CN109541306A - A kind of harmonic wave harmonic detection method based on TLS-ESPRIT - Google Patents
A kind of harmonic wave harmonic detection method based on TLS-ESPRIT Download PDFInfo
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Abstract
The invention discloses a kind of harmonic wave harmonic detection method based on TLS-ESPRIT, by the sampled data x of voltage signal0, x1..., xN‑1It is arranged in L × M dimension sampled data matrix X；Signal frequency component number k is estimated using Gai Shi circule method；Singular value decomposition X=R ∑ U is carried out to the sampled data matrix XT, the preceding k of right singular matrix U is taken to arrange to obtain signal subspace US；The frequency of each component in sampled signal is obtained using total least square method；The amplitude and phase angle of each component in sampled signal are obtained using least square method.The present invention can not only be provided simultaneously with short period window and upper frequency resolution ratio, and stability with higher and higher detection accuracy, compared to traditional window function and interpolation algorithm, the algorithm apply power distribution network dynamic process m-Acetyl chlorophosphonazo detection in precision it is higher, can more monitor the dynamic process of system.
Description
Technical field
The present invention relates to electric power quality technical fields, more particularly to one kind to be based on TLS-ESPRIT
(TotalLeastSquare-EstimationofSignalParametersviaRotationInvarianceTechniqu
Es, total least square method-invariable rotary Subspace algorithm) harmonic wave harmonic detection method.
Background technique
In recent years, power distribution network scale constantly increased, the flexibilities such as solar energy, the wind energy distributed energy and electric car
A large amount of access power distribution networks of load, thus make power distribution network in addition to it is short out with distribution wire, can be few with measurement point, synchronous and communicate item
The existing features such as part is incomplete, and increased the features such as m-Acetyl chlorophosphonazo, noise content are big, dynamic process is fast newly, therefore power distribution network is humorous
Wave and m-Acetyl chlorophosphonazo detection have become important research contents.
Currently, existing harmonic wave and harmonic detection method are mainly based upon Fast Fourier Transform (FFT) (Fast Fourier
Transform, FFT) and its innovatory algorithm, but in the case where non-synchronous sampling and signal dynamics change, these measurement methods
There are fence effect and it is long when window equalization effect, to detection accuracy can be made to be greatly reduced, it is therefore necessary to research in short-term
Window, high-resolution harmonic wave and inter-harmonic wave measuring method.
Estimation of Spatial Spectrum is one of main direction of studying of array signal processing, lays particular emphasis on what research arranged in certain sequence
Accurate estimation of the space array to airspace signal many kinds of parameters.Invariable rotary subspace (EstimationofSignalParame
TersviaRotationInvarianceTechniques, ESPRIT) algorithm is one of important branch of Estimation of Spatial Spectrum, be
A kind of high resolution algorithm based on feature decomposition can break through the time window and frequency resolution correlation of Fourier transformation
Limitation, is provided simultaneously with short time-window and high-resolution characteristic.But in low signal-to-noise ratio, this invariable rotary Subspace algorithm
To the more difficult judgement of signal frequency composition quantity, to affect the stability of the algorithm.
Summary of the invention
For above-mentioned shortcoming in the prior art, the present invention provides humorous between a kind of harmonic wave based on TLS-ESPRIT
Wave detecting method.The detection method can not only be provided simultaneously with short period window and upper frequency resolution ratio, and with higher
Stability and higher detection accuracy, compared to traditional window function and interpolation algorithm, which is applied in power distribution network dynamic mistake
Precision is higher in the m-Acetyl chlorophosphonazo detection of journey, can more monitor the dynamic process of system.
The purpose of the present invention is what is be achieved through the following technical solutions:
A kind of harmonic wave harmonic detection method based on TLS-ESPRIT, comprising the following steps:
Step 1: by the sampled data x of voltage signal0, x1..., xN-1It is arranged in L × M dimension sampled data matrix X:
Step 2: estimating signal frequency component number k using Gai Shi circule method；
Step 3: carrying out singular value decomposition X=R ∑ U to the sampled data matrix XT, the preceding k of right singular matrix U is taken to arrange
Obtain signal subspace US；
Step 4: obtaining the frequency of each component in sampled signal using total least square method；
Step 5: obtaining the amplitude and phase angle of each component in sampled signal using least square method.
Preferably, described to include: using Gai Shi circule method estimation signal frequency component number k
(1) data covariance matrix R is constructed:
(2) piecemeal is carried out to the data covariance matrix R,
(3) its feature space U is obtained to M-1 dimension square matrix R ' carry out feature decompositionG:
(4) with the feature space UGConstruct unitary transformation matrix T:
(5) unitary transformation is carried out to the data covariance matrix R
(6) it enablesWhen n from small to large when, it is assumed that there is negative for the first time in GDE (n)
When number be n0, then signal frequency component number k=n-1.
Preferably, described that the preceding k of right singular matrix U is taken to arrange to obtain signal subspace USIt include: to draw right singular matrix U
It is divided into signal subspace USWith noise subspace Un,
U=[Us|Un]
Wherein, USIt is arranged for the preceding k of right singular matrix U, k is the signal frequency component number.
Preferably, the frequency for obtaining each component in sampled signal using total least square method includes:
(1) signal subspace U is takenSPreceding M-1 row constitute matrix U1, and take signal subspace USM-1 row constitutes matrix afterwards
U2, order matrix D=[U1 U2]；
(2) singular value decomposition is carried out to matrix DAnd by right singular matrix UtIt is divided into the side of 4 k × k dimension
Battle array:
(3) according to the solution procedure structural matrix ψ of total least square methodtls:
And to matrix ψtlsEigenvalues Decomposition is carried out, characteristic value φ is obtained1、φ2、…、φk, then each component frequencies be
Preferably, described to obtain the amplitude of each component and phase angle in sampled signal using least square method and include:
(1) it enables
X '=[x0 x1 … xN-1]T；
(2) had according to least square method
A=(φTφ)-1φTX′；
(3) each component amplitude and phase angle are u in sampled signali=2 | Ai|
As seen from the above technical solution provided by the invention, the harmonic wave provided by the present invention based on TLS-ESPRIT
Sampled data is first arranged in data matrix by harmonic detection method, and estimates signal frequency component number using Gai Shi circule method, so
Signal subspace is obtained by carrying out singular value decomposition to data matrix afterwards, total least square method is recycled to obtain sampled signal
In each component frequency, the amplitude and phase angle of each component in sampled signal are obtained using least square method, so as to use
Harmonic in Power System and the frequency of m-Acetyl chlorophosphonazo, amplitude, phase angle are estimated with higher frequency resolution under conditions of short time window
Etc. parameters.The detection method provided by the present invention is provided simultaneously with the advantages of short time window and upper frequency resolution ratio, and has
There are higher stability and higher detection accuracy, is more suitable for than traditional window function and interpolation algorithm for monitoring the dynamic of electric system
State process.
Detailed description of the invention
In order to illustrate the technical solution of the embodiments of the present invention more clearly, required use in being described below to embodiment
Attached drawing be briefly described, it should be apparent that, drawings in the following description are only some embodiments of the invention, for this
For the those of ordinary skill in field, without creative efforts, it can also be obtained according to these attached drawings other
Attached drawing.
Fig. 1 provides the flow diagram of the harmonic wave harmonic detection method based on TLS-ESPRIT for the embodiment of the present invention.
Specific embodiment
With reference to the attached drawing in the embodiment of the present invention, technical solution in the embodiment of the present invention carries out clear, complete
Ground description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.Based on this
The embodiment of invention, every other implementation obtained by those of ordinary skill in the art without making creative efforts
Example, belongs to protection scope of the present invention.
The harmonic wave harmonic detection method to provided by the present invention based on TLS-ESPRIT is described in detail below.This
The content being not described in detail in inventive embodiments belongs to the prior art well known to professional and technical personnel in the field.
Embodiment 1
As shown in Figure 1, a kind of harmonic wave harmonic detection method based on TLS-ESPRIT, may comprise steps of:
Step 1: sampled to voltage signal to be measured, and by the sampled data x of acquisition0, x1..., xN-1It is arranged in L × M
Tie up sampled data matrix X.
Step 2: estimating signal frequency component number k using Gai Shi circule method.
Step 3: carrying out singular value decomposition to the sampled data matrix X, the preceding k of right singular matrix U is taken to arrange to obtain signal
Subspace US。
Step 4: obtaining the frequency of each component in sampled signal using total least square method.
Step 5: obtaining the amplitude and phase angle of each component in sampled signal using least square method.
Specifically, being somebody's turn to do the harmonic wave harmonic detection method based on TLS-ESPRIT includes following embodiments:
(1) L × M described in step 1 ties up sampled data matrix X are as follows:
Wherein, x is sampled data, and N is sampled data number, and L is the line number of sampled data matrix X, and M is sampled data square
The columns of battle array X；M+L-1=N.
Wherein, when M and L specific value is arranged, the value that M and L can be set is greater than signal frequency component number k to be asked
Value, i.e. M > k, L > k；Specifically, in practical applications, the frequency content (except noise) in practical power systems signal is no
Can be too many, therefore k can be estimated out and be greater than the maximum value when M and L is arranged in this way less than a certain maximum value, such as implemented
M takes 121, L to take and 120 can guarantee to be much larger than corresponding signal frequency component number k in example.
(2) estimating signal frequency component number k using Gai Shi circule method described in step 2 may include:
1. the sampled data matrix X according to step 1 constructs data covariance matrix R:
Wherein, R is the data covariance matrix of sampled data matrix X, and L is the line number of sampled data matrix X, and X is step
Sampled data matrix described in one, XHThe conjugate transposition of representing matrix X.
2. piecemeal is carried out to the data covariance matrix R,
Wherein, R is the data covariance matrix of sampled data matrix X, and R ' is that the M-1 in the upper left corner R ties up square matrix, and r is M-1 dimension
Column vector, rHRow vector is tieed up for M-1,For the element in the lower right corner R, M is the columns of sampled data matrix X.
3. the M-1 dimension square matrix R ' carry out feature decomposition to the R upper left obtains its feature space UG:
Wherein, R ' is that the M-1 of R upper left ties up square matrix；UGIt is characterized space, and is metI is unit
Battle array；∑GIt is characterized space UGCorresponding eigenvalue matrix, off-diagonal element 0.
4. with the feature space UGConstruct unitary transformation matrix T:
Wherein, T is characterized space UGUnitary transformation matrix, UGIt is characterized space, 0 ties up null vector for M-1.
5. carrying out unitary transformation to the data covariance matrix R
Wherein, RTFor the matrix for obtain after unitary transformation to R, R is the data covariance matrix of sampled data matrix X, T
It is characterized space UGUnitary transformation matrix, ∑ RTThe M-1 in the upper left corner ties up square matrix,Square matrix is tieed up for the M-1 in the upper left corner R
The feature space of R ', r are the M-1 dimensional vector on the right side of R, rMMFor RTThe element in the lower right corner, λ1For the main diagonal element of ∑,
ρ1, ρ2..., ρM-1ForIn element,For rHUGIn element, M is sampled data matrix X
Columns.
6. enablingWhen n from small to large when, it is assumed that when there is negative for the first time in GDE (n)
Number be n0, then signal frequency component number k=n0-1；
Wherein, GDE (n) is the function for judging signal frequency component number, and n=1,2 ..., M-1, r are positioned at data association side
The M-1 dimensional vector of m column in poor matrix R, M are the columns of sampled data matrix X, and the value of i is 1 to M-1；D (L) is one
Dynamic gene related with L, its value range is between 0 to 1, and D (L) is smaller when L is bigger, and when L tends to infinity, D (L) is taken
0。
(3) singular value decomposition is carried out to the sampled data matrix X in step 3:
X=R ∑ UT
Then its right singular matrix U is divided into signal subspace USWith noise subspace Un,
U=[Us|Un]
Wherein, X is sampled data matrix described in step 1, and R is the data covariance matrix of sampled data matrix X, ∑
Singular value for X arranges from big to small and the diagonal matrix that forms, and U is the right singular matrix of sampled data matrix X, UTRepresenting matrix
The transposition of U；UnFor noise subspace, USFor signal subspace, the preceding k of right singular matrix U is taken to arrange, k is signal described in step 2
Frequency content number.
(4) it can wrap described in step 4 using the frequency that total least square method obtains each component in sampled signal
It includes:
1. taking signal subspace U described in step 3SPreceding M-1 row constitute matrix U1, and take signal subspace USM-1 afterwards
Row constitutes matrix U2, order matrix D=[U1 U2]。
2. carrying out singular value decomposition to the matrix D:
And by the right singular matrix U of the matrix DtIt is divided into the square matrix of 4 k × k dimension:
Wherein, RtFor the left singular matrix of the matrix D, ∑tSingular value for the matrix D arranges and group from big to small
At diagonal matrix, UtFor the right singular matrix of the matrix D, Ut11、Ut12、Ut21、Ut22It is right singular matrix UtK × the k being divided into
Square matrix is tieed up, k is signal frequency component number described in step 2.
3. according to the solution procedure structural matrix ψ of total least square methodtls:
And to matrix ψtlsEigenvalues Decomposition is carried out, characteristic value φ is obtained1、φ2、…、φk, then each component frequencies be
Wherein, fiFor the frequency of component i in sampled signal, φiFor plural number, TSFor signal sampling time interval, k is step
Signal frequency component number described in two.
(5) obtaining the amplitude of each component and phase angle in sampled signal using least square method described in step 5 includes:
1. enabling
X '=[x0 x1 … xN-1]T
Wherein,For by φ1, φ2..., φkThe coefficient square of equal elements composition
Battle array, N be sampled data number, k be step 2 described in signal frequency component number, X ' be by N number of groups of samples at matrix, x
For sampled data.
2. being had according to least square method
A=(φTφ)-1φTX′
Wherein, A=(φTφ)-1φTX ' be etc. Formula X '=φ A least square solution.
3. each component amplitude and phase angle are u in sampled signali=2 | Ai|
Wherein, i=1,2 ..., k, k are signal frequency component number described in step 2, uiFor component width in sampled signal
Value,For component phase angle, A in sampled signaliFor i-th of element in matrix A.
Further, signal frequency composition quantity estimation method common in the art has method of information theory, smooth order
The methods of with matrix decomposition, these methods require to obtain the characteristic value of matrix after matrix or amendment, then recycle characteristic value
To estimate signal frequency component number.And Gai Shi circle method of the present invention is estimated using Gerschgorin circles theorem
The method for counting each characteristic value position of matrix, can estimate signal frequency component number, and be not required to using the position of characteristic value
Specifically to know characteristic value numerical value, there is certain superiority.Total least square method of the present invention
(TotalLeastSquare, TLS) is a kind of relatively advanced least square method structure, and total least square method is thought to return square
There is interference in battle array, this factor is considered when calculating least square, thus obtain than not accounting for the general of factor influence
The more superior performance of least square method.Harmonic wave harmonic detection method provided by the present invention based on TLS-ESPRIT will first be adopted
Sample data arrangement estimates signal frequency component number at data matrix, and using Gai Shi circule method, then by carrying out to data matrix
Singular value decomposition obtains signal subspace, and total least square method is recycled to obtain the frequency of each component in sampled signal, utilizes
Least square method obtains the amplitude and phase angle of each component in sampled signal, so as under conditions of using short time window with compared with
The parameters such as high frequency, amplitude, the phase angle of frequency resolution estimation Harmonic in Power System and m-Acetyl chlorophosphonazo.It is provided by the present invention
The detection method is provided simultaneously with the advantages of short time window and upper frequency resolution ratio, and stability with higher and higher
Detection accuracy is more suitable for the dynamic process for monitoring electric system than traditional window function and interpolation algorithm.
To sum up, the embodiment of the present invention can not only be provided simultaneously with short period window and upper frequency resolution ratio, and have
There are higher stability and higher detection accuracy, compared to traditional window function and interpolation algorithm, which applies dynamic in power distribution network
Precision is higher in the m-Acetyl chlorophosphonazo detection of state process, can more monitor the dynamic process of system.
In order to more clearly from show technical solution provided by the present invention and generated technical effect, below with imitative
The harmonic wave harmonic detection method provided by the present invention based on TLS-ESPRIT is described in detail in true test case.
Emulation testing example
Emulation testing is carried out to the harmonic wave harmonic detection method based on TLS-ESPRIT that the embodiment of the present invention 1 provides,
It can specifically include the following contents:
1, an emulation testing sampled signal is defined, in signal under each frequency component parameter as shown in table 1:
Table 1
2, the short time-window of detection method, high-resolution characteristic in the embodiment of the present invention 1 are examined
Use the embodiment of the present invention 1 provide the harmonic wave harmonic detection method based on TLS-ESPRIT sample frequency for
1200Hz, sampling number 240, sampled data matrix X line number L take the columns M of 120, sampled data matrix X to take 121, sampling
Under conditions of signal adds 60dB white Gaussian noise, the emulation testing is detected with sampled signal, to obtain the following table 2 institute
Each frequency component parameter estimated value of emulation testing sampled signal when show plus 60dB white Gaussian noise:
Table 2
By Tables 1 and 2 it can be seen that under conditions of 60dB white Gaussian noise, the embodiment of the present invention 1 provide based on
The harmonic wave harmonic detection method of TLS-ESPRIT uses the time window of 0.2s that can accurately estimate minimum frequency space for 3Hz's
The parameter of frequency content quantity and each ingredient that signal includes.
3, in the embodiment of the present invention 1 detection method with using 10s time window existing windowing FFT algorithm performance compared with
The harmonic wave harmonic detection method based on TLS-ESPRIT that the embodiment of the present invention 1 is provided is in sample frequency
1200Hz, sampling number 240, sampled data matrix X line number L take the columns M of 120, sampled data matrix X to take 121, sampling
Signal adds the testing result under conditions of 60dB white Gaussian noise, 10s time window plus 5 rank rife-vincent windows with using
Testing result of existing windowing FFT algorithm under conditions of adding 60dB white Gaussian noise carries out application condition, to obtain the following table 3
Shown in plus two kinds of Algorithm Error comparison results when 60dB white Gaussian noise:
Table 3
As can be seen from Table 3: under conditions of 60dB white Gaussian noise, compared to the existing windowing FFT with 10s time window
Algorithm is existed using the harmonic wave harmonic detection method based on TLS-ESPRIT that the embodiment of the present invention 1 of 0.2s time window provides
An order of magnitude is higher by frequency estimation accuracy, the similar performance in Amplitude Estimation precision.
To sum up, the embodiment of the present invention can not only be provided simultaneously with short period window and upper frequency resolution ratio, and have
There are higher stability and higher detection accuracy, compared to traditional window function and interpolation algorithm, which applies dynamic in power distribution network
Precision is higher in the m-Acetyl chlorophosphonazo detection of state process, can more monitor the dynamic process of system.
The foregoing is only a preferred embodiment of the present invention, but scope of protection of the present invention is not limited thereto,
Within the technical scope of the present disclosure, any changes or substitutions that can be easily thought of by anyone skilled in the art,
It should be covered by the protection scope of the present invention.Therefore, protection scope of the present invention should be with the protection model of claims
Subject to enclosing.
Claims (5)
1. a kind of harmonic wave harmonic detection method based on TLS-ESPRIT, which comprises the following steps:
Step 1: by the sampled data x of voltage signal0,x1,…,xN-1It is arranged in L × M dimension sampled data matrix X:
Step 2: estimating signal frequency component number k using Gai Shi circule method；
Step 3: carrying out singular value decomposition X=R ∑ U to the sampled data matrix XT, the preceding k of right singular matrix U is taken to arrange to obtain
Signal subspace US；
Step 4: obtaining the frequency of each component in sampled signal using total least square method；
Step 5: obtaining the amplitude and phase angle of each component in sampled signal using least square method.
2. the harmonic wave harmonic detection method according to claim 1 based on TLS-ESPRIT, which is characterized in that the benefit
Include: with Gai Shi circule method estimation signal frequency component number k
(1) data covariance matrix R is constructed:
(2) piecemeal is carried out to the data covariance matrix R,
(3) its feature space U is obtained to M-1 dimension square matrix R ' carry out feature decompositionG:
(4) with the feature space UGConstruct unitary transformation matrix T:
(5) unitary transformation is carried out to the data covariance matrix R
(6) it enablesWhen n from small to large when, it is assumed that when there is negative for the first time in GDE (n)
Number is n0, then signal frequency component number k=n-1.
3. the harmonic wave harmonic detection method according to any one of claim 1 to 2 based on TLS-ESPRIT, feature
It is, described takes the preceding k of right singular matrix U to arrange to obtain signal subspace USIt include: that right singular matrix U is divided into signal subspace
Space USWith noise subspace Un,
U=[Us|Un]
Wherein, USIt is arranged for the preceding k of right singular matrix U, k is the signal frequency component number.
4. the harmonic wave harmonic detection method according to any one of claim 1 to 2 based on TLS-ESPRIT, feature
It is, the frequency for obtaining each component in sampled signal using total least square method includes:
(1) signal subspace U is takenSPreceding M-1 row constitute matrix U1, and take signal subspace USM-1 row constitutes matrix U afterwards2, enable square
Battle array D=[U1 U2]；
(2) singular value decomposition is carried out to matrix DAnd by right singular matrix UtIt is divided into the square matrix of 4 k × k dimension:
(3) according to the solution procedure structural matrix ψ of total least square methodtls:
And to matrix ψtlsEigenvalues Decomposition is carried out, characteristic value φ is obtained1、φ2、…、φk, then each component frequencies be
5. the harmonic wave harmonic detection method according to any one of claim 1 to 2 based on TLS-ESPRIT, feature
It is, it is described to obtain the amplitude of each component and phase angle in sampled signal using least square method and include:
(1) it enables
X '=[x0 x1 … xN-1]T；
(2) had according to least square method
A=(φTφ)-1φTX′；
(3) each component amplitude and phase angle are in sampled signal
ui=2 | Ai|
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Application publication date: 20190329 |