CN104360170A - Capacitive equipment dielectric loss angle calculation method based on iterative matching pursuit - Google Patents

Abstract

The invention relates to a capacitive equipment dielectric loss angle calculation method based on iterative matching pursuit. The method includes 1, acquiring current and voltage signal modulus; 2, initializing parameters, and setting an iteration number according to a formula that Num = 1; 3, calculating the frequency resolution and phase angle resolution; 4, establishing discrete sinusoidal signal atoms; 5, selecting optimal atoms; 6, calculating the optimal frequency and phase angle; 7, updating the number of iterations according to the formula Num = Num + 1; 8, judging whether the calculation error requirements are met or not; 9, calculating the capacitive equipment dielectric loss angle. The method has the advantages that the influence on dielectric loss angle calculation by synchronous sampling and field noise is avoided, and accurate measurement of the dielectric loss angle can be implemented; the exact value of the fundamental wave phase angle can be acquired by iteration and iteration matching pursuit algorithm.

Description

A kind of based on iterative matching pursuit capacitive equipment dielectric loss angle computing method

Technical field

The present invention relates to a kind of Dielectric loss angle computing method, specifically relate to a kind of based on iterative matching pursuit capacitive equipment dielectric loss angle computing method.

Background technology

In high voltage electric power equip ment, major part is capacitor type insulating equipment, and the parameter of the dielectric loss angle δ of its insulating property Dielectric loss angle is weighed, and it accurately reflects the overall performance of insulation.Can reliable basis be provided for fault diagnosis to the precise monitoring of Dielectric loss angle and provide important leverage for power system safety and stability runs.

Under normal circumstances, the value of Dielectric loss angle is very little, is about 0.001 ~ 0.02rad, because true value is too small in actual measurement, Chang Rongyi flood by error.The monitoring method of Dielectric loss angle mainly contains Hardware Method and Software Method at present.Hardware Method mainly comprises Schering bridge method and digitizing zero passage method, measures Dielectric loss angle computing velocity fast based on Hardware Method, but there is the shortcomings such as poor anti jamming capability, measuring accuracy are low, cumulative errors.The main method that analysis and treament has become current Dielectric Loss Angle is carried out to measured signal based on Software Method.Wherein, fast Fourier analysis method (FFT) is most widely used at present, this method is mainly through carrying out windowing and block and try to achieve voltage signal, current signal phasing degree by FFT conversion capacitive apparatus voltage, current digital signal, and then try to achieve Dielectric loss angle.But usually fluctuate due to the frequency of electric system, be difficult to ensure accurately to accomplish that synchronized sampling or complete cycle block to signal to be analyzed, FFT is made to there is spectral leakage and fence effect, its analysis result especially phase result error is very large, is difficult to the measurement directly Fourier analysis being used for Dielectric loss angle.Usually windowing can be adopted to block and Spectrum Correction to reduce the error of calculation.But, adopt windowing method fundamentally can not overcome the impact of spectral leakage; Meanwhile, still there is fence effect after windowing; And this method has certain requirement to sample frequency, and can not be too short for reducing the sampling length that affects of negative frequency.These reasons all limit the raising of the computational solution precision of traditional Dielectric loss angle computing method based on FFT theory.Further analysis can be known, based on the signal method for expressing of Fourier analysis, attempt to represent arbitrary signal by the set of limited orthogonal basis function, once after base decides, the method for expressing of signal is also just determined thereupon, be difficult to carry out adaptive change along with the change of signal, thus tradition based on Fourier analysis signal method for expressing its represent the limited in one's ability of signal.And then based on the Dielectric Loss Angle algorithm of Fourier analysis principle, its computational solution precision is also affected.

Summary of the invention

For the deficiencies in the prior art, the present invention proposes a kind of based on iterative matching pursuit capacitive equipment dielectric loss angle computing method, carries out modulus sampling, obtain discrete signal to tested current and voltage signals; In sinusoidal signal over-complete dictionary of atoms, iterative matching pursuit is carried out with accurate Calculation dielectric loss angle value by measured signal.Wherein, modulus sampling refers to by carrying out analog to digital conversion to tested current signal, voltage signal, obtains two signal discrete sequences, as long as due to accurate analysis fundamental signal, is not strict with high sample frequency, can adopts 1 ~ 2.5kHz, to reduce hardware requirement.This method avoid non-synchronous sampling and on-the-spot noise to the impact of Dielectric loss angle result of calculation, the Measurement accuracy to Dielectric loss angle can be realized.

The object of the invention is to adopt following technical proposals to realize:

A kind of based on iterative matching pursuit capacitive equipment dielectric loss angle computing method, its improvements are, described method comprises

(1) current and voltage signals modulus is gathered;

(2) initiation parameter, if iterations Num=1;

(3) calculated rate resolution and phase angular resolution;

(4) discrete sine signal atom is built;

(5) best atom is chosen;

(6) optimum frequency and optimum phase angle is calculated;

(7) iterations shown in newer Num=Num+1;

(8) judge whether to meet error of calculation requirement;

(9) capacitive equipment dielectric loss angle is calculated.

Preferably, described step (1) comprises measures capacitive apparatus voltage signal and current signal, and is f by sample frequency _sanalog to digital conversion link obtain discrete voltage signal X _uwith discrete current signals X _i, make sampling length be N.

Preferably, described step (2) comprises parameter initialization, if current iteration times N um=1; Order $f_{\mathrm{Num}}^H={f_1}^H=55\mathrm{Hz},f_{\mathrm{Num}}^L={f_1}^L=45\mathrm{Hz},{\mathrm{\φ}}_{\mathrm{Num}}^H=\mathrm{\π},{\mathrm{\φ}}_{\mathrm{Num}}^L=-\mathrm{\π};$ The numerical value of positive integer M and J is set; Setup algorithm resultant error limit ε.

Preferably, described step (3) comprises and uses formula $\left\{\begin{array}{c}{\mathrm{\Δf}}_{\mathrm{Num}}=\frac{f_{\mathrm{Num}}^H-f_{\mathrm{Num}}^L}{M}\\ {\mathrm{\Δ\φ}}_{\mathrm{Num}}=\frac{{\mathrm{\φ}}_{\mathrm{Num}}^H-{\mathrm{\φ}}_{\mathrm{Num}}^L}{J}\end{array}\right.$ Calculate current iteration number of times lower frequency resolution and phase angular resolution.

Preferably, described step (4) comprises by sinusoidal signal atom g=k _nsin (2 π f _mt+ φ _j) build discrete sine signal atom $G_{\mathrm{Num}}(m,j)=k_n\sin (2\mathrm{\π}\frac{m{\mathrm{\Δf}}_{\mathrm{Num}}+f_{\mathrm{Num}}^L}{f_s}n+j{\mathrm{\Δ\φ}}_{\mathrm{Num}}+{\mathrm{\φ}}_{\mathrm{Num}}^L),n=\mathrm{0,1},...,N-1,$

Wherein, 2 π f _mt+ φ _jfor sinusoidal signal, f _sfor sample frequency; N is the sampling length of discrete signal, and has m=0,1,2 ..., M; J=0,1,2 ..., J; k _nfor positive integer multiplying power normalization coefficient, make atom meet normalizing condition, its computing method are:

$k_n=\frac{1}{\left|\right|G_{\mathrm{Num}}(m,j)\left|\right|}.$

Preferably, described step (5) comprises according to matching pursuit algorithm, best atom under choosing current iteration number of times by following formula,

$|<X,G_{\mathrm{Num}}(m_{\mathrm{Num}}^{\mathrm{best}},j_{\mathrm{Num}}^{\mathrm{best}})>|=\sup |<X,G_{\mathrm{Num}}(m,j)>|$

Wherein, for best atom position, | <X, G _num(m, j) >| is signal X and atom G _numthe absolute value of the inner product of (m, j), sup|<X, G _num(m, j) >| is | <X, G _numthe maximal value of (m, j) >|, and have m=0,1,2 ..., M, j=0,1,2 ..., J.

Preferably, described step (6) comprises and uses formula $\left\{\begin{array}{c}{f}_{\mathrm{Num}}^{\mathrm{best}}=f_{\mathrm{Num}}^L+m_{\mathrm{Num}}^{\mathrm{best}}{\mathrm{\&Delta;f}}_{\mathrm{Num}}\\ {\mathrm{\&phi;}}_{\mathrm{Num}}^{\mathrm{best}}={\mathrm{\&phi;}}_{\mathrm{Num}}^L+j_{\mathrm{Num}}^{\mathrm{best}}{\mathrm{\&Delta;\&phi;}}_{\mathrm{Num}}\end{array}\right.$ Calculate the optimum frequency under current iteration number of times and optimum phase angle.

Preferably, described step (7) comprises the current iteration number of times shown in newer Num=Num+1; Upgrade $f_{\mathrm{Num}}^H,f_{\mathrm{Num}}^L,{\mathrm{\&phi;}}_{\mathrm{Num}}^H,{\mathrm{\&phi;}}_{\mathrm{Num}}^L,$

$\left\{\begin{array}{c}{f}_{\mathrm{Num}}^H=f_{\mathrm{Num}-1}^{\mathrm{best}}+{\mathrm{\&Delta;f}}_{\mathrm{Num}-1}\\ f_{\mathrm{Num}}^L=f_{\mathrm{Num}-1}^{\mathrm{best}}-{\mathrm{\&Delta;f}}_{\mathrm{Num}-1}\\ {\mathrm{\&phi;}}_{\mathrm{Num}}^H={\mathrm{\&phi;}}_{\mathrm{Num}-1}^{\mathrm{best}}+{\mathrm{\&Delta;\&phi;}}_{\mathrm{Num}-1}\\ {\mathrm{\&phi;}}_{\mathrm{Num}}^L={\mathrm{\&phi;}}_{\mathrm{Num}-1}^{\mathrm{best}}-{\mathrm{\&Delta;\&phi;}}_{\mathrm{Num}-1}\end{array}\right..$

Preferably, described step (8) comprises and judges whether to meet error of calculation requirement, namely return step 3; then iteration stopping, obtains this signal fundamental phase angle

Preferably, described step (9) comprises calculating current and voltage dispersion signal, obtains its current signal fundamental phase angle voltage signal fundamental phase angle then this capacitive equipment dielectric loss angle is

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

A kind of Dielectric loss angle computing method based on iterative matching pursuit that the present invention proposes, avoid non-synchronous sampling and on-the-spot noise to the impact of Dielectric loss angle result of calculation, can realize the Measurement accuracy to Dielectric loss angle.

In order to improve fundamental phase angle computational accuracy, reduce calculating consuming time, first technical scheme of the present invention searches for optimum matching atom in larger frequency range and larger phase angle range, constantly updating by searching for the optimum matching atom pair frequency range, phase angle range, frequency resolution and the phase angular resolution that obtain, being obtained the exact value at fundamental phase angle by successive ignition and iterative matching pursuit algorithm.

Accompanying drawing explanation

Fig. 1 is that one provided by the invention is based on iterative matching pursuit capacitive equipment dielectric loss angle computing method process flow diagram.

Fig. 2 is capacitive insulator arrangement equivalent-circuit model provided by the invention.

Embodiment

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described in further detail.

The present invention is directed to the deficiency of existing Dielectric Loss Angle method, propose a kind of Dielectric loss angle computing method based on iterative matching pursuit, this method avoid non-synchronous sampling and on-the-spot noise to the impact of Dielectric loss angle result of calculation, achieve the Measurement accuracy to Dielectric loss angle.Its ultimate principle is:

When carrying out Dielectric Loss Angle to capacitive apparatus, power frequency measured signal can be expressed as:

X(t)＝A sin(2πf ₀t+φ ₁) [1]

Wherein, A is fundamental signal amplitude, φ ₁for first-harmonic initial phase angle, f ₀for fundamental frequency, be 50Hz under normal circumstances.

Due to normal containing harmonic components in voltage, current signal, test site also exists a large amount of noise simultaneously, therefore when testing Dielectric loss angle, measuring-signal can be expressed as the mixed signal comprising a series of sinusoidal signal:

$x\left(t\right)=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{A}_k\sin (2\mathrm{\&pi;k}{f}_{0}t+{\mathrm{\&phi;}}_k)---\left[2\right]$

Wherein, A _kfor k subharmonic amplitude, φ _kfor k subharmonic phase place.

Consider that on-the-spot meeting exists a large amount of noise, therefore final measuring-signal can be expressed as form:

$x\left(t\right)=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{A}_n\sin (2\mathrm{\&pi;}{f}_{k}t+{\mathrm{\&phi;}}_k)+f_n\left(t\right)---\left[3\right]$

Wherein f _nt () is measuring-signal institute Noise.

Discrete sampling is carried out to voltage, current signal, voltage, electric current discrete digital signal can be obtained:

$X\left(n\right)=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{A}_k\sin (2\mathrm{\&pi;}\frac{f_k}{f_s}n+{\mathrm{\&phi;}}_k)+F_n\left(n\right)---\left[4\right]$

Wherein, f _sfor sample frequency; F _nn () is noise signal discrete form; N is the sampling length of discrete signal, and has n=0,1 ..., N-1.

Be different from traditional method utilizing whole orthogonal basis function to represent signal based on Fourier analysis, Its Sparse Decomposition selects the atom the most similar to signal to represent signal adaptively in over-complete dictionary of atoms, and the atom number selected is few as much as possible, and its ultimate principle is as follows:

A given set D={g _q, q=1,2 ..., Q}.Its element is g _q, g _qa whole Hilbert space H=R of one-tenth ⁿunit vector, C is g _qall lower target set, i.e. C={1,2 ..., Q}, and have Q > > N, claim set D to be over-complete dictionary of atoms, element g _qfor atom.For signal x ∈ H any given in space, can represent with over-complete dictionary of atoms D Atom, namely

$x=\underset{q\&Element;I_m\&Subset;C}{\mathrm{\&Sigma;}}{\mathrm{\&alpha;}}_q{g}_q---\left[5\right]$

Wherein, α _qfor the expansion coefficient of corresponding atom; For set I _mfor the subscript collection of selected atom, card (I _m)=m, and have m < < Q.

Because atom D was complete, atom g _qdo not meet orthogonality, therefore the method for expressing of [1] formula is unique, rarefaction representation is exactly that from various possible decomposition method, find out coefficient of dissociation the most sparse, and the one that namely m value is minimum is expressed.

Match tracing (Matching Pursuit, MP) algorithm is the main method of current Its Sparse Decomposition, and its ultimate principle is: set signal to be decomposed as f, and its length is N; Over-complete dictionary of atoms D={g _q, q=1,2 ..., Q}, and atomic length is also N, and have || g _q||=1.First from over-complete dictionary of atoms, choose the atom mated the most with signal f to be decomposed and meet:

$|<f,g_{q_{b_1}}>|=\sup |<f,g_q>|---\left[6\right]$

Wherein, q=1,2 ..., Q, and have <f, g _q> is signal f and atom g _qinner product, sup|<f, g _q>| represents signal f and atom g _qthe maximal value of inner product.Formula (2) shows, in Hilbert space, in all atoms of over-complete dictionary of atoms, the atom of this space closest to signal f direction, namely it is the atom that can mate with signal f in Hilbert space.

If according to the basic thought of Its Sparse Decomposition and match tracing, build sinusoidal signal atom as follows

g＝k _nsin(2πf _mt+φ _j) [7]

Wherein, f _mfor frequency parameter; φ _jfor phase parameter; k _nfor normalization coefficient, and meet:

$k_n=\frac{1}{\left|\right|g\left|\right|}---\left[8\right]$

Offset of sinusoidal signal atom discretize, obtains discrete sine signal atom:

$G(m,j)=k_n\sin (2\mathrm{\&pi;}\frac{\mathrm{m\&Delta;f}+f^L}{f_s}n+\mathrm{j\&Delta;\&phi;}+{\mathrm{\&phi;}}^L),n=\mathrm{0,1},...,N-1---\left[9\right]$

Wherein, f ^lfor frequency searching lower limit, φ ^lfor phase angle searches lower limit, Δ f frequency searching resolution, Δ φ is that phase angle searches resolution, m=0,1,2 ..., M-1, j=0,1,2 ..., J-1, and have:

$\left\{\begin{array}{c}\mathrm{\&Delta;f}=\frac{f^H-f^L}{M}\\ \mathrm{\&Delta;\&phi;}=\frac{{\mathrm{\&phi;}}^H-{\mathrm{\&phi;}}^L}{J}\end{array}\right.---\left[10\right]$

Wherein, f ^hfor the frequency searching upper limit, φ ^hfor phase angle searches the upper limit.

Different according to m with j value, M × J sinusoidal signal atom can be generated, by these atomic building sinusoidal signal over-complete dictionary of atoms D={G (m, j) | m=0,1,2,, M-1, j=0,1,2 ..., J-1}, based on matching pursuit algorithm, find the optimum atom G (m matched with signal first-harmonic ^best, j ^best), it meets:

|<X,G(m ^best,j ^best)>|＝sup|<X,G(m,j)>| [11]

Look for optimum atom and just can know signal fundamental phase:

φ ₁＝j ^bestΔφ+φ ^L[12]

Ask for current signal, voltage signal fundamental phase respectively then capacitive equipment dielectric loss angle is:

$\mathrm{\&delta;}=\frac{\mathrm{\&pi;}}{2}-|{\mathrm{\&phi;}}_1^U-{\mathrm{\&phi;}}_1^I|---\left[13\right]$

In order to improve fundamental phase angle computational accuracy, reduce calculating consuming time, first in larger frequency range and larger phase angle range, optimum matching atom is searched for, constantly update by searching for the optimum matching atom pair frequency range, phase angle range, frequency resolution and the phase angular resolution that obtain, obtained the exact value at fundamental phase angle by successive ignition and iterative matching pursuit algorithm, its concrete grammar is:

Step 1: capacitive apparatus voltage signal to be measured, current signal are measured, and be f by sample frequency _sanalog to digital conversion link obtain discrete voltage signal X _u, discrete current signals X _i, and make sampling length be N.

Step 2: each parameter of initialization, if current iteration times N um=1.Order the concrete numerical value (M and J is not less than 50) of positive integer M and J is set; Setup algorithm resultant error limit ε simultaneously.

Step 3: calculate current iteration number of times lower frequency resolution and phase angular resolution

$\left\{\begin{array}{c}{\mathrm{\&Delta;f}}_{\mathrm{Num}}=\frac{f_{\mathrm{Num}}^H-f_{\mathrm{Num}}^L}{M}\\ {\mathrm{\&Delta;\&phi;}}_{\mathrm{Num}}=\frac{{\mathrm{\&phi;}}_{\mathrm{Num}}^H-{\mathrm{\&phi;}}_{\mathrm{Num}}^L}{J}\end{array}\right.---\left[10\right]$

Step 4: by sinusoidal signal atom g=k _nsin (2 π f _mt+ φ _j) build discrete sine signal atom

$G_{\mathrm{Num}}(m,j)=k_n\sin (2\mathrm{\&pi;}\frac{m{\mathrm{\&Delta;f}}_{\mathrm{Num}}+f_{\mathrm{Num}}^L}{f_s}n+j{\mathrm{\&Delta;\&phi;}}_{\mathrm{Num}}+{\mathrm{\&phi;}}_{\mathrm{Num}}^L),n=\mathrm{0,1},...,N-1---\left[11\right]$

Wherein, f _sfor sample frequency; N is the sampling length of discrete signal, and has m=0,1,2 ..., M-1; J=0,1,2 ..., J-1; k _nfor normalization coefficient, make atom meet normalizing condition, its computing method are:

$k_n=\frac{1}{\left|\right|G_{\mathrm{Num}}(m,j)\left|\right|}---\left[12\right]$

Step 5: best atom under choosing current iteration number of times according to matching pursuit algorithm, matching pursuit algorithm chooses the method for best atom as shown in [3] formula.

$|<X,G_{\mathrm{Num}}(m_{\mathrm{Num}}^{\mathrm{best}},j_{\mathrm{Num}}^{\mathrm{best}})>|=\sup |<X,G_{\mathrm{Num}}(m,j)>|---\left[13\right]$

Wherein, | <X, G _num(m, j) >| is signal X and atom G _numthe absolute value of the inner product of (m, j), sup|<X, G _num(m, j) >| is | <X, G _numthe maximal value of (m, j) >|, and have m=0,1,2 ..., M, j=0,1,2 ..., J.

Step 6: calculate the optimum frequency under current iteration number of times and optimum phase angle:

$\left\{\begin{array}{c}{f}_{\mathrm{Num}}^{\mathrm{best}}=f_{\mathrm{Num}}^L+m_{\mathrm{Num}}^{\mathrm{best}}{\mathrm{\&Delta;f}}_{\mathrm{Num}}\\ {\mathrm{\&phi;}}_{\mathrm{Num}}^{\mathrm{best}}={\mathrm{\&phi;}}_{\mathrm{Num}}^L+j_{\mathrm{Num}}^{\mathrm{best}}{\mathrm{\&Delta;\&phi;}}_{\mathrm{Num}}\end{array}\right.---\left[14\right]$

Step 7: upgrade current iteration number of times, i.e. Num=Num+1, upgrades simultaneously

$\left\{\begin{array}{c}{f}_{\mathrm{Num}}^H=f_{\mathrm{Num}-1}^{\mathrm{best}}+{\mathrm{\&Delta;f}}_{\mathrm{Num}-1}\\ f_{\mathrm{Num}}^L=f_{\mathrm{Num}-1}^{\mathrm{best}}-{\mathrm{\&Delta;f}}_{\mathrm{Num}-1}\\ {\mathrm{\&phi;}}_{\mathrm{Num}}^H={\mathrm{\&phi;}}_{\mathrm{Num}-1}^{\mathrm{best}}+{\mathrm{\&Delta;\&phi;}}_{\mathrm{Num}-1}\\ {\mathrm{\&phi;}}_{\mathrm{Num}}^L={\mathrm{\&phi;}}_{\mathrm{Num}-1}^{\mathrm{best}}-{\mathrm{\&Delta;\&phi;}}_{\mathrm{Num}-1}\end{array}\right.---\left[15\right]$

Step 8: return step 3, by described in step 3 to step 6 successively, obtain optimum frequency under current iteration number of times and optimum phase angle

Step 9: judge whether to meet error of calculation requirement, even return step 7; If then iteration stopping, obtains this signal fundamental phase angle

Step 10: calculate by above-mentioned steps respectively electric current, voltage dispersion signal, obtains its current signal fundamental phase angle voltage signal fundamental phase angle then this capacitive equipment dielectric loss angle is

$\mathrm{\&delta;}=\frac{\mathrm{\&pi;}}{2}-|{\mathrm{\&phi;}}_1^U-{\mathrm{\&phi;}}_1^I|---\left[16\right]$

Embodiment

Capacitive insulator arrangement adopts resistance, Capacitance parallel connection equivalent-circuit model.Wherein electric capacity C=88 μ F, resistance value is respectively R=3k Ω, 5k Ω, 6k Ω, 9k Ω, 10k Ω, 15k Ω.Dielectric loss angle true data calculation formula is:

$\mathrm{\&delta;}=\arctan \left(\frac{1}{2\mathrm{\&pi;}{f}_0\mathrm{RC}}\right)---\left[17\right]$

Wherein, f ₀for fundamental frequency

(1) discrete sampling and analog to digital conversion link

Surveyed electric current, voltage analog signal are converted to digital quantity by high-speed AD converter, and sample frequency is f _s=1.5kHz, sampling length is 1000.

(2) f is made ₁ ^h=55Hz, f ₁ ^l=45Hz, m=100, J=100, limits of error ε=10 ^-9.Dielectric loss angle value is calculated according to iterative matching pursuit Dielectric loss angle computing method.

(3) Dielectric loss angle is calculated

According to result of calculation in (2), calculate Dielectric loss angle true value by formula [16].

In this example, capacitive insulator arrangement equivalent model resistance value is 9k Ω, when fundamental frequency is in 49.6Hz to 50.4Hz range.Dielectric loss angle result of calculation is following, and (wherein, aEb represents a × 10 ^b)

Dielectric loss angle result of calculation during the change of table 1 first-harmonic

In this example, in capacitive insulator arrangement equivalent model, resistance R change can realize the change of dielectric loss value true value, and when resistance is different numerical value, when fundamental frequency is 50.1Hz, Dielectric loss angle result of calculation is as shown in subscript.

The result of calculation during change of table 2 Dielectric loss angle true value

In this example, in capacitive insulator arrangement equivalent model, resistance value is 9k Ω, and fundamental frequency is 49.9Hz, and third harmonic accounts for first-harmonic ratio when changing, and Dielectric loss angle result of calculation is as shown in the table.

Dielectric loss angle result of calculation during the change of table 3 third harmonic ratio

Third harmonic accounts for first-harmonic ratio	δ absolute error/rad	Relative error/%
			10％	6.7772E-10	1.6896E-05
8％	5.4239E-10	1.3522E-05
			6％	4.0695E-10	1.0146E-05
4％	2.7141E-10	6.7666E-06
			2％	1.3577E-10	3.3849E-06
0％	1.4740E-10	3.6382E-06

In this example, in capacitive insulator arrangement equivalent model, resistance value is 9k Ω, and fundamental frequency is 50.1Hz, and it is 10% that third harmonic accounts for first-harmonic ratio, and it is 5% that quintuple harmonics accounts for first-harmonic ratio.The noise when white Gaussian noise adding different-energy is tested with simulated field, when measured signal signal to noise ratio (S/N ratio) changes, Dielectric loss angle result of calculation is as shown in the table

Dielectric loss angle result of calculation under the different signal to noise ratio (S/N ratio) of table 4

Signal to noise ratio (S/N ratio) (SNR)/dB	δ absolute error/rad	Relative error/%
			-2	-2.2484E-10	-5.5832E-06
-4	2.4278E-10	6.0287E-06
			-6	4.4534E-10	1.1059E-05
-8	6.1918E-10	1.5375E-05
			-10	7.6125E-10	1.8903E-05
-15	8.4320E-10	2.0938E-05

Finally should be noted that: above embodiment is only in order to illustrate that technical scheme of the present invention is not intended to limit; those of ordinary skill in the field still can modify to the specific embodiment of the present invention with reference to above-described embodiment or equivalent replacement; these do not depart from any amendment of spirit and scope of the invention or equivalent replacement, are all applying within the claims of the present invention awaited the reply.

Claims (10)

1., based on iterative matching pursuit capacitive equipment dielectric loss angle computing method, it is characterized in that, described method comprises

(1) current and voltage signals modulus is gathered;

(2) initiation parameter, if iterations Num=1;

(3) calculated rate resolution and phase angular resolution;

(4) discrete sine signal atom is built;

(5) best atom is chosen;

(6) optimum frequency and optimum phase angle is calculated;

(7) iterations shown in newer Num=Num+1;

(8) judge whether to meet error of calculation requirement;

(9) capacitive equipment dielectric loss angle is calculated.

2. one as claimed in claim 1 is based on iterative matching pursuit capacitive equipment dielectric loss angle computing method, it is characterized in that, described step (1) comprises measures capacitive apparatus voltage signal and current signal, and is f by sample frequency _sanalog to digital conversion link obtain discrete voltage signal X _uwith discrete current signals X _i, make sampling length be N.

3. as claimed in claim 1 a kind of based on iterative matching pursuit capacitive equipment dielectric loss angle computing method, it is characterized in that, described step (2) comprises parameter initialization, if current iteration times N um=1; Order $f_{\mathrm{Num}}^L={f_1}^L=45\mathrm{Hz},{\mathrm{\&phi;}}_{\mathrm{Num}}^H=\mathrm{\&pi;},{\mathrm{\&phi;}}_{\mathrm{Num}}^L=-\mathrm{\&pi;};$ The numerical value of positive integer M and J is set; Setup algorithm resultant error limit ε.

4. as claimed in claim 1 a kind of based on iterative matching pursuit capacitive equipment dielectric loss angle computing method, it is characterized in that, described step (3) comprises uses formula $\left\{\begin{array}{c}\mathrm{\&Delta;}{f}_{\mathrm{Num}}=\frac{f_{\mathrm{Num}}^H-f_{\mathrm{Num}}^L}{M}\\ \mathrm{\&Delta;}{\mathrm{\&phi;}}_{\mathrm{Num}}=\frac{{\mathrm{\&phi;}}_{\mathrm{Num}}^H-{\mathrm{\&phi;}}_{\mathrm{Num}}^L}{J}\end{array}\right.$ Calculate current iteration number of times lower frequency resolution and phase angular resolution.

5. as claimed in claim 1 a kind of based on iterative matching pursuit capacitive equipment dielectric loss angle computing method, it is characterized in that, described step (4) comprises by sinusoidal signal atom g=k _nsin (2 π f _mt+ φ _j) build discrete sine signal atom $G_{\mathrm{Num}}(m,j)=k_n\sin (2\mathrm{\&pi;}\frac{\mathrm{m\&Delta;}{f}_{\mathrm{Num}}+f_{\mathrm{Num}}^L}{f_s}n+\mathrm{j\&Delta;}{\mathrm{\&phi;}}_{\mathrm{Num}}+{\mathrm{\&phi;}}_{\mathrm{Num}}^L),$ n＝0,1,…,N-1，

Wherein, 2 π f _mt+ φ _jfor sinusoidal signal, f _sfor sample frequency; N is the sampling length of discrete signal, and has m=0,1,2 ..., M; J=0,1,2 ..., J; k _nfor positive integer multiplying power normalization coefficient, make atom meet normalizing condition, its computing method are:

$k_n=\frac{1}{\left|\right|G_{\mathrm{Num}}(m,j)\left|\right|}.$

6. one as claimed in claim 1 is based on iterative matching pursuit capacitive equipment dielectric loss angle computing method, and it is characterized in that, described step (5) comprises according to matching pursuit algorithm, best atom under choosing current iteration number of times by following formula,

$|\&lang;X,G_{\mathrm{Num}}(m_{\mathrm{Num}}^{\mathrm{best}},j_{\mathrm{Num}}^{\mathrm{best}})\&rang;|=\sup |\&lang;X,G_{\mathrm{Num}}(m,j)\&rang;|$

Wherein, for best atom position, | <X, G _num(m, j) >| is signal X and atom G _numthe absolute value of the inner product of (m, j), sup|<X, G _num(m, j) >| is | <X, G _numthe maximal value of (m, j) >|, and have m=0,1,2 ..., M, j=0,1,2 ..., J.

7. as claimed in claim 1 a kind of based on iterative matching pursuit capacitive equipment dielectric loss angle computing method, it is characterized in that, described step (6) comprises uses formula $\left\{\begin{array}{c}{f}_{\mathrm{Num}}^{\mathrm{best}}=f_{\mathrm{Num}}^L+m_{\mathrm{Num}}^{\mathrm{best}}\mathrm{\&Delta;}{f}_{\mathrm{Num}}\\ {\mathrm{\&phi;}}_{\mathrm{Num}}^{\mathrm{best}}={\mathrm{\&phi;}}_{\mathrm{Num}}^L+j_{\mathrm{Num}}^{\mathrm{best}}\mathrm{\&Delta;}{\mathrm{\&phi;}}_{\mathrm{Num}}\end{array}\right.$ Calculate the optimum frequency under current iteration number of times and optimum phase angle.

8. one as claimed in claim 1 is based on iterative matching pursuit capacitive equipment dielectric loss angle computing method, and it is characterized in that, described step (7) comprises the current iteration number of times shown in newer Num=Num+1; Upgrade

$\left\{\begin{array}{c}{f}_{\mathrm{Num}}^H=f_{\mathrm{Num}-1}^{\mathrm{best}}+\mathrm{\&Delta;}{f}_{\mathrm{Num}-1}\\ f_{\mathrm{Num}}^L=f_{\mathrm{Num}-1}^{\mathrm{best}}-\mathrm{\&Delta;}{f}_{\mathrm{Num}-1}\\ {\mathrm{\&phi;}}_{\mathrm{Num}}^H={\mathrm{\&phi;}}_{\mathrm{Num}-1}^{\mathrm{best}}+\mathrm{\&Delta;}{\mathrm{\&phi;}}_{\mathrm{Num}-1}\\ {\mathrm{\&phi;}}_{\mathrm{Num}}^L={\mathrm{\&phi;}}_{\mathrm{Num}-1}^{\mathrm{best}}-\mathrm{\&Delta;}{\mathrm{\&phi;}}_{\mathrm{Num}-1}\end{array}\right..$

9. as claimed in claim 1 a kind of based on iterative matching pursuit capacitive equipment dielectric loss angle computing method, it is characterized in that, described step (8) comprises and judges whether to meet error of calculation requirement, namely return step 3; $|{\mathrm{\&phi;}}_{\mathrm{Num}}^{\mathrm{best}}-{\mathrm{\&phi;}}_{\mathrm{Num}-1}^{\mathrm{best}}|<\mathrm{\&epsiv;},$ Then iteration stopping, obtains this signal fundamental phase angle ${\mathrm{\&phi;}}_1={\mathrm{\&phi;}}_{\mathrm{Num}}^{\mathrm{best}}.$

10. as claimed in claim 1 a kind of based on iterative matching pursuit capacitive equipment dielectric loss angle computing method, it is characterized in that, described step (9) comprises calculating current and voltage dispersion signal, obtains its current signal fundamental phase angle voltage signal fundamental phase angle then this capacitive equipment dielectric loss angle is