
And
Figure GDA0002490267390000053
coefficient of first iterationγi is determined by an integration method, an ideal period sampling point N and iteration times N;
Figure GDA0002490267390000054
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 GDA0002490267390000061
analyzing W +1 data to obtain fundamental wave information of the voltage signal V
Figure GDA0002490267390000062
And
Figure GDA0002490267390000063
applying the formula:
Figure GDA0002490267390000064
calculating a frequency drift mu of the voltage signal VV；
Using formulas
Figure GDA0002490267390000065
Calculating a fundamental wave initial phase angle of the voltage signal V;
using formulas
Figure GDA0002490267390000066
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 GDA0002490267390000067
analyzing W +1 data to obtain fundamental wave information of the current signal I
Figure GDA0002490267390000068
And
Figure GDA0002490267390000069
applying a quasi-synchronous DFT formula from the sampling point I of the current signal I to 1:
Figure GDA00024902673900000610
analyzing W +1 data to obtain fundamental wave information of the current signal I
Figure GDA00024902673900000611
And
Figure GDA00024902673900000612
applying the formula:
Figure GDA00024902673900000613
calculating a frequency drift mu of the current signal II；
Using formulas
Figure GDA00024902673900000614
Calculating a fundamental wave initial phase angle of the current signal I;
using formulas
Figure GDA00024902673900000615
And linearly correcting the initial phase angle of the fundamental wave of the current signal I.
(4) According to the formula
Figure GDA0002490267390000071
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 measurement method based on a linear correction algorithm 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 trapezoidal integration method, and W is equal to nN;
(2) applying a quasi-synchronous DFT formula starting from a sampling point i of the voltage signal V being 0:
Figure FDA0002490267380000011
analyzing W +1 data to obtain fundamental wave information of the voltage signal V
Figure FDA0002490267380000012
And
Figure FDA0002490267380000013
applying a quasi-synchronous DFT formula from the sampling point i of the voltage signal V to 1:
Figure FDA0002490267380000014
analyzing W +1 data to obtain fundamental wave information of the voltage signal V
Figure FDA0002490267380000015
And
Figure FDA0002490267380000016
applying the formula:
Figure FDA0002490267380000017
calculating a frequency drift mu of the voltage signal Vv；
Using formulas
Figure FDA0002490267380000018
Calculating a fundamental wave initial phase angle of the voltage signal V;
using formulas
Figure FDA0002490267380000019
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 FDA0002490267380000021
analyzing W +1 data to obtain fundamental wave information of the current signal I
Figure FDA0002490267380000022
And
Figure DEST_PATH_IMAGE002
applying a quasi-synchronous DFT formula from the sampling point I of the current signal I to 1:
Figure FDA0002490267380000024
analyzing W +1 data to obtain fundamental wave information of the current signal I
Figure FDA0002490267380000025
And
Figure FDA0002490267380000026
applying the formula:
Figure FDA0002490267380000027
calculating a frequency drift mu of the current signal Il；
Using formulas
Figure FDA0002490267380000028
Calculating a fundamental wave initial phase angle of the current signal I;
using formulas
Figure FDA0002490267380000029
Linearly correcting the fundamental wave initial phase angle of the current signal I;
(4) according to the formula
Figure FDA00024902673800000210
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 FDA00024902673800000211
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 based on the linear correction algorithm 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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