CN109342816A - The detection method of spectral leakage in electric energy quality monitoring - Google Patents
The detection method of spectral leakage in electric energy quality monitoring Download PDFInfo
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- CN109342816A CN109342816A CN201811475977.3A CN201811475977A CN109342816A CN 109342816 A CN109342816 A CN 109342816A CN 201811475977 A CN201811475977 A CN 201811475977A CN 109342816 A CN109342816 A CN 109342816A
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- G—PHYSICS
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- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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- G01R23/16—Spectrum analysis; Fourier analysis
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Abstract
The detection method of spectral leakage in a kind of electric energy quality monitoring, including discretization, by signal by rectangular window windowing process, Fourier transformation and Euler's variation are carried out, and judges four steps of spectral leakage situation when signal carries out Fourier transformation according to spectral leakage coefficient.The present invention is simple to operation, must can effectively detect spectral leakage phenomenon and leak degree of the signal after FFT transform, and the correctness for the voltage calculated result of electric energy quality monitoring terminal provides safeguard.
Description
Technical field
The present invention relates to data acquisition and procession fields, and in particular to the detection of spectral leakage in a kind of electric energy quality monitoring
Method.
Background technique
In recent years, the nonlinear-loads such as rectification adverser, frequency converter constantly put into operation, lead to power load day
Become diversification and complication, so that voltage deviation, frequency departure, voltage fluctuation and flicker, three-phase imbalance, harmonic wave are abnormal in power grid
The power quality problems such as change are got worse, and threaten the electricity consumption reliability and safety in production of power consumer.In order to improve electric energy matter
Amount, it is necessary to which research meets the monitoring algorithm and monitoring device that Modern Electric Power Quality analysis requires, and carries out to power quality index real
When monitor.
It is actually answered in engineering field for analyzing the algorithm of power quality indexes based on Fourier transformation (FFT)
Fft algorithm need to carry out windowing process to signal, and result can come spectrum component from normal spread spectrum, that is, frequency occurs
Spectrum leakage.Currently, analysis and improvement are concentrated mainly on for the research of spectral leakage both at home and abroad, for example, by using different window functions
Reduce spectral leakage etc., and spectral leakage is few to be referred to for how to detect.
Summary of the invention
The purpose of the present invention is to provide a kind of detection methods of spectral leakage in electric energy quality monitoring, can effectively obtain inspection
Survey spectral leakage phenomenon and leak degree of the signal after FFT transform.
The purpose of the present invention can be achieved, and design a kind of detection method of spectral leakage in electric energy quality monitoring, packet
Include following steps:
S1, in the monitoring calculation of power quality terminal, choose any single frequency sinusoidal signal x (t) superposition modulated wave, formed
One source signal；
S2, above-mentioned source signal is exported to electric energy quality monitoring terminal, and record N number of continuous 10 cycle electricity of monitoring terminal
Press measured value URMS(0)…URMS(N), the amplitude A (k) of the kth spectral line of the discrete f (t) of the source signal is obtained, as shown in Equation 1:
In formula, j is imaginary unit, and Fourier transformation is that time domain is converted into complex frequency domain, and the plural number in complex frequency domain is a+jb
Form, j here do not need to do specified otherwise.N=0,1 ..., N.
S3, kth is set0Spectral line is the signal spectrum on the basis of vibration frequency, obtains K0Numerical value；
S4, judge that signal carries out Fourier's change inside electric energy quality monitoring terminal according to the calculated result of formula 2 and formula 3
Spectral leakage situation when changing；
QRMSLabeled as spectral leakage coefficient, value is bigger, indicates that the degree of spectral leakage is bigger；
In formula, UNFor the virtual value of source sinusoidal signal, A1For the amplitude of modulating wave.
Value not within the above range, then judge spectral leakage.
Further, any single frequency sinusoidal signal x (t) superposition modulated wave forms the source signal of virtual value fluctuation, source signal
F (t) is in (1 ± 0.05) UNBetween the signal that fluctuates.
Further, N number of continuous 10 cycle voltage measuring value is 100, and source signal is as shown in Equation 4；
In formula, f (t) is in (1 ± 0.05) UNBetween the signal that fluctuates, the frequency of fluctuation signal is 2.3Hz；UNFor source
The virtual value of sinusoidal signal.
The amplitude A (k) of the kth spectral line of signal f (t) is as shown in Equation 5:
If kth0Spectral line is the spectral line of 2.3Hz reference signal, obtains K by formula 60It is 46,
In formula, N=100 indicates the continuous 100 terminal voltage population of measured values recorded, ts=10 × 20ms=0.2s
Indicate the 10 cycle voltage sample times of terminal；
According to the calculated result of formula 1 and formula 2 are as follows:
Spectral leakage is judged according to the above results.
Further, to the sampling of frequency spectrum and adding window the step of are as follows:
Use discrete means with Δ f=f at equal intervalss/ N is to continuous frequency spectrum Xc1(f) spectral sampling is carried out, N is sampling number,
Discrete series X can be obtainedc1(k) expression formula is as shown in Equation 7,
Window function selects rectangular window, is analyzed by weighting truncation and Fourier transformation；
The spectrum expression formula of selected rectangular window is represented by formula 8:
With rectangular window wR(n) windowing signal x is obtained to signal x (n) weighting truncationR(n), the discrete frequency near positive frequency point
Compose XR1(k) as shown in Equation 9:
According to Power Quality Monitoring Technology specification, A grades of electric energy quality monitoring terminals, which record every cycle, should at least sample 256
Point, formula 9 can be approximately formula 10:
Measured signal frequency can be slightly offset in practical applications, i.e. k0'=k0+Δk0, formula 10 is substituted into, reality is simulated
The discrete spectrum figure for adding rectangular window FFT, according to spectrogram analysis spectrum leak case.
The present invention is calculated and is analyzed by simple data, in conjunction with the constraint condition of spectral leakage coefficient and spectral line amplitude,
Spectral leakage phenomenon and leak degree of the signal after FFT transform must can be effectively detected, the detection method is simple to operation, is
The correctness of the voltage calculated result of electric energy quality monitoring terminal provides safeguard.
Specific embodiment
The invention will be further described with reference to embodiments.
The detection method of spectral leakage in a kind of electric energy quality monitoring, comprising the following steps:
S1, in the monitoring calculation of power quality terminal, choose any single frequency sinusoidal signal x (t) superposition modulated wave, formed
One source signal；
S2, above-mentioned source signal is exported to electric energy quality monitoring terminal, and record N number of continuous 10 cycle electricity of monitoring terminal
Press measured value URMS(0)…URMS(N), the amplitude A (k) of the kth spectral line of the discrete f (t) of the source signal is obtained, as shown in Equation 1:
In formula, j is imaginary unit, and Fourier transformation is that time domain is converted into complex frequency domain, and the plural number in complex frequency domain is a+jb
Form, j here do not need to do specified otherwise.N=0,1 ..., N.
S3, kth is set0Spectral line is the signal spectrum on the basis of vibration frequency, obtains K0Numerical value；
S4, judge that signal carries out Fourier's change inside electric energy quality monitoring terminal according to the calculated result of formula 2 and formula 3
Spectral leakage situation when changing；
QRMSLabeled as spectral leakage coefficient, value is bigger, indicates that the degree of spectral leakage is bigger；
In formula, UNFor the virtual value of source sinusoidal signal, A1For the amplitude of modulating wave.
Value not within the above range, then judge spectral leakage.
Any single frequency sinusoidal signal x (t) superposition modulated wave, formed virtual value fluctuation source signal, source signal f (t) be
(1±0.05)UNBetween the signal that fluctuates.
N number of continuous 10 cycle voltage measuring value is 100, and source signal is as shown in Equation 4；
In formula, f (t) is in (1 ± 0.05) UNBetween the signal that fluctuates, the frequency of fluctuation signal is 2.3Hz；UNFor source
The virtual value of sinusoidal signal.
The amplitude A (k) of the kth spectral line of signal f (t) is as shown in Equation 5:
If kth0Spectral line is the spectral line of 2.3Hz reference signal, obtains K by formula 60It is 46,
In formula, N=100 indicates the continuous 100 terminal voltage population of measured values recorded, ts=10 × 20ms=0.2s
Indicate the 10 cycle voltage sample times of terminal；
According to the calculated result of formula 1 and formula 2 are as follows:
Spectral leakage is judged according to the above results.
The step of to the sampling and adding window of frequency spectrum are as follows:
Use discrete means with Δ f=f at equal intervalss/ N (corresponding at [0,2 π] with Δ ω=2 π/N at equal intervals) is to continuous frequency
Compose Xc1(f) spectral sampling is carried out, N is sampling number, and discrete series X can be obtainedc1(k) expression formula is as shown in Equation 7,
Window function selects rectangular window, is analyzed by weighting truncation and Fourier transformation；
The spectrum expression formula of selected rectangular window is represented by formula 8:
In formula, N is sampling number.
With rectangular window wR(n) windowing signal x is obtained to signal x (n) weighting truncationR(n), the discrete frequency near positive frequency point
Compose XR1(k) as shown in Equation 9:
In formula, A0For the amplitude of source signal,For the initial phase of source signal, k0Indicate the true spectral line of discrete spectrum.
According to Power Quality Monitoring Technology specification, A grades of electric energy quality monitoring terminals, which record every cycle, should at least sample 256
Point, formula 9 can be approximately formula 10:
Measured signal frequency can be slightly offset in practical applications, i.e. k0'=k0+Δk0, formula 10 is substituted into, reality is simulated
The discrete spectrum figure for adding rectangular window FFT, according to spectrogram analysis spectrum leak case.
Power quality is analyzed with Fourier transformation (FFT), the fft algorithm of practical application need to carry out windowing process to signal.
In the spectrum monitoring of power quality terminal calculates, with sample frequency fsSingle frequency sinusoidal signal x (t) discretization is obtained into sequence x
(n) as shown in Equation 11,
Wherein sample frequency fs=1/Ts, ω0=2 π f0/fs；
In formula, A0For the amplitude of source signal, ω0For discrete sampling frequency,For the initial phase of source signal, TSFor sampling
Period, f0For signal frequency, n is hits.
Truncation processing is done to x (n) by time-domain windowed, is allowed to become finite length sequence xc(n), and to it Fourier is carried out
It is as shown in Equation 12 that transform analysis can obtain frequency spectrum,
By Euler's formulaIt converts, then frequency-domain expression are as follows:
The practical continuous frequency spectrum only considered near positive frequency point, function expression are as follows:
Continuous frequency spectrum is formed, realizes and real-time monitoring is carried out to power quality index.
Finally, it should be noted that although the contents of the present invention have passed through above preferred embodiment and have been discussed in detail,
It cannot be construed as a limitation to the scope of the present invention.For those of ordinary skill in the art, Ke Yili
Solution can also make various deformation, replacement and improvement in the case where not departing from present inventive concept and principle, these belong to this
The protection scope of invention.
Claims (4)
1. the detection method of spectral leakage in a kind of electric energy quality monitoring, which comprises the following steps:
S1, in the monitoring calculation of power quality terminal, choose any single frequency sinusoidal signal x (t) superposition modulated wave, form a source
Signal；
S2, above-mentioned source signal is exported to electric energy quality monitoring terminal, and the N number of continuous 10 weeks wave voltages for recording monitoring terminal are surveyed
Magnitude URMS(0)…URMS(N), the amplitude A (k) of the kth spectral line of the discrete f (t) of the source signal is obtained, as shown in Equation 1:
In formula, j is imaginary unit, and Fourier transformation is that time domain is converted into complex frequency domain, and the plural number in complex frequency domain is the shape of a+jb
Formula, j here do not need to do specified otherwise；N=0,1 ..., N；
S3, kth is set0Spectral line is the signal spectrum on the basis of vibration frequency, obtains K0Numerical value；
S4, when judging that signal carries out Fourier transformation inside electric energy quality monitoring terminal according to the calculated result of formula 2 and formula 3
Spectral leakage situation；
QRMSLabeled as spectral leakage coefficient, value is bigger, indicates that the degree of spectral leakage is bigger；
In formula, UNFor the virtual value of source sinusoidal signal, A1For the amplitude of modulating wave；
Value not within the above range, then judge spectral leakage.
2. the detection method of spectral leakage in electric energy quality monitoring according to claim 1, it is characterised in that: any single-frequency
Sinusoidal signal x (t) superposition modulated wave forms the source signal of virtual value fluctuation, and source signal f (t) is in (1 ± 0.05) UNBetween wave
Dynamic signal.
3. the detection method of spectral leakage in electric energy quality monitoring according to claim 1, it is characterised in that: described N number of
Continuous 10 cycle voltage measuring value is 100, and source signal is as shown in Equation 4；
In formula, f (t) is in (1 ± 0.05) UNBetween the signal that fluctuates, the frequency of fluctuation signal is 2.3Hz；UNFor source sine
The virtual value of signal；
The amplitude A (k) of the kth spectral line of signal f (t) is as shown in Equation 5:
If kth0Spectral line is the spectral line of 2.3Hz reference signal, obtains K by formula 60It is 46,
In formula, N=100 indicates the continuous 100 terminal voltage population of measured values recorded, ts=10 × 20ms=0.2s is indicated
The 10 cycle voltage sample times of terminal；
According to the calculated result of formula 1 and formula 2 are as follows:
Spectral leakage is judged according to the above results.
4. the detection method of spectral leakage in electric energy quality monitoring according to claim 1, which is characterized in that frequency spectrum
The step of sampling and adding window are as follows:
Use discrete means with Δ f=f at equal intervalss/ N is to continuous frequency spectrum Xc1(f) spectral sampling is carried out, N is sampling number, can be obtained
To discrete series Xc1(k) expression formula is as shown in Equation 7；
Window function selects rectangular window, is analyzed by weighting truncation and Fourier transformation；
The spectrum expression formula of selected rectangular window is represented by formula 8:
In formula, N is sampling number；ω is discrete sampling frequency；
With rectangular window wR(n) windowing signal x is obtained to signal x (n) weighting truncationR(n), the discrete spectrum x near positive frequency pointR1
(k) as shown in Equation 9:
In formula, A0For the amplitude of source signal,For the initial phase of source signal, k0Indicate the true spectral line of discrete spectrum；
According to Power Quality Monitoring Technology specification, A grades of electric energy quality monitoring terminals, which record every cycle, should at least sample at 256 points, formula 9
Can be approximately formula 10:
Measured signal frequency can be slightly offset in practical applications, i.e. k0'=k0+Δk0, formula 10 is substituted into, practical plus square is simulated
The discrete spectrum figure of shape window FFT, according to spectrogram analysis spectrum leak case.
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| CN112946374A (en) * | 2021-01-27 | 2021-06-11 | 华北电力大学 | Three-phase unbalance detection method and device based on convolution window function |
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