CN103592512A - Harmonic analysis method of power quality harmonic analyzer - Google Patents

Abstract

The invention discloses a harmonic analysis method of a power quality harmonic analyzer. The harmonic analysis method of the power quality harmonic analyzer is realized through improvement based on a quasi-synchronous DFT. The harmonic analysis method of the power quality harmonic analyzer comprises the steps that an electrical signal X on which harmonic analysis needs to be conducted is sampled in a power grid, and data of W+2 sampling points are sampled at equal intervals; the position for frequency domain sampling is changed according to the drifting Mu a signal frequency, when the harmonic analysis is conducted by means of the quasi-synchronous DFT, namely the position for the frequency domain sampling is Mu2pi/N. According to the harmonic analysis method of the power quality harmonic analyzer, after the amplitude and the initial phase angle of each harmonic wave of the electric signal X are calculated, the percentage and the phase angle difference between the amplitude value Pk of a higher harmonic and the amplitude value of a fundamental harmonic P1 of a voltage signal V and the percentage and the phase angle difference between the amplitude value Pk of a higher harmonic and the amplitude value of a fundamental harmonic P1 of a current signal I are calculated respectively, output and displayed.

Description

A kind of harmonic analysis method of electric energy quality harmonic analyser

The application divides an application, the application number of original application: 201110322629.4, and invention and created name: a kind of harmonic analysis method of electric energy quality harmonic analyser, the applying date: 2011-10-21.

Technical field

The present invention relates to the technical field that electric energy quality harmonic is analyzed, specifically a kind of high-precision harmonic analysis method.

Background technology

Frequency analysis technology is widely used in various fields such as electric energy quality monitoring, electronic product production testing, electric equipment monitoring, is the important technical of carrying out power system monitor, quality inspection, monitoring of tools.

In power supply grid, the generation of harmonic phenomena is mainly due to large-capacity power equipment, cause with electric rectification or converter and other nonlinear-loads.Along with the develop rapidly of Power Electronic Technique, many industrial enterprises introduce a large amount of impact load, asymmetric load and nonlinear load in recent years, and they inevitably occur harmonic pollution phenomenon when access electrical network.Therefore, the voltage of power supply grid, current signal are carried out to frequency analysis, can observe better electric network pollution situation, and then provide theoretical foundation for power network compensation and purification.

The most widely used technology of frequency analysis is discrete Fourier transformation (DFT) and Fast Fourier Transform (FFT) (FFT) at present.The frequency analysis technology that accurate synchronous sampling technique and DFT technology combine (that is: accurate synchronous DFT frequency analysis technology) can improve the precision of frequency analysis, and its formula is:

$\left\{\begin{array}{c}{a}_k={2F}_{\mathrm{ak}}^n=\frac{2}{Q}\underset{i=0}{\overset{W}{\mathrm{\Σ}}}{\mathrm{\γ}}_{i}f\left(i\right)\cos \left(k\frac{2\mathrm{\π}}{N}i\right)\\ b_k={2F}_{\mathrm{bk}}^n=\frac{2}{Q}\underset{i=0}{\overset{W}{\mathrm{\Σ}}}{\mathrm{\γ}}_{i}f\left(i\right)\sin \left(k\frac{2\mathrm{\π}}{N}i\right)\end{array}\right.,$

In formula: k is for needing the number of times (as first-harmonic k=1,3 subharmonic k=3) of the harmonic wave of acquisition; Sin and cos are respectively sine and cosine functions; And a _kand b _kbe respectively real part and the imaginary part of k subharmonic; N is iterations; W determines by integration method, while adopting complexification trapezoidal integration method, and W=nN; γ _iit is a weighting coefficient; for all weighting coefficient sums; I the sampled value that f (i) is analysis waveform; N is sampling number in the cycle.

In engineering application, frequency analysis is always carried out the sampling of finite point and is difficult to accomplish the synchronized sampling of stricti jurise.Like this, when the accurate synchronous DFT of application carries out frequency analysis, the short scope leakage that will exist the long scope causing due to truncation effect to leak and cause due to fence effect, makes analysis result precision not high, even not credible.

Summary of the invention

The technical problem to be solved in the present invention is to provide the harmonic analysis method of the electric energy quality harmonic analyser that a kind of precision is higher, effectively to improve the analytical error of accurate synchronous DFT frequency analysis technology, obtain high-precision frequency analysis result, thereby improve the reliability of the electric energy quality monitoring equipment based on frequency analysis theory and the validity of state judgement.

For solving the problems of the technologies described above, the invention provides a kind of harmonic analysis method of electric energy quality harmonic analyser, described electric energy quality harmonic analyser comprises successively and to be connected: sensor, signal conditioning circuit, data acquisition circuit and CPU element; Described harmonic analysis method comprises the steps:

(1) in described CPU element sampling electrical network, need the electric signal X of frequency analysis, and equal interval sampling W+2 sampling number is according to { f (i), i=0,1, w+1}(W is determined by selected integration method, the present invention does not specify a certain integration method, conventional integration method has complexification trapezoidal integration method W=nN, complexification rectangular integration method W=n (N-1), iterative Simpson integration method W=n (N-1)/2 etc., and the actual conditions that can apply according to the present invention are selected suitable integration method.Generally more satisfactory with complexification trapezoidal integration method effect);

(2) CPU element starts the accurate synchronous DFT formula of application from the sampled point i=0 of described electric signal X:

$\left\{\begin{array}{c}{a}_k={2F}_{\mathrm{ak}}^n=\frac{2}{Q}\underset{i=0}{\overset{W}{\mathrm{\Σ}}}{\mathrm{\γ}}_{i}f\left(i\right)\cos \left(k\frac{2\mathrm{\π}}{N}i\right)\\ b_k={2F}_{\mathrm{bk}}^n=\frac{2}{Q}\underset{i=0}{\overset{W}{\mathrm{\Σ}}}{\mathrm{\γ}}_{i}f\left(i\right)\sin \left(k\frac{2\mathrm{\π}}{N}i\right)\end{array}\right.,$

Analyze W+1 data acquisition first-harmonic information

with

Then, CPU element starts the accurate synchronous DFT formula of application from the sampled point i=1 of described electric signal X:

$\left\{\begin{array}{c}{a}_k={2F}_{\mathrm{ak}}^n=\frac{2}{Q}\underset{i=0}{\overset{W+1}{\mathrm{\Σ}}}{\mathrm{\γ}}_{i}f\left(i\right)\cos \left(k\frac{2\mathrm{\π}}{N}(i-1)\right)\\ b_k={2F}_{\mathrm{bk}}^n=\frac{2}{Q}\underset{i=0}{\overset{W+1}{\mathrm{\Σ}}}{\mathrm{\γ}}_{i}f\left(i\right)\sin \left(k\frac{2\mathrm{\π}}{N}(i-1)\right)\end{array}\right.,$

Analyze W+1 data acquisition first-harmonic information

with

;

Application of formula $\mathrm{\μ}=N\frac{{\mathrm{tg}}^{-1}\left[\frac{F_{a0}^n\left(1\right)}{F_{b0}^n\left(1\right)}\right]-{\mathrm{tg}}^{-1}\left[\frac{F_{a0}^n\left(0\right)}{F_{b0}^n\left(0\right)}\right]}{2\mathrm{\π}}$ Calculate the frequency drift μ of described electric signal X;

Application of formula $\left\{\begin{array}{c}{a}_k=\frac{2}{Q}\underset{i=0}{\overset{W}{\mathrm{\Σ}}}{\mathrm{\γ}}_{i}f\left(i\right)\cos \left(k\frac{\mathrm{\μ}2\mathrm{\π}}{N}i\right)\\ b_k=\frac{2}{Q}\underset{i=0}{\overset{W}{\mathrm{\Σ}}}{\mathrm{\γ}}_{i}f\left(i\right)\sin \left(k\frac{\mathrm{\μ}2\mathrm{\π}}{N}i\right)\end{array}\right.,$ Draw respectively the first-harmonic of described electric signal X and the real part a of higher hamonic wave _xwith imaginary part b _k;

(3), CPU element calculates respectively the first-harmonic of described electric signal X and the amplitude of higher hamonic wave $P_k=\sqrt{a_k^2+b_k^2}$ And initial phase angle

(5), CPU element calculates respectively the amplitude P of the higher hamonic wave of described electric signal X _kwith first-harmonic P ₁amplitude number percent

and phase angle difference

and output display (the general LCD unit being connected with this CPU element that adopts shows).

Described electric signal X is generally grid ac voltage signal or grid alternating current stream signal.

Accurate synchronous DFT frequency analysis can effectively suppress long scope and leak, the main cause of its spectrum leakage is that the short scope that signal frequency drift causes is leaked, and signal frequency drift causes principal character that short scope leaks is spectrum peak-to-peak value occurs position along with signal frequency drift synchronous change, so variable fence frequency domain sample can effectively catch according to signal drift the position that spectrum peak-to-peak value occurs, thereby obtains high-precision harmonic information.

Equal interval sampling is according to period T and the frequency f (if power frequency component frequency f is 50Hz, the cycle is 20mS) of carrying out the ideal signal of frequency analysis, the N point of sampling in one-period, and sample frequency is f _s=Nf, and N>=64.

Described sampling W+2 sampling number is according to being to do corresponding selection according to selected integration method, if adopt complexification trapezoidal integration method, W=nN; If adopt complexification rectangular integration method, W=n (N-1); If adopt iterative Simpson integration method, W=n (N-1)/2.Then according to sample frequency f _s=Nf, acquisition sampled point data sequence f (i), and i=0,1 ..., w+1}, n>=3, finally carry out frequency analysis to this data sequence.

An iteration coefficient γ _iby integration method, ideal period sampled point N and iterations n, determined, concrete derivation referring to document [Dai Xianzhong. the some problems [J] in accurate synchronized sampling application. electrical measurement and instrument, 1988, (2): 2-7.].

for all weighting coefficient sums.A _kand b _kfor imaginary part and the real part of k subharmonic, according to a _kand b _kjust can obtain harmonic amplitude and initial phase angle.

The drift μ of signal frequency obtains according to the fixed relationship of sampling number N in neighbouring sample point first-harmonic phase angle difference and ideal period, and the drift μ of signal frequency also can be used for revising the frequency f of first-harmonic and higher hamonic wave ₁frequency f with higher hamonic wave _k.

The present invention is mainly used in the analysis software of electric energy quality harmonic analyser, for improvement of the quality with improving frequency analysis, obtains amplitude, phase angle and the frequency of high-precision first-harmonic and higher hamonic wave.The present invention carries out sampling and analyzing by analyzed signal, and analysis result (amplitude, phase angle and frequency etc.) is exported according to the requirement of electric energy quality harmonic analyser.The harmonic analysis method that electric energy quality harmonic analyser of the present invention adopts, the frequency analysis technology for based on variable fence thought, has following technical advantage:

(1) high-precision frequency analysis result.No matter the analysis result that frequency analysis technology of the present invention obtains is that amplitude or phase angle error improve 4 more than the order of magnitude.

(2) frequency analysis technology of the present invention has fundamentally solved the low problem of accurate synchronous DFT analysis precision, and without carrying out complicated inverting and correction, algorithm is simple.

(3) with respect to the synchronous DFT of standard, frequency analysis technology of the present invention only need to increase a sampled point and just solve the large problem of accurate synchronous DFT analytical error, is easy to realize.

(4) application the present invention improves existing instrument and equipment, and technical is feasible, and does not need to increase any hardware spending and just can make analysis result can improve 4 more than the order of magnitude.

(5) variable fence thought is also applicable to carry out repeatedly iteration and the frequency analysis process of non-once iteration too, now only an iteration need to be resolved into repeatedly to iteration and realize just passable.Iteration is the same with iteration repeatedly in essence, and just when calculating, repeatedly iteration is carried out substep calculating, and iteration is that the process of iteration is repeatedly merged to iteration coefficient γ _iin once calculated, so the present invention is equally applicable to repeatedly iterative process.

(6) the present invention applies the position that accurate synchronous DFT carries out the sampling of frequency analysis time-frequency domain and changes according to the drift of signal frequency, and described frequency domain sampling position is μ 2 π/N, wherein: the drift that μ is signal frequency, during without drift, μ is 1.The thought of harmonic analysis method of the present invention based on variable fence, realizes by 5 analytical procedures.The thought of variable fence: the main cause of accurate synchronous DFT analytical error is position and the ideal position generation deviation that the drift of signal frequency causes spectrum peak to occur, if the analysis result still obtaining to sample in frequency domain according to 2 π/N is extremely incorrect.Variable fence refers to: the position of frequency domain sampling be not the 2 π/N fixing, but change according to the drift of signal frequency, frequency sampling position is the drift that μ 2 π/N(μ is signal frequency).Frequency domain sampling fence changes along with the drift of signal frequency can accurately estimate the position that higher hamonic wave peak value occurs, and then obtains high-precision amplitude and phase angle information.

Embodiment

Electric energy quality harmonic analyser is mainly comprised of sensor, signal conditioning circuit, data acquisition circuit, CPU, LCD unit and corresponding analysis software.Sensor generally adopts voltage transformer (VT) and current transformer, and the high voltage of tested electrical network and large current signal are changed by a certain percentage; The voltage that signal conditioning circuit is sent sensor here, current signal are transformed to the voltage signal that is applicable to data acquisition circuit sampling; By data acquisition circuit, the signal after conditioning is sampled, then completed the analysis of harmonic wave and detection by analysis software by CPU.

The harmonic analysis method of electric energy quality harmonic analyser of the present invention, comprises the following steps:

First, in CPU element sampling electrical network, need the electric signal X of frequency analysis, and an equal interval sampling W+2 sampled point, with obtain described electric signal X discrete series f (k), k=0,1 ..., w+1}.W is determined jointly by sampling number N in integration method, iterations n and ideal period.Equal interval sampling refers to according to the frequency f (if power frequency component frequency is 50Hz, the cycle is 20mS) of carrying out the ideal signal of frequency analysis determines sample frequency f _s=Nf, at sample frequency f _seffect under the N point of sampling equably in one-period.Usually, periodic sampling point N=64 or just can obtain good frequency analysis result above, and iterations n=3-5 just can obtain comparatively ideal frequency analysis result.Integration method has complexification trapezoidal integration method W=nN, complexification rectangular integration method W=n (N-1), Simpson's integration method W=n (N-1)/2 etc. multiple, can select according to actual conditions.

Secondly, CPU element starts the accurate synchronous DFT formula of application from the sampled point i=0 of described electric signal X: $\left\{\begin{array}{c}{a}_k={2F}_{\mathrm{ak}}^n=\frac{2}{Q}\underset{i=0}{\overset{W}{\mathrm{\Σ}}}{\mathrm{\γ}}_{i}f\left(i\right)\cos \left(k\frac{2\mathrm{\π}}{N}i\right)\\ b_k={2F}_{\mathrm{bk}}^n=\frac{2}{Q}\underset{i=0}{\overset{W}{\mathrm{\Σ}}}{\mathrm{\γ}}_{i}f\left(i\right)\sin \left(k\frac{2\mathrm{\π}}{N}i\right)\end{array}\right.,$ Analyze W+1 data acquisition first-harmonic information

with

wherein, an iteration coefficient γ _iby integration method, ideal period sampled point N and iterations n, determined, and

for all weighting coefficient sums.

Then, CPU element starts the accurate synchronous DFT formula of application from the sampled point i=1 of described electric signal X:

$\left\{\begin{array}{c}{a}_k={2F}_{\mathrm{ak}}^n=\frac{2}{Q}\underset{i=0}{\overset{W+1}{\mathrm{\Σ}}}{\mathrm{\γ}}_{i}f\left(i\right)\cos \left(k\frac{2\mathrm{\π}}{N}(i-1)\right)\\ b_k={2F}_{\mathrm{bk}}^n=\frac{2}{Q}\underset{i=0}{\overset{W+1}{\mathrm{\Σ}}}{\mathrm{\γ}}_{i}f\left(i\right)\sin \left(k\frac{2\mathrm{\π}}{N}(i-1)\right)\end{array}\right.,$ Analyze W+1 data acquisition first-harmonic information

with

.

Then, application of formula $\mathrm{\μ}=N\frac{{\mathrm{tg}}^{-1}\left[\frac{F_{a0}^n\left(1\right)}{F_{b0}^n\left(1\right)}\right]-{\mathrm{tg}}^{-1}\left[\frac{F_{a0}^n\left(0\right)}{F_{b0}^n\left(0\right)}\right]}{2\mathrm{\π}}$ The frequency drift μ that calculates described electric signal X obtains after frequency drift μ, can be according to sample frequency f _scalculate and obtain the first-harmonic of analyzed signal and the frequency f of higher hamonic wave with sampling number N in ideal period.

Then, application of formula $\left\{\begin{array}{c}{a}_k=\frac{2}{Q}\underset{i=0}{\overset{W}{\mathrm{\Σ}}}{\mathrm{\γ}}_{i}f\left(i\right)\cos \left(k\frac{\mathrm{\μ}2\mathrm{\π}}{N}i\right)\\ b_k=\frac{2}{Q}\underset{i=0}{\overset{W}{\mathrm{\Σ}}}{\mathrm{\γ}}_{i}f\left(i\right)\sin \left(k\frac{\mathrm{\μ}2\mathrm{\π}}{N}i\right)\end{array}\right.,$ Calculate respectively the first-harmonic of described electric signal X and the real part a of higher hamonic wave _kwith imaginary part b _k;

CPU element and then according to formula:

calculate respectively the first-harmonic of described electric signal X and the amplitude P of higher hamonic wave _kand initial phase angle:

Finally, CPU element calculates respectively the amplitude P of the higher hamonic wave of described electric signal X _kwith first-harmonic P ₁amplitude number percent

and phase angle difference

and output display (the general LCD unit being connected with this CPU element that adopts shows).

Those skilled in the art will be appreciated that, above embodiment is only for the present invention is described, and not as limitation of the invention, the present invention can also be varied to more mode, as long as within the scope of connotation of the present invention, to the variation of the above embodiment, modification, all will drop within the scope of claims of the present invention.

Claims (1)

1. a harmonic analysis method for electric energy quality harmonic analyser, is characterized in that comprising the following steps:

(1), need the electric signal X of frequency analysis equal interval sampling W+2 sampling number certificate in the CPU element of electric energy quality harmonic analyser sampling electrical network: f (i), i=0,1 ..., w+1};

(2), CPU element starts the accurate synchronous DFT formula of application from the sampled point i=0 of described electric signal X:

$\left\{\begin{array}{c}{a}_k={2F}_{\mathrm{ak}}^n=\frac{2}{Q}\underset{i=0}{\overset{W}{\mathrm{\Σ}}}{\mathrm{\γ}}_{i}f\left(i\right)\cos \left(k\frac{2\mathrm{\π}}{N}i\right)\\ b_k={2F}_{\mathrm{bk}}^n=\frac{2}{Q}\underset{i=0}{\overset{W}{\mathrm{\Σ}}}{\mathrm{\γ}}_{i}f\left(i\right)\sin \left(k\frac{2\mathrm{\π}}{N}i\right)\end{array}\right.,$ Analyze W+1 data acquisition first-harmonic information

with

Then, CPU element starts the accurate synchronous DFT formula of application from the sampled point i=1 of described electric signal X:

$\left\{\begin{array}{c}{a}_k={2F}_{\mathrm{ak}}^n=\frac{2}{Q}\underset{i=0}{\overset{W+1}{\mathrm{\Σ}}}{\mathrm{\γ}}_{i}f\left(i\right)\cos \left(k\frac{2\mathrm{\π}}{N}(i-1)\right)\\ b_k={2F}_{\mathrm{bk}}^n=\frac{2}{Q}\underset{i=0}{\overset{W+1}{\mathrm{\Σ}}}{\mathrm{\γ}}_{i}f\left(i\right)\sin \left(k\frac{2\mathrm{\π}}{N}(i-1)\right)\end{array}\right.,$ , analyze W+1 data acquisition first-harmonic information with

;

Application of formula: $\mathrm{\μ}=N\frac{{\mathrm{tg}}^{-1}\left[\frac{F_{a0}^n\left(1\right)}{F_{b0}^n\left(1\right)}\right]-{\mathrm{tg}}^{-1}\left[\frac{F_{a0}^n\left(0\right)}{F_{b0}^n\left(0\right)}\right]}{2\mathrm{\π}},$

Calculate the frequency drift μ of described electric signal X;

Application of formula: $\left\{\begin{array}{c}{a}_k=\frac{2}{Q}\underset{i=0}{\overset{W}{\mathrm{\Σ}}}{\mathrm{\γ}}_{i}f\left(i\right)\cos \left(k\frac{\mathrm{\μ}2\mathrm{\π}}{N}i\right)\\ b_k=\frac{2}{Q}\underset{i=0}{\overset{W}{\mathrm{\Σ}}}{\mathrm{\γ}}_{i}f\left(i\right)\sin \left(k\frac{\mathrm{\μ}2\mathrm{\π}}{N}i\right)\end{array}\right.,$ Draw respectively the first-harmonic of described electric signal X and the real part a of higher hamonic wave _xwith imaginary part b _k;

(3), CPU element calculates respectively the first-harmonic of described electric signal X and the amplitude of higher hamonic wave $P_k=\sqrt{a_k^2+b_k^2}$ And initial phase angle

(4), CPU element calculates respectively the amplitude P of the higher hamonic wave of described electric signal X _kwith first-harmonic P ₁amplitude number percent

and phase angle difference

and output display;

Described equal interval sampling is according to period T and the frequency f of carrying out the ideal signal of frequency analysis, the N point of sampling in one-period, and sample frequency is f _s=Nf, and N>=64;

Frequency drift μ obtains according to the fixed relationship of sampling number N in neighbouring sample point first-harmonic phase angle difference and ideal period, and frequency drift μ is for revising the frequency f of first-harmonic ₁frequency f with higher hamonic wave _k.