CN202339381U - Harmonic electric energy metering system based on Nuttall self-convolution window weighed FFT (Fast Fourier Transform) - Google Patents

Abstract

The utility model relates to a harmonic electric energy metering system based on Nuttall self-convolution window weighed FFT (Fast Fourier Transform). A Nuttall self-convolution window unit is connected with a signal sampling unit and an FFT arithmetic unit, a frequency range calculation unit of a hth-time harmonic wave is connected with the FFT arithmetic unit and a local searching unit with maximum amplitude and secondly maximum spectrum line, a frequency spectrum interpolation value calculation unit is connected with the local searching unit with the maximum amplitude and the secondly maximum spectrum line and a frequency offset calculation unit, and a harmonic parameter calculation unit is connected with the frequency offset calculation unit and the harmonic electric energy output unit. Through utilizing the harmonic electric energy metering system based on the Nuttall self-convolution window weighed FFT, integer-time harmonic electric wave measurement of a complex electric energy signal can be realized.

Description

A kind of harmonic electric energy metering system of Nuttall self-convolution window weighting Fourier transform

Technical field

The utility model relates to a kind of harmonic electric energy metering system, specifically is a kind of electric harmonic electric energy metered system of Nuttall self-convolution window weighting Fourier transform.Belong to the signal Processing field.

Background technology

The high-precision signal analysis be treated to harmonic trend calculating, Equipment Inspection, Harmonious Waves in Power Systems compensation and inhibition, analysis of vibration signal and random fault processing etc. scientific basis be provided.When adopting the Fourier transform theory to carry out signal Processing, because there is fluctuation in signal frequency or disturbs, strict synchronized sampling can't realize that spectrum leakage and fence effect can be introduced than mistake.

Find that through the document retrieval adopt window function can effectively reduce spectrum leakage to signal weighting, the main lobe of window function frequency spectrum is directly relevant with frequency resolution, main lobe is wide, frequency resolution is low; Secondary lobe is directly relevant with leakage, and secondary lobe is big, and leakage is many; The speed of side lobe attenuation slope reflection side lobe attenuation, side lobe attenuation is fast more, and is strong more to leak suppressing.Chinese scholars has proposed a series of window functions, like Hanning window, Blackman-Harris window, Rife-Vincent (I) window, Nuttall window and rectangle convolution window etc., and they is applied in the signal weighting Processing Algorithm, has improved the signal Processing precision.

Signal weighting analytical algorithm based on classical window function (Hanning window, Blackman-Harris window, Rife-Vincent (I) window, Nuttall window and rectangle convolution window etc.) utilizes the frequency spectrum secondary lobe dropping characteristic of window function can reduce spectrum leakage to a certain extent.But because the sidelobe performance of classical window is still not ideal enough, still limited to the inhibiting effect of spectrum leakage, the phase mutual interference between harmonic wave can not ignore, and the signal analysis and processing precision is restricted.

Summary of the invention

The utility model purpose is to overcome the defective of existing windowing Fourier transform harmonic electric energy metering system; A kind of easy Nuttall self-convolution window weighting Fourier transform harmonic electric energy metering system is provided; Solving signal weighting processing procedure intermediate frequency spectrum leaks excessive; The problem of phase mutual interference between harmonic wave, thus accuracy and the practicality that signal harmonic is analyzed improved, for signal parameter identification and the harmonic electric energy metering of further carrying out provides reliable basis.

The utility model is realized above-mentioned purpose through following technical scheme: a kind of harmonic electric energy metering system of Nuttall self-convolution window weighting Fourier transform; Local Search unit, frequency spectrum interpolation computing unit, frequency offset computing unit, harmonic parameters computing unit and harmonic electric energy output unit by signal sampling unit, the frequency range computing unit that adds Nuttall self-convolution window unit, FFT arithmetic element, h subharmonic, amplitude maximum and inferior big spectral line are formed; Add Nuttall self-convolution window unit and connect signal sampling unit and FFT arithmetic element; The frequency range computing unit of h subharmonic connects FFT arithmetic element and the maximum and inferior Local Search unit of spectral line greatly of amplitude; The frequency spectrum interpolation computing unit connects amplitude maximum and inferior the Local Search unit and the frequency offset computing unit of spectral line greatly, and the harmonic parameters computing unit connects frequency offset computing unit and harmonic electric energy output unit.

The said Nuttall self-convolution window unit that adds is that structure length is the discrete Nuttall window sequence of M earlier; Then p discrete Nuttall window sequence made convolution algorithm p-1 time; Obtain convolution sequence; Head or p-1 of tail benefit in convolution sequence are zero, and promptly obtaining length is the discrete Nuttall self-convolution window in p rank of N=pM.

Said frequency spectrum interpolation computing unit is that the utilization least square method is carried out match near the amplitude the harmonic frequency is maximum with time big spectral line, obtains the accurate frequency spectrum of this harmonic frequency.

This system's performing step is following: at first make up length and be discrete Nuttall window sequence, the Nuttall window convolution algorithm that will disperse then obtains convolution sequence; Head or tail zero padding in convolution sequence; Obtain discrete Nuttall self-convolution window, adopt Nuttall self-convolution window sequence that the discrete electrical force signal is computed weighted, adopt Fourier transform to obtain the discrete spectrum of electric power signal again; Near the maximum and inferior big spectral line of the searching amplitude corresponding harmonic frequency of discrete spectrum; The utilization least square method is carried out match to the peak value spectral line, obtains amplitude, frequency and the initial phase angle of electric harmonic, thereby realizes the integral frequency harmonizing wave electric energy metrical in the complicated electric power signal.

The principle of the utility model is:

The Nuttall window is the cosine composite window, and its time domain expression formula does

$w\left(n\right)=\underset{g=0}{\overset{G-1}{\mathrm{\Σ}}}{(-1)}^g{b}_g\cos (2\mathrm{\πn}\·g/N)$

In the formula, M is the item number of window function; N=0,1 ..., N-1; Bg satisfies constraint condition

$\left\{\begin{array}{c}\underset{g=0}{\overset{G-1}{\mathrm{\Σ}}}{b}_g=1\\ \underset{g=0}{\overset{G-1}{\mathrm{\Σ}}}{(-1)}^g{b}_g=0\end{array}\right.$

Table 1 has provided the coefficient of typical Nuttall window function

The coefficient of table 1 Nuttall window function

The Nuttall self-convolution window of time domain discrete does

Wherein, Subscript p representes to participate in the number of the Nuttall self-convolution window of convolution algorithm, and subscript N representes to participate in the Nuttall window of convolution, for ease of the realization of Fast Fourier Transform (FFT); Convolution results is carried out the zero padding operation, and then the length of discrete Nuttall self-convolution window is N=pM.

If only contain single-frequency signal components x (t), be f through SF _sAnalog to digital conversion after, obtain discrete series:

$x\left(m\right)=A_0\sin (2\mathrm{\π}\frac{f_0}{f_s}m+{\mathrm{\φ}}_0),$ m＝0，1，2，…，+∞

In the formula, A ₀, f ₀, φ ₀Be respectively amplitude, frequency and the initial phase angle of signal.

Signal after the discretize is added the p rank Nuttall self-convolution window w that length is N _N-p(n) (n=0,1 ..., N-1), the sequence that obtains after the brachymemma does

x(n)＝x(m)w _N-p(n)，n＝0，1，…，N-1

After sequence x (n) carried out discrete Fourier transformation, obtain its discrete spectrum and do

$X\left(k\right)=A_0{e}^{j{\mathrm{\φ}}_0}\frac{2^p{e}^{-j\left({k-k}_0\right)\mathrm{\π}}}{M^p}{\left\{\frac{\sin [\mathrm{\π}\left({k-k}_0\right)/2p]}{\sin [\mathrm{\π}\left({k-k}_0\right)/N]}\right\}}^{2p}$

In the formula, k ₀=f ₀N/f _s

If in the discrete spectrum, frequency f ₀Near local amplitude is maximum to be respectively k with time maximum spectral line ₁And k ₂Root satisfies k ₁≤k ₀≤k ₂=k ₁+ 1.In frequency f ₀Near the local peaking's search strategy that adopts finds this two spectral lines, can confirm k ₁And k ₂If these two spectral line amplitudes are respectively y ₁And y ₂, promptly

${\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HSA00000596565200012.png"\; state="\{\{state\}\}">y</figure-callout>}}_1=\left|X\left(k_1\right)\right|=\frac{{A_{0}2}^p}{M^p}{\left\{\frac{\sin [\mathrm{\&pi;}\left(k_1-k_0\right)/2p]}{\sin [\mathrm{\&pi;}\left(k_1-k_0\right)/N]}\right\}}^{2p}$

${\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HSA00000596565200012.png"\; state="\{\{state\}\}">y</figure-callout>}}_2=\left|X\left(k_2\right)\right|=\frac{{A_{0}2}^p}{M^p}{\left\{\frac{\sin [\mathrm{\&pi;}\left(k_2-k_0\right)/2p]}{\sin [\mathrm{\&pi;}\left(k_2-k_0\right)/N]}\right\}}^{2p}$

Consider 0≤k ₀-k ₁≤1, the definition alpha does

α＝k ₀-k ₁-0.5，-0.5≤α≤0.5

Y then ₁And y ₂Can be rewritten as function about α:

${\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HSA00000596565200012.png"\; state="\{\{state\}\}">y</figure-callout>}}_1=\frac{{A_{0}2}^p}{M^p}{\left\{\frac{\sin [\mathrm{\&pi;}(-\mathrm{\&alpha;}-0.5)/2p]}{\sin [\mathrm{\&pi;}(-\mathrm{\&alpha;}-0.5)/N]}\right\}}^{2p}$

${\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HSA00000596565200012.png"\; state="\{\{state\}\}">y</figure-callout>}}_2=\frac{{A_{0}2}^p}{M^p}{\left\{\frac{\sin [\mathrm{\&pi;}(-\mathrm{\&alpha;}+0.5)/2p]}{\sin [\mathrm{\&pi;}(-\mathrm{\&alpha;}+0.5)/N]}\right\}}^{2p}$

The definition factor beta does

$\mathrm{\&beta;}=\frac{y_2-y_1}{y_2+y_1}$

With the y in the formula following formula ₁And y ₂Replace, then β can be written as the function about α:

$\mathrm{\&beta;}=\frac{\left|W_{N-p}\right[2\mathrm{\&pi;}(-\mathrm{\&alpha;}+0.5)/N\left]\right|-\left|W_{N-p}\right[2\mathrm{\&pi;}(-\mathrm{\&alpha;}-0.5)/N\left]\right|}{\left|W_{N-p}\right[2\mathrm{\&pi;}(-\mathrm{\&alpha;}-0.5)/N\left]\right|+\left|W_{N-p}\right[2\mathrm{\&pi;}(-\mathrm{\&alpha;}+0.5)/N\left]\right|}=g\left(\mathrm{\&alpha;}\right)$

In α ∈ [0.5,0.5] scope,, utilize each α with the periodic sampling some spots _jValue calculates corresponding β _i, confirm to treat fitting of a polynomial number of times K, utilize and find the solution coefficient a on the formula _k(k=0,1 ..., K-1), thereby set up frequency spectrum interpolation polynomial expression S _K(x), can be designated as

α＝g ^-1(β)≈a ₁β+a ₂β ²+a ₃β ³+…+a _Kβ ^K

In the formula, a ₁, a ₂..., a _KCoefficient for polynomial fitting.

Frequency f ₀Calculating formula do

$f_0=k_0\frac{f_s}{N}=(\mathrm{\&alpha;}+k_1+0.5)\frac{f_s}{N}$

Amplitude does

$A_0=\frac{{2\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HSA00000596565200012.png"\; state="\{\{state\}\}">y</figure-callout>}}_1}{\left|W_{N-p}\right[2\mathrm{\&pi;}(-\mathrm{\&alpha;}-0.5)/N\left]\right|}$

Or

$A_0=\frac{{2\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HSA00000596565200012.png"\; state="\{\{state\}\}">y</figure-callout>}}_2}{\left|W_{N-p}\right[2\mathrm{\&pi;}(-\mathrm{\&alpha;}+0.5)/N\left]\right|}$

Initial phase angle does

${\mathrm{\&phi;}}_0=\arg \left[X\left(k_1\right)\right]+\frac{\mathrm{\&pi;}}{2}-\arg \left\{W_{N-p}\right[\frac{2\mathrm{\&pi;}(-\mathrm{\&alpha;}-0.5)}{N}\left]\right\}$

For the each harmonic component, all can find the solution parameter as stated above.

Description of drawings

Fig. 1 is the block scheme of the harmonic electric energy metering system of the described Nuttall self-convolution window weighting of the utility model Fourier transform.

Fig. 2 is the discrete spectrum interpolation processing synoptic diagram of the utility model.

Embodiment

Below through embodiment the technical scheme of the utility model is further specified.

As shown in Figure 1; A kind of harmonic electric energy metering system of Nuttall self-convolution window weighting Fourier transform; Local Search unit, frequency spectrum interpolation computing unit, frequency offset computing unit, harmonic parameters computing unit and harmonic electric energy output unit by signal sampling unit, the frequency range computing unit that adds Nuttall self-convolution window unit, FFT arithmetic element, h subharmonic, amplitude maximum and inferior big spectral line are formed; Add Nuttall self-convolution window unit and connect signal sampling unit and FFT arithmetic element; The frequency range computing unit of h subharmonic connects FFT arithmetic element and the maximum and inferior Local Search unit of spectral line greatly of amplitude; The frequency spectrum interpolation computing unit connects amplitude maximum and inferior the Local Search unit and the frequency offset computing unit of spectral line greatly, and the harmonic parameters computing unit connects frequency offset computing unit and harmonic electric energy output unit.

The implementation method of the harmonic electric energy metering system of the described Nuttall self-convolution window weighting of the utility model Fourier transform is carried out as follows:

At first set up discrete 4 minimum secondary lobe Nuttall windows of M=64, G=3, promptly select b0=0.3635819, b1=0.4891775, b2=0.1365995, b3=0.0106411, through the sequence of 4 minimum secondary lobe Nuttall windows of computes:

$w\left(n\right)=\underset{g=0}{\overset{G-1}{\mathrm{\&Sigma;}}}{(-1)}^g{b}_g\cos (2\mathrm{\&pi;n}\&CenterDot;g/N)$

Secondly, w (n) is carried out 2～4 rank from convolution algorithm, promptly p respectively value be 2,3 and 4, carry out corresponding zero padding operation again, make the length of 4 the minimum secondary lobe Nuttall self-convolution windows in 2～4 rank be respectively 128,192 and 256.

The voltage signal that is provided with a multi-frequency composition does

$x\left(n\right)=A_0+A_1\sin (2\mathrm{\&pi;}\frac{f_{1}n}{N}+{\mathrm{\&phi;}}_1)+A_3\sin (2\mathrm{\&pi;}\frac{f_{3}n}{N}+{\mathrm{\&phi;}}_3)$

In the formula, A ₀=0.2V; A ₁=6V; f ₁=20.2Hz; φ ₁=0.1rad; A ₃=1; f ₃=60.6Hz; φ ₃=0rad.

Adopt 4 the minimum secondary lobe Nuttall self-convolution windows in 4 rank set up that discrete series x (n) is carried out weighting, carry out discrete Fourier transformation again, obtain the discrete spectrum after the voltage signal weighting.Discrete spectrum is carried out normalization handle, near the spectrum amplitude the frequency f 1 distributes as shown in Figure 2.Signal frequency f ₁Do not overlap, and be positioned at the maximum spectral line k of discrete spectrum amplitude with discrete spectral line ₁=4 with time big spectral line k ₂Between=5.After confirming that k1 and k2 are respectively maximum and second largest peak value spectral line; Obtain corresponding range value y1 and y2; According to the least square peaks spectrum fit procedure in the aforementioned summary of the invention; Calculate the high reps of polynomial expression when being set to K=5, add 4 the minimum secondary lobe Nuttall self-convolution windows in 4 rank after, the discrete spectrum interpolation polynomial does

α4 _th＝0.4026β ⁵+0.7644β ³+11.9048β

Will Bring following formula into, promptly calculating f1 is 20.1999999996Hz, and A0 is 0.20000000007V, and A1 is 5.9999999999V, φ ₁Be 0.10000008rad.And the like, can calculate A3 is 0.99999999997V, f3 is 60.60000000001Hz, φ ₃For-0.00000002rad.

As shown in Figure 2, discrete spectrum interpolation processing principle is:

Be located in the discrete spectrum, near the local amplitude the frequency f 0 is maximum to be respectively k with time maximum spectral line ₁And k ₂Root, establishing these two spectral line amplitudes is respectively y ₁And y ₂Consider 0≤k ₀-k ₁≤1, the definition alpha does

α＝k ₀-k ₁-0.5，-0.5≤α≤0.5

Y then ₁And y ₂Can be rewritten as the function about α, the definition factor beta does

$\mathrm{\&beta;}=\frac{y_2-y_1}{{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HSA00000596565200012.png"\; state="\{\{state\}\}">y</figure-callout>}}_2+{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HSA00000596565200012.png"\; state="\{\{state\}\}">y</figure-callout>}}_1}$

With the y in the following formula ₁And y ₂Replace, then β can be written as the function about α:

$\mathrm{\&beta;}=\frac{\left|W_{N-p}\right[2\mathrm{\&pi;}(-\mathrm{\&alpha;}+0.5)/N\left]\right|-\left|W_{N-p}\right[2\mathrm{\&pi;}(-\mathrm{\&alpha;}-0.5)/N\left]\right|}{\left|W_{N-p}\right[2\mathrm{\&pi;}(-\mathrm{\&alpha;}-0.5)/N\left]\right|+\left|W_{N-p}\right[2\mathrm{\&pi;}(-\mathrm{\&alpha;}+0.5)/N\left]\right|}=g\left(\mathrm{\&alpha;}\right)$

In α ∈ [0.5,0.5] scope,, utilize each α with the periodic sampling some spots _iValue calculates corresponding β _i, confirm to treat fitting of a polynomial number of times K, utilize and find the solution coefficient a on the formula _k(k=0,1 ..., K-1), thereby set up frequency spectrum interpolation polynomial expression S _K(x), can be designated as

α＝g ^-1(β)≈a ₁β+a ₂β ²+a ₃β ³+…+a _Kβ ^K

In the formula, a ₁, a ₂..., a _KCoefficient for polynomial fitting.Thereby realize the discrete spectrum interpolation processing.

Claims (3)

1. the harmonic electric energy metering system of a Nuttall self-convolution window weighting Fourier transform; It is characterized in that; This system is made up of Local Search unit, frequency spectrum interpolation computing unit, frequency offset computing unit, harmonic parameters computing unit and the harmonic electric energy output unit of signal sampling unit, the frequency range computing unit that adds Nuttall self-convolution window unit, FFT arithmetic element, h subharmonic, amplitude maximum and inferior big spectral line; Add Nuttall self-convolution window unit and connect signal sampling unit and FFT arithmetic element; The frequency range computing unit of h subharmonic connects FFT arithmetic element and the maximum and inferior Local Search unit of spectral line greatly of amplitude; The frequency spectrum interpolation computing unit connects amplitude maximum and inferior the Local Search unit and the frequency offset computing unit of spectral line greatly, and the harmonic parameters computing unit connects frequency offset computing unit and harmonic electric energy output unit.

2. the harmonic electric energy metering system of Nuttall self-convolution window weighting Fourier transform according to claim 1; It is characterized in that; The said Nuttall self-convolution window unit that adds is that structure length is the discrete Nuttall window sequence of M earlier, then p discrete Nuttall window sequence is made convolution algorithm p-1 time, obtains convolution sequence; Head or p-1 of tail benefit in convolution sequence are zero, and promptly obtaining length is the discrete Nuttall self-convolution window in p rank of N=pM.

3. the harmonic electric energy metering system of Nuttall self-convolution window weighting Fourier transform according to claim 1; It is characterized in that; Said frequency spectrum interpolation computing unit is that the utilization least square method is carried out match near the amplitude the harmonic frequency is maximum with time big spectral line, obtains the accurate frequency spectrum of this harmonic frequency.

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