CN105137175B - A kind of adding window Short Time Fourier Transform three point interpolation Dynamic Frequency Measurement method - Google Patents
A kind of adding window Short Time Fourier Transform three point interpolation Dynamic Frequency Measurement method Download PDFInfo
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Abstract
The invention discloses a kind of adding window Short Time Fourier Transform Dynamic Frequency Measurement method, this method is mainly comprised the following steps：First, discrete sampling is carried out to power network time domain continuous signal, N point sampling sequence U (n) are obtained；Second, window function is selected, using Short Time Fourier Transform, the Short Time Fourier Transform matrix F of sample sequence is obtainedSTFT(i,j)；3rd, obtain the maximum correspondence spectral line k of matrix pth row1With adjacent spectral line k2、k3；4th, k is passed through1、k2、k3, using polynomial approximation method, obtain peak value line parameters αp；5th, using formula fmp=(αp+k1) Δ f, obtain the crest frequency f of signalmp；6th, calculate signal frequency rate of change fc‑p, it is determined that the row that required increase is calculated, and calculate corresponding crest frequency fmp；7th, according to crest frequency fmp, obtain the dynamic frequency function f that signal is changed over timem(p).This method is based on adding window Short Time Fourier Transform, using interpolation method, while quick measurement frequency, and also signal time domain can be analyzed, and precision is high, calculate simple.
Description
Technical field
The invention belongs to power system frequency field of measuring technique, it is related to a kind of adding window Short Time Fourier Transform three point interpolation
Dynamic Frequency Measurement method.
Background technology
Frequency is the important operational factor of power system and electrical equipment, and the rated frequency of China's power system is 50Hz,
Frequency departure scope specified in " power industry technologies laws and regulations on the management " is ± 0.2- ± 0.5Hz, and its purpose is to ensure electricity
The stable operation of Force system and the electric energy that high-quality is supplied to user.Because electric energy can not be stored, and load changes at any time,
The change of load will cause the change of power system frequency, and system dynamic frequency directly affects the quality of power supply and the peace of operation of power networks
Quan Xing, stability.Frequency measurement is power system and electric equipment operation, monitoring, control and the basis of relay protection.With
China's power system is continued to develop, and coal electricity, Hydropower Base and the construction in nuclear power base, remote, extensive power transmission network make
Transmission line of electricity tends to heavy duty, and transmission line of electricity increases because of the threat that accident is disconnected to receiving-end system frequency stability；With nuclear fuel material, coal
Charcoal etc. is the power supply rigidization increase of fuel, and the response performance of load variations is deteriorated；Requirement of the Large-scale machine set to frequency shift (FS)
Harsher, frequency is too high or too low may all to cause protection device to act, and easily cause cause frequency significantly to offset chain
Accident；Interconnect synchronised grids region wide, substantially, this requires special to system frequency to network system frequency response spatial-temporal distribution characteristic
Property and dynamic behaviour are studied, to ensure the safe and stable operation of system.However, current frequency measurement method is difficult to meet
System is to the analysis demand of frequency response spatial and temporal distributions characteristic, and this proposes new choose to power network dynamic frequency analysis measuring method
War.
Method proposed by the present invention, overcomes legacy frequencies measuring method and is difficult to while meeting frequency-domain analysis and time-domain analysis
Shortcoming.Using adding window Short Time Fourier Transform, time frequency analysis can be carried out to signal, in the same of accurate measurement signal frequency
When, the time-domain analysis result of signal can be provided, by calculating frequency change rate, time-domain analysis precision is added, using 3 points
Interpolation algorithm, improves signal frequency measurement accuracy, and calculates simple, and providing one for Dynamic Frequency In Power Systems measurement has
The approach of effect.
The content of the invention
The invention provides a kind of adding window Short Time Fourier Transform three point interpolation Dynamic Frequency Measurement method, tradition is overcome
Frequency measurement method is difficult to while meeting the shortcoming of frequency-domain analysis and time-domain analysis., can be with using adding window Short Time Fourier Transform
Time frequency analysis is carried out to signal, while accurate measurement signal frequency, the time-domain analysis result of signal can be provided, passes through meter
Frequency change rate is calculated, time-domain analysis precision is added, using three point interpolation algorithm, signal frequency measurement accuracy, and meter is improved
Calculate simple.
In order to solve the above technical problems, solution proposed by the present invention is：First, power network time domain continuous signal is carried out
Discrete sampling, obtains N point sampling sequence U (n)；Second, window function is selected, using Short Time Fourier Transform, sample sequence is obtained
Short Time Fourier Transform matrix FSTFT(i,j)；3rd, obtain the maximum correspondence spectral line k of matrix pth row1With adjacent spectral line
k2、k3；4th, k is passed through1、k2、k3, using polynomial approximation method, obtain peak value line parameters αp；5th, using formula fmp=
(αp+k1) Δ f, obtain the crest frequency f of signalmp；6th, calculate signal frequency rate of change fc-p, it is determined that what required increase was calculated
Row, and calculate corresponding crest frequency fmp；7th, according to crest frequency fmp, obtain the dynamic frequency letter that signal is changed over time
Number fm(p)。
Technical scheme is as follows：
A kind of adding window Short Time Fourier Transform three point interpolation Dynamic Frequency Measurement method, it is characterised in that：Using three angular moments
Shape convolution window, carries out Short Time Fourier Transform to power network signal, the Short Time Fourier Transform matrix of signal is obtained, according to Chief Signal Boatswain
Degree and window function window are long, it is determined that the column position of required calculating, since arranging the 1st, finds the corresponding spectral line of maximum in the row, with
And two adjacent spectral lines, using obtained spectral line, the crest frequency of the row is calculated, then signal frequency rate of change is calculated, obtain
Need increase to calculate the row of crest frequency, so as to obtain the dynamic frequency function of signal, specifically include following steps：
A. to the continuous power network signal u (t) of time domain with sample frequency fsSampled, the N points of signal are obtained after over-sampling
Discrete sampling sequence U (n), n=0,1,2 ..., N-1；
B. the quarter window for being R/2 with length carries out convolution with rectangular window, obtains the triangle rectangle time domain that length is R and rolls up
Product window w (n), using fourier formula in short-term, carries out Short Time Fourier Transform to signal discrete sample sequence, obtains the short of signal
When Fourier transform matrix FSTFT(i,j)；
C. according to signal length N and the long R of window function window, it is determined that the matrix F of required calculatingSTFTThe row p of (i, j)；
D. interpolation method is applied, according to the Short Time Fourier Transform matrix F of signalSTFT(i, j), obtains pth row maximum institute
Corresponding spectral line, is designated as k1, with k1Adjacent spectral line is designated as k respectively2And k3, k1The frequency content of expression is f1=k1Δ f, k2Table
The frequency content shown is f2=k2Δ f, k3The frequency content of expression is f3=k3Δ f, k1、k2、k3The amplitude of expression is respectively y1、
y2、y3；
E. by formulaAnd αp=km-k1, wherein kmFor the position corresponding to crest frequency, formula can be obtained：Using polynomial approximation method, peak value line parameters α is solvedp, αpSpan for [-
0.5,0.5]；
F. formula f is appliedmp=(αp+k1) Δ f, wherein Δ f=fs/ N, obtains the crest frequency f of signalmp；
G. according to crest frequency fmpCalculate the frequency change rate f of signalc-p, calculation formula isAccording to fc-pIt is determined that needing to increase the row for calculating crest frequency；
H. according to the crest frequency f of signalmp, finally give the dynamic frequency function f that signal is changed over timem(p)。
In described method, it is characterised in that it is determined that the required formula arranged that calculates isN=0,1,
2 ..., N-1, symbolExpression is rounded downwards.
In described method, it is characterised in that when frequency changes, the row that increase calculates crest frequency are become by frequency
Rate fc-pIt is determined that, work as fc-p>=0.002 or fc-pWhen≤- 0.002, if p=1, increase calculates the crest frequency f of 2,3,4 rowm2、
fm3、fm4If, p>1, then increase calculates (p-3), (p-2), the crest frequency f of (p-1) rowm(p-3)、fm(p-2)、fm(p-1)。
The invention provides a kind of adding window Short Time Fourier Transform three point interpolation Dynamic Frequency Measurement method, tradition is overcome
Frequency measurement method is difficult to while meeting the shortcoming of frequency-domain analysis and time-domain analysis., can be with using adding window Short Time Fourier Transform
Time frequency analysis is carried out to signal, while accurate measurement signal frequency, the time-domain analysis result of signal can be provided, passes through meter
Frequency change rate is calculated, time-domain analysis precision is added, using three point interpolation algorithm, signal frequency measurement accuracy, and meter is improved
Calculate simple, an effective approach is provided for Dynamic Frequency In Power Systems measurement.
Brief description of the drawings
Fig. 1 is the theory diagram of Dynamic Frequency Measurement in the present invention.
Fig. 2 is realizes the program flow diagram of adding window Short Time Fourier Transform Dynamic Frequency Measurement method in the present invention.
Embodiment
The present invention proposes a kind of adding window Short Time Fourier Transform three point interpolation Dynamic Frequency Measurement method.Below in conjunction with attached
Figure elaborates：
The theory diagram of the Dynamic Frequency Measurement of the present invention as shown in figure 1, first, obtained after time-domain signal discrete sampling from
Scattered signal, then by the processing of adding window Short Time Fourier Transform, obtains the time frequency analysis matrix of signal, then pass through three point interpolation
Method, improves frequency-domain analysis result accuracy, so as to complete the Dynamic Frequency Measurement of signal.
As shown in Fig. 2 a kind of adding window Short Time Fourier Transform three point interpolation Dynamic Frequency Measurement method flow is as follows：
The first step, with fsFor sample frequency, time domain continuous signal is sampled, the time-domain expression of signal is：
In formula, K is highest overtone order, and k is overtone order, and fundamental wave is represented during k=1；AkFor kth subharmonic amplitude；T is
Time；F is the frequency of signal fundamental wave；For the phase of kth subharmonic.Invented for test, power transformation when signal is in the present embodiment
Signal is pressed, 0<During t≤1s, f is 50.1Hz, 1<During t≤2s, f is 50.2Hz, 2<During t≤3s, f is 49.9Hz, fundamental wave
Amplitude is 220V, and the initial phase of fundamental wave is 30 °, K=1, according to fs>=2Kf, sample frequency is set to 2000Hz；
Discrete sampling is carried out to signal, signal length N=6001 voltage dispersion sequence is obtained：
In formula, n=0,1,2 ..., N-1；
Second step, because mains frequency is 50Hz, the quarter window for being R/2 with length carries out convolution with rectangular window, obtained
To the triangle rectangle convolution window w (n) that length is R, using fourier formula in short-term, to line voltage discrete sampling sequence U
(n) Short Time Fourier Transform is carried out, Short Time Fourier Transform formula is：
In formula, w*(n) it is the conjugation of window function, τ is imaginary unit；
The Short Time Fourier Transform matrix F of voltage signal can be obtained by formula (3)STFT(i,j)；In the present embodiment,
The length R of triangle rectangle convolution window is 512；The resulting transformation matrices of Fourier in short-term FSTFT(i, j) dimension is 1025
× 208, i.e. i=1,2,3 ..., 1025；J=1,2,3 ..., 208；
3rd step, using three point interpolation method, according to the Short Time Fourier Transform matrix F of voltage signalSTFT(i, j), is obtained
Spectral line corresponding to pth row maximum, is designated as k1, with k1Adjacent spectral line is designated as k respectively2And k3, p expression formula is：
In formula, n=2R, 2R+1,2R+2 ..., N-1, L is that window function moves interval, symbolExpression is rounded downwards；
In the present embodiment, window function movement interval L is 24, and selected columns p is 37 and 41；
k1、k2、k3The frequency content f of expression1、f2、f3Respectively：
f1=k1Δf (5)
f2=k2Δf (6)
f3=k3In Δ f (7) formula, sampling interval Δ f=fs/N；
k1、k2、k3The amplitude y of expression1、y2、y3Respectively：
In formula, A0For the amplitude of signal, f0For the frequency of signal,For the initial phase of signal, WRFor the frequency spectrum letter of window function
Number；
4th step, it is assumed that peak value line parameters α, β is as follows：
αp=kmp-k1 (11)
Wherein, kmpFor the position corresponding to crest frequency；
Formula (8), (9), (10) and (11) is substituted into formula (12), can be obtained：
Using polynomial approximation method, peak value line parameters α is solvedp, αpSpan be [- 0.5,0.5]；The present embodiment
In, k1=26, k2=25, k3=27, Δ f=1.9512, the peak value line parameters α tried to achieve37=-0.326, α41=-0.318；
5th step, according to peak value line parameters αp, using formula：
fmp=(αp+k1)Δf (14)
The crest frequency f of voltage signal can be obtainedmp；In the present embodiment, crest frequency fm37=50.095Hz, fm41=
50.111Hz；
6th step, using crest frequency fmp, calculate frequency change rate fc-p, formula is：
According to fc-pIt is determined that needing to increase the row for calculating crest frequency, work as fc-p>=0.002 or fc-pWhen≤- 0.002, if p=
1, then increase calculates the crest frequency f of 2,3,4 rowm2、fm3、fm4If, p>1, then increase calculating (p-3), (p-2), (p-1) are arranged
Crest frequency fm(p-3)、fm(p-2)、fm(p-1)；F in the present embodimentc-41=0.0003, it is not necessary to which increase calculates row；
6th step, according to the crest frequency f of voltage signalmp, finally give the dynamic frequency that voltage signal is changed over time
Function fm(p)。
So far, the measurement of power network signal dynamic frequency is completed.
In summary, the invention provides a kind of adding window Short Time Fourier Transform three point interpolation Dynamic Frequency Measurement method,
Legacy frequencies measuring method is overcome to be difficult to while meeting the shortcoming of frequency-domain analysis and time-domain analysis.Using adding window Fourier in short-term
Conversion, can carry out time frequency analysis to signal, while accurate measurement signal frequency, can provide the time-domain analysis knot of signal
Really, by calculating frequency change rate, time-domain analysis precision is added, using three point interpolation algorithm, signal frequency measurement is improved
Precision, and calculate simple.
Claims (3)
1. a kind of adding window Short Time Fourier Transform three point interpolation Dynamic Frequency Measurement method, it is characterised in that：Using triangle rectangle
Convolution window, carries out Short Time Fourier Transform to power network signal, the Short Time Fourier Transform matrix of signal is obtained, according to signal length
And window function window is long, it is determined that the column position of required calculating, since arranging the 1st, finds the corresponding spectral line of maximum in the row, and
Two adjacent spectral lines, using obtained spectral line, calculate the crest frequency of the row, then calculate signal frequency rate of change, are needed
Increase the row for calculating crest frequency, so as to obtain the dynamic frequency function of signal, specifically include following steps：
A. to the continuous power network signal u (t) of time domain with sample frequency fsSampled, the N points that signal is obtained after over-sampling discrete are adopted
Sample sequence U (n), n=0,1,2 ..., N-1；
B. the quarter window for being R/2 with length carries out convolution with rectangular window, obtains the triangle rectangle convolution window that length is R
W (n), using fourier formula in short-term, carries out Short Time Fourier Transform to signal discrete sample sequence, obtains Fu in short-term of signal
In leaf transformation matrix FSTFT(i,j)；
C. according to signal length N and the long R of window function window, it is determined that the matrix F of required calculatingSTFTThe row p of (i, j)；
D. interpolation method is applied, according to the Short Time Fourier Transform matrix F of signalSTFT(i, j), is obtained corresponding to pth row maximum
Spectral line, is designated as k1, with k1Adjacent spectral line is designated as k respectively2And k3, k1The frequency content of expression is f1=k1Δ f, k2The frequency of expression
Rate composition is f2=k2Δ f, k3The frequency content of expression is f3=k3Δ f, k1、k2、k3The amplitude of expression is respectively y1、y2、y3；
E. by formulaAnd αp=km-k1, wherein kmFor the position corresponding to crest frequency, formula can be obtained：Using polynomial approximation method, peak value line parameters α is solvedp, αpSpan be
[- 0.5,0.5]；
F. formula f is appliedmp=(αp+k1) Δ f, wherein Δ f=fs/ N, obtains the crest frequency f of signalmp；
G. according to crest frequency fmpCalculate the frequency change rate f of signalc-p, calculation formula isAccording to fc-pIt is determined that needing to increase the row for calculating crest frequency；
H. according to the crest frequency f of signalmp, finally give the dynamic frequency function f that signal is changed over timem(p)。
2. according to the method described in claim 1, it is characterised in that it is determined that the required formula arranged that calculates isN=0,1,2 ..., N-1, symbolExpression is rounded downwards.
3. according to the method described in claim 1, it is characterised in that when frequency changes, increase calculates crest frequency
Row are by frequency change rate fc-pIt is determined that, work as fc-p>=0.002 or fc-pWhen≤- 0.002, if p=1, increase calculates 2,3,4 row
Crest frequency fm2、fm3、fm4If, p>1, then increase calculates (p-3), (p-2), the crest frequency f of (p-1) rowm(p-3)、fm(p-2)、
fm(p-1)。
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