CN113295923A - VFTO signal spectrum analysis method based on improved s-transform - Google Patents

VFTO signal spectrum analysis method based on improved s-transform Download PDF

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CN113295923A
CN113295923A CN202110409569.3A CN202110409569A CN113295923A CN 113295923 A CN113295923 A CN 113295923A CN 202110409569 A CN202110409569 A CN 202110409569A CN 113295923 A CN113295923 A CN 113295923A
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spectrum
signal
frequency
window function
vfto
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张安学
李昊博
杨倩
张明
陈圻铭
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Xian Jiaotong University
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    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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Abstract

The invention discloses a VFTO signal spectrum analysis method based on improved s-transform, which is used for carrying out time domain sampling on an input signal to obtain a discrete sequence; performing FFT (fast Fourier transform) on the discrete sequence to obtain a signal frequency spectrum; determining a window length control function and a window function according to the signal frequency spectrum and the resolution requirement; performing FFT on the window function to obtain a window function frequency spectrum; carrying out periodic extension on the signal frequency spectrum, and multiplying the signal frequency spectrum after dimension expansion by a window function frequency spectrum; carrying out inverse Fourier transform on the multiplied result to obtain a time distribution result of a single frequency point; and finishing the calculation of all frequency points, and finally obtaining a two-dimensional matrix time spectrum. The VFTO signal spectrum analysis method based on the improved s transformation can better adapt to the VFTO spectrum characteristics, reflects the local characteristics of the frequency component changing along with time, and is more suitable for the VFTO spectrum analysis process.

Description

VFTO signal spectrum analysis method based on improved s-transform
Technical Field
The invention belongs to the technical field of transient electromagnetic signal processing, and particularly relates to a VFTO signal spectrum analysis method based on improved s-transform.
Background
Among the various fast transient phenomena, the hazards of VFTO caused by DS operation are the most serious and most interesting. The VFTO spectral analysis relies on a well-behaved signal processing method to convert the VFTO signal from the time domain to the frequency domain and further analyze its spectral characteristics. From a frequency domain perspective, VFTO is a non-stationary signal that contains frequency components whose amplitudes vary with time. The fourier transform is an integral transform, and can be represented by a time domain or a frequency domain, but cannot represent the change of frequency in the signal with time, so that the fourier transform can only be used for rough analysis of a VFTO spectrum.
Disclosure of Invention
The present invention aims to provide a VFTO signal spectrum analysis method based on improved s-transform to solve the above problems.
In order to achieve the purpose, the invention adopts the following technical scheme:
a VFTO signal spectrum analysis method based on improved s transformation comprises the following steps:
step 1: performing time domain sampling on an input signal to obtain a discrete sequence;
step 2: performing FFT (fast Fourier transform) on the discrete sequence to obtain a signal frequency spectrum;
and step 3: determining a window length control function and a window function according to the signal frequency spectrum and the resolution requirement;
and 4, step 4: performing FFT on the window function to obtain a window function frequency spectrum;
and 5: carrying out periodic extension on the signal frequency spectrum, and multiplying the signal frequency spectrum after dimension expansion by a window function frequency spectrum;
step 6: performing inverse Fourier transform on the multiplied result of the step 5 to obtain a time distribution result of a single frequency point;
and 7: introducing an adjusting factor lambda into the window function, and replacing f with lambda so as to control the changing speed of f through the action of the adjusting factor lambda;
and 8: and (4) repeating the steps 4-7 until the calculation of all the frequency points is completed, and finally obtaining the time spectrum of the two-dimensional matrix.
Further, in step 1, the input signal s (t) is sampled in time domain with a sampling frequency offsThe sampling time interval is
Figure BDA0003023622110000021
The number of sampling points is
Figure BDA0003023622110000022
Wherein t is the signal duration, obtaining a discrete sequence s [ kT ]]，k＝0,1,2,…,N- 1。
Further, in step 2, for the discrete sequence s [ kT ]]FFT to obtain signal spectrum
Figure 100002_1
Further, in step 3, the specific method for determining the window length control function and the window function is as follows:
step 3-1, determining parameters a, b and c according to the signal spectrum and the resolution requirement;
let the signal sampling rate be fs，
Figure BDA0003023622110000025
Get
Figure BDA0003023622110000026
Let the maximum and minimum frequencies of the signal be fmaxAnd fminMaximum and minimum values Δ f of the width of the frequency domain of the window function allowed by the practical analysismaxAnd Δ fminThen, the value ranges of a and c are determined by the following inequalities:
Figure BDA0003023622110000027
and 3-2, determining values of a and c in a value range, substituting each parameter value into a window length control function:
Figure BDA0003023622110000028
3-3, substituting the window length control function into the Gaussian window function to obtain an improved window function expression:
Figure BDA0003023622110000029
where α (f) is a window function scale factor.
Further, in step 4, the frequency spectrum of the window function is
Figure BDA0003023622110000031
The specific formula is as follows:
Figure 100002_2
wherein N starts to take a value from 0, N is the number of frequency points, and T is the sampling period.
Further, in step 5, multiplying the signal spectrum after the dimension expansion by a window function spectrum, specifically:
step 5-1, making signal frequency spectrum
Figure BDA0003023622110000033
Dimension expansion to obtain signal spectrum
Figure BDA0003023622110000034
Wherein m is 0,1,2,3 … N-1;
step 5-2, the signal frequency spectrum after dimension expansion
Figure BDA0003023622110000035
Multiplied by the window function spectrum G (m, n).
Further, in step 6, inverse fourier transform is performed on the multiplication result to obtain time domain information of the nth frequency point
Figure BDA0003023622110000036
Wherein m is 0,1,2,3 … N-1.
Further, in step 7, the window function is improved by introducing an adjustment factor λ, and the specific expression is as follows:
Figure BDA0003023622110000037
the modified S transform is defined as:
Figure 100002_3
wherein λ is an adjustment factor, and λ > 0.
Further, in step 8, the specific judgment method for judging whether all the frequency points have been calculated is as follows: judging whether N is larger than or equal to N-1, if not, adding 1 to N, and repeating the steps 4, 5 and 6; and if so, outputting a time-frequency spectrum result.
Compared with the prior art, the invention has the following technical effects:
the method can realize high-resolution time-frequency analysis and has real-time performance according to the signal frequency self-adaptive adjustment window function;
the method is different from the WVD conversion, belongs to quadratic time frequency conversion, and does not have the problem of cross item interference;
the time-frequency resolution is better, and two sections of closer frequency components can be distinguished from the time domain. In conclusion, the VFTO waveform has the characteristics of wide frequency band, large amplitude span of frequency components and the like, the VFTO signal spectrum analysis method based on the improved s transformation can better adapt to the VFTO spectrum characteristics, reflects the local characteristics of the frequency components changing along with time, and is more suitable for the VFTO spectrum analysis process.
Drawings
Fig. 1 is a flow chart of a VFTO signal spectrum analysis method based on improved s-transform of the present invention;
FIG. 2 is a waveform diagram of a VFTO composite signal;
FIG. 3 is a graph of a VFTO composite signal spectrum;
FIG. 4 is a converted gray scale plot of the VFTO composite signal S;
FIG. 5 is a modified S transform gray scale diagram of the VFTO composite signal;
fig. 6 is a VFTO waveform of a load side when the fast disconnecting switch is switched on;
fig. 7 is a VFTO waveform of a first breakdown of a load side when a fast disconnecting switch is switched on;
fig. 8 is a VFTO spectrum diagram of a first breakdown of a load side when a fast disconnecting switch is switched on;
FIG. 9 is an improved S-transform time-frequency grayscale plot of a first pre-click VFTO waveform;
fig. 10 is a graph of the amplitude variation of the VFTO frequency component.
Detailed Description
The invention is further described below with reference to the accompanying drawings:
referring to fig. 1 to 10, a VFTO signal spectrum analysis method based on modified s-transform includes the following steps:
step 1, performing time domain sampling on an input signal s (t), wherein the sampling frequency is fsThe sampling time interval is
Figure BDA0003023622110000041
The number of sampling points is
Figure BDA0003023622110000042
Wherein t is the signal duration, obtaining a discrete sequence s [ kT ]]，k＝0,1,2,…,N-1；
Step 2, for the discrete sequence s [ kT ]]FFT to obtain signal spectrum
Figure BDA0003023622110000043
n＝0,1,2,…,N-1；
Step 3, determining the values of the parameters a, b and c according to the frequency spectrum characteristics, wherein the specific method for determining the window length control function and the window function comprises the following steps:
step 3-1, determining parameters a, b and c according to the signal spectrum and the resolution requirement;
let the signal sampling rate be fsDue to the fact that
Figure BDA0003023622110000051
Thus taking
Figure BDA0003023622110000052
Let the maximum and minimum frequencies of the signal be fmaxAnd fminMaximum and minimum values Δ f of the width of the frequency domain of the window function allowed by the practical analysismaxAnd Δ fminThen, the value ranges of a and c are determined by the following inequalities:
Figure BDA0003023622110000053
and 3-2, determining values of a and c in a value range, substituting each parameter value into a window length control function:
Figure BDA0003023622110000054
3-3, substituting the window length control function into the Gaussian window function to obtain an improved window function expression:
Figure BDA0003023622110000055
step 4, FFT is carried out on the window function to obtain a window function frequency spectrum which is
Figure BDA0003023622110000056
The specific formula is as follows:
Figure 4
step 5, multiplying the signal frequency spectrum after the dimension expansion by a window function frequency spectrum, which specifically comprises the following steps:
step 5-1, making signal frequency spectrum
Figure BDA0003023622110000058
Dimension expansion to obtain signal spectrum
Figure BDA0003023622110000059
Wherein m is 0,1,2,3 … N-1;
step 5-2, the signal frequency spectrum after dimension expansion
Figure BDA00030236221100000510
Multiplying by a window function spectrum G (m, n);
step 6, carrying out inverse Fourier transform on the multiplication result to obtain time domain information of the nth frequency point
Figure BDA00030236221100000511
Step 7, improving the window function by introducing an adjusting factor lambda, wherein the specific expression is as follows:
Figure BDA0003023622110000061
step 8, judging whether all frequency points are calculated by the specific judgment method: judging whether N is larger than or equal to N-1, if not, adding 1 to N, and repeating the steps 4, 5 and 6; and if so, outputting a time-frequency spectrum result.
The time-frequency analysis method of the present invention is illustrated below by way of example in three cases.
The first embodiment is as follows: VFTO synthetic test signal simulation analysis
And (3) imitating the characteristics of a VFTO waveform, and synthesizing a simple signal with the characteristic of a single-breakdown VFTO waveform by using MATLAB software. The frequency components and the duration of the VFTO composite signal are shown in table 1, and the corresponding waveform is shown in fig. 2, wherein the voltage amplitudes are shown as the VFTO composite signal is a multi-frequency damped oscillation wave as a whole. The Fourier spectrum of the VFTO synthesized signal is shown in fig. 3, and includes 6 frequency components of 0.00005, 1, 10, 40, 80 and 100MHz, but the Fourier spectrum cannot give the local characteristics of the signal, i.e. cannot reflect the characteristics of the frequency spectrum of the signal changing with time.
TABLE 1VFTO composite Signal frequency component
Figure BDA0003023622110000062
FIG. 4 is an S-transform time-frequency analysis of the synthesized signal, which shows that the frequency resolution varies with frequency, the low frequency has better Δ f, the high frequency has better Δ t, but the high frequency Δ f is worse, and the two components of 80MHz and 100MHz cannot be distinguished from the frequency domain; fig. 5 is a modified S-transform spectrum analysis of a synthesized signal, where λ is 0.3, and the frequency resolution performance is mainly different in that the speed of time-frequency resolution changing with frequency is slowed down, and the modified S-transform makes up for the deficiency of the S-transform in high frequency by λ, and can distinguish two frequency components of 80MHz and 100MHz from the frequency domain.
Example two: VFTO measured waveform analysis
Fig. 6 is a VFTO actual measurement waveform of a load side when the rapid isolation switch of the GIS substation is switched on. The vertical axis is the measured voltage per unit pu, and the reference is the peak-to-peak voltage.
As can be seen from fig. 6, in the closing process of the disconnector, the contact gap undergoes multiple pre-breakdowns, and each breakdown forms a step. On one hand, the data size of the waveform of fig. 6 is very large due to the extremely short sampling interval (1.6ns), and if the spectrum analysis is performed on all the data, the workload is very large and the pertinence is lacked; on the other hand, the single breakdown waveform duration is about several to several tens μ s, and the time interval of adjacent two breakdowns is in steps, and the adjacent single breakdown waveforms do not overlap. Therefore, when the spectral characteristics of the VFTO waveform are studied, the spectral characteristics can be decomposed into spectral analysis of each breakdown waveform.
Fig. 7 is a waveform diagram (waveform amplified at 20 ms) 2 μ s before the first breakdown in fig. 6, and it can be seen that the single breakdown VFTO waveform is a multi-frequency ringing wave.
As can be seen from fig. 8, the waveform contains abundant frequency components, specifically, frequency components of 0.31, 0.94, 1.25, 4.7, 6.9, 11.3, 14.1, 34.4, 42, 44 and 60MHz, and further includes a dc component. The amplitude of the 6.9MHz frequency component is relatively high compared with other frequency components, the VFTO main frequency component is broken through once, the influence on the waveform shape of the VFTO is large, and the main frequency is obtained. The fourier spectrum can only describe the frequency components contained in the VFTO waveform as a whole, and cannot reflect the time-varying characteristics of the waveform frequency components.
Fig. 9 is a time-frequency grayscale diagram of a time-frequency analysis result of a VFTO waveform first-time breakdown of the load side when the disconnector is switched on. As can be seen from fig. 9, the VFTO measured waveform has non-stationary characteristics, rich frequency components, and different durations of the frequency components.
The low-frequency component exists all the time, and is formed by basic electric oscillation, the high-frequency component is subjected to speed attenuation, which is determined by the refraction and reflection of the traveling wave caused by the high-frequency component, and the analysis results are consistent with the theoretical analysis of the VFTO.
To further analyze the non-stationary characteristics of each frequency component, fig. 10 further shows a frequency slice diagram of each frequency component, i.e., an amplitude-time curve of each frequency component.
As can be seen from fig. 10, in 2 of the VFTO waveform, the amplitudes of 4 low frequency components such as dc, 310kHz, 940kHz and 1250kHz are basically kept unchanged, while the amplitudes of 5 frequency components such as 4.7MHz, 69MHz, 113MH, 14.1MHz and 344MHz are attenuated with time but at a slower rate, wherein 6.9MHz is the dominant frequency component of the VFTO, and has the largest amplitude, and the attenuation is relatively slow; while the amplitudes of the 3 frequency components at 42MHz, 44MHz, and 60MHz decay rapidly to zero for a short period of time, it can be seen that the duration of the VFTO high frequency component is very limited. Thus, the greater the frequency of the VFTO frequency component, the faster the amplitude decays, and the shorter the duration.

Claims (9)

1. A VFTO signal spectrum analysis method based on improved s transformation is characterized by comprising the following steps:
step 1: performing time domain sampling on an input signal to obtain a discrete sequence;
step 2: performing FFT (fast Fourier transform) on the discrete sequence to obtain a signal frequency spectrum;
and step 3: determining a window length control function and a window function according to the signal frequency spectrum and the resolution requirement;
and 4, step 4: performing FFT on the window function to obtain a window function frequency spectrum;
and 5: carrying out periodic extension on the signal frequency spectrum, and multiplying the signal frequency spectrum after dimension expansion by a window function frequency spectrum;
step 6: performing inverse Fourier transform on the multiplied result of the step 5 to obtain a time distribution result of a single frequency point;
and 7: introducing an adjusting factor lambda into the window function, and replacing f with lambda so as to control the changing speed of f through the action of the adjusting factor lambda;
and 8: and (4) repeating the steps 4-7 until the calculation of all the frequency points is completed, and finally obtaining the time spectrum of the two-dimensional matrix.
2. A VFTO signal spectrum analyzing method based on modified s-transform as claimed in claim 1, wherein in step 1, the input signal s (t) is sampled in time domain with sampling frequency fsThe sampling time interval is
Figure FDA0003023622100000011
The number of sampling points is
Figure FDA0003023622100000012
Wherein t is the signal duration, obtaining a discrete sequence s [ kT ]]，k＝0,1,2,…,N-1。
3. A VFTO signal spectrum analysis method based on modified s-transform as claimed in claim 1, wherein in step 2, the discrete sequence s [ kT ] is analyzed]FFT to obtain signal spectrum
Figure 1
4. The VFTO signal spectrum analyzing method based on the improved s-transform as claimed in claim 1, wherein in step 3, the specific method for determining the window length control function and the window function is:
step 3-1, determining parameters a, b and c according to the signal spectrum and the resolution requirement;
let the signal sampling rate be fs，
Figure FDA0003023622100000014
Get
Figure FDA0003023622100000015
Let the maximum and minimum frequencies of the signal be fmaxAnd fminMaximum and minimum values Δ f of the width of the frequency domain of the window function allowed by the practical analysismaxAnd Δ fminThen, the value ranges of a and c are determined by the following inequalities:
Figure FDA0003023622100000021
and 3-2, determining values of a and c in a value range, substituting each parameter value into a window length control function:
Figure FDA0003023622100000022
3-3, substituting the window length control function into the Gaussian window function to obtain an improved window function expression:
Figure FDA0003023622100000023
where α (f) is a window function scale factor.
5. A VFTO signal spectrum analyzing method based on modified s-transform as claimed in claim 1 wherein in step 4, the window function spectrum is such that
Figure FDA0003023622100000024
The specific formula is as follows:
Figure 2
wherein N starts to take a value from 0, N is the number of frequency points, and T is the sampling period.
6. The VFTO signal spectrum analyzing method based on the improved s-transform as claimed in claim 1, wherein in step 5, the signal spectrum after the dimension expansion is multiplied by the window function spectrum, specifically:
step 5-1, making signal frequency spectrum
Figure FDA0003023622100000026
Dimension expansion to obtain signal spectrum
Figure FDA0003023622100000027
Wherein m is 0,1,2,3 … N-1;
step 5-2, the signal frequency spectrum after dimension expansion
Figure FDA0003023622100000028
Multiplied by the window function spectrum G (m, n).
7. The VFTO signal spectrum analysis method based on improved s-transform as claimed in claim 1, wherein in step 6, inverse Fourier transform is performed to the multiplied result to obtain the time domain information of the nth frequency point
Figure FDA0003023622100000029
Wherein m is 0,1,2,3 … N-1.
8. The method of claim 1, wherein in step 7, the window function is modified by introducing an adjustment factor λ, and the specific expression is as follows:
Figure FDA0003023622100000031
the modified S transform is defined as:
Figure 3
wherein λ is an adjustment factor, and λ > 0.
9. The method as claimed in claim 1, wherein in step 8, the specific judgment method for judging whether all frequency points are calculated is: judging whether N is larger than or equal to N-1, if not, adding 1 to N, and repeating the steps 4, 5 and 6; and if so, outputting a time-frequency spectrum result.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115420949A (en) * 2022-11-04 2022-12-02 中国电力科学研究院有限公司 VFTO time frequency analysis method, device, medium and equipment
CN116449077A (en) * 2023-04-23 2023-07-18 国网江苏省电力有限公司 Method for performing time-frequency analysis on PT secondary side disturbance voltage based on Wigner-Ville distribution algorithm

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115420949A (en) * 2022-11-04 2022-12-02 中国电力科学研究院有限公司 VFTO time frequency analysis method, device, medium and equipment
CN115420949B (en) * 2022-11-04 2022-12-30 中国电力科学研究院有限公司 VFTO time frequency analysis method, device, medium and equipment
CN116449077A (en) * 2023-04-23 2023-07-18 国网江苏省电力有限公司 Method for performing time-frequency analysis on PT secondary side disturbance voltage based on Wigner-Ville distribution algorithm
CN116449077B (en) * 2023-04-23 2024-03-26 国网江苏省电力有限公司 Method for performing time-frequency analysis on PT secondary side disturbance voltage based on Wigner-Ville distribution algorithm

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