CN104360170B - One kind is based on iterative matching pursuit capacitive equipment dielectric loss angle computational methods - Google Patents
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Abstract
Iterative matching pursuit capacitive equipment dielectric loss angle computational methods are based on the present invention relates to one kind, methods described includes (1) and gathers current and voltage signals modulus；(2) initiation parameter, if iterations Num=1；(3) frequency resolution and phase angular resolution are calculated；(4) discrete sine signal atom is built；(5) optimal atom is chosen；(6) optimum frequency and optimum phase angle are calculated；(7) iterations shown in newer Num=Num+1；(8) judge whether to meet calculation error requirement；(9) capacitive equipment dielectric loss angle is calculated.Influence present invention, avoiding non-synchronous sampling and live noise to dielectric loss angle result of calculation, can realize the accurate measurement to dielectric loss angle.The present invention obtains the exact value of fundamental phase angle by successive ignition and iterative matching pursuit algorithm.
Description
Technical field
It is in particular to a kind of to be based on iterative matching pursuit capacitive equipment dielectric the present invention relates to a kind of dielectric loss angle computational methods
Damage angle computational methods.
Background technology
It is largely capacitor type insulating equipment, the dielectric loss angle δ of its insulating properties dielectric loss angle in high-tension electricity equipment
Parameter weigh, it has accurately reflected the overall performance of insulation.Accurate monitoring to dielectric loss angle can examine for electrical equipment malfunction
It is disconnected that reliable basis are provided and important leverage are provided for power system security stable operation.
Under normal circumstances, the value very little of dielectric loss angle, about 0.001~0.02rad, because true value is too small in actual measurement,
Chang Rongyi is flooded by error.The monitoring method of dielectric loss angle mainly has Hardware Method and Software Method at present.Hardware Method mainly includes west
Woods bridge method and digitlization zero passage method, it is fast based on Hardware Method measurement dielectric loss angle calculating speed, but there is poor anti jamming capability, measurement
Precision is low, cumulative errors the shortcomings of.Analyzed and handled to measured signal based on Software Method turns into current Dielectric Loss Angle
Main method.Wherein, fast Fourier analysis method (FFT) at present it is most widely used, the method mainly by capacitive apparatus voltage,
Current digital signal carries out adding window and blocks and try to achieve voltage signal, current signal phase angle by FFT, and then tries to achieve Jie
Damage angle.Frequency yet with power system is it occur frequently that fluctuation, it is difficult to which synchronous adopt accurately is accomplished in guarantee to signal to be analyzed
Sample or complete cycle block, and FFT is there is spectral leakage and fence effect, and its analysis result especially phase result error is very
Greatly, it is difficult to which Fourier analysis is directly used for the measurement of dielectric loss angle.It can generally use that adding window is blocked and Spectrum Correction is to reduce
Calculation error.But, the influence of spectral leakage can not be fundamentally overcome using adding window method；Meanwhile, still exist after adding window
Fence effect；Moreover, the method has certain requirement to sample frequency, and can not mistake for the influence sampling length for reducing negative frequency
It is short.These reasons all limit the raising of the computational solution precision of traditional dielectric loss angle computational methods theoretical based on FFT.Enter one
It is can be known to walk analysis, the signal method for expressing based on Fourier analysis, it is intended to by the set of limited orthogonal basic function come table
Show arbitrary signal, after base is decided, the method for expressing of signal is also just determined therewith, it is difficult to be carried out with the change of signal
Adaptive change, thus traditional signal method for expressing based on Fourier analysis its represent the limited in one's ability of signal.And then, it is based on
The Dielectric Loss Angle algorithm of Fourier analysis principle, its computational solution precision is also impacted.
The content of the invention
In view of the shortcomings of the prior art, the present invention proposes a kind of based on iterative matching pursuit capacitive equipment dielectric loss angle calculating side
Tested current and voltage signals are carried out modulus sampling, obtain discrete signal by method；By measured signal in the excessively complete original of sinusoidal signal
Match tracing is iterated in word bank accurately to calculate dielectric loss angle value.Wherein, modulus sampling refer to by tested current signal,
Voltage signal carries out analog-to-digital conversion, two signal discrete sequences is obtained, as long as due to accurately analyzing fundamental signal, not being strict with
High sample frequency, can use 1~2.5kHz, to reduce hardware requirement.This method avoid non-synchronous sampling and live noise
Influence to dielectric loss angle result of calculation, can realize the accurate measurement to dielectric loss angle.
The purpose of the present invention is realized using following technical proposals：
One kind is based on iterative matching pursuit capacitive equipment dielectric loss angle computational methods, and it is theed improvement is that, methods described bag
Include
(1) current and voltage signals modulus is gathered；
(2) initiation parameter, if iterations Num=1；
(3) frequency resolution and phase angular resolution are calculated；
(4) discrete sine signal atom is built；
(5) optimal atom is chosen；
(6) optimum frequency and optimum phase angle are calculated；
(7) iterations shown in newer Num=Num+1；
(8) judge whether to meet calculation error requirement；
(9) capacitive equipment dielectric loss angle is calculated.
It is preferred that, the step (1) includes measurement capacitive apparatus voltage signal and current signal, and is f with sample frequencys
Analog-to-digital conversion link obtain discrete voltage signal XUWith discrete current signals XI, it is N to make sampling length.
It is preferred that, the step (2) is included to parameter initialization, if current iteration times N um=1；OrderPositive integer M and J numerical value are set；Setting meter
Calculate resultant error limit ε.
It is preferred that, the step (3) includes using formulaCurrent iteration number of times lower frequency is calculated to differentiate
Rate and phase angular resolution.
It is preferred that, the step (4) is included by sinusoidal signal atom g=knsin(2πfmt+φj) build discrete sine letter
Number atom
Wherein, 2 π fmt+φjFor sinusoidal signal, fsFor sample frequency；N is the sampling length of discrete signal, and has a m=0,
1,2,…,M；J=0,1,2 ..., J；knFor positive integer multiplying power normalization coefficient so that atom meets normalizing condition, it is calculated
Method is：
It is preferred that, the step (5) is included according to matching pursuit algorithm, chooses optimal former under current iteration number of times as the following formula
Son,
Wherein,For optimal atom position, |<X,GNum(m,j)>| for signal X and atom GNum(m,j)
Inner product absolute value, sup |<X,GNum(m,j)>| it is |<X,GNum(m,j)>| maximum, and have m=0,1,2 ..., M, j
=0,1,2 ..., J.
It is preferred that, the step (6) includes using formulaCalculate under current iteration number of times
Optimum frequency and optimum phase angle.
It is preferred that, the step (7) includes the current iteration number of times shown in newer Num=Num+1,；Update
It is preferred that, the step (8) comprises determining whether to meet calculation error requirement, i.e.,Return
Step 3；Then iteration stopping, obtains the signal fundamental phase angle
It is preferred that, the step (9) includes calculating current and voltage dispersion signal, obtains its current signal fundamental phase angleVoltage signal fundamental phase angleThen the capacitive equipment dielectric loss angle is
Compared with the prior art, the beneficial effects of the invention are as follows：
A kind of dielectric loss angle computational methods based on iterative matching pursuit proposed by the present invention, it is to avoid non-synchronous sampling and
Influence of the live noise to dielectric loss angle result of calculation, can realize the accurate measurement to dielectric loss angle.
In order to improve fundamental phase angle computational accuracy, reduce and calculate time-consuming, technical scheme is first in larger frequency
Best match atom is scanned in rate scope and larger phase angle range, the best match atom pair frequency obtained by search
Scope, phase angle range, frequency resolution and phase angular resolution are constantly updated, and pass through successive ignition and iterative matching pursuit
Algorithm obtains the exact value of fundamental phase angle.
Brief description of the drawings
Fig. 1 is based on iterative matching pursuit capacitive equipment dielectric loss angle computational methods flow chart for one kind that the present invention is provided.
The capacitive insulator arrangement equivalent-circuit model that Fig. 2 provides for the present invention.
Embodiment
The embodiment to the present invention is described in further detail below in conjunction with the accompanying drawings.
A kind of deficiency of the present invention for existing Dielectric Loss Angle method, it is proposed that dielectric loss angle based on iterative matching pursuit
Computational methods, the influence this method avoid non-synchronous sampling and live noise to dielectric loss angle result of calculation, are realized to being situated between
Damage the accurate measurement at angle.Its general principle is：
When carrying out Dielectric Loss Angle to capacitive apparatus, power frequency measured signal can be expressed as：
X (t)=A sin (2 π f0t+φ1) [1]
Wherein, A is fundamental signal amplitude, φ1For fundamental wave initial phase angle, f0For fundamental frequency, normally 50Hz.
Due to often containing harmonic components in voltage, current signal, while test site has substantial amounts of noise jamming, therefore
When testing dielectric loss angle, measurement signal is represented by including a series of mixed signal of sinusoidal signals：
Wherein, AkFor k subharmonic amplitudes, φkFor k subharmonic phases.
There is substantial amounts of noise jamming in view of on-the-spot meeting, therefore final measurement signal is represented by following form：
Wherein fn(t) it is measurement signal institute Noise.
Discrete sampling is carried out to voltage, current signal, voltage, electric current discrete digital signal can be obtained：
Wherein, fsFor sample frequency；Fn(n) it is noise signal discrete form；N is the sampling length of discrete signal, and has
N=0,1 ..., N-1.
It is sparse different from traditional method being indicated based on Fourier analysis using whole orthogonal basis functions to signal
Decomposition is adaptive selected the atom most like with signal in over-complete dictionary of atoms and represents signal, and the atom number selected
Few as far as possible, its general principle is as follows：
Give a set D={ gq, q=1,2 ..., Q }.Its element is gq, gqIt is into whole Hilbert spaces H=
RNUnit vector, C is gqAll lower target set, i.e. C={ 1,2 ..., Q }, and there is Q ＞ ＞ N, set D to be called complete original
Word bank, element gqFor atom., can be with atom in over-complete dictionary of atoms D come table for any given signal x ∈ H in space
Show, i.e.,
Wherein, αqFor the expansion coefficient of correspondence atom；For set ImFor the subscript collection of selected atom, card (Im)=m, and
There are m ＜ ＜ Q.
Because atom D was complete, atom gqOrthogonality is unsatisfactory for, therefore the method for expressing of [1] formula is not unique, it is dilute
Dredge and represent to be exactly to find out that decomposition coefficient is the most sparse from various possible decomposition methods, i.e. the minimum a kind of expression of m values.
Match tracing (Matching Pursuit, MP) algorithm is the main method of current Its Sparse Decomposition, its general principle
For：If signal to be decomposed is f, its length is N；Over-complete dictionary of atoms D={ gq, q=1,2 ..., Q }, and atomic length is also N,
And have | | gq| |=1.The atom matched the most with signal f to be decomposed is chosen first from over-complete dictionary of atomsAnd meet：
Wherein, q=1,2 ..., Q, and have<f,gq>For signal f and atom gqInner product, sup |<f,
gq>| represent signal f and atom gqInner product maximum.Formula (2) shows, in Hilbert spaces, the institute of over-complete dictionary of atoms
Have in atom,It is atom of the space closest to signal f directions, i.e.,It is that can most be matched with signal f in Hilbert spaces
Atom.
If according to Its Sparse Decomposition and the basic thought of match tracing, building sinusoidal signal atom as follows
G=knsin(2πfmt+φj) [7]
Wherein, fmFor frequency parameter；φjFor phase parameter；knFor normalization coefficient, and meet：
To sinusoidal signal atom discretization, discrete sine signal atom is obtained：
Wherein, fLFor frequency searching lower limit, φLLower limit is searched for phase angle, Δ f frequency searching resolution ratio, Δ φ searches for phase angle
Resolution ratio, m=0,1,2 ..., M-1, j=0,1,2 ..., J-1 are sought, and is had：
Wherein, fHFor the frequency searching upper limit, φHThe upper limit is searched for phase angle.
It is different according to m with j values, M × J sinusoidal signal atom can be generated, these atomic building sinusoidal signals are excessively complete
Standby atom D=G (m, j) | and m=0,1,2 ..., M-1, j=0,1,2 ..., J-1 }, based on matching pursuit algorithm, find and letter
The optimal atom G (m that number fundamental wave matchesbest,jbest), it meets：
|<X,G(mbest,jbest)>|=sup |<X,G(m,j)>| [11]
Look for optimal atom and just may know that signal fundamental phase：
φ1=jbestΔφ+φL [12]
Current signal, voltage signal fundamental phase are asked for respectivelyThen capacitive equipment dielectric loss angle is：
In order to improve fundamental phase angle computational accuracy, reduce and calculate time-consuming, first in larger frequency range and larger phase
Best match atom is scanned in angular region, the best match atom pair frequency range that is obtained by search, phase angle range, frequency
Rate resolution ratio and phase angular resolution are constantly updated, and fundamental phase is obtained by successive ignition and iterative matching pursuit algorithm
The exact value at angle, its specific method is：
Step 1：Capacitive apparatus voltage signal to be measured, current signal are measured, and are f by sample frequencysMould
Number conversion links obtain discrete voltage signal XU, discrete current signals XI, and make sampling length be N.
Step 2：Each parameter is initialized, if current iteration times N um=1.Order Positive integer M and J concrete numerical value (M and J is not less than 50) are set；Concurrently set result of calculation mistake
Difference limit ε.
Step 3：Calculate current iteration number of times lower frequency resolution ratio and phase angular resolution
Step 4：By sinusoidal signal atom g=knsin(2πfmt+φj) build discrete sine signal atom
Wherein, fsFor sample frequency；N is the sampling length of discrete signal, and has m=0,1,2 ..., M-1；J=0,1,
2,…,J-1；knFor normalization coefficient so that atom meets normalizing condition, its computational methods is：
Step 5：Optimal atom under current iteration number of times is chosen according to matching pursuit algorithm, matching pursuit algorithm is chosen optimal
The method of atom is as shown in [3] formula.
Wherein, |<X,GNum(m,j)>| for signal X and atom GNumThe absolute value of the inner product of (m, j), sup |<X,GNum(m,
j)>| it is |<X,GNum(m,j)>| maximum, and have m=0,1,2 ..., M, j=0,1,2 ..., J.
Step 6：Calculate the optimum frequency and optimum phase angle under current iteration number of times：
Step 7：Current iteration number of times, i.e. Num=Num+1 are updated, is updated simultaneously
Step 8：Return to step 3, as described in step 3 to step 6 successively, obtains optimum frequency under current iteration number of times
And optimum phase angle
Step 9：Judge whether to meet calculation error requirement, evenReturn to step 7；IfThen iteration stopping, obtains the signal fundamental phase angle
Step 10：Electric current, voltage dispersion signal are calculated by above-mentioned steps respectively, its current signal fundamental wave phase is obtained
Parallactic angleVoltage signal fundamental phase angleThen the capacitive equipment dielectric loss angle is
Embodiment
Capacitive insulator arrangement uses resistance, electric capacity parallel equivalent circuit model.Wherein electric capacity C=88 μ F, resistance value difference
For R=3k Ω, 5k Ω, 6k Ω, 9k Ω, 10k Ω, 15k Ω.Dielectric loss angle true data calculation formula is：
Wherein, f0For 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 fs=
1.5kHz, sampling length is 1000.
(2) f is made1 H=55Hz, f1 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 computational methods.
(3) dielectric loss angle is calculated
According to result of calculation in (2), dielectric loss angle true value is calculated 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
During range.Dielectric loss angle result of calculation is following, and (wherein, aEb represents a × 10b)
Dielectric loss angle result of calculation when the fundamental wave of table 1 changes
In this example, the change of dielectric loss value true value can be achieved in resistance R changes in capacitive insulator arrangement equivalent model, works as resistance
During for different numerical value, when fundamental frequency is 50.1Hz, dielectric loss angle result of calculation is as shown in subscript.
Result of calculation when the dielectric loss angle true value of table 2 changes
In this example, resistance value is 9k Ω in capacitive insulator arrangement equivalent model, and fundamental frequency is 49.9Hz, triple-frequency harmonics
When accounting for fundamental wave ratio and changing, dielectric loss angle result of calculation is as shown in the table.
Dielectric loss angle result of calculation when the triple-frequency harmonics ratio of table 3 changes
| Triple-frequency harmonics accounts for fundamental wave ratio | δ absolute errors/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, resistance value is 9k Ω in capacitive insulator arrangement equivalent model, and fundamental frequency is 50.1Hz, triple-frequency harmonics
It is 10% to account for fundamental wave ratio, and it is 5% that quintuple harmonics, which accounts for fundamental wave ratio,.The white Gaussian noise of different-energy is added to simulate live survey
Noise jamming during examination, when measured signal signal to noise 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 of table 4
| Signal to noise ratio (SNR)/dB | δ absolute errors/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 it should be noted that：The above embodiments are merely illustrative of the technical scheme of the present invention and are not intended to be limiting thereof, institute
The those of ordinary skill in category field with reference to above-described embodiment still can to the present invention embodiment modify or
Equivalent substitution, these any modifications or equivalent substitution without departing from spirit and scope of the invention are applying for this pending hair
Within bright claims.
Claims (7)
1. one kind is based on iterative matching pursuit capacitive equipment dielectric loss angle computational methods, it is characterised in that methods described includes
(1) current and voltage signals are gathered and analog-to-digital conversion is carried out；
(2) initiation parameter, if current iteration times N um=1；
(3) frequency resolution and phase angular resolution are calculated；
(4) discrete sine signal atom is built；
The step (4) is included by sinusoidal signal atom g=knsin(2πfmt+φj) build discrete sine signal atom
Wherein, fmFor frequency parameter；For phase parameter；fsFor sample frequency；N is the sampling length of discrete signal, and has m=
0,1,2,……,M；J=0,1,2 ... ..., J；knFor positive integer multiplying power normalization coefficient so that atom meets normalizing condition,
Its computational methods is：
Wherein, M and J are meant that：Any positive integer and M and J is not less than 50, Δ fNumIt is meant that：The Num times iteration frequency
Search resolution ratio；It is meant that：The Num times iteration phase angle searches resolution ratio；It is meant that：The Num times iteration
Frequency searching lower limit；It is meant that：The Num times iteration phase angle searches lower limit；
(5) optimal atom is chosen；
The step (5) includes, according to matching pursuit algorithm, optimal atom under current iteration number of times being chosen as the following formula,
Wherein,For optimal atom position, |<X,GNum(m,j)>| for signal X and atom GNum(m's, j) is interior
Long-pending absolute value, sup |<X,GNum(m,j)>| it is |<X,GNum(m,j)>| maximum, and have m=0,1,2 ... ..., M；J=
0,1,2 ... ..., J；
(6) optimum frequency and optimum phase angle are calculated；
The step (6) includes using formulaCalculate the optimum frequency and most under current iteration number of times
Good phase angle；
(7) iterations shown in newer Num=Num+1；
(8) judge whether to meet calculation error requirement；
(9) capacitive equipment dielectric loss angle is calculated.
2. it is as claimed in claim 1 a kind of based on iterative matching pursuit capacitive equipment dielectric loss angle computational methods, it is characterised in that
The step (1) includes measurement capacitive apparatus voltage signal and current signal, and is f with sample frequencysAnalog-to-digital conversion link
Obtain discrete voltage signal XUWith discrete current signals XI, it is N to make sampling length.
3. it is as claimed in claim 1 a kind of based on iterative matching pursuit capacitive equipment dielectric loss angle computational methods, it is characterised in that
The step (2) is included to parameter initialization, if current iteration times N um=1；Order f 1 H=55Hz,= f 1 L=
45Hz,Positive integer M and J numerical value are set；Setup algorithm resultant error limits ε.
4. it is as claimed in claim 3 a kind of based on iterative matching pursuit capacitive equipment dielectric loss angle computational methods, it is characterised in that
The step (3) includes using formulaCalculate current iteration number of times lower frequency resolution ratio and phase angular resolution
Rate；
Wherein,The upper limit is searched for the Num times iteration frequency,The upper limit is searched for the Num times iteration phase angle.
5. it is as claimed in claim 4 a kind of based on iterative matching pursuit capacitive equipment dielectric loss angle computational methods, it is characterised in that
The step (7) includes the current iteration number of times shown in newer Num=Num+1；Update
Wherein, Δ φNum-1It is meant that：The Num-1 times iteration phase angle searches resolution ratio, Δ fNum-1It is meant that：The Num-1 times
Iteration frequency searches resolution ratio,It is meant that：The optimum frequency that the Num-1 times iterated search is obtained,Implication
It is：The optimum phase angle that the Num-1 times iterated search is obtained.
6. it is as claimed in claim 5 a kind of based on iterative matching pursuit capacitive equipment dielectric loss angle computational methods, it is characterised in that
The step (8) comprises determining whether that meeting calculation error requires, i.e.,Return to step 3；Then iteration stopping, obtains the signal fundamental phase angle
7. it is as claimed in claim 6 a kind of based on iterative matching pursuit capacitive equipment dielectric loss angle computational methods, it is characterised in that
The step (9) includes calculating current and voltage dispersion signal, obtains its current signal fundamental phase angleVoltage signal fundamental wave
Phase angleThen the capacitive equipment dielectric loss angle is
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| CN102565542A (en) * | 2012-02-10 | 2012-07-11 | 国电南瑞科技股份有限公司 | Capacitive equipment medium loss online monitoring method based on IEC61850-9-2 standard |
| CN103576002A (en) * | 2013-11-11 | 2014-02-12 | 华北电力大学（保定） | Method for calculating dielectric loss angle of compatible insulating device |
| CN103760425A (en) * | 2014-01-22 | 2014-04-30 | 湖南大学 | Method and device for rapidly measuring dielectric loss angle based on time domain quasi-synchronization |
| CN105137198A (en) * | 2015-09-15 | 2015-12-09 | 福州大学 | Novel dielectric loss measurement method based on Nuttall window - five-point converting FFT |
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| CN102565542A (en) * | 2012-02-10 | 2012-07-11 | 国电南瑞科技股份有限公司 | Capacitive equipment medium loss online monitoring method based on IEC61850-9-2 standard |
| CN103576002A (en) * | 2013-11-11 | 2014-02-12 | 华北电力大学（保定） | Method for calculating dielectric loss angle of compatible insulating device |
| CN103760425A (en) * | 2014-01-22 | 2014-04-30 | 湖南大学 | Method and device for rapidly measuring dielectric loss angle based on time domain quasi-synchronization |
| CN105137198A (en) * | 2015-09-15 | 2015-12-09 | 福州大学 | Novel dielectric loss measurement method based on Nuttall window - five-point converting FFT |
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