CN105388361B - Two-way interpolation synchronizes the FFT electric harmonic detection methods of sample sequence - Google Patents
Two-way interpolation synchronizes the FFT electric harmonic detection methods of sample sequence Download PDFInfo
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Abstract
The invention discloses the FFT electric harmonic detection methods that a kind of two-way interpolation synchronizes sample sequence, including：Step 1, mutual inductor sample harmonic signal obtains the signal x (n) of discretization, and processing is filtered to signal x (n) and obtains fundamental signal x0(n)；Step 2, the fundamental signal of ten continuous cycles is taken as sampled data；Step 3, carry out that positive Newton interpolation obtains sampled data amplitude the 1st time and the 21st time across position at the time of threshold value a to sampled data, the two at moment position be designated as t respectivelystartAnd tend；Step 4, with moment position tstartAnd tendBetween Along ent be interpolation point, reverse Newton interpolation is carried out to sampled data, obtains the signal amplitude at each interpolation point, that is, obtains and synchronizes sample sequence；Step 5, Fast Fourier Transform (FFT) is carried out to syncul sequence.The present invention can fast and accurately detection signal harmonic component, can continuously detect measured signal for a long time, have good ageing.
Description
Technical field
The present invention relates to Measurement of Harmonics in Power System technical field, and in particular to a kind of two-way interpolation synchronizes sample sequence
FFT electric harmonic detection methods.
Background technology
The extensive use of the substantial increase of nonlinear-load, particularly power electronic equipment, makes in power network in power system
Harmonic components increase, the severe exacerbation quality of power supply.Occurring harmonic wave in power distribution network may not only make resonance occur in power network to show
As can also increase the loss of motor and transformer, aggravate power cable aging, the lost of life.To the quick, accurate of harmonic component
Really detection is beneficial to the analysis and improvement of the quality of power supply.Fast Fourier Transform (FFT) is due to its ripe theory and to be easy to power network embedding
Enter the reason for formula is realized turns into the most important method of current electric harmonic analysis.But directly using Fast Fourier Transform (FFT) to electricity
Because non-integer-period interception and non-synchronous sampling can produce spectral leakage and fence effect when net harmonic wave is analyzed, have a strong impact on
The accuracy of signal parameter measurement result, so that it cannot reach the Standard of harmonic measure.
To solve the above problems, currently used harmonic analysis method has：Harmonic parameters estimation based on interpolation FFT method,
Based on FFT methods subharmonic measurement with analysis, the high-precision window function double spectral line interpolation Electric Power Harmonic Analysis method based on FFT,
Rectangle convolution window method, triangle convolution window method etc..
However, although spectral leakage can effectively be reduced by carrying out fast Fourier analysis after adding window again, due to window function
Frequency domain in a large amount of secondary lobes be present, well spectral leakage can not be suppressed, and the larger secondary lobe of amplitude-frequency response is to original
The detection of weaker frequency content has interference effect in beginning signal.And there is interpolation and repair in the window function with excellent sidelobe performance
Positive formula is complicated, to spectral line detection process time-consuming the shortcomings that, have a strong impact on ageing.
The content of the invention
For the deficiencies in the prior art, the present invention proposes a kind of two-way Newton interpolation and synchronizes sample sequence
FFT electric harmonic detection methods.
The present invention obtains the signal primitive period, then according to letter in the case of non-synchronous sampling using positive interpolation calculation
Number primitive period sets reverse interpolation point position at equal intervals so that the sample sequence after adjustment is similar to obtain in the case of synchronized sampling
Sample sequence, spectrum leakage during so as to reduce fast Fourier analysis.
In order to solve the above technical problems, the present invention adopts the following technical scheme that：
A kind of two-way interpolation synchronizes the FFT electric harmonic detection methods of sample sequence, including：
Step 1, mutual inductor sample harmonic signal obtains the signal x (n) of discretization, and processing is filtered to signal x (n) and is obtained
Fundamental signal x0(n)；
Step 2, the fundamental signals of ten continuous cycles is taken to be specially as sampled data：
Threshold value a, detection fundamental signal x are set0(n) amplitude crosses over a number, and the 1st time and the 21st time across between threshold value a
Data are the fundamental signal of ten continuous cycles, and a is fundamental signal x0(n) arbitrary value between peak value；
Step 3, sampled data amplitude is obtained the 1st time to the positive Newton interpolation of sampled data progress and the 21st time is crossed over threshold value a
At the time of position, the two at moment position be designated as t respectivelystartAnd tend；
Step 4, with moment position tstartAnd tendBetween N0Individual Along ent is interpolation point, and reverse ox is carried out to sampled data
Interpolation, obtains the signal amplitude at each interpolation point, that is, obtains and synchronize sample sequence, N0=f0/ 50Hz × 10, f0For fundamental wave
Frequency；
Step 5, Fast Fourier Transform (FFT) is carried out to syncul sequence.
In step 1, processing is filtered to signal x (n) using second order Butterworth lowpass filters.
Preferably, threshold value a=0.
Step 3 is specially：
Each two sample point datas carry out positive Newton interpolation before and after taking at the 1st leap threshold value a of sampled data amplitude, obtain
Moment tstart；Similarly, each two sample point datas carry out positive newton before and after taking at the 21st leap threshold value a of sampled data amplitude
Interpolation, obtain moment tend, tstartAnd tendDifference be sampled data time domain length, i.e. sampled data complete cycle.
Step 4 is specially：
To each interpolation point, the reverse Newton interpolation of three ranks is carried out using each 2 data before and after being distributed in interpolation point, obtains each interpolation
Signal amplitude at point, so as to obtain synchronization sample sequence.
Compared with prior art, the present invention has advantages below and beneficial effect：
The present invention is inserted by detecting sampled data length corresponding to cycle signal under fundamental frequency change situation using forward direction
Value carries out accurate interception complete cycle to cycle signal, and interpolation point position is set in the position at equal intervals of primitive period using reverse interpolation
Put so that the sample sequence after adjustment is similar to the sample sequence obtained in the case of synchronized sampling, so as to reduce fast Fourier
Spectrum leakage during analysis.
The present invention is easy to Project Realization, only carries out simple two-way interpolation arithmetic by the sampled data of ten power frequency periods
With regard to that can solve the problems, such as due to non-integer-period sampled caused spectral leakage.In the feelings of power network fundamental frequency a small range change
Under condition, by the way that the sampling data synchronization of change frequency to fundamental frequency is fast for that on 50Hz isometric degree series, can improve
The operation efficiency of fast Fourier transformation, and then have preferably ageing.
Embodiment
The present invention's comprises the following steps that：
Step 1, sample harmonic signal x (t), discretization signal x (n) is obtained.
Transformer is with fixed frequency f0The signal of power system is sampled, signal can be that voltage signal or electric current are believed
Number；Sampled signal is transferred into combining unit to be packed by the period, is transferred to signal x (n) by digital information network
Power Quality Detection instrument.
Step 2, discretization signal x (n) filtering process is obtained, obtains fundamental signal x0(n)。
By discretization signal x (n) by low pass filter, obtain power network fundamental frequency and change in the range of 50 ± 0.2Hz
Fundamental signal x0(n), in this specific implementation, low pass filter is second order Butterworth lowpass filters.
Step 3, the fundamental signal of ten continuous cycles is taken as sampled data.
This step is specially：
Threshold value a, a is set to be set to fundamental signal x0(n) arbitrary value between peak value, because different threshold value a can influence to lead to
The precision of positive interpolation calculation system signal accurate complete cycle is crossed, is normally set up a=0 to obtain higher computational accuracy.In electricity
In the case that net fundamental frequency changes, by detecting fundamental signal x0(n) amplitude crosses over threshold value a number, crosses over threshold value the 1st time
Data between a and the 21st leap threshold value a are the fundamental signal of ten continuous cycles, and its length is set to N.
Step 4, positive Newton interpolation is carried out to the sampled data that step 3 obtains.
This step is known technology, for ease of understanding, a kind of embodiment of this step will be carried out below detailed
Explanation.
By the sampled data x that length is N0(n) starting point and end are designated as respectively at the 1st time and the 21st time leap threshold value a of amplitude
Point, take 2 data respectively in beginning and end both sides, carry out the positive Newton interpolation of three ranks, obtain corresponding to beginning and end
Moment, i.e. sampled data x0(n) at the time of the 1st time and the 21st time leap threshold value a of amplitude, t is designated as respectivelystartAnd tend。
By taking Newton Interpolation Algorithm as an example, newton interpolation polynomial can be expressed as form：
P (x)=f [x0]+f[x0,x1](x-x0)+f[x0,x1,x2](x-x0)(x-x1)+...
(1)
+f[x0,x1,...xn](x-x0)(x-x1)...(x-xn-1)
In formula (1), xiRepresent ith sample point position on a timeline, f (xi) amplitude of ith sample point is represented, n is
Sampling number.
K rank inequalityWherein, given number
According to (xi,f(xi)) be defined on interpolation section [u, v], i=0,1 ... N.If simple function P in function class be present
(x) so that P (xi)=f (xi), then P (xi) be f (x) interpolating function, x1、x2、…、xnFor interpolation knot, [u, v] is interpolation
Section.
If four sampled points for crossing threshold value a both sides are followed successively by kn-2、kn-1、kn、kn+ 1, use the Newton interpolation of 3 rank inequality
Method, t is calculated respectivelystartAnd tendExact value.3 rank inequality tables of aforementioned four sampled point are shown in Table 1, wherein, x0、x1、x2、x3
Represent sampled data in k respectivelyn-2、kn-1、kn、knThe amplitude of+1 sample point.
3 rank inequality tables of 1 positive Newton interpolation of table sampled point near threshold value a both sides
| xi | f(xi) | 1 rank inequality | 2 rank inequality | 3 rank inequality |
| x0=x (kn-2) | f(x0)=kn-2 | |||
| x1=x (kn-1) | f(x1)=kn-1 | f[x0,x1] | ||
| x2=x (kn) | f(x2)=kn | f[x1,x2] | f[x0,x1,x2] | |
| x3=x (kn+1) | f(x3)=kn+1 | f[x2,x3] | f[x1,x2,x3] | f[x0,x1,x2,x3] |
Inequality result in table 1 is substituted into formula (1), obtains fundamental signal x0(n) the time t that ith passes through threshold value ai：
ti≈ P (i)=f [x0]+f[x0, x1](i-x0)+f[x0, x1, x2](i-x0)(i-x1)+
(2)
f[x0, x1, x2, x3](i-x0)(i-x1)(i-x2)
Fundamental signal x can similarly be obtained0(n) the i-th+20 times time t for passing through threshold value ai+20, choose the t for now calculating gainedi
For tstart, calculate gained ti+20For tend, and then try to achieve the time domain length of 10 cycle signals of sample sequence.
Step 5, reverse Newton interpolation is carried out to sampled data to obtain synchronizing sample sequence.
In the case of power network fundamental frequency 50Hz, the sampled data length of ten continuous cycles fundamental signals is：
N0=f0/50Hz×10 (3)
During due to Implementation of Embedded System Fast Fourier Transform (FFT), the points converted every time are changeless, and are being become
Calculation times are minimum when the points changed are 2 integral number power, fastest.Therefore the complete cycleization of gained in step 4 is sampled
Sequence obtains being equal to N for length by reverse Newton interpolation0Syncul sequence.
The interpolation point of reverse interpolation is tend-tstartN0On individual Along ent, equally by taking reverse Newton interpolating method as an example, profit
The reverse Newton interpolation of three ranks is carried out with each 2 sample point datas in each interpolation point both sides, obtains the signal amplitude at each interpolation point, from
And obtain length N0Syncul sequence xs(n0).Interpolation point both sides sampled point is designated as k successivelyn-2、kn-1、kn、kn+ 1, f (x0)、f
(x1)、f(x2)、f(x3) it is sampled point kn-2、kn-1、kn、kn+ 1 place's signal amplitude.
3 rank inequality tables of the 2 reverse Newton interpolation of table in new Along ent
| xi | f(xi) | 1 rank inequality | 2 rank inequality | 3 rank inequality |
| x0=kn-2 | f(x0)=x (kn-2) | |||
| x1=kn-1 | f(x1)=x (kn-1) | f[x0,x1] | ||
| x2=kn | f(x2)=x (kn) | f[x1,x2] | f[x0,x1,x2] | |
| x3=kn+1 | f(x3)=x (kn+1) | f[x2,x3] | f[x1,x2,x3] | f[x0,x1,x2,x3] |
Inequality result in table 2 is substituted into formula (1), obtains amplitude x of the signal in i-th of interpolation points(i) calculating
Value：
xs(i) ≈ P (i)=f [x0]+f[x0, x1](i-x0)+f[x0, x1, x2](i-x0)(i-x1)+
(4)
f[x0, x1, x2, x3](i-x0)(i-x1)(i-x2)
Step 6, to syncul sequence xs(n0) carry out Fast Fourier Transform (FFT).
Time window be 10 primitive period length, sample frequency be Dot × fr(fr=50Hz), Dot is every cycle sampling
In the case of points, the calculation formula of harmonic parameters is as follows：
In formula (5), f1·10·Dot·TsThe position for being fundamental frequency on frequency spectrum, X (mf1·10·Dot·Ts) be
The FFT result of m subharmonic.
Embodiment
The voltage signal x (t) containing higher hamonic wave is chosen, illustrates the inventive method by taking the voltage signal as an example.
Step 1, fixed sampling frequency f0=25600Hz sample harmonic signal x (t) obtain the signal x (n) of discretization.
Step 2, processing is filtered to signal x (n), is specially：By signal x (n) by cut-off frequency be 75Hz two
Rank Butterworth lowpass filters, obtain fundamental signal x0(n)。
Step 3, threshold value a=0, detection fundamental signal x are set0(n) zero crossing situation is obtained under current electric grid fundamental frequency
The fundamental signal of ten continuous cycles, i.e. sampled data, sampled data length are designated as N.
Step 4, positive Newton interpolation is carried out to sampled data.
Whole period processing is carried out to the head and the tail both ends of sampled data, is specially：To sampled data x0(n) head and the tail both ends are crossed over
4 data at threshold value a carry out the positive Newton interpolation of three ranks, and threshold value a is accurately crossed over so as to obtain fundamental signal head and the tail both ends
At the time of, respectively tstartAnd tend.Four sampled points for crossing both sides at threshold value a are designated as k successivelyn-2、kn-1、kn、kn+ 1, make
With the Newton interpolating method of three rank inequality, t is calculatedstartAnd tendExact value, 3 ranks as shown in Table 3 and Table 4 are drawn according to table 1
Inequality table.
3 positive Newton interpolation of table is in tstartThree rank inequality tables of neighbouring sampled point
| xi | f(xi) | 1 rank inequality | 2 rank inequality | 3 rank inequality |
| x0=4.82e-4 | f(x0)=90 | |||
| x1=2.20e-4 | f(x1)=91 | -3.8107e3 | ||
| x2=-5.04e-5 | f(x2)=92 | -3.6987e3 | -2.1034e5 | |
| x3=-3.13e-4 | f(x3)=93 | -3.8031e3 | 1.9579e5 | 3.0889e5 |
The inequality result of table 3 is substituted into formula (1), obtains tstartCalculated value.
tstart≈ P (a)=f [x0]+f[x0, x1](a-x0)+f[x0, x1, x2](a-x0)(a-x1)+
(6)
f[x0, x1, x2, x3](a-x0)(a-x1)(a-x2)=91.8159
4 positive Newton interpolation of table is in crosspoint tendThree rank inequality tables of neighbouring sampled point
| xi | f(xi) | 1 rank inequality | 2 rank inequality | 3 rank inequality |
| x0=5.15e-4 | f(x0)=5149 | |||
| x1=2.58e-4 | f(x1)=5150 | -3.8832e3 | ||
| x2=-1.17e-6 | f(x2)=5151 | -3.7088e3 | -3.3073e5 | |
| x3=-2.78e-4 | f(x3)=5152 | -3.7506e3 | 7.7890e4 | 6.5646e6 |
Inequality result in table 4 is substituted into formula (1), obtains tendCalculated value.
tend≈ P (a)=f [x0]+f[x0, x1](a-x0)+f[x0, x1, x2](a-x0)(a-x1)+
(7)
f[x0, x1, x2, x3](a-x0)(a-x1)(a-x2)=5150.9576
And then by tend-tstartThe time domain length for trying to achieve the cycle signal of sample sequence 10 is 5059.1417.
Step 5, syncul sequence is obtained to the reverse Newton interpolation of sampled data.In the situation that power network fundamental frequency is 50Hz
Under, the sampled signal length of ten cycles is：
N0=f0/ 50Hz × 10=5120 (8)
During due to Implementation of Embedded System Fast Fourier Transform (FFT), the points converted every time are changeless, and are being become
Calculation times are minimum when the points changed are 2 integral number power, fastest.Therefore the complete cycle of gained in step 4 is adopted
Sample sequence obtains being equal to N for length by reverse Newton interpolation0Syncul sequence.
The interpolation point for carrying out reverse Newton interpolation is tend-tstartN0On individual Along ent.Utilize 4 near each interpolation point
Individual sample point data, the three rank inequality methods according to table 2 carry out the reverse Newton interpolation of three ranks, obtain original at each interpolation point adopt
The amplitude of sample signal.
Below by taking the 2500th interpolation point as an example, there is provided the n of the interpolation point position2500Computational methods, it is as follows：
The position of 4 near the interpolation point sampled points is taken to be followed successively by x0=2469, x1=2470, x2=2471, x3=
2472, according to three rank Newton interpolating methods by former sequence this four sampling point positions sampled value, calculate adjustment after sequence exist
Signal amplitude at 2500th point, its computational methods are as shown in table 5.
3 rank inequality tables of the 5 reverse Newton interpolation of table in n-th (n=2500) individual interpolation point
| xi | f(xi) | 1 rank inequality | 2 rank inequality | 3 rank inequality |
| x0=2469 | f(x0)=190.5057 | |||
| x1=2470 | F (x1)=192.1845 | 1.6788 | ||
| X2=2471 | F (x2)=194.2564 | 2.0719 | 0.1966 | |
| x3=2472 | f(x3)=196.6452 | 2.3888 | 0.1584 | -0.0127 |
The mean deviation result of table 5 is substituted into formula (1), obtains amplitude x of the signal in n-th (n=2500) individual interpolation points
(2500) calculated value：
xs(2500) ≈ P (2470.2840)=f [x0]+f[x0, x1](2470.2840-x0)+f[x0, x1, x2]
(2470.2840-x0)(2470.2840-x1)+f[x0, x1, x2, x3](2470.2840-x0) (10)
(2470.2840-x1)(2470.2840-x2)=192.7363
Other interpolation points can similarly be handled, it is n to obtain length0Syncul sequence xs(n0)。
Step 6, to the syncul sequence x of gained in step 5s(n0) carry out Fast Fourier Transform (FFT).
The signal frequency of this implementation is 50.6 hertz, and it is 2.44 × 10 that fundamental frequency, which calculates relative error,-10, amplitude and phase
Position and error analysis are as shown in table 6.
The error analysis table of the harmonic signal of table 6
Claims (5)
1. two-way interpolation synchronizes the FFT electric harmonic detection methods of sample sequence, it is characterized in that, including：
Step 1, mutual inductor sample harmonic signal obtains the signal x (n) of discretization, and processing is filtered to signal x (n) and obtains fundamental wave
Signal x0(n)；
Step 2, the fundamental signals of ten continuous cycles is taken to be specially as sampled data：
Threshold value a, detection fundamental signal x are set0(n) amplitude crosses over a number, the 1st time and the 21st time data crossed between threshold value a
The fundamental signal of i.e. ten continuous cycles, a are fundamental signal x0(n) arbitrary value between peak value；
Step 3, sampled data is carried out positive Newton interpolation obtain sampled data amplitude the 1st time and the 21st time across threshold value a when
Carve position, the two at moment position be designated as t respectivelystartAnd tend；
Step 4, with moment position tstartAnd tendBetween N0Individual Along ent is interpolation point, and carrying out reverse newton to sampled data inserts
Value, obtains the signal amplitude at each interpolation point, that is, obtains and synchronize sample sequence, N0=f0/ 50Hz × 10, f0For fundamental frequency；
Step 5, Fast Fourier Transform (FFT) is carried out to syncul sequence.
2. two-way interpolation as claimed in claim 1 synchronizes the FFT electric harmonic detection methods of sample sequence, it is characterized in that：
In step 1, processing is filtered to signal x (n) using second order Butterworth lowpass filters.
3. two-way interpolation as claimed in claim 1 synchronizes the FFT electric harmonic detection methods of sample sequence, it is characterized in that：
Described threshold value a=0.
4. two-way interpolation as claimed in claim 1 synchronizes the FFT electric harmonic detection methods of sample sequence, it is characterized in that：
Step 3 is specially：
Each two sample point datas carry out positive Newton interpolation before and after taking at the 1st leap threshold value a of sampled data amplitude, obtain the moment
tstart；Similarly, the positive newton of each two sample point datas progress inserts before and after taking at the 21st leap threshold value a of sampled data amplitude
Value, obtains moment tend, tstartAnd tendDifference be sampled data time domain length, i.e. sampled data complete cycle.
5. two-way interpolation as claimed in claim 1 synchronizes the FFT electric harmonic detection methods of sample sequence, it is characterized in that：
Step 3 is specially：
To each interpolation point, the reverse Newton interpolation of three ranks is carried out using each 2 data before and after being distributed in interpolation point, is obtained at each interpolation point
Signal amplitude, so as to obtain synchronization sample sequence.
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