CN104808069A - Relative comparison method in combination with correlation analysis filtering performance - Google Patents
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Abstract
The invention discloses a relative comparison method which is high in anti-jamming capability and measuring accuracy, wide in application range and used for measuring relative dielectric loss (delta tan delta) of a capacitive apparatus. Before the delta tan delta of the capacitive apparatus is measured by means of the relative comparison method, firstly, filtering performance of a correlation function is fully utilized, leakage current of two selected apparatuses is correlated to standard fundamental waves respectively, the leakage current is subjected to filtering processing, then relative dielectric loss of the apparatuses is obtained by means of time delay feature of a cross-correlation function, and thereby, an algorithm is quite accurate. The relative comparison method in combination with correlation analysis filtering performance has the advantages that the anti-jamming capability and measuring accuracy are high, the application range is wide, and certain practical application value is achieved.
Description
Technical Field
The invention relates to a measurement algorithm applied to the on-line monitoring of the dielectric loss of high-voltage capacitive equipment, belonging to the technical field of the on-line monitoring of the high-voltage capacitive equipment.
Background
Capacitive devices (current transformers, coupling capacitors, capacitive voltage transformers, high-voltage bushings and the like) account for a considerable proportion of the power system equipment, and the safety and reliability of the devices are the basis for realizing the operation of the whole power system. A large part of the accidents of damage to electrical equipment, especially high voltage equipment, are caused by insulation damage, and the overall defect or large concentrated local defect of an insulation system of the electrical equipment at an early development stage can be found by measuring the dielectric loss (tan, hereinafter referred to as dielectric loss) or relative dielectric loss. Therefore, the measurement of the high-voltage capacitive device tan is of great importance for the safe and economic operation of the substation and even the whole power system.
At present, the dielectric loss measurement mainly comprises a zero-crossing comparison method, a harmonic analysis method, a relative comparison method and the like. The basic principle of the zero-crossing comparison method is as follows: voltage and current signals pass through the same two-path signal preprocessing circuit and then enter a zero-crossing comparator to shape the alternating current signal into a square wave signal in a zero-crossing mode, and the phase difference of the two signals is obtained by comparing the time difference between the rising edge and the falling edge of the two square wave signals, so that dielectric loss is obtained. The principle of the harmonic analysis method is as follows: voltage and current signals of a tested product are respectively obtained by using a voltage transformer and a current transformer, then harmonic decomposition is carried out on the voltage and current signals by using Discrete Fourier Transform (DFT), phase difference between fundamental wave current and the voltage signals is obtained, and dielectric loss of the tested product is further solved. The principle of the relative comparison method is: and selecting two capacitive equipment leakage current values, setting one group of the two capacitive equipment leakage current values as a reference standard, and carrying out relative comparison to obtain relative dielectric loss so as to carry out fault diagnosis.
The advantages of the relative comparison method are: firstly, considering the similarity of the operation conditions, voltage references and environmental influences among devices with the same phase and the same voltage class, the dielectric loss measurement data of the devices should have the signs of simultaneous change. If the insulation condition of the equipment is good, the two test results are basically the same; if there is a significant difference between the test data, an abnormal insulation condition of one of the devices may occur. Therefore, the change of the dielectric loss relative value of the two components is used as the basis of fault diagnosis, the stability is better, and the sensitivity of fault diagnosis can be greatly improved. Secondly, the influence of temperature and humidity change, interphase interference, Potential Transformer (PT) angle difference and other factors can be counteracted to a certain extent, and therefore the insulation state can be judged more accurately. Therefore, the method has better application prospect compared with a comparative method.
The traditional relative comparison method mostly adopts correlation analysis to obtain the relative dielectric loss. The relative dielectric loss can be obtained according to the phase difference of the leakage currents of the two devices, and the phase difference can be obtained through the time difference,as shown in figure 1Shown, the formula is: Δ ═ 2 π Δ T/T. The time difference Delta T of two leakage currents and the waveform diagram of the cross-correlation function of two leakage current signals can be obtained by utilizing the time delay characteristic of the cross-correlation functionAs shown in fig. 2The highest peak on the waveform diagram is referred to as a correlation peak, and the difference between the position of the correlation peak and the origin is the time difference Δ T between the two leakage current signals.
However, the dielectric loss of the capacitive device is a tiny value under normal conditions, so that the interference of the system (harmonic interference) and the interference of the outside world (environmental interference) are the measuring parties for solving the relative dielectric loss of the traditional methodFa HuiThe conventional relative comparison method is not accurate under certain conditions (such as large harmonic interference or environmental interference). Therefore, finding a relative dielectric loss measurement method with strong anti-interference capability and high precision is always a key point and a hot point of research.
Disclosure of Invention
The invention aims to provide a relative comparison method combining the filtering performance of correlation analysis, which filters most of interference by utilizing the filtering performance of the correlation analysis before the relative comparison of dielectric loss of equipment, so that the relative comparison method has the remarkable advantages of strong anti-interference capability, high measurement precision, wide application range and the like when measuring the relative dielectric loss of capacitive equipment.
The technical scheme adopted for realizing the purpose of the invention is as follows: and filtering by adopting a filtering algorithm combined with correlation analysis, and then calculating the relative dielectric loss of the equipment so as to diagnose.
The invention comprises the following steps:
(1) collecting leakage current signals of two selected devices as i1(t)、i2(t) setting the standard fundamental wave signal as i0(t)；
(2) Using standard fundamental wave signals i respectively0(t) and two leakage current signals i1(t)、i2(t) performing cross-correlation processing to obtain two leakage current signals i1(t)、i2(t) filtered leakage current signal i10(t)、i20(t): the method comprises the following specific steps:
(21) are respectively corresponding to standard fundamental wave signals as i0(t) two leakage current signals i1(t)、i2(t) Fourier transforming to obtain frequency domain signal I0(f)、I1(f) And I2(f)；
(22) Respectively obtaining standard fundamental frequency domain signals I according to a correlation theorem0(f) And leakage frequency domain signal I1(f) Standard fundamental frequency domain signal I0(f) And leakage frequency domain signal I2(f) Cross spectral density function between:
wherein,I10(f) as a standard fundamental frequency domain signal I0(f) And leakage frequency domain signal I1(f) The cross-spectral density function of (a),is I1(f) Conjugation of (1); i is20(f) As a standard fundamental frequency domain signal I0(f) And leakage frequency domain signal I2(f) The cross-spectral density function of (a),is I2(f) Conjugation of (1).
(23) Calculating to obtain two filtered leakage current frequency domain signals I10(f)、I20(f) And respectively carrying out Fourier inverse transformation on the obtained leakage current frequency domain signals to obtain filtered leakage current signals i10(t)、i20(t)；
(3) For filtered leakage current signal i10(t)、i20(t) performing a cross-correlation process to determine i using the time delay characteristics of the correlation function10(t) and i20Time delay t between (t)delay；
(4) According to the formula Δ tdelayObtaining the relative dielectric loss angle of the equipment by multiplying 360/N; where N is the number of sample points per cycle.
The invention firstly carries out filtering by utilizing improved correlation analysis and then obtains the relative dielectric loss, so that the anti-interference capability of the relative comparison method is stronger and the measurement precision is higher after filtering processing. Interference in the actual operation process of the power system has a great influence on the measurement result, and mainly interferes with harmonic waves in the system and external environment interference. Generally, when harmonic interference or external environmental interference increases, the accuracy of the relative comparison method cannot meet the requirement. After the filtering algorithm combined with the improved correlation analysis of the invention is used for filtering, the waveform of the signal is obviously improved, most of interference is filtered out, the waveform is smooth and has no burrs,as shown in fig. 3(ii) a Under severe interference conditions (amplification of harmonic and environmental interference, when signal-to-noise ratio is present)5dB), the result measured by the relative comparison method after filtering by the filter algorithm combined with the improved correlation analysis of the invention is more accurate, and the diagnostic requirement and the comparison are metAs shown in figure 5，FIG. 5(a) The waveform in (1) has large burrs, which have great influence on detecting correlation peaks and further solving time delay, and the measured result is extremely inaccurateFIG. 5(b) The waveform in the method filters interference, is smooth and free of burrs, and can accurately measure the position of a related peak, so that the relative dielectric loss can be accurately obtained. Therefore, the invention adopts the standard fundamental wave as the intermediate variable in combination with the relative comparison method for improving the correlation analysis, fully combines the filtering performance and the time delay characteristic of the correlation analysis, improves the anti-interference capability and the measurement precision of the algorithm, has wider application range and has certain practical application value.
Drawings
FIG. 1 shows a schematic view of aIs the principle of the relative comparison method of the present inventionDrawing (A)；
FIG. 2Is a signal waveform diagram of two devices adopted by the invention;
FIG. 3Is a correlation function waveform diagram;
FIG. 4Is a comparison of the waveforms before and after filteringDrawing (A)Wherein: the solid line is a waveform diagram before filtering by adopting the filtering algorithm combined with correlation analysis of the invention, and the dotted line is a waveform diagram after filtering;
FIG. 5Is the correlation processing result in case of severe interference;
wherein (a) is a processing result directly compared without using the filtering algorithm of the binding correlation analysis of the present invention, and (b) is a processing result after using the filtering algorithm of the binding correlation analysis of the present invention.
Detailed Description
For the purpose of illustrating the structural features and operational principles of the present invention, reference is made to the following detailed description of the preferred embodiments.
The relative comparison method of the invention comprises the following steps:
(1) collecting leakage current signals of two selected devices as i1(t)、i2(t) setting the standard fundamental wave signal as i0(t)；
The standard fundamental wave signal is power frequency signal, amplitude and phase angle are arbitrarily selected, and because the standard fundamental wave signal is applied to the power system, the standard fundamental wave signal is power frequency (50Hz) signal, and the signal subjected to correlation analysis processing is common frequency signal (same frequency), namely i1(t)、i2(t) is also a power frequency signal, and the amplitude and phase angle thereof have no influence on the calculation result and can be selected optionally.
(2) Using standard fundamental wave signals i respectively0(t) and two leakage current signals i1(t)、i2(t) performing cross-correlation processing to obtain two leakage current signals i1(t)、i2(t) filtered leakage current signal i10(t)、i20(t)：
Because the direct calculation of the cross-correlation function is calculated in the time domain, the calculation amount is large, and the real-time requirement under the online monitoring condition is difficult to meet, the correlation theorem is utilized in the actual calculation, namely the cross-correlation function and the cross-spectral density function of the signal are a pair of Fourier transform, the time domain calculation is converted into the frequency domain calculation through the correlation theorem,
the calculation is greatly simplified, and the requirement of real-time property is met. With Y1(f) And Y2(f) Respectively represent functions y1(t) and y2(t)
And the cross-spectral density function of the signal is expressed by
Determining the formula:
Therefore, the method of calculating the cross-spectral density function of two signals and then performing inverse Fourier transform on the two signals can be adopted to realize the engineering quick calculation of the cross-correlation function.
The method comprises the following specific steps:
(21) are respectively corresponding to standard fundamental wave signals as i0(t) two leakage current signals i1(t)、i2(t) Fourier transform to obtain frequency domain signal I0(f)、I1(f) And I2(f)；
(22) Respectively obtaining standard fundamental frequency domain signals I according to a correlation theorem0(f) And leakage frequency domain signal I1(f) Standard fundamental frequency domain signal I0(f) And leakage frequency domain signal I2(f) Cross spectral density function between:
wherein, I10(f) As a standard fundamental frequency domain signal I0(f) And leakage frequency domain signal I1(f) The cross-spectral density function of (a),is I1(f) Conjugation of (1); i is20(f) As a standard fundamental frequency domain signal I0(f) And leakage frequency domain signal I2(f) The cross-spectral density function of (a),is I2(f) Conjugation of (1).
(23) Calculating to obtain a filtered leakage current frequency domain signal I10(f)、I20(f) And respectively carrying out Fourier inverse transformation on the obtained leakage current frequency domain signals to obtain filtered leakage current signals i10(t)、i20(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 finite number of discontinuities of the first type (the function has finite left and right limits as t approaches this discontinuity from left or right);
2) within a period, the function has a finite number of maxima or minima;
3) f (t) absolute integrable in a single cycle, i.e.
The following is true.
The above equation is referred to as the fourier transform of the integration operation F (t) and the inverse fourier transform of F (ω). Wherein, F (ω) is called an image function of F (t), F (t) is called an image primitive function of F (ω), F (ω) is an image of F (t), and F (t) is an image primitive of F (ω) (ω 2 π F, so ω and F have the same meaning and represent independent variables in the frequency domain.
The formula for the fourier transform in step (21) is derived as:
the formula for the inverse fourier transform in step (23) is derived as:
the cross-correlation process is as follows:
the correlation function reflects the degree of similarity between two co-frequency signals or between the signals themselves at different times. The two signals obtained by detection are compared to obtain a correlation function, and the analysis based on the correlation function is called correlation analysis.
Let two signals be y1(t)、y2(t), then y1(t)、y2(t) correlation function, i.e. formula
Suppose that the signal s (t) is interfered by the outside to form a composite signal y1(t) and y2(t), i.e. y1(t)＝s(t)+n(t)，y2(t) s (t + τ) + m (t),(s) (t) is the wanted signal, and n (t), m (t) are two noisy signals), then the cross-correlation function will contain y alone1(t)、y2(t) while excluding the interference of extraneous noise, i.e. when the cross-correlation function is:
Ry1y2(τ)＝E[y1(t)y2(t+τ)]＝αRxx(τ-τ1)
where α is the relative absorption coefficient, i.e., the magnitude of the peak-to-peak correlation of the two signals. For function Ry1y2(τ) it is α, τ1And RxxAnd when τ is τ ═ τ1Since the signal has a correlation of 1 with itself (i.e., R)xx(0) 1) has Ry1y2(τ)＝αRxx(0) α, has the maximum value, i.e., is the correlation peak point. Then, the time difference can be estimated by using a cross-correlation function, and the difference between the position of the correlation peak and the origin is the time difference of the two corresponding paths of signals.
The filtering algorithm is as follows:
because interference exists in the signals, when the interference is continuously increased in practical application, the accuracy of phase difference of the two signals obtained by directly adopting a relative comparison method is rapidly reduced. Analysis finds that the reason is that n (t), m (t) have certain correlation, and the correlation is enhanced after interference enhancement, so that the measurement result is not accurate enough.
In order to eliminate the influence caused by the correlation of n (t) and m (t), the invention introduces an intermediate variable, namely standard fundamental wave (only including common-frequency fundamental wave) y0(t), i.e. y0(t)＝s(t0). Using y separately0(t) and signal y containing an interference signal1(t)、y2(t) correlation, the signal y is extracted1(t)、y2Fundamental component y of (t)10(t)、y20(t), which is the filtering of the correlation function. After the two signals are respectively related to the same standard fundamental wave, the waveform is smooth and complete and phase difference information is retained, and the filtered fundamental wave component y is10(t)、y20(t) performing correlation again, and then obtaining the phase difference of the two signals by using the time delay characteristic of the correlation function, which is the core of the filtering algorithm of the invention combined with the improved correlation analysis.
(3) For filtered leakage current signal i10(t)、i20(t) performing a cross-correlation process to determine i using the time delay characteristics of the correlation function10(t) and i20Time delay t between (t)delay；
(4) According to the formula Δ tdelayObtaining the relative dielectric loss angle of the equipment by multiplying 360/N; where N is the number of sample points per cycle.
When it is small, the tangent of the dielectric loss angle is close to the dielectric loss angle, and
Δtan＝|tanx1-tanx2|＝tan|(x1-x2)|≈|(x1-x2)|＝Δ
wherein,x1、x2the dielectric loss angle of two same-phase capacitive equipment with the same bus is disclosed. The phase comparison of the leakage current of two devices with the same bus can obtain the relative dielectric loss angle delta, and the index reflects the relative insulation condition of the devices. When the two devices to be compared are well insulated, the relative dielectric loss angle delta of the two devices is generally very small; if one of the devices has an insulation defect, Δ will increase significantly, resulting in a significant change in Δ tan. By analogy, insulation defects of the equipment can be found by comparing multiple groups of equipment.
The concrete calculation example is as follows:
since the relative dielectric loss (Δ tan) of a capacitive device is normally small, the calculation example will directly calculate the relative dielectric loss angle (Δ) for greater intuition. Most of the capacitance devices are usually in the range of 0.001-0.02, so the requirement for measurement accuracy is high. The absolute value of the error is controlled to be 0.001 to 0.002 when the threshold is 0.01.
Interference in the actual operation process of the power system has a great influence on the measurement result, and mainly interferes with harmonic waves in the system and external environment interference. In practice, however, the harmonic size is determined by the system itself and can be set to a fixed value during research; the environmental interference is uncontrollable, and weather, temperature, humidity, noise and the like can influence the environmental interference, so whether the measurement algorithm can operate correctly under the serious environmental interference is an important index for measuring the performance of the algorithm. According to the calculation example, the accuracy of the measurement algorithm is measured after the filtering algorithm is added at the moment by continuously amplifying the environmental interference.
In order to test the specific experimental effect of the environmental interference amplification, the harmonic interference is set to be constant, the environmental interference is amplified continuously, and the experimental results (delta is in the range of 0-0.02 during calculation) of the time when no filtering algorithm is available are compared, wherein delta is1As a result of the filtering-free algorithm, Δ2For the calculation result adopting the filtering algorithm, the specific data are shown inTABLE 1。
In the tableThe data not meeting the error requirement (0.001-0.002) are thickened.
TABLE 1Experimental results in amplifying environmental disturbances
Analysis ofTABLE 1It can be known that when the signal-to-noise ratio is 30dB, the accuracy of the result obtained by the filter-free algorithm no longer meets the requirement; the measurement result adopting the filtering algorithm can still meet the requirement when the signal-to-noise ratio is 5dB, and the superiority of the algorithm is fully embodied.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.
Claims (1)
1. A relative comparison method of filterability in conjunction with correlation analysis, the method comprising: the method comprises the following steps:
(1) collecting leakage current signals of two selected devices as i1(t)、i2(t) setting the standard fundamental wave signal as i0(t)；
(2) Using standard fundamental wave signals i respectively0(t) and two leakage current signals i1(t)、i2(t) performing cross-correlation processing to obtain two leakage current signals i1(t)、i2(t) filtered signal i10(t)、i20(t): the method comprises the following specific steps:
(21) are respectively corresponding to standard fundamental wave signals as i0(t) two leakage current signals i1(t)、i2(t) Fourier transform to obtain frequency domain signal I0(f)、I1(f) And I2(f)；
(22) Respectively obtaining standard fundamental frequency domain signals I according to a correlation theorem0(f) And leakage frequency domain signal I1(f) Standard fundamental frequency domain signal I0(f) And leakage frequency domain signal I2(f) Cross spectral density function between:
wherein, I10(f) As a standard fundamental frequency domain signal I0(f) And leakage frequency domain signal I1(f) The cross-spectral density function of (a),is I1(f) Conjugation of (1); i is20(f) As a standard fundamental frequency domain signal I0(f) And leakage frequency domain signal I2(f) The cross-spectral density function of (a),I2(f) conjugation of (1);
(23) calculating to obtain two filtered leakage current frequency domain signals I10(f)、I20(f) (ii) a And respectively carrying out Fourier inverse transformation on the obtained leakage current frequency domain signals to obtain filtered leakage current signals i10(t)、i20(t)；
(3) For filtered leakage current signal i10(t)、i20(t) performing a cross-correlation process to determine i using the time delay characteristics of the correlation function10(t) and i20Time delay t between (t)delay；
(4) According to the formula Δ tdelayObtaining the relative dielectric loss angle of the equipment by multiplying 360/N; where N is the number of sample points per cycle.
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