CN106980043A - A kind of improvement phase difference correction method based on Hanning window - Google Patents

Abstract

The invention discloses a kind of improvement phase difference correction method based on Hanning window, this method is larger mainly for existing phase difference correction method measurement error in the case where haveing the shortcomings that m-Acetyl chlorophosphonazo, while sidelobe performance is improved, the frequency-domain expression of a demand solution Hanning window possesses higher precision.This method is substantially in the new spectrum sequence after polynomial transformation, obtained and a new sample window for being different from Hanning window has been weighted on simple signal, and its first side lobe height and subsequent side lobe attenuation speed are better than Hanning window.

Description

A kind of improvement phase difference correction method based on Hanning window

Technical field

The invention belongs to Electric Power Harmonic Analysis technical field, more particularly to a kind of improvement phase difference correction based on Hanning window Method.

Background technology

In recent years, with the construction and the popularization of new energy technology of intelligent grid, various distributed power sources and energy storage device Also it is widely applied, while feature and the reduction disposal of pollutants that power network is powered is enhanced, is also brought to power network Substantial amounts of harmonic wave.Electric harmonic parameter is accurate, real-time on-line monitoring is weight during development intelligent grid, improvement harmonic pollution The technological means wanted.Fast Fourier Transform (FFT) (FFT) is because calculating speed is fast, be easy to the advantages such as Project Realization, in electric harmonic It is widely used in monitoring.In the case of synchronized sampling, FFT is minimum to the measurement error of fundamental wave and each harmonic, And when system fundamental frequency dynamic change so as to when producing larger frequency shift (FS), the frequency that signal cutout is caused under non-synchronous sampling Spectrum leakage can produce large effect to measurement accuracy, in some instances it may even be possible to cause measurement to fail.For this problem, propose in recent years Many improved methods based on FFT.

For example with time domain interpolation method, its principle is the fundamental frequency for first calculating signal, then based on synchronized ideal Sample frequency enters row interpolation restructuring, it is adaptable to the higher occasion of requirement of real-time.But overtone order it is higher or between having it is humorous Error is larger in the presence of ripple.

Again for example with multiline interpolation algorithm, its computational accuracy is higher, but needs to solve parameter in calculating process Approximation by polynomi-als formula, and correction formula after each window function curve matching differs, computationally intensive, is difficult to realize.

In addition, also there is a kind of phase difference correction method, this method by the phase difference of front and rear FFT twice corresponding spectral line come Frequency correction amount is calculated, algorithm is simple.Principle is as follows：

For a certain harmonic component in signal, have：

If the frequency domain analytic expression of gravity center of symmetric window function is W (f), then to the harmonic component adding window and Fourier transformation is done, had：

Wherein, T is the length of window function, and above formula only considers the positive half of its frequency spectrum, and assumes other harmonic components Interference is sufficiently small, can be ignored.Under the premise of this, its phase is：

If frequency error isThen above formula can be written as：

If original signal is delayed into t in time domain₀, then the initial phase of the harmonic component also change therewith It can similarly be obtained, now had according to above-mentioned derivation：

Formula (5) subtracts formula (4), obtains

It can thus be concluded that the correcting value of frequency is：

Amplitude can be extrapolated accordingly and the updating formula of phase is as follows：

Y in above formula (typically selects after FFT at the maximum of spectral line) amplitude at place for frequency f.

In above formulaFor the phase at frequency f.

From formula (8), the amplitude rectification of the correction method depends on the frequency domain analytic expression of window function, and some window functions Fourier transformation analytical expression can not be derived, therefore be dfficult to apply to phase difference correction method.And phase difference correction method exists Using some expression formulas excessively complicated window function (such as convolution window) when it is also rather inconvenient, this is a big limitation of this method.

In addition, the premise that above-mentioned derivation is set up is：Only consider the positive half of frequency spectrum, and assume the dry of other harmonic components Disturb sufficiently small.But in fact, due to spectrum leakage and to there may be the interference between m-Acetyl chlorophosphonazo, each harmonic be very important , this will cause the error of result of calculation.

The content of the invention

For the phase difference correction method in background technology, in the case where there is m-Acetyl chlorophosphonazo, measurement error is larger, and the present invention is carried A kind of improvement phase difference algorithm based on Hanning window is gone out.While sidelobe performance is improved, the frequency of a demand solution Hanning window Domain expression formula, possesses higher precision.

For signal shown in formula (1), if using Hanning window w_H(t) it is weighted and blocks in time domain, sampled signal x can be obtained_H (t), its frequency spectrum is：

X_H(f)=X (f) * W_H(f) (10)

In actual applications, it is general that its discrete spectrum X is asked for using FFT_H(k), can regard as on continuous frequency spectrum with Δ f=f_s/ N carries out discrete sampling, has

Wherein, N represents the points of fft analysis, k '_m=f_m/Δf.When N is very big, above formula can be written as form：

Further simplify, have：

In formula：

σ=k-k '_m=k- (k_m+Δk_m) (14)

Wherein, k_mFor k '_mRound and obtain nearby, Δ k_m∈(-1,1)。

Following algorithm improvement is carried out for Hanning window：

From formula (13), | X_H(k) | and | σ (σ²- 1) | between there is inverse relation, the height of spectral line in main lobe both sides Be withVelocity attenuation.In order to improve precision, it should pursue faster side lobe attenuation, to reach that reduction is each humorous The purpose interfered between wave component.Its decay is now made to accelerate, to X_H(k) polynomial transformation is carried out, a new frequency is obtained

Spectral sequence is as follows：

And for the purpose for accelerating decay, make above formula meet following equation：

Simultaneous formula (16) and formula (17), by coefficient of correlation, can solve to obtain a=1/60, b=-1/90, c=1/360.

Observation type (17) is obtained, and the rate of decay of the new sequence obtained by polynomial transformation increases to 1/ | σ (σ²-1) (σ²-4)(σ²- 9) |, spectrum leakage is reduced in theory.

Observation type (12) is understood again, X_H(k)、-X_H(k+1)、-X_H(k-1)、X_H(k+2)、X_H(k-2) phase is all identical , so new spectrum sequence X_H-5And X (k)_H(k) it is also consistent in phase-frequency characteristic, in phase difference correction method before Derivation still set up, new sequence goes for this method.

Brief description of the drawings

Fig. 1 is X_HAnd X_H-5Spectrum curve contrast schematic diagram.

Embodiment

In practical application, adding Hanning window to measured signal with f_sFrequency carry out discrete sampling, take a segment signal length For (L+N), N points obtain first paragraph time series x (n) before taking, and delay L points, then take N points to obtain second segment time series x₀(n), Wherein 0<L≤N.Make N point fft analysis to above-mentioned two time series, and progress polynomial transformation is obtained newly as shown in formula (16) Spectrum sequence X_H-5And X (k)_0H-5(k) the corresponding spectral line k in each maximum place of spectral line amplitude, is found out_m, then normalize Frequency correction amount be Δ k_m。

According to discussion before to phase difference correction method, by x (n) and x₀(n) the corresponding spectral line of the frequency spectrum of two sequences Phase is subtracted each other：

ΔΦ=Φ₀(k_m)-Φ(k_m) (18)

Then from derivation before：

Frequency correction amount Δ k after being normalized again_mAfterwards, frequency, amplitude and phase can be all corrected, wherein Actual frequency after correction is：

f_m=(k_m+Δk_m)f_s/N (20)

And in amplitude rectification, only need to know that the frequency domain analytic expression of Hanning window can be carried out, formula is as follows：

The updating formula of phase is：

DTFT now is carried out to a simple signal in time domain plus after Hanning window, continuous spectrum curve is obtained, for another example formula (16) a new frequency spectrum is drawn shown in, for the ease of observing and comparing, frequency and amplitude have been normalized, and ordinate is used Decibel expression, as shown in Figure 1.

From accompanying drawing 1, substantially add in the new spectrum sequence after polynomial transformation, obtained on simple signal A new sample window for being different from Hanning window is weighed, it is peaceful that its first side lobe height and subsequent side lobe attenuation speed are better than the Chinese Window.Because FFT computings and formula (16) are all linear operations, when analyzing harmonic signal, it can be understood as, first to each frequency point Amount has carried out polynomial transformation, then carries out frequency domain superposition, and the side lobe attenuation speed of each harmonic component is accelerated, when frequency point When resolution is sufficiently high, using X_H-5(k) sequence carries out that the interference between each harmonic, m-Acetyl chlorophosphonazo can be reduced, so as to improve survey Accuracy of measurement.

Claims (1)

1. a kind of improvement phase difference correction method based on Hanning window, it is characterised in that this method is：

For a certain harmonic component in signalUsing Hanning window w_H(t) it is right in time domain Its weighting is blocked, and can obtain sampled signal x_H(t), its frequency spectrum is：

X_H(f)=X (f) * W_H(f) (1)

Its discrete spectrum X is asked for using FFT_H(k), i.e., with Δ f=f on continuous frequency spectrum_s/ N carries out discrete sampling, is reduced to：

$X_H\left(k\right)=\frac{B}{\mathrm{\&sigma;}({\mathrm{\&sigma;}}^2-1)}---\left(2\right)$

In formula：

σ=k-k '_m=k- (k_m+Δk_m) (3)

Wherein, N represents the points of fft analysis, k '_m=f_m/ Δ f, k_mFor k '_mRound and obtain nearby, Δ k_m∈(-1,1)；

Following algorithm improvement is carried out for Hanning window：

From formula (2), | X_H(k) | and | σ (σ²- 1) | between there is inverse relation, the height of spectral line in main lobe both sides be withVelocity attenuation, make its decay accelerate, to X_H(k) polynomial transformation is carried out, a new spectrum sequence is obtained It is as follows：

$\begin{array}{c}{X}_{H-5}\left(k\right)={\mathrm{aX}}_H\left(k\right)+b\&lsqb;X_H(k+1)+X_H(k-1)\&rsqb;\\ +c\&lsqb;X_H\left(k+2\right)+X_H\left(k-2\right)\&rsqb;\end{array}---\left(5\right)$

And make above formula meet following equation：

$X_{H-5}\left(k\right)=\frac{B}{\mathrm{\&sigma;}({\mathrm{\&sigma;}}^2-1)({\mathrm{\&sigma;}}^2-4)({\mathrm{\&sigma;}}^2-9)}---\left(6\right)$

Simultaneous formula (5) and formula (6), by coefficient of correlation, can solve to obtain a=1/60, b=-1/90, c=1/360.