CN105868160A - S-transformation detection method for power quality disturbance signals - Google Patents

Abstract

The invention discloses an S-transformation detection method for power quality disturbance signals. The method is specifically implemented by the following steps of step 1, establishing an S-transformation function; step 2, performing one-dimensional continuous S-inverse transformation on the function defined in the step 1; step 3, performing one-dimensional discrete S-transformation on a function relational expression obtained in the step 2; and step 4, processing various specific signals with deducing methods in the steps 1 to 3, analyzing obtained results, and detecting various power disturbance signals. Therefore, the occurrence positions of disturbances in a power grid can be quickly and accurately located, and characteristic information of amplitudes, frequency components, phase changes and the like of the disturbance signals can be detected.

Description

The S-transformation detection method of Power Quality Disturbance

Technical field

The invention belongs to electric power quality evaluation areas, relate to the S-transformation detection method of a kind of Power Quality Disturbance.

Background technology

What the quality of power supply described is to the quality of the AC energy of user side by utility network, typically refer to quality supply, in recent years, along with the increase of the nonlinear scale spaces load such as electric welding machine, electric arc furnace, RHVC and twin compressor in electrical network, cause the power quality problems such as voltage interruption in power distribution network, voltage dip, voltage swell, harmonic wave, flickering to become serious, cause the quality of power supply to decline.For the power quality problem suppressed and administer in electrical network, power quality compensator need to be added in electrical network, the development of these equipment and adjust and be required to accurate, detailed power quality parameter.Therefore understand the mechanism that disturbing signal produces, detect the characteristic parameter (including amplitude, frequency, start/stop time, phase place etc.) of disturbing signal accurately, to improving power supply quality and guaranteeing that power system security economical operation has very important meaning.

The most conventional detection method has Fourier transform, short time discrete Fourier transform, wavelet transformation, HHT, mathematical morphology and instantaneous reactive power theory etc..The defect of Fourier transform is can not to carry out localization to analyze, it is not suitable for analyzing non-stationary signal, short time discrete Fourier transform method is also been proposed for solving this problem, but choosing of the window function width of short time discrete Fourier transform is relatively difficult, and time-frequency window does not have adaptivity, it is suitable only for analyzes the process that characteristic dimension is roughly the same, is not suitable for analyzing Multiscal process and mutation process.And, the discrete form of this method does not has orthogonal expansion, it is difficult to realize highly effective algorithm.Wavelet transformation overcomes the defect of both the above method, it has the characteristic of Multiresolution Decomposition, and obtain a wide range of applications in electrical energy power quality disturbance analysis, but its defect be computationally intensive, analysis result is easily affected by wavelet basis function, more sensitive to noise ratio, signal optional frequency feature etc. can not be extracted.

As a kind of Time-Frequency Analysis Method, it is short time discrete Fourier transform and the succession of wavelet transformation and development to S-transformation, has more excellent time-frequency characteristic, and noise resisting ability is strong, can extract signal optional frequency characteristic information, be the power quality analysis instrument that the present invention is to be studied.

Summary of the invention

It is an object of the invention to provide the S-transformation detection method of a kind of Power Quality Disturbance, the characteristic informations such as the position that in electrical network, disturbance occurs, detection disturbing signal amplitude, frequency content and phase place change can be positioned fast and accurately.

The technical solution adopted in the present invention is, the S-transformation detection method of a kind of Power Quality Disturbance, specifically implements according to following steps:

Step 1: set up S-transformation function,

Step 2, carries out one-dimensional continuous S inverse transformation to the function defined in step 1,

Step 3, carries out one-dimensional discrete S-transformation to the functional relation obtained in step 2,

Step 4, utilizes the derivation method of step 1～step 3 to process concrete various signals, and is analyzed the result obtained, thus utilizes the various Power Disturbance signals of detection.

The feature of the present invention also resides in,

Step 1 particularly as follows: set up functional expression be,

$S(\mathrm{\τ},f)={\∫}_{-\mathrm{\∞}}^{\mathrm{\∞}}h\left(t\right)g(\mathrm{\τ}-t)e^{(-2\mathrm{\π}ftj)}dt---\left(1\right)$

Wherein,

$g(\mathrm{\τ}-t)=\frac{\left|f\right|}{\sqrt{2\mathrm{\π}}}{e}^{\[\frac{-f^2{(\mathrm{\τ}-t)}^2}{2}\]}---\left(2\right)$

In formula: f is frequency, j is imaginary unit, τ is the parameter controlling Gauss window at time t shaft position, h (t) is primary signal function, (2) formula is the expression formula of Gaussian window, can be obtained by formula (1), (2), conversion is that the height of Gauss window and width vary with frequency in place of being different from short time discrete Fourier transform, thus overcomes the defect that Fu's leaf transformation window height and width are fixed in short-term.

Step 2 particularly as follows:

When the function defining step 1 carries out one-dimensional continuous S inverse transformation,

Because

$h\left(t\right)=\underset{-\mathrm{\∞}}{\overset{\mathrm{\∞}}{\∫}}\[{\∫}_{-\mathrm{\∞}}^{\mathrm{\∞}}S(\mathrm{\τ},f)d\mathrm{\τ}\]e^{\left(2\mathrm{\π}ftj\right)}df---\left(3\right)$

Relation between the S-transformation of signal h (t) and its Fourier transform H (f) is:

$S(\mathrm{\τ},f)=\underset{-\mathrm{\∞}}{\overset{\mathrm{\∞}}{\∫}}H(f+\mathrm{\α})\·e^{\left(\frac{-2{\mathrm{\π}}^2{\mathrm{\α}}^2}{f^2}\right)}\·e^{\left(2\mathrm{\π}\mathrm{\α}\mathrm{\τ}j\right)}d\mathrm{\α}---\left(4\right)$

Wherein, α controls Gaussian window in frequency domain and moves on the frequency axis, and τ moves on a timeline for controlling Gaussian window in frequency domain, and H (f+ α) is the Fourier transform of h (t),Fourier transform for Gaussian window.

Step 3 particularly as follows: set h [KT] (k=0,1,2, ... N-1) it is the discrete-time series obtained that continuous time signal h (t) is sampled, sampling interval is T, and total sampling number is N, then this seasonal effect in time series discrete Fourier transform (DFT) is:

$H\[\frac{n}{NT}\]=\frac{1}{N}\underset{k=0}{\overset{N-1}{\Σ}}h\left(kT\right)e^{\left(\frac{-2\mathrm{\π}nkj}{N}\right)}---\left(5\right)$

When n ≠ 0,

$S(iT,\frac{n}{NT})=\underset{m=0}{\overset{N-1}{\Σ}}H\left(\frac{m+n}{NT}\right)e^{\left(\frac{-2{\mathrm{\π}}^2{m}^2}{n^2}\right)}{e}^{\left(\frac{i2\mathrm{\π}mj}{N}\right)},n\≠0---\left(6\right)$

Wherein: i, m, n=0,1,2 ..., N-1

As n=0,

$S(iT,0)=\frac{1}{N}\underset{m=0}{\overset{N-1}{\Σ}}h\left(\frac{m}{NT}\right)---\left(7\right)$

The algorithm basic step of S-transformation is can get: first calculate the fast fourier transform of h (t) by (5), (6), (7) formulaAgain willMove toThen the fast fourier transform of Gauss function g under each frequency (τ-T) is calculatedAgain by frequency, sampled point calculatesI.e. (m, n), makees convolution to fast fourier transform B of calculating primary signal and Gaussian window, and finally by convolution theorem, (m, inverse fast fourier transform n) obtain S-transformation S (iT, n/NT) to calculate B.

Signal described in described step 4 can be following several signal function,

1) h (t)=sin (ω t),

2) h (t)=sin (ω t+ (π/3) μ (t-0.21)),

3) h (t)=sin (ω t)+0.08sin (3 ω t)+0.15sin (5 ω t)+0.12sin (7 ω t)

4) h (t)={ 1-0.65 [μ (t-0.195)-μ (t-0.335)] } sin ω t

5)

H (t)=(1+0.8 [μ (t-0.195)-μ (t-0.235)]) (sin ω t+0.03sin 3 ω t+0.09sin 5 ω t+0.1sin 7 ω t).

The profitable effect of the present invention is that the detection method of employing was compared more in the past, and testing result is more accurate, and error is less, and can realize quickly location.Additionally, analyzed the phase place disturbing signal, and current research often ignores this problem.

Accompanying drawing explanation

Fig. 1 is the flow chart of the S-transformation detection method of Power Quality Disturbance of the present invention；

Fig. 2 is to sine voltage signal detection figure；

Fig. 3 is to containing phase hit sine voltage signal detection figure；

Fig. 4 is to harmonic signal detection figure；

Fig. 5 is to voltage dip signal detection figure；

Fig. 6 is to rising signal detection figure temporarily containing harmonic voltage；

The comparison diagram that voltage dip start/stop time, amplitude and phase place are changed by Fig. 7 short time discrete Fourier transform and S-transformation.

Detailed description of the invention

The present invention is described in detail with detailed description of the invention below in conjunction with the accompanying drawings.

The S-transformation detection method of a kind of Power Quality Disturbance, specifically implements according to following steps:

Step 1: set up S-transformation function,

$S(\mathrm{\τ},f)={\∫}_{-\mathrm{\∞}}^{\mathrm{\∞}}h\left(t\right)g(\mathrm{\τ}-t)e^{(-2\mathrm{\π}ftj)}dt---\left(1\right)$

Wherein,

$g(\mathrm{\τ}-t)=\frac{\left|f\right|}{\sqrt{2\mathrm{\π}}}{e}^{\[\frac{-f^2{(\mathrm{\τ}-t)}^2}{2}\]}---\left(2\right)$

In formula: f is frequency, j is imaginary unit, τ is the parameter controlling Gauss window at time t shaft position, h (t) is primary signal function, (2) formula is the expression formula of Gaussian window, can be obtained by formula (1), (2), conversion is that the height of Gauss window and width vary with frequency in place of being different from short time discrete Fourier transform, thus overcomes the defect that Fu's leaf transformation window height and width are fixed in short-term.

Step 2, carries out one-dimensional continuous S inverse transformation to the function defined in step 1,

Because

$h\left(t\right)=\underset{-\mathrm{\∞}}{\overset{\mathrm{\∞}}{\∫}}\[{\∫}_{-\mathrm{\∞}}^{\mathrm{\∞}}S(\mathrm{\τ},f)d\mathrm{\τ}\]e^{\left(2\mathrm{\π}ftj\right)}df---\left(3\right)$

Relation between the S-transformation of signal h (t) and its Fourier transform H (f) is:

$S(\mathrm{\τ},f)=\underset{-\mathrm{\∞}}{\overset{\mathrm{\∞}}{\∫}}H(f+\mathrm{\α})\·e^{\left(\frac{-2{\mathrm{\π}}^2{\mathrm{\α}}^2}{f^2}\right)}\·e^{\left(2\mathrm{\π}\mathrm{\α}\mathrm{\τ}j\right)}d\mathrm{\α}---\left(4\right)$

Wherein, α controls Gaussian window in frequency domain and moves on the frequency axis, and τ moves on a timeline for controlling Gaussian window in frequency domain, and H (f+ α) is the Fourier transform of h (t),Fourier transform for Gaussian window.

Step 3, carries out one-dimensional discrete S-transformation to the functional relation (4) in step 2,

If h [KT] (k=0,1,2 ... N-1) it is the discrete-time series obtained that continuous time signal h (t) is sampled, the sampling interval is T, and total sampling number is N, then this seasonal effect in time series discrete Fourier transform (DFT) is:

$H\[\frac{n}{NT}\]=\frac{1}{N}\underset{k=0}{\overset{N-1}{\Σ}}h\left(kT\right)e^{\left(\frac{-2\mathrm{\π}nkj}{N}\right)}---\left(5\right)$

When n ≠ 0,

$S(iT,\frac{n}{NT})=\underset{m=0}{\overset{N-1}{\Σ}}H\left(\frac{m+n}{NT}\right)e^{\left(\frac{-2{\mathrm{\π}}^2{m}^2}{n^2}\right)}{e}^{\left(\frac{i2\mathrm{\π}mj}{N}\right)},n\≠0---\left(6\right)$

Wherein: i, m, n=0,1,2 ..., N-1

As n=0,

$S(iT,0)=\frac{1}{N}\underset{m=0}{\overset{N-1}{\Σ}}h\left(\frac{m}{NT}\right)---\left(7\right)$

The algorithm basic step of S-transformation is can get: first calculate the fast fourier transform of h (t) by (5), (6), (7) formulaAgain willMove toThen the fast fourier transform of Gauss function g under each frequency (τ-T) is calculatedAgain by frequency, sampled point calculatesI.e. (m, n), makees convolution to fast fourier transform B of calculating primary signal and Gaussian window, and finally by convolution theorem, (m, inverse fast fourier transform n) obtain S-transformation S (iT, n/NT) to calculate B.

Step 4, utilizes the derivation method of step 1～step 3 to process concrete various signals, and is analyzed the result obtained, thus utilizes the various Power Disturbance signals of detection.

I.e. h (t) in step 1～3 is specially following several signal functions, and is analyzed, as follows:

1. as h (t)=sin (ω t), the result obtained after carrying out S-transformation is as shown in Figure 2, wherein Fig. 2 (a) represents each row squared magnitude and the average detection figure of module time-frequency matrixes, as can be seen from the figure, Fig. 2 (a) not fluctuation, illustrates this signal stabilization；Fig. 2 (b) represents fundamental frequency amplitude detection figure, it can be seen that the amplitude of sine voltage signal is 1V, Fig. 2 (c) represents frequency amplitude envelope detected figure, as we know from the figure, this curve only frequency be at 50HZ acquirement maximum, illustrate that the frequency of signal is 50Hz, without other frequency contents, Fig. 2 (d) represents phase hit detection figure, it can be seen that phase increment value is around 0 change, without fluctuation.Above-mentioned Fig. 2 (a)～the detection figure of sinusoidal signal function that (d) is standard, can be as judging remaining the most problematic contrast standard of signal to be detected, when the detected signal of input is for existing problems or non-standard signal, by the figure that S-transformation obtains just has different displays, by the detection figure Comprehensive Correlation of parameters is evaluated, just the quality of this signal can be evaluated and judge, determine this disturbing signal.

2.h (t)=sin (ω t+ (π/3) μ (t-0.21)), the sinusoidal signal model containing phase hit result after S-transformation is as shown in Figure 3, Fig. 3 (a) represents each row squared magnitude and the average detection figure of module time-frequency matrixes, wherein curve has obvious spike, testing result shows that its maximum is at n=210, i.e. disturbance occurs when sampled point n=210 (or time t=0.21s).Fig. 3 (b) and Fig. 3 (c) represents fundamental frequency amplitude detection figure and frequency amplitude envelope detected figure respectively, illustrate that this signal has disturbance, persistent period is the shortest, disturbance makes amplitude have dropped 0.104, the frequency of signal is that 50Hz, Fig. 3 (d) represent phase hit detection figure, illustrates that phase place there occurs saltus step, understood in this signal by features above analysis and comprise only phase hit, without other disturbances.Above-mentioned Fig. 3 (a)～3 (d) are the detection figure of the sinusoidal standard signal function containing phase hit of standard, can be as judging remaining the most problematic contrast standard of signal to be detected, when the detected signal of input is for existing problems or non-standard signal, by the figure that S-transformation obtains just has different displays, by the detection figure Comprehensive Correlation of parameters is evaluated, just the quality of this signal can be evaluated and judge, determine this disturbing signal.

3. when h (t)=sin (ω t)+0.08sin (3 ω t)+0.15sin (5 ω the t)+0.12sin (7 ω t) result after S-transformation as shown in Figure 3, Fig. 4 (a) represents each row squared magnitude and the average detection figure of module time-frequency matrixes, fluctuate in time, illustrating that disturbing signal exists always, the persistent period is 1s；Fig. 4 (b) and 4 (d) represent fundamental frequency amplitude detection figure and phase hit detection figure respectively, and testing result is identical with sine voltage signal, is stable；Fig. 4 (c) represents frequency amplitude envelope detection figure, it is to reach peak value at 50,150,250,350 in frequency respectively, and peak value is followed successively by 1,0.08,0.15,0.1208, in result explanation harmonic signal in addition to sine wave, also comprise the triple-frequency harmonics of 8%, the quintuple harmonics of 15% and the seventh harmonic of 12%.Above-mentioned Fig. 4 (a)～the detection figure of harmonic standard signal function that (d) is standard, can be as judging remaining the most problematic contrast standard of signal to be detected, when the detected signal of input is for existing problems or non-standard signal, by the figure that S-transformation obtains just has different displays, by the detection figure Comprehensive Correlation of parameters is evaluated, just the quality of this signal can be evaluated and judge, determine this disturbing signal

4. as h (t)={ 1-0.65 [μ (t-0.195)-μ (t-0.335)] } sin ω t, result after S-transformation is as shown in Figure 5, Fig. 5 (a) represents each row squared magnitude and the average detection figure of module time-frequency matrixes, curve has two obvious spikes, the position of spike is at n=195 and n=335, the rising of temporary fall is described, the moment of beginning is respectively t=0.195s and t=0.335s, duration T=0.14s.Fig. 5 (b) represents fundamental frequency amplitude detection figure, and curve is carved with obvious amplitude when disturbance occurs, and the lower value that falls behind, for 0.35V, illustrates that amplitude have dropped 1-0.35=0.65V.Fig. 5 (c), 5 (d) are respectively frequency amplitude envelope detection figure and phase hit detection figure, illustrate that signal frequency is 50Hz, and phase place there occurs change.Cleaning Principle and voltage dip to the signal such as voltage swell, interruption are basically identical.Above-mentioned Fig. 5 (a)～the detection figure of voltage dip standard signal function that 5 (d) is standard, can be as judging remaining the most problematic contrast standard of signal to be detected, when the detected signal of input is for existing problems or non-standard signal, by the figure that S-transformation obtains just has different displays, by the detection figure Comprehensive Correlation of parameters is evaluated, just the quality of this signal can be evaluated and judge, determine this disturbing signal.

5. when h (t)=(1+0.8 [μ (the t-0.195)-μ (t-0.235)]) (sin ω t+0.03sin 3 ω t+0.09sin 5 ω t+0.1sin 7 ω t) result after S-transformation as shown in Figure 6

Fig. 6 (a) and 6 (c) are each row squared magnitude of module time-frequency matrixes and average detection figure and frequency amplitude envelope detection figure respectively, can be seen that in this signal containing harmonic wave, frequency amplitude envelope wherein has 4 peak values, frequency corresponding at peak value is 50,150,250,350, amplitude is 1,0.03,0.09,0.1055, basically identical with frequency content and the content of harmonic wave in model, but slightly error at 7 subharmonic.Each row squared magnitude and the average detection of observing Fig. 6 (a) module time-frequency matrixes are schemed and Fig. 6 (b) fundamental frequency amplitude detection graph discovery, this signal is in addition to harmonic wave, at sampled point n=195 to n=235 place, amplitude increases 0.8, illustrate possibly together with the disturbance making voltage raise in this signal, and this disturbance makes phase place generation saltus step.Above-mentioned Fig. 6 (a)～the harmonic wave making alive that (d) is standard rise the detection figure of signal function temporarily, can be as judging remaining the most problematic contrast standard of signal to be detected, when the detected signal of input is for existing problems or non-standard signal, by the figure that S-transformation obtains just has different displays, by the detection figure Comprehensive Correlation of parameters is evaluated, just the quality of this signal can be evaluated and judge, determine this disturbing signal.

6., according to dropping model temporarily, to voltage dip, it carries out short time discrete Fourier transform and S-transformation respectively, the result of detection as shown in Figure 7:

Rise, the moment of beginning is respectively 0.275s and 0.525s, and temporary range of decrease value is that 0.625pu, Fig. 7 (a1) represent short time discrete Fourier transform time-frequency curve detection figure, illustrate that temporary fall occurs rise, moment beginning is respectively T_ST=0.2725s and T_EN=0.5225s, error is 0.25%, compared with Fig. 7 (a1), from the time-frequency curve detection figure of Fig. 7 (a2) S-transformation, can be seen that S-transformation has good time-frequency resolution capability, and when fall occurs temporarily compared with short time discrete Fourier transform, spike is the thinnest but also long, it is easy to find the maximum of points of sword spike.What testing result showed that temporary fall occurs rise, the moment of beginning is respectively T_ST=0.275s and T_EN=0.525s, error is 0, and result shows that S-transformation is more accurate to the location of voltage dip.Being can be seen that by Fig. 7 (b1) short time discrete Fourier transform fundamental frequency amplitude curve, 7 (b2) S-transformation fundamental frequency amplitude curve occurs moment phase place to have obvious saltus step in fall temporarily, compared with the phase hit that STFT change detection arrives, the phase increment value of S-transformation detection is more accurate.Adding signal to noise ratio in voltage dip signal is the white Gaussian noise of 40dB, and the testing result of voltage dip amplitude is as shown in Fig. 7 (c1) short time discrete Fourier transform phase hit curve, Fig. 7 (c2) S-transformation phase hit curve.Result shows, in the case of containing noise, the fundamental frequency amplitude curve of STFT conversion exists fluctuation, and the amplitude of fall is between 0.622～0.628pu temporarily；The fundamental frequency amplitude curve of S-transformation is substantially without fluctuation, and testing result is 0.625pu, this shows that the anti-noise ability of S-transformation is relatively strong, and testing result is accurate.

The method utilizing the present invention, the signal of various function waveforms is carried out S-transformation by flow chart 1, the characteristic signals such as the time of signal, amplitude, frequency and phase place can be extracted, when in electrical network, disturbance occurs, can realize it is quick and precisely positioned, accurately detect its amplitude, frequency and phase place situation of change.Disturbing signal is positioned by each row squared magnitude and the Mean curve that use matrix, it is characterized in that: the start/stop time curve that disturbance occurs has obvious spike, and this detection method error is minimum.Using a certain moment frequency amplitude envelope to forcing frequency composition detection, use phase increment curve detection signal phase situation of change, it is characterized in that: during disturbance occurs, curve fluctuation is substantially.

Claims (5)

1. the S-transformation detection method of a Power Quality Disturbance, it is characterised in that specifically according to Following steps are implemented:

Step 1: set up S-transformation function,

Step 2, carries out one-dimensional continuous S inverse transformation to the function defined in step 1,

Step 3, carries out one-dimensional discrete S-transformation to the functional relation obtained in step 2,

Step 4, utilizes the derivation method of step 1～step 3 to process concrete various signals, and The result obtained is analyzed, thus utilizes the various Power Disturbance signals of detection.

The S-transformation detection method of Power Quality Disturbance the most according to claim 1, it is special Levy and be, described step 1 particularly as follows:

The functional expression set up is,

$S(\mathrm{\τ},f)={\∫}_{-\mathrm{\∞}}^{\mathrm{\∞}}h\left(t\right)g(\mathrm{\τ}-t)e^{(-2\mathrm{\π}ftj)}dt---\left(1\right)$

Wherein,

$g(\mathrm{\τ}-t)=\frac{\left|f\right|}{\sqrt{2\mathrm{\π}}}{e}^{\[\frac{-f^2{(\mathrm{\τ}-t)}^2}{2}\]}---\left(2\right)$

In formula: f is frequency, j is imaginary unit, and τ is the ginseng controlling Gauss window at time t shaft position Number, h (t) is primary signal function, and (2) formula is the expression formula of Gaussian window, can be obtained by formula (1), (2) Arriving, conversion is that the height of Gauss window and width become with frequency in place of being different from Short Time Fourier Transform Change, thus overcome the defect that Fu's leaf transformation window height and width are fixed in short-term.

The S-transformation detection method of a kind of Power Quality Disturbance the most according to claim 1, its Be characterised by, described step 2 particularly as follows:

When the function defining step 1 carries out one-dimensional continuous S inverse transformation,

Because

$h\left(t\right)=\underset{-\mathrm{\∞}}{\overset{\mathrm{\∞}}{\∫}}\[{\∫}_{-\mathrm{\∞}}^{\mathrm{\∞}}S(\mathrm{\τ},f)d\mathrm{\τ}\]e^{\left(2\mathrm{\π}ftj\right)}df---\left(3\right)$

Relation between the S-transformation of signal h (t) and its Fourier transformation H (f) is:

$S(\mathrm{\τ},f)=\underset{-\mathrm{\∞}}{\overset{\mathrm{\∞}}{\∫}}H(f+\mathrm{\α})\·e^{\left(\frac{-2{\mathrm{\π}}^2{\mathrm{\α}}^2}{f^2}\right)}\·e^{\left(2\mathrm{\π}\mathrm{\α}\mathrm{\τ}j\right)}d\mathrm{\α}---\left(4\right)$

Wherein, α controls Gaussian window in frequency domain and moves on the frequency axis, τ for control in frequency domain Gaussian window time Moving on countershaft, H (f+ α) is the Fourier transformation of h (t),Fourier transformation for Gaussian window.

The S-transformation detection method of a kind of Power Quality Disturbance the most according to claim 1, its Be characterised by, described step 3 particularly as follows: set h [KT] (k=0,1,2 ... N-1) be to continuous time believe Number h (t) carries out the discrete-time series obtained of sampling, and the sampling interval is T, and total sampling number is N, then This seasonal effect in time series discrete Fourier transform is:

$H\[\frac{n}{NT}\]=\frac{1}{N}\underset{k=0}{\overset{N-1}{\Σ}}h\left(kT\right)e^{\left(\frac{-2\mathrm{\π}nkj}{N}\right)}---\left(5\right)$

When n ≠ 0,

$S(iT,\frac{n}{NT})=\underset{m=0}{\overset{N-1}{\Σ}}H\left(\frac{m+n}{NT}\right)e^{\left(\frac{-2{\mathrm{\π}}^2{m}^2}{n^2}\right)}{e}^{\left(\frac{i2\mathrm{\π}mj}{N}\right)},n\≠0---\left(6\right)$

Wherein: i, m, n=0,1,2 ..., N-1

As n=0,

$S(iT,0)=\frac{1}{N}\underset{m=0}{\overset{N-1}{\Σ}}h\left(\frac{m}{NT}\right)---\left(7\right)$

The algorithm basic step of S-transformation is can get: first calculate quick Fu of h (t) by (5), (6), (7) formula In leaf transformationAgain willMove toThen Gaussian window letter under each frequency is calculated The fast Fourier transform of number g (τ-T)Again by frequency, sampled point calculates(m n), rolls up the i.e. fast Fourier transform B of calculating primary signal and Gaussian window Long-pending, finally by convolution theorem, (m, Fast Fourier Transform Inverse n) obtain S-transformation S (iT, n/NT) to calculate B.

The S-transformation detection method of Power Quality Disturbance the most according to claim 1, its feature Being, the signal described in described step 4 can be following several signal function,

1) h (t)=sin (ω t),

2) h (t)=sin (ω t+ (π/3) μ (t-0.21)),

3) h (t)=sin (ω t)+0.08sin (3 ω t)+0.15sin (5 ω t)+0.12sin (7 ω t)

4) h (t)={ 1-0.65 [μ (t-0.195)-μ (t-0.335)] } sin ω t

5)

H (t)=(1+0.8 [μ (t-0.195)-μ (t-0.235)]) (sin ω t+0.03sin3 ω t+0.09sin5 ω t+0.1sin7 ω t) 。