CN103105532A - Harmonic electric energy measuring system of improved Fourier transform and control method thereof - Google Patents

Abstract

Provided are a harmonic electric energy measuring system of an improved Fourier transform and a control method. The harmonic electric energy measuring system for the improved Fourier transform comprises a three-phase power grid data acquisition module, a data processing module, a data management module and a peripheral module, wherein the three-phase power grid data acquisition module is connected with the data processing module through a parallel port, the data processing module is connected with the data management module through an asynchronous series port, and the data management module is directly connected with the peripheral module. By means of the harmonic electric energy measuring system for the improved Fourier transform and the control method thereof, influences of fundamental frequency fluctuation and inter harmonic are overcome well, and accuracy in computing harmonic parameter is improved.

Description

A kind of harmonic electric energy metering system and control method thereof of improving Fourier transform

Technical field

The present invention relates to the signal process field, specifically a kind of harmonic electric energy metering system and control method thereof of improving Fourier transform.

Background technology

Along with intelligent grid build fully under way, various distributed power generations and energy storage device are incorporated into the power networks, and also make the harmonic pollution problem more serious when improving the mains supply reliability.In actual measurement, cause the uncertainty of harmonic frequency due to the mains frequency deviation, the impact of voltage fluctuation and a harmonic wave etc. all can reduce the accuracy of frequency analysis.Pin-point accuracy Harmonic detection and analysis under unstable state can provide scientific basis for the harmonic wave bi-directional current calculates, harmonic electric energy measures, harmonic wave suppresses and compensation etc., to improving energy utilization rate, safeguard the green electric power supply environment, guaranteeing that electric power netting safe running is significant.

Electric Power Harmonic Analysis has developed multiple time domain based on digital signal processing, frequency domain method.Wherein, Fast Fourier Transform (FFT) is widely applied because it calculates simple and is easy to Implementation of Embedded System.But the constant sampling rate of the many employings of existing surveying instrument adds the existence of a harmonic wave, subharmonic etc., and the synchronized sampling under unstable state is difficult to strict realization, and the spectrum leakage that causes and fence effect affect the accuracy of frequency analysis.The window function weighting can reduce the impact of spectrum leakage, can improve to a certain extent the frequency analysis accuracy in conjunction with the corresponding algorithm that improves, but its error of calculation is still larger during the harmonic signal under analyzing unstable state.

Summary of the invention

The object of the invention is to overcome frequency analysis and causes the impact of spectrum leakage and fence effect under unstable state, a kind of harmonic electric energy metering system and control method thereof of improving Fourier transform proposed, can effectively overcome the impact of fundamental frequency fluctuation and a harmonic wave, the harmonic parameters accuracy in computation obviously improves, be suitable for the frequency analysis under unsteady state condition, thereby improve accuracy and practicality that signal harmonic is analyzed, for signal parameter identification and the harmonic electric energy metering of further carrying out provides reliable basis.

The present invention is achieved through the following technical solutions above-mentioned purpose: a kind of harmonic electric energy metering system that improves Fourier transform, formed by three phase network data acquisition module, data processing module, data management module and peripheral module, wherein, the three phase network data acquisition module is connected with data processing module by parallel interface, data processing module is connected by asynchronous serial port with data management module, and data management module directly is connected with peripheral module.

Described three phase network data acquisition module comprises resistance pressure-dividing network, TA and resistor network and sampling A/D chip ADS8364, in order to synchronized sampling and the A/D conversion of completing three phase network voltage, current signal.

Described data processing module adopts signal processor ADSP-BF533, adopts based on the harmonic electric energy metering method of cosine even power window improvement Fourier transform image data is carried out analyzing and processing.

Described data management module adopts single-chip microcomputer M30624FGPFP, the functions such as the demonstration of completion system, storage, communication and function selection.

At first the control method of the harmonic electric energy metering system of described improvement Fourier transform comprises the steps: the multifrequency signal that contains harmonic wave and a harmonic component by sample rate f _sCarry out data acquisition, obtain its discrete series; Then the harmonic analysis method based on cosine even power window improvement Fourier transform carries out windowing process to discrete series, obtains the sign formula of harmonic signal; Use at last least square method to carry out match to the peak value spectral line, derive frequency, amplitude and the phase calculation correction formula of signal first-harmonic and each harmonic, calculate amplitude, frequency, the initial phase angle of harmonic wave by harmonic amplitude, frequency and initial phase angle amendment type analysis meter at last.

Principle of the present invention is:

The discrete time-domain expression formula of typical case's cosine function window is

w _cos(n)＝sin ^α(nπ/N),n＝0,1,2，...,N-1 (1)

In formula, the value of integer α determines the form of window function.When parameter alpha satisfied α=2p (p is natural number), the cosine function window of formula (1) form can be expressed as

$w_{\cos }\left(n\right)=\underset{m=0}{\overset{p}{\mathrm{\Σ}}}{(-1)}^m{J}_m\cos (2\mathrm{\πmn}/N)---\left(2\right)$

In formula, n=0,1,2 ...., N-1; J _mSatisfy constraint condition:

$\underset{m=0}{\overset{p}{\mathrm{\Σ}}}{(-1)}^m{J}_m=0,\underset{m=0}{\overset{p}{\mathrm{\Σ}}}{J}_m=1---\left(3\right)$

Claim that the window function of this moment is cosine even power window, can get its discrete Fourier transformation (DFT) expression formula by formula (2) to be

$W_{\cos }\left(\mathrm{\ω}\right)=\underset{m=0}{\overset{p}{\mathrm{\Σ}}}{(-1)}^m\frac{J_m}{2}[W_R(\mathrm{\ω}-m)+W_R(\mathrm{\ω}+m)]---\left(4\right)$

In formula, W _R(.) is the DFT expression formula of rectangular window

$W_R\left(\mathrm{\ω}\right)=\frac{\sin \left(\mathrm{\ω\π}\right)}{\sin (\mathrm{\ω\π}/N)}{e}^{-j(N-1)\mathrm{\ω\π}/N}---\left(5\right)$

N generally〉〉 1, the DFT that can get the EOCW window simplifies expression formula and is

$W_{\cos }\left(\mathrm{\ω}\right)=\frac{\mathrm{N\ω}}{\mathrm{\π}}\sin \left(\mathrm{\π\ω}\right)e^{-\mathrm{j\π\ω}}\underset{m=0}{\overset{p}{\mathrm{\Σ}}}{(-1)}^m\frac{J_m}{{\mathrm{\ω}}^2-m^2}---\left(6\right)$

The main lobe width of window function reacts its frequency resolution, and main lobe is wider, and frequency resolution is lower; The spectrum leakage of window function suppresses ability can be described by its side lobe peak level and side lobe attenuation speed, and peak level is less and side lobe attenuation speed is larger, and it is stronger that its spectrum leakage suppresses ability.

The main lobe width B of typical case EOCW window _W, side lobe peak level Asl and side lobe attenuation speed D _slWith parameter p, following approximation relation is arranged:

B _W＝4(p+1)π/N (7)

A _sl≈-16(p+1) (8)

D _sl≈6(2p+1) (9)

The multifrequency signal x (t) that contains harmonic wave and a harmonic component is f through sampling rate _sData acquisition system (DAS) after the discrete series that obtains be

In formula, A _k, f _k,

Be respectively amplitude, frequency and the phase place of k subharmonic; x _i(n) be between harmonic component.

For the sake of simplicity, ignore the impact of a harmonic wave, and without loss of generality, take the k subharmonic as example.Signal x (n) is through cosine even power window W _cos(n) obtain the N point after the weighting brachymemma long

In formula, λ ∈ [1, K], f _k=λ _kf ₁, f ₁Be fundamental frequency.

Suppose that following two conditions are met:

1）10f ₁＜f _k＜f _s/2-10f ₁

2）|λ _k-λ _q|＞B _W，k,q∈[1,K]，k≥2，k≠q

The impact of negative frequency secondary lobe (in formula 11 the 2nd) and all the other each harmonics all can be ignored the leakage contribution of k subharmonic (in formula 11 the 3rd), and this up-to-date style (11) can be changed into

The harmonic signal parameter can be passed through X _cos(λ) characterize, during synchronized sampling, the corresponding frequency λ of k subharmonic _kA singlet line at place; Under non-synchronous sampling, energy leakage is to whole frequency band, and due to fence effect, the peak point that the k subharmonic is corresponding departs from discrete frequency.At this moment, λ _kBe non-integer, suppose

λ _k＝l _k+ _k, _k∈[0,1] (13)

In formula, l _kδ _kThe corresponding real part of difference and fraction part.

Near supposing peak point, the corresponding maximum and inferior maximum spectral line of amplitude is respectively l _kAnd l _k+1The bar spectral line, its corresponding amplitude is respectively y _k1=| X _cos(l _k) |, y _k2=| X _cos(l _k+1) |.

Definition μ _k=δ _k-0.5, ε _k=(y _k1-y _k2)/(y _k1+ y _k2), can get through substitution of variable:

${\mathrm{\ϵ}}_k=\frac{W_{\cos }(-{\mathrm{\μ}}_k-0.5)-W_{\cos }(-{\mathrm{\μ}}_k+0.5)}{W_{\cos }(-{\mathrm{\μ}}_k-0.5)+W_{\cos }(-{\mathrm{\μ}}_k+0.5)}=f\left({\mathrm{\μ}}_k\right)---\left(14\right)$

Due to |-μ _k± 0.5|≤1, and N is generally larger, can be got by formula (6):

$\left|W_{\cos }(-{\mathrm{\μ}}_k\±0.5)\right|=\frac{N}{\mathrm{\π}}|\cos \left(\mathrm{\π}{\mathrm{\μ}}_k\right)\×\underset{m=0}{\overset{p}{\mathrm{\Σ}}}{(-1)}^m{J}_m\frac{-{\mathrm{\μ}}_k\±0.5}{{(-{\mathrm{\μ}}_k\±0.5)}^2-m^2}|---\left(15\right)$

Utilize least square curve fitting, can get formula (15) inverse function μ _k=f ₁(ε _k) approximant μ _k=F (ε _k), obtain parameter μ _k, the frequency amendment type of k subharmonic is

f _k＝λ _kf _s/N＝(l _k+μ _k+0.5)f _s/N (16)

To l _kAnd l _k+1The amplitude of bar spectral line is weighted on average, can obtain the amplitude correction formula of k subharmonic

$A_k=\frac{2(y_{k1}+y_{k2})}{\left|W_{\cos }(-\mathrm{\μ}-0.5)\right|+\left|W_{\cos }(-\mathrm{\μ}+0.5)\right|}---\left(17\right)$

When N was larger, the simplification expression formula that can be got formula (17) by formula (15) was A _k=N ^-1(y _k1+ y _k2) v (μ _k), further adopt least square fitting to approach, can get that it is approximant:

A _k＝N ^-1(y _k1+y _k2)R(μ _k) (18)

The phase place amendment type that convolution (12), (15) can obtain the k subharmonic is

Description of drawings

Fig. 1 is the block diagram of the harmonic electric energy metering system of improvement Fourier transform of the present invention.

Fig. 2 is the control method process flow diagram of the harmonic electric energy metering system of improvement Fourier transform of the present invention.

Specific embodiments

Below by drawings and Examples, technical scheme of the present invention is further illustrated.

As shown in Figure 1, the harmonic electric energy metering system of improvement Fourier transform of the present invention comprises three phase network data acquisition module, data processing module, data management module and four parts of peripheral module.Wherein, the three phase network data acquisition module comprises resistance pressure-dividing network, TA and resistor network and ADS8364 chip, realizes the real-time synchronization sampling to electrical network three-phase voltage, current signal; Sampled data is sent in data processing module by parallel interface; Data processing module adopts the ADSP-BF533 chip, improve the Fourier transform harmonic analysis method based on cosine even power window voltage, current waveform are carried out spectrum analysis, isolate first-harmonic and each harmonic component, complete electric parameter metering, frequency analysis and harmonic electric energy metering, result sends to data management module by asynchronous serial port, complete data statistics, storage, communication and function selection etc. by the M30624FGPFP chip, complete at last the demonstration output of data by peripheral module.

As shown in Figure 2, the control method flow process of improvement Fourier transform harmonic wave metering system of the present invention is as follows: at first to the multifrequency signal that contains harmonic wave and a harmonic component by sample rate f _sCarry out data acquisition, obtain its discrete series; Then improve the Fourier transform harmonic analysis method based on cosine even power window discrete series is carried out windowing process, obtain the sign formula of harmonic signal; Use again least square method to carry out match to the peak value spectral line, derive frequency, amplitude and the phase calculation amendment type of signal first-harmonic and each harmonic; Calculate amplitude, frequency, the initial phase angle of harmonic wave by harmonic amplitude, frequency and initial phase angle amendment type analysis meter at last.

Claims (5)

1. harmonic electric energy metering system that improves Fourier transform, it is characterized in that, this system is comprised of three phase network data acquisition module, data processing module, data management module and peripheral module, wherein, the three phase network data acquisition module is connected with data processing module by parallel interface, data processing module is connected by asynchronous serial port with data management module, and data management module directly is connected with peripheral module.

2. the harmonic electric energy metering system of improvement Fourier transform as claimed in claim 1, is characterized in that, described three phase network data acquisition module comprises resistance pressure-dividing network, TA and resistor network and sampling A/D chip ADS8364.

3. the harmonic electric energy metering system of improvement Fourier transform as claimed in claim 1, is characterized in that, described data processing module adopts signal processor ADSP-BF533.

4. the harmonic electric energy metering system of improvement Fourier transform as claimed in claim 1, is characterized in that, described data management module adopts single-chip microcomputer M30624FGPFP.

5. the control method of the harmonic electric energy metering system of improvement Fourier transform as claimed in claim 1, is characterized in that, comprises the steps: at first the multifrequency signal that contains harmonic wave and a harmonic component by sample rate f _sCarry out data acquisition, obtain its discrete series; Then the harmonic analysis method based on cosine even power window improvement Fourier transform carries out windowing process to discrete series, obtains the sign formula of harmonic signal; Use at last least square method to carry out match to the peak value spectral line, derive frequency, amplitude and the phase calculation correction formula of signal first-harmonic and each harmonic, calculate amplitude, frequency, the initial phase angle of harmonic wave by harmonic amplitude, frequency and initial phase angle amendment type analysis meter at last.

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