CN110095650A  The complicated harmonic detecting analysis method of four spectral line interpolation FFTs based on five RifeVincent (I) windows  Google Patents
The complicated harmonic detecting analysis method of four spectral line interpolation FFTs based on five RifeVincent (I) windows Download PDFInfo
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 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
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Abstract
The complicated harmonic detecting analysis method of four spectral line interpolation FFTs based on five RifeVincent (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 RifeVincent (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 fastdeveloping, and various novel devices are applied in power grid successively, and especially power electronic equipment is wide
The substantial increase of general application and nonlinearload 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 nonsynchronous 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 RifeVincent 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 RifeVincent (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 RifeVincent (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 RifeVincent (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 ... N1 are sampling number, f_{s}It is to adopt
Sample frequency, A_{h}、f_{h}WithThe respectively amplitude, frequency and phase of h subharmonic.
In the step 2, the adding window discrete series signal obtained after adding window is x_{w}(n)=x (n) w (n).
Wherein, w (n) is five RifeVincent (I) windows, and the timedomain expression of five RifeVincent (I) windows is
Wherein, m is the item number of window function, a_{m}For the coefficient of window function, n=1,2 ... N1；N is sampling number.
In the step 2, the window function coefficient a of five RifeVincent (I) windows_{m}The condition of satisfaction has: 1.:2.: a_{0}=1, a_{1}=1.6, a_{2}=0.8, a_{3}=0.22857, a_{4}=0.02857.
In the step 3, the specific steps of discrete Fourier transform are as follows:
Step 31: to the discrete series signal x after adding window_{w}(n) it carries out Fourier transformation and acquires discrete frequency domain function.
Step 32: 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 subharmonic_{h}Neighbouring four
Spectral line k_{h1}、k_{h2}、k_{h3}And k_{h4}, the amplitude of this four spectral lines is respectively as follows: y_{2}= X (k_{h2})、y_{1}= X (k_{h1})、y_{3}= X (k_{h3})
 and y_{4}= X (k_{h4}) , the positional relationship of this four spectral lines lefttoright is successively: k from making_{h1}、k_{h2}、k_{h3}、k_{h4}, size relation are as follows:
k_{h1}=k_{h2} 1, k_{h2}=k_{h3} 1, k_{h3}=k_{h4}1。
The step 5 the following steps are included:
Step 51: offset β=k of document border spectral line value and theoretical value_{h}k_{h2}The range of 0.5, β are [ 0.5,0.5].
The relational expression α for establishing four spectral lines solves offset β, if α=(y_{3}+y_{4}y_{1}y_{2})/(y_{3}+y_{4}+y_{1}+y_{2}), 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 52: to find out offset β, using obtaining β=γ after polyfit Function Fitting^{1}(α's) is approximant are as follows:
β≈d_{1}α+d_{3}α^{3}+…+d_{2r+1}α^{2r+1}(5)；
Wherein, d_{1}、d_{3}、…d_{2r+1}The 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 antifitting, wherein 7 represent fitting number, to meet fitting precision
Demand, fitting number cannot be very few.The γ found out^{1}The coefficient of (α) is as follows:
The α of β=0.199099^{7}+0.302882α^{5}+0.612560α^{3}+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 53:h subharmonic is calculated by the average weighted of four spectral lines near peak point, due to
The spectral line k of inside two_{h2}、k_{h3}Closer to k_{h}, give k_{h2}、k_{h3}Bigger weight, the h times amplitude estimation formula is as follows:
When n is large, above formula can be expressed as A_{h}=N^{1}(y_{1}+3y_{2}+3y_{3}+y_{4}) 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:
A_{h}≈N^{1}(y_{1}+3y_{2}+3y_{3}+y_{4})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 β^{6}+0.004239β^{4}+0.048335β^{2}+0.290677 (12)
The magnitude parameters of h subharmonic can be calculated using formula (11), (12).
The timedomain function expression formula of five RifeVincent (I) window are as follows:
W (n)=11.6cos (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 RifeVincent 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 RifeVincent (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 RifeVincent 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 RifeVincent (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 RifeVincent (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 RifeVincent 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 RifeVincent (I) windows have the smallest side compared with three, four RifeVincent 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 RifeVincent (I) window, four spectral line interpolation results
Figure.
Fig. 2 (b) is the phase relative error comparison of five three spectral lines of RifeVincent (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 RifeVincent (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 RifeVincent (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 ... N1 are sampling number, f_{s}It is to adopt
Sample frequency, A_{h}、f_{h}WithThe respectively amplitude, frequency and phase of h subharmonic.
In the step 2, the discrete series signal obtained after adding window is x_{w}(n)=x (n) w (n).Wherein, w (n) is five Rife
Vincent (I) window.The timedomain expression of five RifeVincent (I) windows is
Wherein, m is the item number of window function, a_{m}For the coefficient of window function, n=1,2 ... N1；N is sampling number.
In the step 2, the coefficient a of five RifeVincent (I) windows_{m}The condition that must satisfy has: 1.:②a_{0}=1, a_{1}=1.6, a ,=0.8, a_{3}=0.22857, a_{4}=0.02857.
In step 2, five RifeVincent (I) windows have minimum compared with three, four RifeVincent 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 31: to the discrete series signal x after adding window_{w}(n) it carries out Fourier transformation and acquires discrete frequency domain function are as follows:
Wherein, k=0,1 ..., N1, Δ f=f_{s}/ N is discrete sampling interval, and k is the serial number of sampling frequency point, A_{h}、f_{h}WithRespectively the amplitude, frequency and phase of h subharmonic, N are sampling number.
It is h subharmonic phaseComplex expression, W is discrete Fourier transform formula, f_{s}It 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^{jπk}For the complex expression of phase angle π k,For phase angleComplex expression, m be window function item number, a_{m}For 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, a_{m}For the coefficient of window function.
Step 32: ignoring the influence of negative frequency point peak value, and discrete frequency domain function can indicate are as follows:
Wherein, k=0,1 ..., N1, 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 32  X (k) , find the frequency of h subharmonic
Point k_{h}Four neighbouring spectral line k_{h1}、k_{h2}、k_{h3}And k_{h4}, the amplitude of this four spectral lines is respectively as follows: y_{2}= X (k_{h2})、y_{1}= X (k_{h1})
、y_{3}= X (k_{h3})  and y_{4}= X (k_{h4}).The positional relationship of this four spectral lines, from making lefttoright to be successively k_{h1}、k_{h2}、k_{h3}、k_{h4},
Size relation is k_{h1}=k_{h2} 1, k_{h2}=k_{h3} 1, k_{h3}=k_{h4}1。
The specific steps of step 5 are as follows:
Step 51: offset β=k of document border spectral line value and theoretical value_{h}k_{h2}The range of 0.5, β are [ 0.5,0.5].
The relational expression α for establishing four spectral lines solves offset β, if α=(y_{3}+y_{4}y_{1}y_{2})/(y_{3}+y_{4}+y_{1}+y_{2}), 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 52: to find out offset β, using obtaining β=γ after polyfit Function Fitting^{1}(α's) is approximant are as follows:
β≈d_{1}α+d_{3}α3+…+d_{2r+1}α^{2r+1} (5)
Wherein, d_{1}、d_{3}、…d_{2r+1}The 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 antifitting, wherein 7 represent fitting number, to meet fitting precision
Demand, fitting number cannot be very few.The γ found out^{1}The coefficient of (α) is as follows:
The α of β=0.199099^{7}+0.302882α^{5}+0.612560α^{3}+2.475000α (6)
Therefore the frequency of h subharmonic, phase formula can be corrected are as follows:
Wherein, f_{h}、The respectively frequency and phase of h subharmonic, k_{h2}For the frequency point k of h subharmonic_{h}The second of the left side
Spectral line, β are the offset of practical spectral line value and theoretical spectrum value, f_{s}For sample frequency, N is sampling number, X (k_{h2}) it is h
Subharmonic frequency point k_{h}Corresponding 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 53:h subharmonic is calculated by the average weighted of four spectral lines near peak point, due to
The spectral line k of inside two_{h2}、k_{h3}Closer to k_{h}, give k_{h2}、k_{h3}Bigger weight, the h times amplitude estimation formula is as follows:
When n is large, above formula can be expressed as A_{h}=N^{1}(y_{1}+3y_{2}+3y_{3}+y_{4}) 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:
A_{h}≈N^{1}(y_{1}+3y_{2}+3y_{3}+y_{4})ρ(β) (11)
Wherein, A_{h}For the amplitude of h subharmonic, y_{1}、y_{2}、y_{3}、y_{4}The respectively frequency point k of h subharmonic_{h}Four neighbouring spectrums
Line k_{h1}、k_{h2}、k_{h3}、k_{h4}Corresponding 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 β^{6}+0.004239β^{4}+0.048335β^{2}+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 f_{s}=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 RifeVincent (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
RifeVincent (I) window, these window functions are higher using most and precision in harmonic detecting.By these window functions and this paper
After five RifeVincent (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 therein_{Ah}、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 table_{Ah}/ %
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 E_{Ah}≤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 valuebased 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 RifeVincent (I) windows proposed by the present invention
Survey analysis method, the timedomain expression of five RifeVincent (I) window function therein are as follows:
W (n)=11.6cos (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 timedomain expression of five RifeVincent (I) windows, and N is sampling number.
The window has preferable side lobe performance, and side lobe peak level is compared with three, four RifeVincent 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 RifeVincent (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 RifeVincent (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 RifeVincent (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 ... N1 are sampling number, f_{s}It is sampling frequency
Rate, A_{h}、f_{h}WithThe respectively amplitude, frequency and phase of h subharmonic.
3. the complicated harmonic detecting of four spectral line interpolation FFTs based on five RifeVincent (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 x_{w}(n)=x (n) w
(n)；Wherein, w (n) is five RifeVincent (I) windows, and the timedomain expression of five RifeVincent (I) windows is
Wherein, m is the item number of window function, a_{m}For the coefficient of window function, n=1,2 ... N1；N is sampling number.
4. the complicated harmonic detecting of four spectral line interpolation FFTs based on five RifeVincent (I) windows according to claim 3
Analysis method, it is characterised in that: in the step 2, the window function coefficient a of five RifeVincent (I) windows_{m}The condition of satisfaction
Have:
1.:2.: a_{0}=1, a_{1}=1.6, a_{2}=0.8, a_{3}=0.22857, a_{4}=0.02857.
5. the complicated harmonic detecting of four spectral line interpolation FFTs based on five RifeVincent (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 31: to the discrete series signal x after adding window_{w}(n) it carries out Fourier transformation and acquires discrete frequency domain function；
Step 32: 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 RifeVincent (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 k_{h}Four neighbouring spectral line k_{h1}、k_{h2}、k_{h3}And k_{h4}, the amplitude of this four spectral lines is respectively as follows: y_{2}= X (k_{h2})、y_{1}= X (k_{h1})
、y_{3}= X (k_{h3})  and y_{4}= X (k_{h4}) , the positional relationship of this four spectral lines lefttoright is successively: k from making_{h1}、k_{h2}、k_{h3}、
k_{h4}, size relation are as follows: k_{h1}=k_{h2} 1, k_{h2}=k_{h3} 1, k_{h3}=k_{h4}1。
7. the complicated harmonic detecting of four spectral line interpolation FFTs based on five RifeVincent (I) windows according to claim 1
Analysis method, it is characterised in that: the step 5 the following steps are included:
Step 51: offset β=k of document border spectral line value and theoretical value_{h}k_{h2}The 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=(y_{3}+y_{4}y_{1}y_{2})/(y_{3}+y_{4}+y_{1}+y_{2}), 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 52: to find out offset β, using obtaining β=γ after polyfit Function Fitting^{1}(α's) is approximant are as follows:
β≈d_{1}α+d_{3}α^{3}+…+d_{2r+1}α^{2r+1}(5)；
Wherein, d_{1}、d_{3}、…d_{2r+1}The 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 antifitting, wherein 7 represent fitting number, for the need for meeting fitting precision
It asks, fitting number cannot be very few；The γ found out^{1}The coefficient of (α) is as follows:
The α of β=0.199099^{7}+0.302882α^{5}+0.612560α^{3}+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 53:h subharmonic is calculated by the average weighted of four spectral lines near peak point, due to inside
Two spectral line k_{h2}、k_{h3}Closer to k_{h}, give k_{h2}、k_{h3}Bigger weight, the h times amplitude estimation formula is as follows:
When n is large, above formula can be expressed as A_{h}=N^{1}(y_{1}+3y_{2}+3y_{3}+y_{4}) 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:
A_{h}≈N^{1}(y_{1}+3y_{2}+3y_{3}+y_{4})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 β^{6}+0.004239β^{4}+0.048335β^{2}+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 RifeVincent (I) windows according to claim 1
Analysis method, it is characterised in that: the timedomain function expression formula of five RifeVincent (I) window are as follows:
W (n)=11.6cos (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 RifeVincent windows compared to be it is the smallest, be
74.5dB。
9. application of five RifeVincent (I) windows in mains by harmonics measurement.
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