CN110095650A - The complicated harmonic detecting analysis method of four spectral line interpolation FFTs based on five Rife-Vincent (I) windows - Google Patents
The complicated harmonic detecting analysis method of four spectral line interpolation FFTs based on five Rife-Vincent (I) windows Download PDFInfo
- Publication number
- CN110095650A CN110095650A CN201910369164.4A CN201910369164A CN110095650A CN 110095650 A CN110095650 A CN 110095650A CN 201910369164 A CN201910369164 A CN 201910369164A CN 110095650 A CN110095650 A CN 110095650A
- Authority
- CN
- China
- Prior art keywords
- rife
- vincent
- harmonic
- spectral line
- discrete
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 230000003595 spectral Effects 0.000 title claims abstract description 86
- 238000004458 analytical method Methods 0.000 title claims abstract description 19
- 238000005070 sampling Methods 0.000 claims abstract description 30
- 238000001228 spectrum Methods 0.000 claims abstract description 26
- 238000005259 measurement Methods 0.000 claims description 15
- 230000000875 corresponding Effects 0.000 claims description 3
- 230000001131 transforming Effects 0.000 claims description 3
- 238000001514 detection method Methods 0.000 abstract description 7
- 230000000694 effects Effects 0.000 description 4
- 238000000034 method Methods 0.000 description 2
- 230000002401 inhibitory effect Effects 0.000 description 1
- 238000007689 inspection Methods 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
- 230000001360 synchronised Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
- G01R23/16—Spectrum analysis; Fourier analysis
Abstract
The complicated harmonic detecting analysis method of four spectral line interpolation FFTs based on five Rife-Vincent (I) windows, comprising: discrete sampling is carried out to the signal containing repeatedly complicated harmonic wave, obtains discrete series signal；The discrete series signal obtained to sampling adds five Rife-Vincent (I) windows, obtains adding window discrete series signal；Discrete Fourier transform is carried out to obtained adding window discrete series signal and obtains discrete harmonic signal spectrum value；According to obtained harmonic signal spectrum value, four spectral lines near each harmonic frequency point are found；Four spectral line Spectrum Relationships are established according to four spectral lines near harmonic wave frequency point, obtain the offset of practical spectral line value and theoretical spectral line value, and derive the correction formula of harmonic parameters, and then find out the revised harmonic parameters of four spectral line interpolations.Compared with existing power grid harmonic wave detection method, the method for the present invention better performances, harmonic wave precision has obtained significantly improving.
Description
Technical field
It is specifically a kind of to be based on five Rife- the invention belongs to the multiple complicated harmonic detecting technique field of power grid
The complicated harmonic detecting analysis method of four spectral line interpolation FFTs of Vincent (I) window.
Background technique
Nowadays, power grid is fast-developing, and various novel devices are applied in power grid successively, and especially power electronic equipment is wide
The substantial increase of general application and nonlinear-load so that the voltage and current characteristic of electric system constantly complicates, electric energy it is humorous
Wave pollution is got worse, and can endanger the safety of system.Therefore, the harmonic content accurately in measurement power grid can be the improvement of harmonic wave
Effective scientific basis, the safety of maintenance system are provided.Currently, there is many harmonic analysis methods both at home and abroad, wherein FFT (Fast
Fourier Transform) it is most important method.Because it can be realized in embedded systems and operation efficiency is high.But by
It can occur minor fluctuations in real power network signal frequency, signal is not always smoothly, so strictly to synchronize to signal
Sampling is difficult to realize.Under non-synchronous sampling, FFT will appear spectrum leakage and fence effect, this has severely impacted humorous
The accuracy of wave testing result.
Adding window can reduce spectrum leakage, and interpolation can eliminate error caused by fence effect, so window function and interpolation algorithm
The interference of the interference and clutter between harmonic wave can effectively be inhibited, application is wide.Common window function has quarter window, rectangle
Window, Hanning window, Blackman window, Nuttall window, rectangle convolution window and Rife-Vincent window etc..But these window functions exist
Precision when detecting repeatedly complicated harmonic signal is not high.Interpolation algorithm has singlet interpolation algorithm, double spectral line interpolation algorithm and three
Spectral line interpolation algorithm.
Patent document (CN 105353215) proposes a kind of harmonic detecting based on four spectral line interpolation FFT of Nuttall window
Method can not inhibit well spectrum leakage to give harmonic measure bring since the side lobe attenuation rate of Nuttall window is smaller
Interference, so to repeatedly the measurement accuracy of complexity harmonic wave need to be improved in power grid.And the patent only to odd times harmonic into
It has gone measurement, has not measured even harmonics, while the magnitude parameters of harmonic signal are larger, algorithm cannot be embodied to weak amplitude
The measurement accuracy of parameter.
Summary of the invention
To solve the above problems, the present invention provides a kind of four spectral line interpolation FFTs for being based on five Rife-Vincent (I) windows
Complicated harmonic detecting analysis method, compared with existing power grid harmonic wave detection method, this method have excellent performance, it is humorous
Wave detection accuracy is effectively improved.
The technical scheme adopted by the invention is as follows:
The complicated harmonic detecting analysis method of four spectral line interpolation FFTs based on five Rife-Vincent (I) windows, including with
Lower step:
Step 1: discrete sampling being carried out to the signal containing repeatedly complicated harmonic wave, obtains discrete series signal；
Step 2: five Rife-Vincent (I) windows are added to the obtained discrete series signal of step 1 sampling, obtain adding window from
Dissipate sequence signal；
Step 3: the adding window discrete series signal obtained to step 2 carries out discrete Fourier transform, obtains discrete harmonic wave
Signal spectrum value.
Step 4: the discrete harmonic signal spectrum value obtained to step 3 finds four spectrums near each harmonic frequency point
Line；
Step 5: four spectral lines near the frequency point obtained to step 4 establish four spectral line spectrum value relationships, pass through four spectral lines
Spectrum Relationship obtains the departure of spectral line value Yu theoretical spectrum value, and derives the correction formula of harmonic parameters, and then find out four
The revised harmonic parameters of spectral line interpolation.
In the step 1, repeatedly complexity harmonic signal isDiscrete sampling obtain from
Scattered sequence signal is
Wherein, h is overtone order, and H is the number of highest subharmonic, and n=0,1,2 ... N-1 are sampling number, fsIt is to adopt
Sample frequency, Ah、fhWithThe respectively amplitude, frequency and phase of h subharmonic.
In the step 2, the adding window discrete series signal obtained after adding window is xw(n)=x (n) w (n).
Wherein, w (n) is five Rife-Vincent (I) windows, and the time-domain expression of five Rife-Vincent (I) windows is
Wherein, m is the item number of window function, amFor the coefficient of window function, n=1,2 ... N-1；N is sampling number.
In the step 2, the window function coefficient a of five Rife-Vincent (I) windowsmThe condition of satisfaction has: 1.:2.: a0=1, a1=1.6, a2=0.8, a3=0.22857, a4=0.02857.
In the step 3, the specific steps of discrete Fourier transform are as follows:
Step 3-1: to the discrete series signal x after adding windoww(n) it carries out Fourier transformation and acquires discrete frequency domain function.
Step 3-2: ignore the influence of negative frequency point peak value, there is shown discrete frequency domain function.
In the step 4, according to obtained harmonic signal value | X (k) |, find the frequency point k of h subharmonichNeighbouring four
Spectral line kh1、kh2、kh3And kh4, the amplitude of this four spectral lines is respectively as follows: y2=| X (kh2)|、y1=| X (kh1)|、y3=| X (kh3)
| and y4=| X (kh4) |, the positional relationship of this four spectral lines left-to-right is successively: k from makingh1、kh2、kh3、kh4, size relation are as follows:
kh1=kh2- 1, kh2=kh3- 1, kh3=kh4-1。
The step 5 the following steps are included:
Step 5-1: offset β=k of document border spectral line value and theoretical valueh-kh2The range of -0.5, β are [- 0.5,0.5].
The relational expression α for establishing four spectral lines solves offset β, if α=(y3+y4-y1-y2)/(y3+y4+y1+y2), then it obtains:
Above formula, regards α as the function of β, that is, has α=γ (β), and inverse function is β=γ-1(α), offset β is according to anti-
Function solves.
Step 5-2: to find out offset β, using obtaining β=γ after polyfit Function Fitting-1(α's) is approximant are as follows:
β≈d1α+d3α3+…+d2r+1α2r+1(5)；
Wherein, d1、d3、…d2r+1The odd times term coefficient of respectively 2r+1 times approximating polynomial.Because of β ∈ [- 0.5,0.5],
It takes several groups of β, α and function polyfit (α, β, 7) is called to carry out anti-fitting, wherein 7 represent fitting number, to meet fitting precision
Demand, fitting number cannot be very few.The γ found out-1The coefficient of (α) is as follows:
The α of β=0.1990997+0.302882α5+0.612560α3+2.475000α (6)；
Therefore the frequency of h subharmonic, phase formula can be corrected are as follows:
The frequency and phase parameter of h subharmonic can be calculated using formula (7), (8).
The amplitude of step 5-3:h subharmonic is calculated by the average weighted of four spectral lines near peak point, due to
The spectral line k of inside twoh2、kh3Closer to kh, give kh2、kh3Bigger weight, the h times amplitude estimation formula is as follows:
When n is large, above formula can be expressed as Ah=N-1(y1+3y2+3y3+y4) μ (β), wherein μ (β) are as follows:
The approximate formula ρ (β) that μ (β) is found out using fitting of a polynomial, then had:
Ah≈N-1(y1+3y2+3y3+y4)ρ(β) (11)
Number of the β in [- 0.5,0.5] is taken, is substituted into formula (10), corresponding μ (β) value is acquired, calls polyfit (β, μ
(β), 7) function, find out the coefficient of ρ (β):
ρ (β)=0.000268 β6+0.004239β4+0.048335β2+0.290677 (12)
The magnitude parameters of h subharmonic can be calculated using formula (11), (12).
The time-domain function expression formula of five Rife-Vincent (I) window are as follows:
W (n)=1-1.6cos (2 π n/N)+0.8cos (4 π n/N) -0.22857xos (6 π n/N)+0.02857cos (8 π n/
N) window has a preferable side lobe performance, side lobe peak level be compared with three, four Rife-Vincent windows it is the smallest,
For -74.5dB.
The present invention is a kind of complicated harmonic detecting point of four spectral line interpolation FFTs based on five Rife-Vincent (I) windows
Analysis method, technical effect are as follows:
1), the window has preferable side lobe performance, and side lobe peak level is compared with three, four Rife-Vincent windows
It is the smallest, is -74.5dB, the influence of each harmonic interference bring spectrum leakage can be inhibited well.
2), four spectral line interpolations algorithm proposed by the present invention calculates simple and precision height, is mentioned using iunction for curve fitting
The high speed calculated.It is weighted using with four spectral lines similar in harmonic wave frequency point, preferably fence can be inhibited to imitate
The influence for coping with harmonic measure precision, improves the accuracy of harmonic measure.
3) a kind of, the complicated harmonic wave of four spectral line interpolation FFTs based on five Rife-Vincent (I) windows proposed by the present invention
Determination method carries out the experimental result of 21 subharmonic detections are as follows: the amplitude measurement relative error order of magnitude is 10-5%~10-8%, the phase measurement relative error order of magnitude are 10-3%~10-7%, amplitude and phase measurement accuracy are relatively high.
5), five Rife-Vincent (I) window proposed by the present invention is a kind of preferable window of window function characteristic, secondary lobe peak
Value level be in three, four and five Rife-Vincent windows it is the smallest, reach -74.5dB, can inhibit well
The influence of each harmonic interference bring spectrum leakage.Simultaneously using the correction of four spectral line interpolations to the amplitude, frequency, phase of harmonic wave
It is modified, obtains more accurate parameter, improve mains by harmonics measurement accuracy.
4), five Rife-Vincent (I) windows have the smallest side compared with three, four Rife-Vincent windows
Valve peak level is -74.5dB, and side lobe attenuation rate is most fast, is 30dB/oct, has preferable side lobe performance, to reach
Inhibit influence of the spectrum leakage to Harmonic Detection precision.
Detailed description of the invention
Fig. 1 is flow chart of the invention.
Fig. 2 (a) is the amplitude relative error comparison of five three spectral lines of Rife-Vincent (I) window, four spectral line interpolation results
Figure.
Fig. 2 (b) is the phase relative error comparison of five three spectral lines of Rife-Vincent (I) window, four spectral line interpolation results
Figure.
Specific embodiment
The present invention relates to a kind of complicated harmonic detectings of four spectral line interpolation FFTs based on five Rife-Vincent (I) windows
Analysis method, as shown in Figure 1, the present invention mainly includes following 5 steps:
(1): discrete sampling being carried out to the signal containing repeatedly complicated harmonic wave, then obtains discrete series signal.
(2): the discrete series signal obtained to step 1 sampling adds five Rife-Vincent (I) windows, and it is discrete to obtain adding window
Sequence signal.
(3): the adding window discrete series signal obtained to step 2 carries out discrete Fourier transform and obtains discrete harmonic wave letter
Number spectrum value.
(4): the harmonic signal spectrum value obtained to step 3 finds four spectral lines near each harmonic peak point.
(5): four spectral lines near the peak point obtained to step 4 establish four spectral line spectrum value relationships, pass through four spectral lines
Spectrum Relationship obtains the departure of spectral line value Yu theoretical spectrum value, and derives the correction formula of harmonic parameters, and then find out four
The revised harmonic parameters of spectral line interpolation.
In step 1, repeatedly complexity harmonic signal isThe discrete sequence that discrete sampling obtains
Column signal is
Wherein, h is overtone order, and H is the number of highest subharmonic, and n=0,1,2 ... N-1 are sampling number, fsIt is to adopt
Sample frequency, Ah、fhWithThe respectively amplitude, frequency and phase of h subharmonic.
In the step 2, the discrete series signal obtained after adding window is xw(n)=x (n) w (n).Wherein, w (n) is five Rife-
Vincent (I) window.The time-domain expression of five Rife-Vincent (I) windows is
Wherein, m is the item number of window function, amFor the coefficient of window function, n=1,2 ... N-1；N is sampling number.
In the step 2, the coefficient a of five Rife-Vincent (I) windowsmThe condition that must satisfy has: 1.:②a0=1, a1=1.6, a ,=0.8, a3=0.22857, a4=0.02857.
In step 2, five Rife-Vincent (I) windows have minimum compared with three, four Rife-Vincent windows
Side lobe peak level, be -74.5dB, side lobe attenuation rate is most fast, be 30dB/oct, have preferable side lobe performance, thus
Reach the influence for inhibiting spectrum leakage to Harmonic Detection precision.
In step 3, the specific steps of discrete Fourier transform are as follows:
Step 3-1: to the discrete series signal x after adding windoww(n) it carries out Fourier transformation and acquires discrete frequency domain function are as follows:
Wherein, k=0,1 ..., N-1, Δ f=fs/ N is discrete sampling interval, and k is the serial number of sampling frequency point, Ah、fhWithRespectively the amplitude, frequency and phase of h subharmonic, N are sampling number.
It is h subharmonic phaseComplex expression, W is discrete Fourier transform formula, fsIt is sample frequency.
In view of N >=1, the discrete Fourier transform of window function can be with approximate representation are as follows:
Wherein, W (k) is the discrete Fourier transform formula of window function, and N is sampling number, and k is the serial number of sampling frequency point, e-jπkFor the complex expression of phase angle π k,For phase angleComplex expression, m be window function item number, amFor window function
Coefficient.
The amplitude of window function are as follows:
Wherein, | W (k) | it is the amplitude of window function, N is sampling number, and k is the serial number of sampling frequency point, and m is the item of window function
Number, amFor the coefficient of window function.
Step 3-2: ignoring the influence of negative frequency point peak value, and discrete frequency domain function can indicate are as follows:
Wherein, k=0,1 ..., N-1, the spectral line expression formula of h subharmonic is in discrete frequency domain function
The specific steps of step 4 are as follows: the harmonic signal value obtained according to step 3-2 | X (k) |, find the frequency of h subharmonic
Point khFour neighbouring spectral line kh1、kh2、kh3And kh4, the amplitude of this four spectral lines is respectively as follows: y2=| X (kh2)|、y1=| X (kh1)
|、y3=| X (kh3) | and y4=| X (kh4)|.The positional relationship of this four spectral lines, from making left-to-right to be successively kh1、kh2、kh3、kh4,
Size relation is kh1=kh2- 1, kh2=kh3- 1, kh3=kh4-1。
The specific steps of step 5 are as follows:
Step 5-1: offset β=k of document border spectral line value and theoretical valueh-kh2The range of -0.5, β are [- 0.5,0.5].
The relational expression α for establishing four spectral lines solves offset β, if α=(y3+y4-y1-y2)/(y3+y4+y1+y2), then it can be obtained
Above formula, regards α as the function of β, that is, has α=γ (β), and inverse function is β=γ-1(α), offset β is according to anti-
Function solves.
Step 5-2: to find out offset β, using obtaining β=γ after polyfit Function Fitting-1(α's) is approximant are as follows:
β≈d1α+d3α3+…+d2r+1α2r+1 (5)
Wherein, d1、d3、…d2r+1The odd times term coefficient of respectively 2r+1 times approximating polynomial.Because of β ∈ [- 0.5,0.5],
It takes several groups of β, α and function polyfit (α, β, 7) is called to carry out anti-fitting, wherein 7 represent fitting number, to meet fitting precision
Demand, fitting number cannot be very few.The γ found out-1The coefficient of (α) is as follows:
The α of β=0.1990997+0.302882α5+0.612560α3+2.475000α (6)
Therefore the frequency of h subharmonic, phase formula can be corrected are as follows:
Wherein, fh、The respectively frequency and phase of h subharmonic, kh2For the frequency point k of h subharmonichThe second of the left side
Spectral line, β are the offset of practical spectral line value and theoretical spectrum value, fsFor sample frequency, N is sampling number, X (kh2) it is h
Subharmonic frequency point khCorresponding windowing signal spectral magnitude, X (β) are by magnitude shift amount.
The frequency and phase parameter of h subharmonic can be calculated using formula (7), (8).
The amplitude of step 5-3:h subharmonic is calculated by the average weighted of four spectral lines near peak point, due to
The spectral line k of inside twoh2、kh3Closer to kh, give kh2、kh3Bigger weight, the h times amplitude estimation formula is as follows:
When n is large, above formula can be expressed as Ah=N-1(y1+3y2+3y3+y4) μ (β), wherein μ (β) are as follows:
The approximate formula ρ (β) that μ (β) is found out using fitting of a polynomial, then had:
Ah≈N-1(y1+3y2+3y3+y4)ρ(β) (11)
Wherein, AhFor the amplitude of h subharmonic, y1、y2、y3、y4The respectively frequency point k of h subharmonichFour neighbouring spectrums
Line kh1、kh2、kh3、kh4Corresponding windowing signal spectral magnitude.ρ (β) is amplitude correction coefficient, and N is sampling number.
Number of the β in [- 0.5,0.5] is taken, is substituted into formula (10), corresponding μ (β) value is acquired, calls polyfit (β, μ
(β), 7) function, find out the coefficient of ρ (β):
ρ (β)=0.000268 β6+0.004239β4+0.048335β2+0.290677 (12)
The magnitude parameters of h subharmonic can be calculated using formula (11), (12).
The verifying example that the present invention is arranged is as follows:
The setting of the harmonic signal of complexity containing high order: this verifying example uses the signal containing 21 complicated harmonic waves, table
It is up to formulaWherein fundamental frequency is 50.10Hz, sample frequency fs=5012Hz, is adopted
Number of samples N=1024, the parameter of harmonic signal such as the following table 1.
The model parameter table of 1 harmonic signal of table
Four spectral line interpolation algorithms of five Rife-Vincent (I) windows of the invention and three spectral line interpolation algorithms are carried out pair
Than amplitude error and the phase error such as following figure compared:
Fig. 2 (a) is amplitude relative error, Fig. 2 (b) is phase relative error.The phase it can be seen from Fig. 2 (a), Fig. 2 (b)
The precision of same window function, the three spectral line interpolation algorithm of ratio of precision of four spectral line interpolation algorithms is high, i.e., composes with two near peak value
The neighbouring spectral line of line also contains important information related with harmonic wave, can provide effective information for parameter correction.
For the accuracy for verifying this paper algorithm, Hanning window, four Nuttall windows, four are added to sophisticated signal
Rife-Vincent (I) window, these window functions are higher using most and precision in harmonic detecting.By these window functions and this paper
After five Rife-Vincent (I) windows processing chosen, discrete spectrum is obtained by FFT transform, four spectral lines is finally carried out and inserts
Value correction obtains each harmonic signal parameter, compares and analyzes to final result.
Simulation result such as the following table 2, table 3, E thereinAh、Respectively the opposite of the amplitude and phase of h subharmonic is missed
Difference, error are with respect to for actual parameter.
2 each harmonic amplitude relative error table E of tableAh/ %
3 each harmonic phase relative error table of table
Algorithm by this paper it can be seen from table 2, table 3 is in detecting 21 subharmonic, amplitude relative error EAh≤6.52434
×10-5%, phase relative errorCompared to Hanning window, Nuttall window and four RV (I)
Window, the measurement accuracy using five RV (I) windows are higher.In such as phase parameter measurement result of the 17th subharmonic, Hanning window,
The error of Nuttall window and four RV (I) windows is larger, and respectively 3.19496 × 10-3%, 2.39468 × 10-5% and
4.18018×10-6%, and the measurement error of five RV (I) windows is 7.18028 × 10-7%.Although four RV (I) windows the 7th,
The precision of five RV (I) windows of amplitude relative error ratio of precision in the detection of 15 and 19 subharmonic is slightly higher, but other secondary amplitudes are opposite
The precision of than five RV (I) windows of error is low, and the phase relative error precision of four RV (I) windows nearly all than five RV
(I) precision of window is low.Therefore, precision of five RV (I) window proposed by the present invention in the detection of higher hamonic wave parameter is higher, real
The high accuracy analysis of complicated harmonic signal parameter is showed.
The comparison of 4 Riming time of algorithm of table
Table 4 gives the runing time of the algorithms of different under identical experiment environment, and as can be seen from Table 4, four spectral lines are inserted
Long operational time of the runing time of value-based algorithm than three spectral line interpolation algorithms.Different window functions, the fortune of four spectral line interpolation algorithms
Difference very little between the row time, five RV (I) windows have large increase to harmonic measure precision, it is to the precision of harmonic detecting
Raising effect is to be worth affirmative, and the influence of runing time bring can be ignored.
A kind of complicated harmonic wave inspection of four spectral line interpolation FFTs based on five Rife-Vincent (I) windows proposed by the present invention
Survey analysis method, the time-domain expression of five Rife-Vincent (I) window function therein are as follows:
W (n)=1-1.6cos (2 π n/N)+0.8cos (4 π n/N) -0.22857cos (6 π n/N)+0.02857cos (8 π n/
N) wherein, w (n) is the time-domain expression of five Rife-Vincent (I) windows, and N is sampling number.
The window has preferable side lobe performance, and side lobe peak level is compared with three, four Rife-Vincent windows
It is the smallest, it is -74.5dB.The result that the experiment containing 21 complicated harmonic detecting signals carried out obtains are as follows: amplitude measurement is opposite
Margin of error magnitude is 10-5%~10-8%, the phase measurement relative error order of magnitude are 10-3%~10-7%, amplitude and phase measurement
Precision has a distinct increment.
Claims (9)
1. the complicated harmonic detecting analysis method of four spectral line interpolation FFTs based on five Rife-Vincent (I) windows, feature exist
In the following steps are included:
Step 1: discrete sampling being carried out to the signal containing repeatedly complicated harmonic wave, obtains discrete series signal；
Step 2: the discrete series signal obtained to step 1 sampling adds five Rife-Vincent (I) windows, obtains the discrete sequence of adding window
Column signal；
Step 3: the adding window discrete series signal obtained to step 2 carries out discrete Fourier transform, obtains discrete harmonic signal
Spectrum value；
Step 4: the discrete harmonic signal spectrum value obtained to step 3 finds four spectral lines near each harmonic frequency point；
Step 5: four spectral lines near the frequency point obtained to step 4 establish four spectral line spectrum value relationships, pass through four spectral line frequency spectrums
Relationship obtains the departure of spectral line value Yu theoretical spectrum value, and derives the correction formula of harmonic parameters, and then finds out four spectral lines
The revised harmonic parameters of interpolation.
2. the complicated harmonic detecting of four spectral line interpolation FFTs based on five Rife-Vincent (I) windows according to claim 1
Analysis method, it is characterised in that: in the step 1, repeatedly complexity harmonic signal isIt is discrete
Sampling obtained discrete series signal is
Wherein, h is overtone order, and H is the number of highest subharmonic, and n=0,1,2 ... N-1 are sampling number, fsIt is sampling frequency
Rate, Ah、fhWithThe respectively amplitude, frequency and phase of h subharmonic.
3. the complicated harmonic detecting of four spectral line interpolation FFTs based on five Rife-Vincent (I) windows according to claim 1
Analysis method, it is characterised in that: in the step 2, the adding window discrete series signal obtained after adding window is xw(n)=x (n) w
(n)；Wherein, w (n) is five Rife-Vincent (I) windows, and the time-domain expression of five Rife-Vincent (I) windows is
Wherein, m is the item number of window function, amFor the coefficient of window function, n=1,2 ... N-1；N is sampling number.
4. the complicated harmonic detecting of four spectral line interpolation FFTs based on five Rife-Vincent (I) windows according to claim 3
Analysis method, it is characterised in that: in the step 2, the window function coefficient a of five Rife-Vincent (I) windowsmThe condition of satisfaction
Have:
1.:2.: a0=1, a1=1.6, a2=0.8, a3=0.22857, a4=0.02857.
5. the complicated harmonic detecting of four spectral line interpolation FFTs based on five Rife-Vincent (I) windows according to claim 1
Analysis method, it is characterised in that: in the step 3, the specific steps of discrete Fourier transform are as follows:
Step 3-1: to the discrete series signal x after adding windoww(n) it carries out Fourier transformation and acquires discrete frequency domain function；
Step 3-2: ignore the influence of negative frequency point peak value, there is shown discrete frequency domain function.
6. the complicated harmonic detecting of four spectral line interpolation FFTs based on five Rife-Vincent (I) windows according to claim 1
Analysis method, it is characterised in that: in the step 4, according to obtained harmonic signal value | X (k) |, find the frequency of h subharmonic
Point khFour neighbouring spectral line kh1、kh2、kh3And kh4, the amplitude of this four spectral lines is respectively as follows: y2=| X (kh2)|、y1=| X (kh1)
|、y3=| X (kh3) | and y4=| X (kh4) |, the positional relationship of this four spectral lines left-to-right is successively: k from makingh1、kh2、kh3、
kh4, size relation are as follows: kh1=kh2- 1, kh2=kh3- 1, kh3=kh4-1。
7. the complicated harmonic detecting of four spectral line interpolation FFTs based on five Rife-Vincent (I) windows according to claim 1
Analysis method, it is characterised in that: the step 5 the following steps are included:
Step 5-1: offset β=k of document border spectral line value and theoretical valueh-kh2The range of -0.5, β are [- 0.5,0.5]；It establishes
The relational expression α of four spectral lines solves offset β, if α=(y3+y4-y1-y2)/(y3+y4+y1+y2), then it obtains:
Above formula, regards α as the function of β, that is, has α=γ (β), and inverse function is β=γ-1(α), offset β is according to inverse function
It solves；
Step 5-2: to find out offset β, using obtaining β=γ after polyfit Function Fitting-1(α's) is approximant are as follows:
β≈d1α+d3α3+…+d2r+1α2r+1(5)；
Wherein, d1、d3、…d2r+1The odd times term coefficient of respectively 2r+1 times approximating polynomial；Because β ∈ [- 0.5,0.5], takes several
Group β, α simultaneously calls function polyfit (α, β, 7) to carry out anti-fitting, wherein 7 represent fitting number, for the need for meeting fitting precision
It asks, fitting number cannot be very few；The γ found out-1The coefficient of (α) is as follows:
The α of β=0.1990997+0.302882α5+0.612560α3+2.475000α (6)；
Therefore the frequency of h subharmonic, phase formula can be corrected are as follows:
The frequency and phase parameter of h subharmonic can be calculated using formula (7), (8)；
The amplitude of step 5-3:h subharmonic is calculated by the average weighted of four spectral lines near peak point, due to inside
Two spectral line kh2、kh3Closer to kh, give kh2、kh3Bigger weight, the h times amplitude estimation formula is as follows:
When n is large, above formula can be expressed as Ah=N-1(y1+3y2+3y3+y4) μ (β), wherein μ (β) are as follows:
The approximate formula ρ (β) that μ (β) is found out using fitting of a polynomial, then had:
Ah≈N-1(y1+3y2+3y3+y4)ρ(β) (11)
Number of the β in [- 0.5,0.5] is taken, is substituted into formula (10), corresponding μ (β) value is acquired, is called polyfit (β, μ (β), 7)
Function finds out the coefficient of ρ (β):
ρ (β)=0.000268 β6+0.004239β4+0.048335β2+0.290677 (12)
The magnitude parameters of h subharmonic can be calculated using formula (11), (12).
8. the complicated harmonic detecting of four spectral line interpolation FFTs based on five Rife-Vincent (I) windows according to claim 1
Analysis method, it is characterised in that: the time-domain function expression formula of five Rife-Vincent (I) window are as follows:
W (n)=1-1.6cos (2 π n/N)+0.8cos (4 π n/N) -0.22857cos (6 π n/N)+0.02857cos (8 π n/N) should
Window has a preferable side lobe performance, side lobe peak level with three, four Rife-Vincent windows compared to be it is the smallest, be-
74.5dB。
9. application of five Rife-Vincent (I) windows in mains by harmonics measurement.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910369164.4A CN110095650A (en) | 2019-05-05 | 2019-05-05 | The complicated harmonic detecting analysis method of four spectral line interpolation FFTs based on five Rife-Vincent (I) windows |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910369164.4A CN110095650A (en) | 2019-05-05 | 2019-05-05 | The complicated harmonic detecting analysis method of four spectral line interpolation FFTs based on five Rife-Vincent (I) windows |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN110095650A true CN110095650A (en) | 2019-08-06 |
Family
ID=67446915
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910369164.4A Pending CN110095650A (en) | 2019-05-05 | 2019-05-05 | The complicated harmonic detecting analysis method of four spectral line interpolation FFTs based on five Rife-Vincent (I) windows |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110095650A (en) |
Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110598269A (en) * | 2019-08-21 | 2019-12-20 | 南京理工大学 | Discrete spectrum parameter correction method in low sampling point |
| CN111025015A (en) * | 2019-12-30 | 2020-04-17 | 广东电网有限责任公司 | Harmonic detection method, device, equipment and storage medium |
| CN111177823A (en) * | 2019-12-10 | 2020-05-19 | 南京理工大学 | Cavity expansion theoretical calculation method suitable for brick masonry penetration |
| CN111984920A (en) * | 2020-08-31 | 2020-11-24 | 广东电网有限责任公司广州供电局 | Subsynchronous/supersynchronous harmonic parameter identification method, subsynchronous/supersynchronous harmonic parameter identification device, subsynchronous/supersynchronous harmonic parameter identification equipment and medium |
| CN111999635A (en) * | 2020-08-23 | 2020-11-27 | 国网山东省电力公司莱芜供电公司 | Board card fault signal analysis method and terminal based on 4-item 5-order Nuttall window |
| CN113189398A (en) * | 2021-04-29 | 2021-07-30 | 云南电网有限责任公司电力科学研究院 | High-order harmonic analysis method and device for zero-point frequency domain windowing |
| CN113899444A (en) * | 2021-10-08 | 2022-01-07 | 招商局重庆交通科研设计院有限公司 | Resonance frequency measurement method of vibrating wire sensor based on Hanning double windows |
Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US3932737A (en) * | 1972-11-07 | 1976-01-13 | Thomson-Csf | Spectrum analyzer establishing a nonlinear frequency distribution of power-density spectra |
| JP2003085157A (en) * | 2001-09-10 | 2003-03-20 | Omron Corp | Frequency analyzer by applying fft algorithm and abnormality determining device and abnormality determining system |
| CN101261292A (en) * | 2008-04-14 | 2008-09-10 | 湖南大学 | Base wave and harmonic detection method based on fiver item Rife-Vincent(1)window double spectral line interpolation FFT |
| CN101334431A (en) * | 2007-12-20 | 2008-12-31 | 复旦大学 | Electric network harmonic frequency spectrum interpolation correction analytical method |
| CN103399204A (en) * | 2013-07-31 | 2013-11-20 | 武汉大学 | Rife-Vincent (II) window interpolation FFT (Fast Fourier Transform)-based harmonic and inter-harmonic detection method |
| CN104897960A (en) * | 2015-06-15 | 2015-09-09 | 中南民族大学 | Harmonic rapid analysis method and system based on windowing four-spectral-line interpolation FFT |
| CN105137180A (en) * | 2015-08-24 | 2015-12-09 | 三峡大学 | High precision harmonic wave analysis method based on six item cosine window four spectral line interpolation |
| CN106526312A (en) * | 2016-10-10 | 2017-03-22 | 清华大学 | Electric energy metering method based on R-V(III) window FFT double-peak interpolation |
| CN107179439A (en) * | 2017-06-26 | 2017-09-19 | 贵州电网有限责任公司贵阳供电局 | Electric energy gauging method based on five peak interpolations of Cosine Window FFT tri- |
-
2019
- 2019-05-05 CN CN201910369164.4A patent/CN110095650A/en active Pending
Patent Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US3932737A (en) * | 1972-11-07 | 1976-01-13 | Thomson-Csf | Spectrum analyzer establishing a nonlinear frequency distribution of power-density spectra |
| JP2003085157A (en) * | 2001-09-10 | 2003-03-20 | Omron Corp | Frequency analyzer by applying fft algorithm and abnormality determining device and abnormality determining system |
| CN101334431A (en) * | 2007-12-20 | 2008-12-31 | 复旦大学 | Electric network harmonic frequency spectrum interpolation correction analytical method |
| CN101261292A (en) * | 2008-04-14 | 2008-09-10 | 湖南大学 | Base wave and harmonic detection method based on fiver item Rife-Vincent(1)window double spectral line interpolation FFT |
| CN103399204A (en) * | 2013-07-31 | 2013-11-20 | 武汉大学 | Rife-Vincent (II) window interpolation FFT (Fast Fourier Transform)-based harmonic and inter-harmonic detection method |
| CN104897960A (en) * | 2015-06-15 | 2015-09-09 | 中南民族大学 | Harmonic rapid analysis method and system based on windowing four-spectral-line interpolation FFT |
| CN105137180A (en) * | 2015-08-24 | 2015-12-09 | 三峡大学 | High precision harmonic wave analysis method based on six item cosine window four spectral line interpolation |
| CN106526312A (en) * | 2016-10-10 | 2017-03-22 | 清华大学 | Electric energy metering method based on R-V(III) window FFT double-peak interpolation |
| CN107179439A (en) * | 2017-06-26 | 2017-09-19 | 贵州电网有限责任公司贵阳供电局 | Electric energy gauging method based on five peak interpolations of Cosine Window FFT tri- |
Non-Patent Citations (3)
| Title |
|---|
| 徐艳春 等: "基于六项余弦窗四谱线插值FFT的高精度谐波检测算法", 《电力系统保护与控制》 * |
| 曾博 等: "基于Rife-Vincent窗的高准确度电力谐波相量计算方法", 《电工技术学报》 * |
| 朱俊伟 等: "基于五项莱夫-文森特窗的三谱线插值FFT谐波分析", 《电气技术》 * |
Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110598269A (en) * | 2019-08-21 | 2019-12-20 | 南京理工大学 | Discrete spectrum parameter correction method in low sampling point |
| CN110598269B (en) * | 2019-08-21 | 2022-11-18 | 南京理工大学 | Discrete spectrum parameter correction method in low sampling point |
| CN111177823A (en) * | 2019-12-10 | 2020-05-19 | 南京理工大学 | Cavity expansion theoretical calculation method suitable for brick masonry penetration |
| CN111177823B (en) * | 2019-12-10 | 2022-09-27 | 南京理工大学 | Cavity expansion theoretical calculation method suitable for brick masonry penetration |
| CN111025015A (en) * | 2019-12-30 | 2020-04-17 | 广东电网有限责任公司 | Harmonic detection method, device, equipment and storage medium |
| CN111999635A (en) * | 2020-08-23 | 2020-11-27 | 国网山东省电力公司莱芜供电公司 | Board card fault signal analysis method and terminal based on 4-item 5-order Nuttall window |
| CN111984920A (en) * | 2020-08-31 | 2020-11-24 | 广东电网有限责任公司广州供电局 | Subsynchronous/supersynchronous harmonic parameter identification method, subsynchronous/supersynchronous harmonic parameter identification device, subsynchronous/supersynchronous harmonic parameter identification equipment and medium |
| CN113189398A (en) * | 2021-04-29 | 2021-07-30 | 云南电网有限责任公司电力科学研究院 | High-order harmonic analysis method and device for zero-point frequency domain windowing |
| CN113899444A (en) * | 2021-10-08 | 2022-01-07 | 招商局重庆交通科研设计院有限公司 | Resonance frequency measurement method of vibrating wire sensor based on Hanning double windows |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110095650A (en) | The complicated harmonic detecting analysis method of four spectral line interpolation FFTs based on five Rife-Vincent (I) windows | |
| CN102435844B (en) | Sinusoidal signal phasor calculating method being independent of frequency | |
| CN102288807B (en) | Method for measuring electric network voltage flicker | |
| CN101701984B (en) | Fundamental wave and harmonic wave detecting method based on three-coefficient Nuttall windowed interpolation FFT | |
| CN109030941A (en) | Tri- spectral line interpolation harmonic analysis method of Hanning involution convolution window FFT | |
| CN106483374A (en) | A kind of harmonic wave harmonic detection method based on Nuttall double window whole phase FFT | |
| CN103308804A (en) | Method for extracting time-frequency parameters of power quality disturbance signals on basis of fast K-S (Kaiser-S) transformation | |
| CN101701982A (en) | Method for detecting harmonic waves of electric system based on window and interpolated FFT | |
| CN109782063A (en) | A kind of dynamic m-Acetyl chlorophosphonazo analysis method based on three spectral line interpolation FFT of Nuttall self-convolution window | |
| CN108535613A (en) | A kind of voltage flicker parameter detection method based on combination window function | |
| CN107643446B (en) | A kind of multiline interpolation harmonic analysis method and system based on main lobe width | |
| CN105137181A (en) | Double-spectrum-line interpolation harmonic analysis algorithm based on Nuttall-Kaiser composite window | |
| CN104714075A (en) | Method for extracting power grid voltage flicker envelope parameters | |
| CN106771591B (en) | A kind of method for parameter estimation of Complex Power harmonic wave | |
| CN103575984A (en) | Harmonic analysis method based on Kaiser window double-spectral-line interpolation FFT | |
| CN105353215A (en) | Harmonic detection method based on Nuttall window four-spectral-line interpolation FFT (fast Fourier transform) | |
| CN105137180A (en) | High precision harmonic wave analysis method based on six item cosine window four spectral line interpolation | |
| CN109490627A (en) | Novel electric power system harmonics analysis method based on mixing convolution window | |
| CN103941090A (en) | Harmonic wave measurement method based on spectral energy interpolation | |
| CN102998528B (en) | Method for extracting frequency components in dynamic distorted sinusoidal signals and device for implementing method | |
| CN109655665A (en) | All phase Fourier's harmonic analysis method based on Blackman window | |
| CN109541312A (en) | A kind of new energy collects the subsynchronous harmonic detecting method in area | |
| CN105866543A (en) | Interharmonic detection method for eliminating interference caused by fundamental waves and harmonic waves to interharmonic detection | |
| CN103543331B (en) | A kind of method calculating electric signal harmonic wave and m-Acetyl chlorophosphonazo | |
| CN110221116A (en) | Voltage flicker envelope detection method based on windowed interpolation and parsing Mode Decomposition |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| RJ01 | Rejection of invention patent application after publication | ||
| RJ01 | Rejection of invention patent application after publication |
Application publication date: 20190806 |