CN105467209A - Novel method for analyzing leaked current of metal oxide lightning arrester - Google Patents

Abstract

The invention discloses a kind of new metal oxide arrester leakage current analysis methods, first to the dis-crete sample values of power network signal Meet 10 cycle adding window as defined in IEC standard, Hanning window added when executing asynchronous, then correspond to the spectrum value at spectral line k after DFT/FFT is converted By spectrum value twice multiplied by the rotatable phase factor The amplitude at frequency point obtained after transformation is vector superposed, to obtain the frequency of arrester, the exact value of amplitude and phase parameter. The analysis method can eliminate fence effect and inhibition spectrum leakage by the way that the amplitude at the transformed frequency point of twiddle factor is vector superposed in fundamental frequency non-synchronous sampling, eliminating instantaneous big interference bring simultaneously influences, and avoids the mistake that traditional FFT algorithm detects appearance under non-synchronous sampling or instantaneous big interference cases.

Description

A kind of new metal oxide arrester leakage current analytical approach

Technical field

The present invention relates to leakage current of an arrester analysis field, be specifically related to a kind of new metal oxide arrester leakage current analytical approach.

Background technology

Found by research, the change of the running status of lightning arrester is embodied in the change of total current and these two inner parameters of current in resistance property flowing through lightning arrester, namely the running status of actual lightning arrester be can characterize by the total current of lightning arrester and current in resistance property, monitoring when lightning arrester runs and early warning realized.

For the analysis of voltage, current signal in the circuit containing connection lightning arrester, first need to measure accurately it.Voltage signal is only containing fundamental signal in theory, and current signal is also containing 3 times, 5 inferior harmonic signals except fundamental signal, traditional fft algorithm is applicable to the situation of strong signal, minor interference, does not have theoretical error when fundamental frequency synchronized sampling, and the result for voltage, electric current is comparatively accurate.And may there is following problem in voltage in side circuit, current signal and cause traditional FFT algorithm to detect losing efficacy: the 1) spectrum leakage that brings of fundamental frequency non-synchronous sampling and fence effect problem, because the electrical network fundamental frequency moment is among fluctuation, its maximum fluctuation scope is within ± 0.5Hz, normal fluctuation situation is within ± 0.2Hz, and the error brought thus is larger, its phase error may reach more than 5 °, causes follow-up calculating to occur gross error; 2) owing to containing lightning arrester in circuit, therefore voltage, current signal may bear the instantaneous large interference of high frequency from thunder and lightning signal, and hardware frequency overlapped-resistable filter may occur that the not thorough or large interfering frequency of signal attenuation is less than the situation of the cutoff frequency of frequency overlapped-resistable filter, the detection tool of large interference now to voltage, current signal has a great impact.For the high-acruracy survey of voltage, current signal, it is crucial for overcoming the above problems.

Summary of the invention

Instant invention overcomes the deficiencies in the prior art, a kind of new metal oxide arrester leakage current analytical approach is provided, the amplitude at the frequency place after being converted by twiddle factor is vector superposed can be eliminated fence effect and suppress spectrum leakage when fundamental frequency non-synchronous sampling, eliminate the impact that instantaneous large interference brings simultaneously, avoid the mistake that traditional FFT algorithm detects appearance under non-synchronous sampling or instantaneous large interference cases.

The present invention is by the following technical solutions:

A new metal oxide arrester leakage current analytical approach, first to the dis-crete sample values of power network signal carry out meeting 10 cycle windowings of IEC standard regulation, when performing asynchronous, add Hanning window, then after DFT/FFT conversion the spectrum value at corresponding spectral line k place

spectrum value is multiplied by the rotatable phase factor for twice the amplitude at the frequency place obtained after conversion is vector superposed, and to obtain the exact value of the frequency of lightning arrester, amplitude and phase parameter, wherein Δ t is unit sampling interval, and M is component number, f _i, A _i, _ifor the frequency of component, amplitude and phase place, n=0,1 ..., N-1, N be sample window length, _i=f _i/ Δ f is unit frequency values, Δ f is sample window length is frequency resolution corresponding during N, W () represents the window spectral function of corresponding windowing, and as N > > 1, the expression formula of corresponding Hanning window spectral function is as follows:

$W_H\left(\mathrm{\θ}\right)=e^{-j\frac{N-1}{N}\mathrm{\π}\mathrm{\θ}}\frac{\sin \left(\mathrm{\π}\mathrm{\θ}\right)}{2\mathrm{\π}\mathrm{\θ}(1-{\mathrm{\θ}}^2)}.$

The formula of concrete calculating frequency, amplitude and phase parameter is accurately respectively:

wherein k _i, _ifor respective frequencies component f _imaximum spectral line sequence number and frequency offseting value, and

Concrete calculating accurately amplitude formula is

$A_i=\frac{(1-{\∂}_i^2)(4-{\∂}_i^2)}{3\sin c\left({\∂}_i\right)}|\stackrel{\‾}{G}(k_i-1)+2\stackrel{\‾}{G}\left(k_i\right)+\stackrel{\‾}{G}(k_i+1)|.$

The formula of concrete calculating phase parameter is accurately

Compared with prior art, the invention has the beneficial effects as follows:

The present invention eliminates the intrinsic fence effect of FFT and spectrum leakage impact by the spectral line vector addition interpolation at multifrequency point place, counteract the large interference of instantaneous high frequency to the interference of spectrum signal simultaneously, thus can the amplitude of measuring voltage, electric current, frequency and phase parameter accurately, final parameters precision is improved.

Accompanying drawing explanation

Fig. 1 changes twiddle factor and leaks schematic diagram to offset;

DFT fence effect during Fig. 2 fundamental frequency non-synchronous sampling and spectrum leakage phenomenon;

Fig. 3 is containing the signal time-domain diagram of the large interference of instantaneous high frequency;

Fig. 4 is containing the signal spectrum figure of the large interference of instantaneous high frequency;

Fig. 5 surveys voltage, current sampling data.

Embodiment

Below in conjunction with accompanying drawing, the invention will be further elaborated.

Embodiment 1

10 cycle windowings when asynchronous (add rectangular window when fundamental frequency is synchronous, add Hanning window) DFT/FFT spectrum analysis sampled data being met to IEC standard regulation obtains spectrum information.

Dis-crete sample values for power network signal is:

In formula, Δ t is unit sampling interval, and M is component number, f _i, A _i, _ifor the frequency of component, amplitude and phase place, n=0,1 ..., N-1, N be sample window length.

After formula (3-1) carries out DFT/FFT conversion, the spectrum value at corresponding spectral line k place is:

In formula _i=f _i/ Δ f is unit frequency values, Δ f is sample window length is frequency resolution corresponding during N, W () represents the window spectral function of corresponding windowing, and as N > > 1, the expression formula of corresponding Hanning window spectral function is as follows:

$W_H\left(\mathrm{\θ}\right)=e^{-j\frac{N-1}{N}\mathrm{\π}\mathrm{\θ}}\frac{\sin \left(\mathrm{\π}\mathrm{\θ}\right)}{2\mathrm{\π}\mathrm{\θ}(1-{\mathrm{\θ}}^2)}---(3-3)$

The rotatable phase factor is taken advantage of to above-mentioned frequency spectrum process to obtain new spectrum information make the phase place in each component main lobe strictly identical, the phase place in secondary lobe is strict contrary, amplitude is close.

Formula (3-2) is expressed as:

Contain in the phase factor of formula intermediate frequency spectrum G (k) component two, it changes along with the difference of position of spectral line, and when k value is larger, impact is comparatively large, in order to the phase value in formula (3-4) does not change with the change of position of spectral line k, is multiplied by the rotatable phase factor to offset its change, that is:

By unitization frequency values _iwrite as following form:

${\mathrm{\β}}_i=k_i+{\∂}_i---(3-6)$

Wherein k _i, _ifor respective frequencies component f _imaximum spectral line sequence number and frequency offseting value, and $-0.5<{\&part;}_i\&le;\mathrm{0.5.}$

Formula (3-5) is expressed as:

Namely

Wherein represent and to take advantage of after the rotatable phase factor on frequency spectrum all the other components to component f _isecondary lobe interference superposition value, to single value Δ (k _m), its secondary lobe amplitude is close, phase directional is strictly contrary.

It changes twiddle factor and offsets the schematic diagram of leakage thought as shown in Figure 1.

By to new frequency spectrum adjacent spectral line is added the thought of leaking to eliminate the superposition of part secondary lobe, suppresses other component to the secondary lobe leakage contribution paying close attention to component, i.e. Δ (k by the spectrum value phase Calais that adjacent spectral line is corresponding _i)+Δ (k _i-1) ≈ 0, Δ (k _i)+Δ (k _i+ 1) ≈ 0, then

So, the 3 spectral line ratios based on twiddle factor are:

${\mathrm{\&alpha;}}_3=\frac{|\stackrel{\&OverBar;}{G}\left(k_i\right)+\stackrel{\&OverBar;}{G}(k_i-1)|}{|\stackrel{\&OverBar;}{G}\left(k_i\right)+\stackrel{\&OverBar;}{G}(k_i+1)|}\&ap;\frac{\left|W(-{\&part;}_i)\right|+\left|W(-1-{\&part;}_i)\right|}{\left|W(-{\&part;}_i)\right|+\left|W(-1-{\&part;}_i)\right|}---(3-11)$

Hanning window is had formula (3-11) abbreviation is:

${\mathrm{\&alpha;}}_3\&ap;\frac{2-{\&part;}_i}{2+{\&part;}_i}---(3-12)$

The anti-frequency offseting value solving 3 spectral line interpolations:

${\&part;}_i=2\frac{\left|\stackrel{\&OverBar;}{G}(k_i+1)\right|-\left|\stackrel{\&OverBar;}{G}(k_i-1)\right|}{|\stackrel{\&OverBar;}{G}(k_i-1)+2\stackrel{\&OverBar;}{G}\left(k_i\right)+\stackrel{\&OverBar;}{G}(k_i+1)|}---(3-13)$

Therefore, the frequency values paying close attention to component is:

$f_i=(k_i+{\&part;}_i)\mathrm{\&Delta;}f={\mathrm{\&beta;}}_i\mathrm{\&Delta;}f---(3-14)$

Utilize three spectral line structures:

According to frequency spectrum sidelobe performance, [Δ (k _i-1)+2 Δ (k _i)+Δ (k _i+ 1)] < < Δ (k _i), then formula (3-15) abbreviation is:

Hanning windowing is had:

$\begin{array}{c}\left|W(-1-{\&part;}_i)\right|+2\left|W(-{\&part;}_i)\right|+\left|W({\&part;}_i-1)\right|\\ =\frac{\sin \left(\mathrm{\&pi;}{\&part;}_i\right)}{2\mathrm{\&pi;}{\&part;}_i}\frac{12}{(1-{\&part;}_i)(4-{\&part;}_i^2)}=\frac{6\sin c\left({\&part;}_i\right)}{(1-{\&part;}_i^2)(4-{\&part;}_i^2)}\end{array}---(3-17)$

Formula (3-16) is converted into:

Therefore

$A_i=\frac{(1-{\&part;}_i^2)(4-{\&part;}_i^2)}{3\sin c\left({\&part;}_i\right)}|\stackrel{\&OverBar;}{G}(k_i-1)+2\stackrel{\&OverBar;}{G}\left(k_i\right)+\stackrel{\&OverBar;}{G}(k_i+1)|---(3-19)$

Wherein angle () represents the angle value returning correspondence, formula (3-14) (3-19) (3-20) is the final computing formula that the multifrequency point interpolation fourier algorithm (be called for short multifrequency point interpolation algorithm) based on twiddle factor conversion is derived, and contrasts institute's analytic signal first-harmonic harmonious wave frequency, amplitude and initial phase respectively.

The fence effect produced during fundamental frequency non-synchronous sampling and spectrum leakage phenomenon be as shown in Figure 2:

If sample frequency f _s=12800Hz, sampling cycle is Mt=10 cycle, every cycle sampling number is N=2560 point, fundamental frequency is 50Hz, each harmonic theoretical value is as shown in table 1, and superpose signal to noise ratio (S/N ratio) is the white Gaussian noise of 20dB simultaneously, superposes the large interference of random instantaneous high frequency in addition, its amplitude is 10 times of fundamental voltage amplitude, and the duration is 1ms.

Table 1 each harmonic wave m-Acetyl chlorophosphonazo parameter theory value

Time and frequency domain analysis is carried out to above-mentioned signal, obtains signal time-domain diagram and spectrogram respectively as shown in Figure 3 and Figure 4.

Utilize the measuring result error contrast of multifrequency point interpolation algorithm and the traditional FFT algorithm carried as shown in table 2.

Table 2 multifrequency point interpolation algorithm and traditional FFT algorithm measurement error

As can be seen from Table 2, traditional FFT algorithm is when containing the large interference of instantaneous high frequency, fundamental frequency non-synchronous sampling, owing to being subject to the impact of fence effect and spectrum leakage, frequency error in its testing result, amplitude error, phase error are all larger, phase error has wherein been greater than 5 °, make to lose efficacy in the occasion higher to phase measurement exact requirements, the normal measurement impact of the large interference of instantaneous high frequency simultaneously on parameter is comparatively large, causes result to occur larger error; The multifrequency point interpolation algorithm carried can the amplitude of measuring voltage, electric current, frequency and phase parameter accurately, particularly can meet the high precision test requirement to phase place in this project, the intrinsic fence effect of FFT and spectrum leakage impact is eliminated by the spectral line vector addition interpolation at multifrequency point place, counteract the large interference of instantaneous high frequency to the interference of spectrum signal simultaneously, final parameters precision is improved.

Measured data is verified:

Voltage, the current data of same lightning arrester two different time sections of sampling, the voltage wherein in a period of time, current waveform figure are illustrated in fig. 5 shown below.

In order to carry out the measurement of follow-up arrester resistance current, accurately extract electric current, voltage phase difference is key, adopt traditional FFT and multifrequency point interpolation method to carry out phase difference measurement contrast, result is as shown in table 3:

Table 3 measured data analysis result

Table 3 shows, actual fundamental frequency has trickle skew 50Hz, in addition there is certain harmonic wave and disturbances in signal, make there is larger deviation when traditional FFT method measure phase difference, and multifrequency point interpolation method eliminates fence effect and inhibits spectrum leakage, therefore the phase differential deviation recorded is less, can meet actual requirement of engineering.

Claims (4)

1. a new metal oxide arrester leakage current analytical approach, is characterized in that, first to the dis-crete sample values of power network signal carry out meeting 10 cycle windowings of IEC standard regulation, when performing asynchronous, add Hanning window, then after DFT/FFT conversion the spectrum value at corresponding spectral line k place

spectrum value is multiplied by the rotatable phase factor for twice the amplitude at the frequency place obtained after conversion is vector superposed, and to obtain the exact value of the frequency of lightning arrester, amplitude and phase parameter, wherein Δ t is unit sampling interval, and M is component number, f _i, A _i, i is the frequency of component, amplitude and phase place, n=0,1 ..., N-1, N be sample window length, i=f _i/ Δ f is unit frequency values, Δ f is sample window length is frequency resolution corresponding during N, W () represents the window spectral function of corresponding windowing, and as N > > 1, the expression formula of corresponding Hanning window spectral function is as follows:

2. analytical approach according to claim 1, is characterized in that: the formula specifically calculating frequency, amplitude and phase parameter is accurately respectively:

wherein k _i, i is respective frequencies component f _imaximum spectral line sequence number and frequency offseting value, and

3. analytical approach according to claim 1, is characterized in that: specifically calculating amplitude formula is accurately

4. analytical approach according to claim 1, is characterized in that: the formula specifically calculating phase parameter is accurately