CN105388361A - FFT power harmonic detection method for bidirectional interpolation synchronization sampling sequence - Google Patents
FFT power harmonic detection method for bidirectional interpolation synchronization sampling sequence Download PDFInfo
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Abstract
The invention discloses an FFT power harmonic detection method for a bidirectional interpolation synchronization sampling sequence, comprising: step 1, a mutual inductor samples a harmonic signal, a discrete signal x(n) is obtained, and the signal x(n) is subjected to filtering processing to acquire a fundamental wave signal x0(n); step 2, fundamental wave signals of ten continuous cyclic waves are taken as sampling data; step 3, the sampling data are subjected to forward Newton interpolation, and moment positions when an amplitude value of the sampling data exceeds a threshold value a for the first time and the twenty first time are acquired, and respectively marked as tstart and tend; step 4, by taking equal diversion points between the moment positions tstart and tend as interpolation points, the sampling data are subjected to reversed Newton interpolation, thus acquiring signal amplitude values of the various interpolation points, namely acquiring the synchronization sampling sequence; step 5, the synchronization sequence is subjected to fast Fourier transform. The FFT power harmonic detection method can be used for quickly and accurately detecting signal harmonic components and continuously detecting the detected signals for a long term, and has good timeliness.
Description
Technical field
The present invention relates to Measurement of Harmonics in Power System technical field, be specifically related to a kind of FFT electric harmonic detection method of two-way interpolation synchronization sample sequence.
Background technology
The rolling up of nonlinear-load in electric system, the particularly widespread use of power electronic equipment, make harmonic components in electrical network increase, the severe exacerbation quality of power supply.Occur in power distribution network that harmonic wave not only may make to occur resonance phenomena in electrical network, also can increase the loss of motor and transformer, make the aging aggravation of power cable, the lost of life.Analysis and the improvement of the quality of power supply will be conducive to quick, the accurate detection of harmonic component.Fast Fourier Transform (FFT) has become the topmost method of current electric harmonic analysis due to the theory of its maturation and the reason that is easy to the embedded realization of electrical network.But because non-integer-period intercepting and non-synchronous sampling can produce spectral leakage and fence effect when directly adopting Fast Fourier Transform (FFT) to analyze mains by harmonics, have a strong impact on the accuracy of signal parameter measurement result, to such an extent as to the Standard of harmonic measure cannot be reached.
For solving the problem, harmonic analysis method conventional at present has: the harmonic parameters based on interpolation FFT method is estimated, the subharmonic measuring and analysis based on FFT method, the high precision window function double spectral line interpolation Electric Power Harmonic Analysis method, rectangle convolution window method, triangle convolution window method etc. based on FFT.
But, although carry out fast Fourier analysis after windowing more effectively can reduce spectral leakage, but owing to there is a large amount of secondary lobe in the frequency domain of window function, can not be good spectral leakage be suppressed, and the larger detection of secondary lobe to frequency content more weak in original signal of amplitude-frequency response has interference effect.And the window function with excellent sidelobe performance exists, and interpolation correction formula is complicated, shortcoming to spectral line testing process length consuming time, have a strong impact on ageing.
Summary of the invention
For the deficiencies in the prior art, the present invention proposes a kind of FFT electric harmonic detection method of two-way Newton interpolation synchronization sample sequence.
The present invention is in non-synchronous sampling situation, forward interpolation calculation is utilized to obtain the signal primitive period, then reverse interpolation point position is set at equal intervals according to the signal primitive period, the sample sequence obtained under making the sample sequence after adjusting be similar to synchronized sampling situation, thus spectrum leakage when reducing fast Fourier analysis.
For solving the problems of the technologies described above, the present invention adopts following technical scheme:
A FFT electric harmonic detection method for two-way interpolation synchronization sample sequence, comprising:
Step 1, mutual inductor sample harmonic signal obtains signal x (n) of discretize, carries out filtering process obtain fundamental signal x to signal x (n)
0(n);
Step 2, the fundamental signal getting ten continuous cycles, as sampled data, is specially:
Threshold value a is set, detects fundamental signal x
0n () amplitude crosses over the number of times of a, the data i.e. fundamental signal of ten continuous cycles crossed between threshold value a for the 1st time and the 21st time, a is fundamental signal x
0arbitrary value between (n) peak value;
Step 3, carry out to sampled data the moment position that forward Newton interpolation obtains sampled data amplitude the 1st time and the 21st leap threshold value a, these two moment positions are designated as t respectively
startand t
end;
Step 4, with moment position t
startand t
endbetween N
0individual Along ent is interpolation point, carries out reverse Newton interpolation to sampled data, obtains the signal amplitude at each interpolation point place, namely obtains synchronization sample sequence, N
0=f
0/ 50Hz × 10, f
0for fundamental frequency;
Step 5, carries out Fast Fourier Transform (FFT) to syncul sequence.
In step 1, second order Butterworth lowpass filters is adopted to carry out filtering process to signal x (n).
As preferably, threshold value a=0.
Step 3 is specially:
Get sampled data amplitude and cross over each two sampling numbers in front and back, threshold value a place for the 1st time according to carrying out forward Newton interpolation, obtain moment t
start; In like manner, get sampled data amplitude and cross over each two sampling numbers in front and back, threshold value a place for the 21st time according to carrying out forward Newton interpolation, obtain moment t
end, t
startand t
enddifference and the time domain length of sampled data, i.e. the complete cycle of sampled data.
Step 4 is specially:
To each interpolation point, utilization is distributed in each 2 data before and after interpolation point and carries out the three reverse Newton interpolations in rank, obtains each interpolation point place signal amplitude, thus obtains synchronization sample sequence.
Compared with prior art, the present invention has the following advantages and beneficial effect:
The present invention is by detecting sampled data length corresponding to cycle signal under fundamental frequency change situation, forward interpolation is utilized to carry out accurate intercepting complete cycle to cycle signal, utilize reverse interpolation that interpolation point position is set in the position at equal intervals of primitive period, the sample sequence obtained under making the sample sequence after adjusting be similar to synchronized sampling situation, thus spectrum leakage when reducing fast Fourier analysis.
The present invention is easy to Project Realization, and the sampled data by means of only ten power frequency periods carries out simple two-way interpolation arithmetic just can solve the problem due to non-integer-period sampled brought spectral leakage.When electrical network fundamental frequency among a small circle in change, by by the sampling data synchronization of change frequency to fundamental frequency be 50Hz equal length sequence on, the operation efficiency of Fast Fourier Transform (FFT) can be improved, and then have ageing preferably.
Embodiment
Concrete steps of the present invention are as follows:
Step 1, sampling harmonic signal x (t), obtains discretize signal x (n).
Mutual inductor is with fixed frequency f
0sample to the signal of electric system, signal can be voltage signal or current signal; Sampled signal is transferred to merge cells pack by the period, by digital information network, signal x (n) is transferred to Power Quality Detection instrument.
Step 2, obtains the filtering process of discretize signal x (n), obtains fundamental signal x
0(n).
By discretize signal x (n) by low-pass filter, obtain the fundamental signal x that electrical network fundamental frequency changes within the scope of 50 ± 0.2Hz
0n (), in this concrete enforcement, low-pass filter is second order Butterworth lowpass filters.
Step 3, gets the fundamental signal of ten continuous cycles as sampled data.
This step is specially:
Arrange threshold value a, a can be set to fundamental signal x
0n the arbitrary value between () peak value, because different threshold value a can affect the precision by forward interpolation calculation system signal accurate complete cycle, setting a=0 is to obtain higher computational accuracy usually.When electrical network fundamental frequency changes, by detecting fundamental signal x
0n () amplitude crosses over the number of times of threshold value a, cross over the data i.e. fundamental signal of ten continuous cycles crossed between threshold value a for threshold value a and the 21st time for the 1st time, its length is set to N.
Step 4, carries out forward Newton interpolation to the sampled data that step 3 obtains.
This step is known technology, for ease of understanding, is described in detail below by a kind of embodiment of this step.
Be the sampled data x of N by length
0n () amplitude the 1st time and cross over threshold value a place for the 21st time and be designated as starting point and terminal respectively, gets 2 data respectively in starting point and terminal both sides, carries out the forward Newton interpolation on three rank, obtain starting point and moment corresponding to terminal, i.e. sampled data x
0n () amplitude crosses over the moment of threshold value a for the 1st time and the 21st time, be designated as t respectively
startand t
end.
For Newton Interpolation Algorithm, newton interpolation polynomial can be expressed as form:
P(x)＝f[x
0]+f[x
0,x
1](x-x
0)+f[x
0,x
1,x
2](x-x
0)(x-x
1)+...
(1)
+f[x
0,x
1,...x
n](x-x
0)(x-x
1)...(x-x
n-1)
In formula (1), x
irepresent i-th sampled point position on a timeline, f (x
i) representing the amplitude of i-th sampled point, n is sampling number.
K rank inequality
Wherein, given data (x
i, f (x
i)) on interpolation section [u, v], there is definition, i=0,1 ... N.If there is simple function P (x) in function class, make P (x
i)=f (x
i), then P (x
i) be the interpolating function of f (x), x
1, x
2..., x
nfor interpolation knot, [u, v] is interpolation section.
If four sampled points crossing threshold value a both sides are followed successively by k
n-2, k
n-1, k
n, k
n+ 1, use the Newton interpolating method of 3 rank inequality, calculate t respectively
startand t
endexact value.3 rank inequality tables of above-mentioned four sampled points in table 1, wherein, x
0, x
1, x
2, x
3represent that sampled data is at k respectively
n-2, k
n-1, k
n, k
nthe amplitude of+1 sample point.
3 rank inequality tables of table 1 forward Newton interpolation sampled point near threshold value a both sides
| x i | f(x i) | 1 rank inequality | 2 rank inequality | 3 rank inequality |
| x 0＝x(k n-2) | f(x 0)＝k n-2 | |||
| x 1＝x(k n-1) | f(x 1)＝k n-1 | f[x 0,x 1] | ||
| x 2＝x(k n) | f(x 2)＝k n | f[x 1,x 2] | f[x 0,x 1,x 2] | |
| x 3＝x(k n+1) | f(x 3)＝k n+1 | f[x 2,x 3] | f[x 1,x 2,x 3] | f[x 0,x 1,x 2,x 3] |
Inequality result in table 1 is substituted in formula (1), obtains fundamental signal x
0(n) i-th time t by threshold value a
i:
t
i≈P(i)＝f[x
0]+f[x
0，x
1](i-x
0)+f[x
0，x
1，x
2](i-x
0)(i-x
1)+
(2)
f[x
0，x
1，x
2，x
3](i-x
0)(i-x
1)(i-x
2)
In like manner can obtain fundamental signal x
0n () passes through the time t of threshold value a for the i-th+20 times
i+20, choose the t now calculating gained
ifor t
start, calculate the t of gained
i+20for t
end, and then try to achieve the time domain length of sample sequence 10 cycle signals.
Step 5, carries out reverse Newton interpolation to sampled data and obtains synchronization sample sequence.
When electrical network fundamental frequency 50Hz, the sampled data length of ten consecutive periods fundamental signals is:
N
0＝f
0/50Hz×10(3)
During due to Implementation of Embedded System Fast Fourier Transform (FFT), each counting of conversion is changeless, and calculation times is minimum, fastest when counting of converting is the integral number power of 2.Therefore sample sequence complete cycle of gained in step 4 is obtained as length equals N by reverse Newton interpolation
0syncul sequence.
The interpolation point of reverse interpolation is t
end-t
startn
0on individual Along ent, equally for reverse Newton interpolating method, utilizing each 2 sampling numbers in each interpolation point both sides according to carrying out the three reverse Newton interpolations in rank, obtaining the signal amplitude at each interpolation point place, thus obtaining length N
0syncul sequence x
s(n
0).Interpolation point both sides sampled point is designated as k successively
n-2, k
n-1, k
n, k
n+ 1, f (x
0), f (x
1), f (x
2), f (x
3) i.e. sampled point k
n-2, k
n-1, k
n, k
n+ 1 place's signal amplitude.
The reverse Newton interpolation of table 2 is at 3 rank inequality tables of new Along ent
| x i | f(x i) | 1 rank inequality | 2 rank inequality | 3 rank inequality |
| x 0＝k n-2 | f(x 0)＝x(k n-2) | |||
| x 1＝k n-1 | f(x 1)＝x(k n-1) | f[x 0,x 1] | ||
| x 2＝k n | f(x 2)＝x(k n) | f[x 1,x 2] | f[x 0,x 1,x 2] | |
| x 3＝k n+1 | f(x 3)＝x(k n+1) | f[x 2,x 3] | f[x 1,x 2,x 3] | f[x 0,x 1,x 2,x 3] |
Inequality result in table 2 is substituted in formula (1), obtains the amplitude x of signal at i-th interpolation point
sthe calculated value of (i):
x
s(i)≈P(i)＝f[x
0]+f[x
0，x
1](i-x
0)+f[x
0，x
1，x
2](i-x
0)(i-x
1)+
(4)
f[x
0，x
1，x
2，x
3](i-x
0)(i-x
1)(i-x
2)
Step 6, to syncul sequence x
s(n
0) carry out Fast Fourier Transform (FFT).
Time window be 10 primitive period length, sample frequency is Dot × f
r(f
r=50Hz), when Dot is every cycle sampling number, the computing formula of harmonic parameters is as follows:
In formula (5), f
110DotT
sfor the position of fundamental frequency on frequency spectrum, X (mf
110DotT
s) be the FFT result of m subharmonic.
Embodiment
Choose voltage signal x (t) containing higher hamonic wave, for this voltage signal, the inventive method is described.
Step 1, fixed sampling frequency f
0=25600Hz sampling harmonic signal x (t) obtains signal x (n) of discretize.
Step 2, carries out filtering process to signal x (n), is specially: the second order Butterworth lowpass filters by signal x (n) by cutoff frequency being 75Hz, obtains fundamental signal x
0(n).
Step 3, arranges threshold value a=0, detects fundamental signal x
0n () zero crossing situation obtains the fundamental signal of current electric grid fundamental frequency lower ten continuous cycles, i.e. sampled data, and sampled data length is designated as N.
Step 4, carries out forward Newton interpolation to sampled data.
Whole period processing is carried out to the head and the tail two ends of sampled data, is specially: to sampled data x
0n 4 data at leap threshold value a place, () head and the tail two ends carry out the forward Newton interpolation on three rank, thus obtain the moment that threshold value a is accurately crossed at fundamental signal head and the tail two ends, are respectively t
startand t
end.Four sampled points crossing both sides, threshold value a place are designated as k successively
n-2, k
n-1, k
n, k
n+ 1, use the Newton interpolating method of three rank inequality, calculate t
startand t
endexact value, draw 3 rank inequality tables as shown in Table 3 and Table 4 according to table 1.
Table 3 forward Newton interpolation is at t
startthree rank inequality tables of neighbouring sampled point
| x i | f(x i) | 1 rank inequality | 2 rank inequality | 3 rank inequality |
| x 0＝4.82e-4 | f(x 0)＝90 | |||
| x 1＝2.20e-4 | f(x 1)＝91 | -3.8107e 3 | ||
| x 2＝-5.04e-5 | f(x 2)＝92 | -3.6987e 3 | -2.1034e 5 | |
| x 3＝-3.13e-4 | f(x 3)＝93 | -3.8031e 3 | 1.9579e 5 | 3.0889e 5 |
The inequality result of table 3 is substituted in formula (1), obtains t
startcalculated value.
t
start≈P(a)＝f[x
0]+f[x
0，x
1](a-x
0)+f[x
0，x
1，x
2](a-x
0)(a-x
1)+
(6)
f[x
0，x
1，x
2，x
3](a-x
0)(a-x
1)(a-x
2)＝91.8159
Table 4 forward Newton interpolation is at point of crossing t
endthree rank inequality tables of neighbouring sampled point
| x i | f(x i) | 1 rank inequality | 2 rank inequality | 3 rank inequality |
| x 0＝5.15e-4 | f(x 0)＝5149 | |||
| x 1＝2.58e-4 | f(x 1)＝5150 | -3.8832e 3 | ||
| x 2＝-1.17e-6 | f(x 2)＝5151 | -3.7088e 3 | -3.3073e 5 | |
| x 3＝-2.78e-4 | f(x 3)＝5152 | -3.7506e 3 | 7.7890e 4 | 6.5646e 6 |
Inequality result in table 4 is substituted in formula (1), obtains t
endcalculated value.
t
end≈P(a)＝f[x
0]+f[x
0，x
1](a-x
0)+f[x
0，x
1，x
2](a-x
0)(a-x
1)+
(7)
f[x
0，x
1，x
2，x
3](a-x
0)(a-x
1)(a-x
2)＝5150.9576
And then by t
end-t
startthe time domain length of trying to achieve sample sequence 10 cycle signal is 5059.1417.
Step 5, obtains syncul sequence to the reverse Newton interpolation of sampled data.When electrical network fundamental frequency is 50Hz, the sampled signal length of ten cycles is:
N
0＝f
0/50Hz×10＝5120(8)
During due to Implementation of Embedded System Fast Fourier Transform (FFT), each counting of conversion is changeless, and calculation times is minimum, fastest when counting of converting is the integral number power of 2.Therefore the sample sequence of the complete cycle of gained in step 4 is obtained as length equals N by reverse Newton interpolation
0syncul sequence.
The interpolation point carrying out reverse Newton interpolation is t
end-t
startn
0on individual Along ent.Utilize 4 sampling number certificates near each interpolation point, carry out the three reverse Newton interpolations in rank according to three rank inequality methods shown in table 2, obtain the amplitude of each interpolation point place original sampled signal.
Below for the 2500th interpolation point, provide this interpolation point position n
2500computing method, as follows:
The position of getting 4 sampled points near this interpolation point is followed successively by x
0=2469, x
1=2470, x
2=2471, x
3=2472, according to three rank Newton interpolating method by the sampled value of former sequence at these four sampling point positions, calculate the signal amplitude of sequence at the 2500th some place after adjustment, its computing method are as shown in table 5.
The reverse Newton interpolation of table 5 is at the 3 rank inequality tables of n-th (n=2500) individual interpolation point
| x i | f(x i) | 1 rank inequality | 2 rank inequality | 3 rank inequality |
| x 0＝2469 | f(x 0)＝190.5057 | |||
| x 1＝2470 | f(x1)＝192.1845 | 1.6788 | ||
| x2＝2471 | f(x2)＝194.2564 | 2.0719 | 0.1966 | |
| x 3＝2472 | f(x 3)＝196.6452 | 2.3888 | 0.1584 | -0.0127 |
Table 5 mean deviation result is substituted in formula (1), obtains the amplitude x of signal at n-th (n=2500) individual interpolation point
s(2500) calculated value:
x
s(2500)≈P(2470.2840)＝f[x
0]+f[x
0，x
1](2470.2840-x
0)+f[x
0，x
1，x
2]
(2470.2840-x
0)(2470.2840-x
1)+f[x
0，x
1，x
2，x
3](2470.2840-x
0)(10)
(2470.2840-x
1)(2470.2840-x
2)＝192.7363
In like manner can to other interpolation point process, obtaining length is n
0syncul sequence x
s(n
0).
Step 6, to the syncul sequence x of gained in step 5
s(n
0) carry out Fast Fourier Transform (FFT).
The signal frequency of this enforcement is 50.6 hertz, and it is 2.44 × 10 that fundamental frequency calculates relative error
-10, amplitude and phase place and error analysis as shown in table 6.
The error analysis table of table 6 harmonic signal
Claims (5)
1. the FFT electric harmonic detection method of two-way interpolation synchronization sample sequence, is characterized in that, comprising:
Step 1, mutual inductor sample harmonic signal obtains signal x (n) of discretize, carries out filtering process obtain fundamental signal x to signal x (n)
0(n);
Step 2, the fundamental signal getting ten continuous cycles, as sampled data, is specially:
Threshold value a is set, detects fundamental signal x
0n () amplitude crosses over the number of times of a, the data i.e. fundamental signal of ten continuous cycles crossed between threshold value a for the 1st time and the 21st time, a is fundamental signal x
0arbitrary value between (n) peak value;
Step 3, carry out to sampled data the moment position that forward Newton interpolation obtains sampled data amplitude the 1st time and the 21st leap threshold value a, these two moment positions are designated as t respectively
startand t
end;
Step 4, with moment position t
startand t
endbetween N
0individual Along ent is interpolation point, carries out reverse Newton interpolation to sampled data, obtains the signal amplitude at each interpolation point place, namely obtains synchronization sample sequence, N
0=f
0/ 50Hz × 10, f
0for fundamental frequency;
Step 5, carries out Fast Fourier Transform (FFT) to syncul sequence.
2. the FFT electric harmonic detection method of two-way interpolation synchronization sample sequence, is characterized in that:
In step 1, second order Butterworth lowpass filters is adopted to carry out filtering process to signal x (n).
3. the FFT electric harmonic detection method of two-way interpolation synchronization sample sequence as claimed in claim 1, is characterized in that:
Described threshold value a=0.
4. the FFT electric harmonic detection method of two-way interpolation synchronization sample sequence as claimed in claim 1, is characterized in that:
Step 3 is specially:
Get sampled data amplitude and cross over each two sampling numbers in front and back, threshold value a place for the 1st time according to carrying out forward Newton interpolation, obtain moment t
start; In like manner, get sampled data amplitude and cross over each two sampling numbers in front and back, threshold value a place for the 21st time according to carrying out forward Newton interpolation, obtain moment t
end, t
startand t
enddifference and the time domain length of sampled data, i.e. the complete cycle of sampled data.
5. the FFT electric harmonic detection method of two-way interpolation synchronization sample sequence as claimed in claim 1, is characterized in that:
Step 3 is specially:
To each interpolation point, utilization is distributed in each 2 data before and after interpolation point and carries out the three reverse Newton interpolations in rank, obtains each interpolation point place signal amplitude, thus obtains synchronization sample sequence.
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