CN109490625A - A kind of harmonic signal analysis method based on sliding window and Semidefinite Programming - Google Patents
A kind of harmonic signal analysis method based on sliding window and Semidefinite Programming Download PDFInfo
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Abstract
The harmonic signal analysis method based on sliding window and Semidefinite Programming that the present invention relates to a kind of, different from traditional frequency domain method for solving, the present invention uses the time domain sparse features of atom norm Harmonious Waves in Power Systems signal first, and harmonic signal analysis mathematical model is successively established to the subset of interception using the form of sliding window, and then the problem is solved by Semidefinite Programming and carries out triangle decomposition, the amplitude and frequency of signal can be obtained, the amplitude and frequency of the signal are obtained eventually by average mode.This method is advantageous in that in Time Domain Processing, overcome frequency domain and spectral leakage and non-synchronous sampling influences to computational accuracy bring, frequency resolution with higher and analysis precision.
Description
Technical field
The present invention relates to power quality analysis and control field, and in particular to a kind of based on sliding window and Semidefinite Programming
Harmonic signal analysis method.
Background technique
In recent years, as the increase of interference load and equipment increase the sensitivity of harmonic wave, harmonic wave is to power train
The influence of system is also more serious, and harmonic pollution has become one the problem of urgently paying close attention to.It is generally believed that the frequency of integral frequency harmonizing wave
Rate is the integral multiple of fundamental frequency.In addition to this, there is also non-integer harmonics abundant, i.e. m-Acetyl chlorophosphonazo, frequencies for power grid
It is not the integral multiple of fundamental frequency, and discrete form or conitnuous forms may be presented in its frequency spectrum.
There are many harmonic analysis methods at present, but they are mostly based on FFT, IEC standard 61000-4-7 also recommends FFT to make
For the most basic method of harmonic measure.Really, these methods are simple and to calculate cost small, under the conditions of synchronized sampling
Realize the high accuracy analysis to harmonic wave, however these are sensitive to frequency shift (FS) based on the method for FFT, it is more severe to the condition of sampling
It carves and the problems such as there are spectral leakage and fence effects, while the method for parameter estimation based on FFT is all by uncertainty principle
Fourier's resolution ratio limitation, particularly, difference on the frequency be Δ ω two sine wave signals, need longer than 2 π/Δ ω
Data length, these defects become apparent from when the analysis to m-Acetyl chlorophosphonazo.Therefore, searching can avoid the limitation of FFT resolution ratio
Method have highly important value.
The present invention realizes Harmonious Waves in Power Systems/m-Acetyl chlorophosphonazo signal using sliding window and Semidefinite Programming and analyzes, and overcomes
The spectral leakage and fence effect of FFT.
Summary of the invention
Insufficient according to prior art, the present invention provides a kind of harmonic signal analysis based on sliding window and Semidefinite Programming
Method realizes Harmonious Waves in Power Systems/m-Acetyl chlorophosphonazo signal using sliding window and Semidefinite Programming and analyzes, overcomes the frequency spectrum of FFT
Leakage and fence effect.
The present invention is realized by following technical scheme:
A kind of harmonic signal analysis method based on sliding window and Semidefinite Programming, this method are as follows:
(1) to signal x (n) since first sampled point, continuous M point forms subset thereafter for selectionThen from
Second point starts, and continuous M point forms subset thereafter for selectionAnd so on, using the form of sliding window, formed
SubsetHere subscript m ∈ [1, N-M+1] indicates subset with x (m) beginning, and the range of subset is
(2) forFollowing Semidefinite Programming is solved using ADMM method
Solve optimal solution in above formula (x, t, u)；
(3) subset can be obtained by carrying out triangle decomposition to T (u)The frequency of Harmonious Waves in Power Systems and m-Acetyl chlorophosphonazo
And amplitude
(4) estimated result for the different windows for being M to N-M+1 size is averaged frequency and width for harmonic wave and m-Acetyl chlorophosphonazo
Value, it may be assumed that
The invention has the advantages that:
This method is advantageous in that in Time Domain Processing, overcomes frequency domain and spectral leakage and non-synchronous sampling to computational accuracy
Bring influences, frequency resolution with higher and analysis precision.
Specific embodiment
To keep the purposes, technical schemes and advantages of the invention implemented clearer, below to the skill in the embodiment of the present invention
Art scheme is further described in more detail.Based on the embodiments of the present invention, those of ordinary skill in the art are not making wound
Every other embodiment obtained under the premise of the property made labour, shall fall within the protection scope of the present invention.Below to reality of the invention
Example is applied to be described in detail.
Traditional Fourier transformation is a kind of complete Orthogonal Decomposition method, and there are spectral leakage phenomenons, reduce harmonic wave
The precision of analysis, for this purpose, the present invention wish to find by continuous parameter space it is minimum (rather than most complete in Fourier's variation
It is standby) atom indicate harmonic information, this is actually a underdetermined problem, but be the characteristics of harmonic analysis in power system,
A small amount of harmonic wave and m-Acetyl chlorophosphonazo component are only existed, and application value is not present in the information of high frequency, therefore this patent is considered as atom
l1Norm solves the problems, such as harmonic analysis in power system.
Enable Γ be an atom set, if its convex closure conv (Γ) relative to origin be one it is centrosymmetric compact, and
Comprising origin as interior point, it means that the either element υ ∈ Γ in Γ will not be located at what the other elements in addition to υ were constituted
In convex closure conv (Γ υ), i.e. element in Γ is all the extreme point of conv (Γ), and υ ∈ Γ is and if only if-υ ∈ Γ.At this time by
The norm that the scaling function of convex closure conv (Γ) defines becomes atom norm, uses | | | |ΓIt indicates, then has:
Atom norm | | | |ΓActually this way of restraint of sparse constraint is increased to set Γ to see set Γ
Make the unlimited dictionary of a description consecutive variations parameter.
If the steady-state signal of k steady state power harmonic wave, m-Acetyl chlorophosphonazo composition are as follows:
Wherein { fi}I=1,2 ... kFor harmonic wave/m-Acetyl chlorophosphonazo frequency, { φi}I=1,2 ... kFor harmonic wave/m-Acetyl chlorophosphonazo phase, J=is enabled
{ 0,1,2 ..., N-1 } defines atomTherefore atom set can be write as Γ=a (f,
φ): f > 0, φ ∈ [0,2 π) }, it is defined according to the atom norm of formula, the atom norm of signal x (n) are as follows:
If harmonic signal sampled point is { 0,1 ..., N-1 }, the sampling period is Δ T, since first sampled point, is used
Size is that the sliding window of M successively intercepts harmonic signal subset T ∈ J, as shown in the table:
Harmonic signal that is obvious, being N for total sampling number has N-M+1 such signal subsets.
According to the sparse property of harmonic signal, following atom norm minimum problem can use to restore the humorous of missing
Wave signal:
Here | | s | |AThe sparse characteristic of Harmonious Waves in Power Systems and m-Acetyl chlorophosphonazo is embodied, since atom norm has half to establish rules
Draw property, take linear Semidefinite Programming theoretical method can be solved in polynomial time atom norm according to
Caratheodory lemma, any positive semidefinite Toeplitz matrix can carry out Vandermonde decomposition, therefore thus by atom model
Number minimization problem is converted into following Semidefinite Programming:
Wherein T (u) is Toeplitz matrix, the first behavior u=[u of T (u)1,u2,...,uN]∈CN, it may be assumed that
When solving above-mentioned Semidefinite Programming, if compression measurement number is enough, while multiple harmonic frequencies are mutual
Between be spaced in except a certain range, then by above-mentioned Semidefinite Programming can Exact recovery missing signal sampling point and
Determine each harmonic frequency.
To solve above-mentioned Semidefinite Programming, this patent is solved using ADMM method, and principle is as follows:
Z≥0
The Lagrangian of the problem are as follows:
In formula, | | | |FFor Frobenius norm
Therefore ADMM solution procedure are as follows:
K is the number of iterations in formula.
Optimal solution in above formula (x, t, u) is solved, Harmonious Waves in Power Systems can be obtained by carrying out triangle decomposition to T (u)
With the frequency f and amplitude of m-Acetyl chlorophosphonazo | s |.
T (u)=A (f) diag (| s |) AH(f)。
With the sliding of window, the estimated result for the different windows that N-M+1 size is M is estimated, flat then is asked to it
The frequency and amplitude of harmonic wave and m-Acetyl chlorophosphonazo can be obtained.
To sum up, specific steps of the invention are as follows:
1, to signal x (n) since first sampled point, continuous M point forms subset thereafter for selectionThen from
Second point starts, and continuous M point forms subset thereafter for selectionAnd so on, using the form of sliding window, formed
SubsetHere subscript m ∈ [1, N-M+1] indicates subset with x (m) beginning, and the range of subset is
2, forFollowing Semidefinite Programming is solved using ADMM method
Solve optimal solution in above formula (x, t, u).
3, subset can be obtained by carrying out triangle decomposition to T (u)The frequency of Harmonious Waves in Power Systems and m-Acetyl chlorophosphonazo
And amplitude
4, the estimated result for the different windows for being M to N-M+1 size is averaged frequency and width for harmonic wave and m-Acetyl chlorophosphonazo
Value, it may be assumed that
One embodiment of the present invention above described embodiment only expresses, the description thereof is more specific and detailed, but simultaneously
Limitations on the scope of the patent of the present invention therefore cannot be interpreted as.It should be pointed out that for those of ordinary skill in the art
For, under the premise of not departing from present inventive concept and principle, various modifications and improvements can be made, these belong to this hair
Bright protection scope.Therefore, the scope of protection of the patent of the invention shall be subject to the appended claims.
Claims (1)
1. a kind of harmonic signal analysis method based on sliding window and Semidefinite Programming, which is characterized in that this method is as follows:
(1) to signal x (n) since first sampled point, continuous M point forms subset thereafter for selectionThen from second
Point starts, and continuous M point forms subset thereafter for selectionAnd so on, using the form of sliding window, form subset
Here subscript m ∈ [1, N-M+1] indicates subset with x (m) beginning, and the range of subset is
(2) forFollowing Semidefinite Programming is solved using ADMM method
Solve optimal solution in above formula (x, t, u)；
(3) subset can be obtained by carrying out triangle decomposition to T (u)The frequency of Harmonious Waves in Power Systems and m-Acetyl chlorophosphonazoAnd width
Value
(4) estimated result for the different windows for being M to N-M+1 size is averaged frequency and amplitude for harmonic wave and m-Acetyl chlorophosphonazo,
That is:
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN112379216A (en) * | 2020-11-05 | 2021-02-19 | 山东大学 | Method and system for restraining measurement error in power transmission line fault location fundamental component extraction |
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| US20170299641A1 (en) * | 2014-10-04 | 2017-10-19 | Intelligent Fusion Technology, Inc. | Sliding window energy detection for spectrum sensing under low snr conditions |
| CN106019026A (en) * | 2016-07-20 | 2016-10-12 | 东南大学 | Distribution method based on waveform matching for harmonic voltage responsibility |
| CN108037361A (en) * | 2017-12-05 | 2018-05-15 | 南京福致通电气自动化有限公司 | A kind of high-precision harmonic parameters method of estimation based on sliding window DFT |
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| CN112379216A (en) * | 2020-11-05 | 2021-02-19 | 山东大学 | Method and system for restraining measurement error in power transmission line fault location fundamental component extraction |
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