CN104808069A - Relative comparison method in combination with correlation analysis filtering performance - Google Patents

Abstract

The invention discloses a relative comparison method with strong anti-interference ability, high measurement precision and wide application range, which is used for measuring the relative dielectric loss (Δtanδ) of capacitive equipment. Before using the relative comparison method to measure the Δtanδ of the capacitive equipment, firstly make full use of the filtering property of the correlation function, and filter the leakage current by correlating the leakage current of the two selected equipment with the standard fundamental wave respectively; then use the cross-correlation The delay characteristic of the function is used to obtain the relative dielectric loss of the equipment, so that the algorithm is more accurate. The invention has the characteristics of strong anti-interference ability, high measurement precision and wide application range, and has certain practical application value.

Description

A Relative Comparison Method Combined with Correlation Analysis and Filtering

technical field

The invention relates to a measurement algorithm applied to on-line monitoring of dielectric loss of high-voltage capacitive equipment, and belongs to the technical field of on-line monitoring of high-voltage capacitive equipment.

Background technique

Capacitive devices (current transformers, coupling capacitors, capacitive voltage transformers and high-voltage bushings, etc.) account for a considerable proportion of power system equipment, and the safety and reliability of these devices is the basis for the operation of the entire power system. A large part of electrical equipment (especially high-voltage equipment) damage accidents is caused by insulation damage, and by measuring dielectric loss (tanδ, hereinafter referred to as dielectric loss) or relative dielectric loss, it can be found that the integrity of the electrical equipment insulation system is in the early development stage Defects or large concentrated local defects. Therefore, the measurement of tanδ of high-voltage capacitive equipment is of great significance to the safe and economical operation of substations and even the entire power system.

At present, the measurement of dielectric loss mainly includes zero-crossing comparison method, harmonic analysis method and relative comparison method. The basic principle of the zero-crossing comparison method is: Let the voltage and current signals pass through the same two-way signal preprocessing circuit, and then enter the zero-crossing comparator to shape the AC signal zero-crossing into a square wave signal. By comparing the two square wave signals The time difference between the rising edge or the falling edge is used to find the phase difference of the two signals, so as to find the dielectric loss. The principle of the harmonic analysis method is: use the voltage transformer and current transformer to obtain the voltage and current signals of the tested product respectively, and then use the discrete Fourier transform (DFT) to perform harmonic decomposition on the voltage and current signals to obtain the fundamental current , The phase difference between the voltage signals, and then find the dielectric loss of the tested product. The principle of the relative comparison method is: select the leakage current values of two capacitive devices, one of which is set as the reference standard, and perform relative comparison to obtain the relative dielectric loss, so as to diagnose the fault.

The advantages of the relative comparison method are: 1. Considering the similarity of operating conditions, voltage references, and environmental influences between equipment with the same voltage level, the dielectric loss measurement data of these equipment should show signs of simultaneous changes. If the equipment insulation is in good condition, the two test results should be basically the same; if there is a significant difference between the test data, the insulation condition of one of the equipment may be abnormal. Therefore, using their relative dielectric loss changes as the basis for fault diagnosis will have better stability and greatly improve the sensitivity of fault diagnosis. Second, it can offset the influence of factors such as temperature and humidity changes, phase-to-phase interference, and potential transformer (PT) angle difference to a certain extent, so that the insulation state will be judged more accurately. Therefore, the relative comparison method has a good application prospect.

Most traditional relative comparison methods use correlation analysis to obtain relative dielectric loss. According to the phase difference of the leakage current of the two devices, the relative dielectric loss can be obtained, and the phase difference can be obtained through the time difference, as shown in Figure 1 , the formula is: Δδ=2πΔT/T. The time difference △T of the two leakage currents can be obtained by using the time delay characteristics of the cross-correlation function. The waveform diagram of the cross-correlation function of the two leakage current signals is shown in Figure 2 . The difference from the origin is the time difference ΔT between the two leakage current signals.

However, the dielectric loss of capacitive equipment is a small value under normal conditions, so the system's own interference (harmonic interference) and external interference (environmental interference) will have a great impact on the traditional measurement method for obtaining relative dielectric loss. , so the traditional relative comparison method will no longer be accurate in some cases (such as when harmonic interference or environmental interference is large). Therefore, it has been the focus and hot spot of research to seek a relative dielectric loss measurement method with strong anti-interference ability and high precision.

Contents of the invention

The purpose of the present invention is to provide a kind of relative comparison method combined with correlation analysis filter property, utilize the filter property of correlation analysis earlier before equipment is done the relative comparison of dielectric loss, filter out most interference, make relative comparison method measure capacitive equipment It has strong anti-interference ability, high measurement accuracy and wide application range.

The technical solution adopted to realize the object of the present invention is: to use a filtering algorithm combined with correlation analysis to perform filtering first, then calculate the relative dielectric loss of the equipment, and then perform diagnosis.

The steps of the present invention are as follows:

(1) Collect the leakage current signals of the two selected devices as i ₁ (t) and i ₂ (t), and set the standard fundamental wave signal as i ₀ (t);

(2) Using the standard fundamental wave signal i ₀ (t) and two leakage current signals i ₁ (t) and i ₂ (t) for cross-correlation processing respectively, two leakage current signals i ₁ (t) and i ₂ (t ) filtered leakage current signals i ₁₀ (t), i ₂₀ (t): the specific steps are as follows:

(21) Perform Fourier transform on the standard fundamental wave signal i ₀ (t) and two leakage current signals i ₁ (t) and i ₂ (t) to obtain the frequency domain signals I ₀ (f), I ₁ ( f) and I ₂ (f);

(22) According to the relevant theorems, the standard fundamental frequency domain signal I ₀ (f) and the leakage frequency domain signal I ₁ (f), the standard fundamental frequency domain signal I ₀ (f) and the leakage frequency domain signal I ₂ ( f) The cross-spectral density function between:

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\stackrel{<span\; class="notranslate">\; *</span>}{<span\; class="notranslate">\; (</span>}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 20</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\stackrel{<span\; class="notranslate">\; *</span>}{<span\; class="notranslate">\; (</span>}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

Among them, I ₁₀ (f) is the cross-spectral density function of the standard fundamental frequency domain signal I ₀ (f) and the leakage frequency domain signal I ₁ (f), is the conjugate of I ₁ (f); I ₂₀ (f) is the cross-spectral density function of the standard fundamental frequency domain signal I ₀ (f) and the leakage frequency domain signal I ₂ (f), It is the conjugate of I ₂ (f).

(23) Calculate the filtered two leakage current frequency domain signals I ₁₀ (f) and I ₂₀ (f), and perform inverse Fourier transform on the obtained leakage current frequency domain signals respectively to obtain the filtered leakage current signal i ₁₀ (t), i ₂₀ (t);

(3) Perform cross-correlation processing on the filtered leakage current signals i ₁₀ (t) and i ₂₀ (t), and use the time-delay characteristics of the correlation function to obtain the relationship between i ₁₀ (t) and i ₂₀ (t) time delay t _delay ;

(4) Calculate the relative dielectric loss angle of the equipment according to the formula Δδ=t _delay ×360/N; where N is the number of sampling points in each period.

The invention utilizes the improved correlation analysis to perform filtering first, and then obtains the relative dielectric loss, so that the anti-interference ability of the relative comparison method after filtering processing is stronger and the measurement accuracy is higher. During the actual operation of the power system, interference has a great influence on the measurement results. The interference mainly includes harmonics in the system and external environmental interference. In general, when the harmonic interference or external environmental interference is increasing, the accuracy of the relative comparison method will not be able to meet the requirements. And after filtering through the filtering algorithm of the present invention in combination with improved correlation analysis, the waveform of the signal is obviously improved, and the signal has filtered most of the interference, and the waveform is smooth without burrs, as shown in Figure 3 ; under severe interference conditions (amplification harmonic interference and Environmental interference, this moment signal-to-noise ratio is 5dB), the result measured by the relative comparison method after the filtering algorithm filtering of combining improved correlation analysis of the present invention is comparatively accurate, meets the diagnosis requirement, and contrast figure is as Fig. 5 , and Fig. 5 (a The waveform in ) has a large burr, which has a great impact on the detection of correlation peaks and the calculation of time delay. The measured results will be extremely inaccurate, while the waveform in Fig . Accurately measure the position of the correlation peak, so as to accurately obtain the relative dielectric loss. Therefore, the present invention uses the standard fundamental wave as an intermediate variable in combination with the relative comparison method of the improved correlation analysis, which fully combines the filtering performance and time delay characteristics of the correlation analysis, improves the anti-interference ability and measurement accuracy of the algorithm, and has a wider application range. Certain practical application value.

Description of drawings

Fig. 1 is the schematic diagram of relative comparison method of the present invention;

Fig. 2 is the signal waveform figure of two kinds of equipments that the present invention adopts;

Fig. 3 is correlation function waveform diagram;

Fig. 4 is the waveform contrast diagram before and after filtering, and wherein: solid line is the waveform diagram before adopting the filtering algorithm filtering of the present invention in conjunction with correlation analysis, and dotted line is the waveform diagram after filtering;

Fig. 5 is the relevant processing result in the case of severe interference;

Wherein (a) is the processing result of direct relative comparison without using the filtering algorithm combined with correlation analysis of the present invention, and (b) is the processing result after adopting the filtering algorithm combined with correlation analysis of the present invention.

Detailed ways

In order to illustrate the structural features and operating principles of the present invention, the following will be described in conjunction with specific embodiments.

Relative comparison method step of the present invention is as follows:

(1) Collect the leakage current signals of the two selected devices as i ₁ (t) and i ₂ (t), and set the standard fundamental wave signal as i ₀ (t);

The standard fundamental wave signal is a power frequency signal, and the amplitude and phase angle are optional. Because it is applied in the power system, it is a power frequency (50Hz) signal, and the correlation analysis is also a common frequency signal (same frequency), that is, i ₁ (t) and i ₂ (t) are also power frequency signals, and their amplitude and phase angle have no influence on the calculation results and can be chosen arbitrarily.

(2) Using the standard fundamental wave signal i ₀ (t) and two leakage current signals i ₁ (t) and i ₂ (t) for cross-correlation processing respectively, two leakage current signals i ₁ (t) and i ₂ (t ) filtered leakage current signal i ₁₀ (t), i ₂₀ (t):

Since the direct calculation of the cross-correlation function is calculated in the time domain, the amount of calculation is large, and it is difficult to meet the real-time requirements under the condition of on-line monitoring. Therefore, the correlation theorem is used in the actual calculation, that is, the cross-correlation function of the signal and the cross-spectral density function are A pair of Fourier transforms, which convert time-domain calculations to frequency-domain calculations through related theorems,

The calculation is greatly simplified and the real-time requirement is met. Denote the functions y ₁ (t) and y ₂ (t) by Y ₁ (f) and Y ₂ (f) respectively

The Fourier transform of , and use * to represent the conjugate of the complex function, the cross-spectral density function of the signal is given by the following formula

The formula is determined:

$G_{i1i2}\left(f\right)=Y{{\left(\stackrel{*}{f}\right)}_{1}Y}_2\left(f\right)$ (Domain f>0)

Therefore, the cross-spectral density function of the two signals can be calculated, and then the method of Fourier inverse transform can be used to realize the fast calculation of the cross-correlation function in engineering.

Specific steps are as follows:

(21) Perform Fourier transform on the standard fundamental wave signal i ₀ (t) and two leakage current signals i ₁ (t) and i ₂ (t) to obtain the frequency domain signals I ₀ (f), I ₁ ( f) and I ₂ (f);

(22) According to the relevant theorems, the standard fundamental frequency domain signal I ₀ (f) and the leakage frequency domain signal I ₁ (f), the standard fundamental frequency domain signal I ₀ (f) and the leakage frequency domain signal I ₂ ( f) The cross-spectral density function between:

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\stackrel{<span\; class="notranslate">\; *</span>}{<span\; class="notranslate">\; (</span>}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 20</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\stackrel{<span\; class="notranslate">\; *</span>}{<span\; class="notranslate">\; (</span>}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

Among them, I ₁₀ (f) is the cross-spectral density function of the standard fundamental frequency domain signal I ₀ (f) and the leakage frequency domain signal I ₁ (f), is the conjugate of I ₁ (f); I ₂₀ (f) is the cross-spectral density function of the standard fundamental frequency domain signal I ₀ (f) and the leakage frequency domain signal I ₂ (f), It is the conjugate of I ₂ (f).

(23) Calculate the filtered leakage current frequency domain signals I ₁₀ (f), I ₂₀ (f), and perform inverse Fourier transform on the obtained leakage current frequency domain signals respectively to obtain the filtered leakage current signal i ₁₀ (t), i ₂₀ (t);

f(t) is a periodic function of t, if t satisfies the Dirichlet condition:

1) The function is continuous in any finite interval, or has only a limited number of discontinuity points of the first type (when t tends to this discontinuity point from left or right, the function has finite left and right limits);

2) In a period, the function has a finite number of maximum or minimum values;

3) f(t) is absolutely integrable in a single period, namely

Then the following formula is established.

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>\underset{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}{\overset{<span\; class="notranslate">\; \&infin;</span>}{<span\; class="notranslate">\; \&Integral;</span>}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; jwt</span>}}\mathrm{<span\; class="notranslate">\; dt</span>}$

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\underset{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}{\overset{<span\; class="notranslate">\; \&infin;</span>}{<span\; class="notranslate">\; \&Integral;</span>}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; jwt</span>}}\mathrm{<span\; class="notranslate">\; d\&omega;</span>}$

The above formula is called the Fourier transform of the integral operation f(t) and the inverse Fourier transform of F(ω). Among them, F(ω) is called the image function of f(t), f(t) is called the original function of F(ω), F(ω) is the image of f(t), f(t) is F(ω) The original image (ω=2πf, so ω has the same meaning as f, and both represent independent variables in the frequency domain).

In step (21), the formula about Fourier transform is derived as:

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\underset{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}{\overset{<span\; class="notranslate">\; \&infin;</span>}{<span\; class="notranslate">\; \&Integral;</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;ft</span>}}\mathrm{<span\; class="notranslate">\; dt</span>}$

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\underset{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}{\overset{<span\; class="notranslate">\; \&infin;</span>}{<span\; class="notranslate">\; \&Integral;</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;ft</span>}}\mathrm{<span\; class="notranslate">\; dt</span>}$

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\underset{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}{\overset{<span\; class="notranslate">\; \&infin;</span>}{<span\; class="notranslate">\; \&Integral;</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;ft</span>}}\mathrm{<span\; class="notranslate">\; dt</span>}$

In the step (23), the formula about the inverse Fourier transform is derived as:

${\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>\underset{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}{\overset{<span\; class="notranslate">\; \&infin;</span>}{<span\; class="notranslate">\; \&Integral;</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;ft</span>}}\mathrm{<span\; class="notranslate">\; df</span>}$

${\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 20</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 20</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>\underset{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}{\overset{<span\; class="notranslate">\; \&infin;</span>}{<span\; class="notranslate">\; \&Integral;</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 20</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;ft</span>}}\mathrm{<span\; class="notranslate">\; df</span>}$

Cross-correlation is handled as follows:

The correlation function reflects the similarity between two signals of the same frequency or the signals themselves at different times. Comparing the two signals obtained by detection to obtain a correlation function, and the analysis based on this is called correlation analysis.

Suppose the two signals are y ₁ (t) and y ₂ (t), then the correlation function of y ₁ (t) and y ₂ (t) is the formula

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; \&Right\; Arrow;</span><span\; class="notranslate">\; \&infin;</span>}{\mathrm{<span\; class="notranslate">\; lim</span>}}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; T</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}^{<span\; class="notranslate">\; +</span><span\; class="notranslate">\; \&infin;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dt</span>}$

Suppose the signal s(t) is disturbed by the outside to form composite signals y ₁ (t) and y ₂ (t), that is, y ₁ (t)=s(t)+n(t), y ₂ (t)=s( t+τ)+m(t), (s(t) is a useful signal, and n(t), m(t) are two noise signals), then the cross-correlation function will only contain y ₁ (t), y ₂ The signal of the relevant part s(t) in (t), and the interference of external noise is excluded, that is, the cross-correlation function at this time is:

R _y1y2 (τ)＝E[y ₁ (t)y ₂ (t+τ)]＝αR _xx (τ-τ ₁ )

In the formula, α is the relative absorption coefficient, that is, the relative peak-to-peak value of the two signals. For the function R _y1y2 (τ), it is a function of α, τ ₁ and R _xx , and when τ=τ ₁ , since the correlation between the signal and itself is 1 (that is, R _xx (0)=1) , there is R _y1y2 (τ)=αR _xx (0)=α, which has a maximum value, which is the correlation peak point. Therefore, the time difference can be estimated by the cross-correlation function, and the difference between the correlation peak position and the origin corresponds to the time difference of the two signals.

The filtering algorithm is as follows:

Due to the presence of interference in the signal, in practical applications, when the interference increases, the accuracy of the phase difference between the two signals directly decreases rapidly by using the relative comparison method. The analysis found that this is because n(t) and m(t) have a certain correlation, and the correlation is enhanced after the interference is enhanced, resulting in inaccurate measurement results.

In order to eliminate the influence brought by the correlation between n(t) and m(t), the present invention introduces an intermediate variable—the standard fundamental wave (only comprising the common-frequency fundamental wave) y ₀ (t), that is, y ₀ (t)= s(t ₀ ). Using y ₀ (t) and the signals y ₁ (t) and y ₂ (t) containing the interference signal _for correlation processing respectively, _the fundamental component y ₁₀ ( t), y ₂₀ (t), this is the filtering property of the correlation function. After the two signals are correlated with the fundamental wave of the same standard, the waveforms are smooth and complete and the phase difference information is retained, and the filtered fundamental wave components y ₁₀ (t) and y ₂₀ (t) are correlated again, and then the correlation function is used The time delay characteristics of the two signals can be obtained, which is the core of the filter algorithm combined with improved correlation analysis of the present invention.

(3) Perform cross-correlation processing on the filtered leakage current signals i ₁₀ (t) and i ₂₀ (t), and use the time-delay characteristics of the correlation function to obtain the relationship between i ₁₀ (t) and i ₂₀ (t) time delay t _delay ;

(4) Calculate the relative dielectric loss angle of the equipment according to the formula Δδ=t _delay ×360/N; where N is the number of sampling points in each period.

When δ is very small, the tangent of the general dielectric loss angle is close to the dielectric loss angle, then there is

Δtanδ=|tanδ _x1 -tanδ _x2 |=tan|(δ _x1 -δ _x2 )|≈|(δ _x1 -δ _x2 )|=Δδ

Among them, δ _x1 and δ _x2 are the dielectric loss angles of two capacitive devices with the same bus. Comparing the leakage currents of two devices on the same bus, the relative dielectric loss angle Δδ can be obtained, which reflects the relative insulation status of the devices. When the insulation of the two devices being compared is good, the relative dielectric loss angle Δδ is generally small; if one of the devices has an insulation defect, its Δδ will increase significantly, resulting in a significant change in Δtanδ. By analogy, by comparing the δ of multiple groups of equipment, the insulation defect of the equipment can be found.

Concrete calculation example:

Since the relative dielectric loss (Δtanδ) of capacitive equipment is usually small, in order to be more intuitive, the calculation example will directly calculate the relative dielectric loss angle (Δδ). Generally, the δ of capacitive equipment is mostly in the range of 0.001 to 0.02, so the accuracy of measuring δ is required to be high. Generally, the specified threshold of δ is 0.01, so the absolute value of the error of δ should be controlled between 0.001 and 0.002.

During the actual operation of the power system, interference has a great influence on the measurement results. The interference mainly includes harmonics in the system and external environmental interference. But in fact, the size of the harmonic is determined by the system itself, which can be set to a fixed value during research; however, environmental interference is uncontrollable, and weather, temperature, humidity, noise, etc. may affect environmental interference, so whether the measurement algorithm can be used in severe environmental interference Correct operation is an important indicator to measure the performance of the algorithm. The calculation example continuously amplifies the environmental interference, and compares the accuracy of the measurement algorithm after adding the filtering algorithm at this time.

In order to test the specific experimental effect when the environmental interference is amplified, the harmonic interference is set to be constant, and the environmental interference is continuously amplified. Compared with the experimental results with or without the filtering algorithm at this time (the calculation Δδ is in the range of 0 to 0.02), where Δδ ₁ is the calculation result without filtering algorithm, and Δδ ₂ is the calculation result using filtering algorithm. The specific data are shown in Table 1 .

The bold data in the table are data that do not meet the error requirements (0.001-0.002).

Table 1 Experimental results when enlarging environmental interference

Analysis of Table 1 shows that when the signal-to-noise ratio is 30dB, the accuracy of the results obtained by the non-filtering algorithm no longer meets the requirements; while the measurement results using the filtering algorithm can still meet the requirements when the signal-to-noise ratio is 5dB, which fully reflects the The superiority of the invented algorithm.

The above is only a preferred embodiment of the present invention, it should be pointed out that for those of ordinary skill in the art, without departing from the principle of the present invention, some improvements and modifications can also be made. It should be regarded as the protection scope of the present invention.

Claims (1)

1. a relative comparison method in conjunction with correlation analysis filter property, it is characterized in that: the steps are as follows: (1) Collect the leakage current signals of the two selected devices as i ₁ (t) and i ₂ (t), and set the standard fundamental wave signal as i ₀ (t); (2) Using the standard fundamental wave signal i ₀ (t) and two leakage current signals i ₁ (t) and i ₂ (t) for cross-correlation processing respectively, two leakage current signals i ₁ (t) and i ₂ (t ) filtered signals i ₁₀ (t), i ₂₀ (t): the specific steps are as follows: (21) Perform Fourier transform on the standard fundamental wave signal i ₀ (t) and two leakage current signals i ₁ (t) and i ₂ (t) to obtain the frequency domain signals I ₀ (f), I ₁ ( f) and I ₂ (f); (22) According to the relevant theorems, the standard fundamental frequency domain signal I ₀ (f) and the leakage frequency domain signal I ₁ (f), the standard fundamental frequency domain signal I ₀ (f) and the leakage frequency domain signal I ₂ ( f) The cross-spectral density function between: ${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 10</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; *</span>}{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span>$ ${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 20</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; *</span>}{{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$ Among them, I ₁₀ (f) is the cross-spectral density function of the standard fundamental frequency domain signal I ₀ (f) and the leakage frequency domain signal I ₁ (f), is the conjugate of I ₁ (f); I ₂₀ (f) is the cross-spectral density function of the standard fundamental frequency domain signal I ₀ (f) and the leakage frequency domain signal I ₂ (f), the conjugate of I ₂ (f); (23) Calculate and obtain the filtered two leakage current frequency domain signals I ₁₀ (f), I ₂₀ (f); and perform inverse Fourier transform on the obtained leakage current frequency domain signals respectively to obtain the filtered leakage current signal i ₁₀ (t), i ₂₀ (t); (3) Perform cross-correlation processing on the filtered leakage current signals i ₁₀ (t) and i ₂₀ (t), and use the time-delay characteristics of the correlation function to obtain the relationship between i ₁₀ (t) and i ₂₀ (t) time delay t _delay ; (4) Calculate the relative dielectric loss angle of the equipment according to the formula Δδ=t _delay ×360/N; where N is the number of sampling points in each period.