CN116894154A - New energy distribution network harmonic and transient oscillation power quality composite disturbance parameter extraction method - Google Patents
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Abstract
A new energy distribution network harmonic and transient oscillation electric energy quality composite disturbance parameter extraction method comprises the steps of firstly adopting SVD to reduce noise, and reconstructing a signal after filtering a sampling signal; then calculating points with the second derivative function of 0 after fitting the singular value sequence fitting function by using an SDM method, and further determining the effective rank order of the Prony algorithm; and finally, extracting the frequency, amplitude and attenuation factor parameters of the harmonic signals by adopting a Prony algorithm. Compared with the original Prony algorithm and SVD-Prony algorithm, the method has the advantages that broadband oscillation and background harmonic parameters can be effectively extracted, and the relative error is smaller.
Description
Technical Field
The invention belongs to the technical field of power quality analysis of power distribution networks, and particularly relates to a method for extracting harmonic and transient oscillation power quality composite disturbance parameters of a new energy power distribution network.
Background
The harmonic wave in the distribution network can increase the system loss rate, and meanwhile, the harmonic wave with more complex components is easy to generate harmonic resonance with the impedance of the distribution network, so that harmonic current amplification is caused, and the normal operation of the parallel capacitor bank in the transformer substation is adversely affected. And when the parallel capacitor bank is put into or cut off, transient oscillation is easy to occur, if reasonable treatment is not obtained, large fluctuation of voltage and current easily causes a large amount of equipment to be disconnected, the safe and stable operation of a power grid is seriously influenced, and the damage is particularly obvious for the power distribution network with larger electric distance interval from a main network.
Therefore, a harmonic detection method capable of simultaneously detecting background harmonic disturbance and transient harmonic oscillation is needed for harmonic analysis and management in a power distribution network. Although the traditional Prony algorithm can extract disturbance information, the traditional Prony algorithm is extremely sensitive to noise, and meanwhile, the accuracy of an extraction result is greatly dependent on the selection of the effective rank order of a model.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a new energy power distribution network harmonic and transient oscillation power quality composite disturbance parameter extraction method.
The invention solves the technical problems by the following technical proposal:
a new energy power distribution network harmonic and transient oscillation power quality composite disturbance parameter extraction method is characterized by comprising the following steps of: the method comprises the following steps:
s1, acquiring current signals containing harmonic waves and transient oscillation disturbance in a power distribution network based on the power distribution network, and adopting a noise reduction method based on singular value decomposition to perform noise reduction processing on the current signals containing noise in the power distribution network and reconstruct a sampling signal sequence;
s2, analyzing the reconstructed signal sequence by using an effective rank calculation method based on a second derivative theory, calculating sequence points with a fitting function second derivative function of 0, and determining the order of a Prony algorithm model;
and S3, extracting harmonic characteristics by adopting a Prony algorithm, acquiring the amplitude and the frequency of a harmonic signal in the power distribution network, and simultaneously extracting the amplitude, the frequency and the attenuation factor of transient harmonic oscillation.
Moreover, the S1 specifically includes:
the method comprises the steps of dividing a sampling signal vector space in a power distribution network into a noise signal space and an effective signal space, wherein the noise signal space and the effective signal space are mutually orthogonal, and aiming at discrete signals x= [ x ] acquired at sampling points of the power distribution network 1 ,x 2 ,…,x N ]The Hankel matrix is constructed as shown below,
wherein: if the number of sampling points N is odd, n= (n+1)/2, m= (n+1)/2, if N is even, n=n/2, m=n/2+1;
then, singular value decomposition is carried out on the matrix X to obtain the following formula:
wherein: the matrix U is an orthogonal matrix in m x m dimensions;
the matrix Σ is an n×n-dimensional matrix;
Δ q×q is a diagonal matrix, and the elements on the diagonal are singular values of matrix X;
the V matrix is an n×n-dimensional reversible orthogonal matrix;
according to the singular value decomposition theory, if k-dimensional effective signal space exists, the diagonal matrix delta q×q The k singular values corresponding to the k singular values are necessarily existed, the remaining q-k singular values are the dimension numbers corresponding to the noise signal space, and k is the order corresponding to the effective signal space;
diagonal matrix delta q×q The elements on the diagonal are singular value sequences corresponding to the matrix X, and the singular value sequences are sequentially arranged according to the absolute values of the singular value elements, which can be simply described as: sigma (sigma) 11 ，σ 22 ，…，σ kk ,σ (k+1)(k+1) ,…,σ nn ；
Wherein: sequence sigma 11 ，σ 22 ，…，σ kk The element value is larger and the variation amplitude of the value is relatively smaller, and the k+1th singular value sigma (k+1)(k+1) The numerical value is higher than the kth singular value sigma kk A substantial drop will occur, followed by sequence sigma (k+1)(k+1) ,σ (k+2)(k+2) …,σ nn The numerical variation will again tend to be smooth without significant fluctuations;
by setting a threshold value, the effective order of the matrix is obtained,
selecting the minimum k value corresponding to the function v (k) larger than the threshold value, namely the effective order;
then for the blocking matrix delta in the matrix sigma q×q Processing, namely setting the q-k order diagonal elements to be zero, and marking the corrected matrix as sigma k Then, the obtained product is transformed to obtain:
using the reconstructed Hankel matrixAnd regenerating a sampling signal sequence to complete the filtering process.
Moreover, the S2 specifically includes:
the singular values of the sampling sample matrix R are ordered according to the order of magnitude, and then the sequence is as follows:
σ 1 ≥σ 2 ≥…≥σ p ≥σ p+1 ≈…≈σ pe
sigma due to the presence of noise in the actual electrical signal p+1 And the singular value is not 0, is a series of values tending to 0, generates a function by fitting discrete singular value data points, then calculates the second derivative of the function, if the following formula is satisfied, that is, the critical point with the second derivative of 0 exists,
the method indicates that the singular values of the matrix are mutated before and after the point, the point is the demarcation point of the effective rank, and the sequence number corresponding to the critical point indicates the effective rank order p.
Moreover, the S3 specifically includes:
assuming the sampling signal function is x (n), then x (0), x (1), …, x are fit by(N-1), designated as
Wherein: p is the order of the model, and N is the number of signal adoption points;
b i and z i The essence is complex number, and the corresponding calculation formula is:
to ensure that the fitted signal is as close as possible to the actual sampled signal, it is necessary to use the sum of squares of the errors as the optimization objective, its corresponding objective function, as follows:
the sampled signal function x (n) is then processed as follows:
wherein: p is p e The order of the sampling sample matrix R is connected, the sampling sample matrix R is constructed according to the above, and the elements and structures in the matrix are as follows:
carrying out singular value decomposition or least square estimation on the matrix R, and solving an effective rank p, wherein the size of the effective rank p depends on the number of signal disturbance quantities, and when the signal is free of noise, the physical meaning of the effective rank p is the number of non-zero elements in the singular value matrix after the singular value of the sample matrix R is decomposed;
and (3) retaining partial elements of the matrix R corresponding to the effective rank order p, and solving the following formula:
1+a 1 z -1 +…+a p z -p ＝0
get its corresponding root z i Then z i Carry-in typeAnd performs the following transformation to obtain the following matrix equation:
wherein: the leftmost matrix is an N x p-dimensional vandermonde matrix, which is full-rank and invertible, and if the leftmost matrix is denoted as matrix V, and matrix V is invertible, the following transformation can be performed:
finally, calculating the characteristic parameters of the mixed disturbance signal, mainly including the amplitude A of transient oscillation i Frequency f i Attenuation factor alpha i And phase theta i The method comprises the steps of carrying out a first treatment on the surface of the Frequency f of harmonic signal i Amplitude parameter A i In parameter calculation, the harmonic signal can be regarded as attenuation factor alpha i Oscillation parameters of =0,
wherein: i=1, 2, …, n, representing the number of disturbance signal components.
The invention has the advantages and beneficial effects that:
the invention aims at two important factors affecting the harmonic detection precision of the Prony algorithm: the method comprises the steps of selecting signal noise and an effective rank order, providing a composite disturbance extraction algorithm based on SVD noise reduction and SDM-Prony algorithm, firstly adopting SVD noise reduction to filter a sampling signal and reconstructing the signal; then, calculating points with a second derivative function of 0 after fitting the singular value sequence fitting function by using an SDM method, and further determining the effective rank order of a Prony algorithm; and finally, extracting the frequency, amplitude and attenuation factor parameters of the harmonic signals by adopting a Prony algorithm. Simulation experiments prove the effectiveness of the method. Meanwhile, the extraction results of the three algorithms on the same disturbance are compared and analyzed, and the SVD-based SDM-Prony algorithm is compared and found to have optimal extraction precision.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a sequence diagram of singular values of a Hankel matrix of a noisy signal according to the present invention;
FIG. 3 is a waveform diagram of a noise-containing raw signal according to the present invention;
fig. 4 is a waveform diagram of the SVD noise reduced signal of the present invention.
Detailed Description
The invention is further illustrated by the following examples, which are intended to be illustrative only and not limiting in any way.
A new energy power distribution network harmonic and transient oscillation power quality composite disturbance parameter extraction method is innovative in that: the method comprises the following steps:
s1, acquiring current signals containing harmonic waves and transient oscillation disturbance in a power distribution network based on the power distribution network, and adopting a noise reduction method based on Singular Value Decomposition (SVD) to perform noise reduction treatment on the current signals containing noise in the power distribution network and reconstruct a sampling signal sequence;
s2, analyzing the reconstructed signal sequence by using an effective rank calculation method based on a second derivative theory (SDM), calculating sequence points with a fitting function second derivative function of 0, and determining the order of a Prony algorithm model;
and S3, extracting harmonic characteristics by adopting a Prony algorithm, acquiring the amplitude and the frequency of a harmonic signal in the power distribution network, and simultaneously extracting the amplitude, the frequency and the attenuation factor of transient harmonic oscillation.
The method comprises the following steps:
the essence of Prony algorithm is a parameter identification method based on polynomial linear fitting, and if the sampled signal data is x (N), then x (0), x (1), …, x (N-1) can be marked asIn the formula (1), p is the order of the model, and N is the number of signal utilization points.
B in formula (1) i And z i The corresponding calculation formulas are shown as formula (2) and formula (3), and the essence of the corresponding calculation formulas is complex.
Also, to ensure that the fitted signal is as close as possible to the actual sampled signal, a minimum sum of squares of errors is used as an optimization objective, the corresponding objective function of which is shown below.
The sampled signal function x (n) is then processed as follows.
Wherein p is e The order of matrix R is followed, and then a matrix R of sampled samples is constructed according to equation (5), with the elements and structure in the matrix being shown in equation (6).
And (3) carrying out singular value decomposition or least square estimation on the matrix R in the formula (6), and obtaining an effective rank p, wherein the size of the effective rank p depends on the number of signal disturbance quantities. When the signal has no noise, the physical meaning of the effective rank p is the number of non-zero elements in the singular value matrix after decomposing the singular value of the sample matrix R.
Then, partial elements of the matrix R corresponding to the effective rank order p are reserved as shown in a formula (7), and then the formula (7) and the formula (8) are solved simultaneously.
1+a 1 z -1 +…+a p z -p ＝0 (8)
A in the formula (6) can be used i Solving the polynomial (8) to obtain the corresponding root z i Is a value of (2). Then z is set i The matrix equation of the formula (9) can be obtained by substituting the formula (1) and performing the following transformation.
The leftmost matrix of equation (9) is an N x p-dimensional vandermonde matrix, which is full rank and reversible. If the leftmost matrix in the expression (9) is denoted as a matrix V, and the matrix V is a reversible matrix, the following conversion can be performed.
Then, the characteristic parameters of the mixed disturbance signal can be calculated, wherein the characteristic parameters mainly comprise the amplitude A of transient oscillation i Frequency f i Attenuation factor alpha i And phase theta i The method comprises the steps of carrying out a first treatment on the surface of the Frequency f of harmonic signal i Amplitude parameter A i . In parameter calculation, the harmonic signal can be regarded as attenuation factor alpha i Oscillation parameters of =0.
In the formula (11), i=1, 2, …, n represents the number of disturbance signal components.
The principle of a noise reduction algorithm (SVD) based on singular value decomposition is to divide an original sampling signal vector space into a noise signal space and an effective signal space, and the noise signal and the effective signal space are orthogonal to each other. For discrete signals acquired at sampling points: x= [ x ] 1 ,x 2 ,…,x N ]The Hankel matrix shown in the following formula (12) may be constructed.
If the number N of sampling points is an odd number, n= (n+1)/2, m= (n+1)/2. When N is even, n=n/2, m=n/2+1. The matrix X is then subjected to singular value decomposition.
In the formula (13), the matrix U is an orthogonal matrix of m×m dimensions. The matrix Σ is an n×n-dimensional matrix, where Δ q×q Is a diagonal matrix, and the elements on the diagonal are the singular values of matrix X. The V matrix is an n x n-dimensional reversible orthogonal matrix.
According to the singular value decomposition theory, if k-dimensional effective signal space exists, the diagonal matrix delta q×q There must be k singular values corresponding thereto. The remaining q-k singular values are the dimensions of the corresponding noise signal space. k is the order corresponding to the effective signal space.
The SVD algorithm is to discriminate the order k corresponding to the effective signal space by using the distribution characteristic of the matrix sigma singular value sequence. Diagonal matrix delta q×q The elements on the diagonal are singular value sequences corresponding to the matrix X, and the singular value sequences are sequentially arranged according to the absolute values of the singular value elements, which can be simply described as: sigma (sigma) 11 ，σ 22 ，…，σ kk ,σ (k+1)(k+1) ,…,σ nn . Wherein the sequence sigma 11 ，σ 22 ，…，σ kk The element values are large and the magnitude of the change in values is relatively small. And the (k+1) th singular value sigma (k+1)(k+1) The numerical value is higher than the kth singular value sigma kk A substantial drop will occur. Subsequent sequence sigma (k+1)(k+1) ,σ (k+2)(k+2) …,σ nn The value change will again tend to settle without significant fluctuations. The reason for this is that the noise component in the sampled signal is much smaller than the effective signal component.
The fundamental electric signals superimposed with 3, 5 and 7 characteristic harmonic disturbances were set in MATLAB simulation experiments, and 20dB of gaussian white noise was applied thereto, with the sampling frequency set at 2000Hz. The Hankel matrix singular value sequence generated from the sampled signals is shown in FIG. 2. If the singular value sequence is regarded as a sequence of numbers arranged according to the size, the position of the mutation point with the numerical value change of the sequence is the effective order k. The effective order is 6, which can be seen visually in fig. 2. In the actual calculation process, the effective order of the matrix is often obtained by setting a threshold value.
I.e. the minimum k value corresponding to the function v (k) larger than the threshold value is the effective order. When the actual SVD algorithm is used, the threshold is usually selected to be 0.9-0.95, and the best effect is achieved.
If the k value is selected to be too small, although the filtering performance is good, part of effective signal components are filtered, so that the characteristic components of the reconstructed sampling signal are lost and the extraction result is inaccurate. If the k value is selected too large, the filtering performance is degraded although the effective signal component is well preserved. Therefore, the threshold value must be flexibly set according to the actual situation.
Then for the blocking matrix delta in the matrix sigma q×q Processing, namely setting the q-k order diagonal elements to be zero, and marking the corrected matrix as sigma k . Then, the obtained product is subjected to a transformation represented by formula (15).
Finally, the reconstructed Hankel matrix is utilizedAnd regenerating a sampling signal sequence, namely finishing the SVD filtering process.
The matrix effective rank extraction method based on the second derivative theory (SDM) is to sort the singular values of the matrix R in the formula (6) according to the order of magnitude, and further obtain a sequence shown in the formula (16).
σ 1 ≥σ 2 ≥…≥σ p ≥σ p+1 ≈…≈σ pe (16)
Sigma due to the presence of noise in the actual electrical signal p+1 And the singular value is not 0, and is a group of sequences with values approaching 0. By fitting discrete singular value data points, a function is generated, and then the second derivative of the function is calculated, e.g., satisfying equation (17), i.e., there are critical points where the second derivative is 0.
Indicating that the singular values of the matrix have been mutated before and after this point. This point can be considered as a demarcation point for the effective rank. The sequence number corresponding to the critical point indicates the effective rank order p. The physical meaning of the effective rank order p is the least characteristic equation order that the Prony algorithm can characterize the disturbance quantity.
The obtained effective rank order p can be substituted into the formulas (7) to (9), so that the calculated amount can be greatly reduced, the number of parameters extracted by the formula (11) is more similar to the number of real disturbance amounts, the number of invalid data is greatly reduced, and the accuracy of a calculation result is further improved.
For the algorithm provided by the invention, the example simulation is carried out on a MATLAB/SIMULINK platform. In the calculation example, 3 groups of power distribution network background harmonic components and 1 group of oscillation components are set, and meanwhile, 20dB of Gaussian white noise is added into the signal. The specific disturbance parameters are set as shown in table 1.
TABLE 1 Signal composite disturbance parameters
The signal disturbance considered in the simulation experiment is the background harmonic wave of the power distribution network and the oscillation generated by the input of the parallel capacitor bank. In the simulation example, the sampling frequency of the signal is set to 2000Hz, and the simulation time is set to 1s. The sample sequence contains 2000 elements in total. The original signal is fitted with a sampling sequence whose waveform of the sampling signal containing gaussian white noise is shown in fig. 3.
The original sampled signal is then noise reduced using an SVD noise reduction algorithm and the sampled signal sequence is re-reconstructed with a waveform as shown in FIG. 4.
Comparing fig. 3 and fig. 4, it can be seen that the noise component of the signal sequence reconstructed after the SVD noise reduction algorithm is filtered is effectively filtered. And the accuracy of parameter extraction by using the Prony algorithm can be improved, and the extraction results are shown in tables 2 and 3.
TABLE 2 transient oscillation parameter extraction results
TABLE 3 harmonic parameter extraction results for Power distribution networks
It can be seen from tables 2 and 3 that, for transient oscillation parameters, since the oscillation amplitude is relatively large and the disturbance characteristics are obvious, the extraction is relatively easy and the result is more accurate. But even though the disturbance features are not very obvious background harmonics, the relative error of the parameter extraction results is within an acceptable error range.
The error mainly comes from SVD noise filtering links, and an effective signal space order k needs to be set in an SVD noise reduction algorithm. If the order k is too large, although the filtering effect is better, the effective components of the signal part are lost, the accuracy of the extraction result of the subsequent Prony algorithm is affected, and even part of parameter information is omitted when serious.
In the simulation example, the original Prony algorithm, the SVD-Prony algorithm and the SDM-Prony algorithm based on the SVD method are respectively adopted for extracting parameters of the sampled signals. The three algorithms are shown in table 4 for the extraction result pairs of the disturbance signal parameter amplitude, frequency and attenuation factor.
Table 4 Prony algorithm and comparison of improved algorithm parameter extraction results
It can be seen that if the SVD noise reduction algorithm is not added, the error of the final extraction result is large, and the higher the frequency of disturbance is, the larger the influence of the noise signal is, and the lower the accuracy of the extraction result is. Transient oscillation has obvious oscillation amplitude, more prominent disturbance characteristics and is less affected by noise.
The new energy power distribution network harmonic and transient oscillation power quality composite disturbance parameter extraction method can filter noise signals to a certain extent, the accuracy is improved to a great extent, and the relative error is still larger. The SVD-based SDM-Prony algorithm further starts from the angle of an effective rank, after the SVD noise reduction operation, the order of a disturbance model is further calculated by using a second derivative theory (SDM) algorithm, and a calculation result is brought into the model of the Prony algorithm, so that the accuracy of parameter extraction is further improved. The relative error of the parameter extraction results of the method is also the smallest in the three methods.
Although the embodiments of the present invention and the accompanying drawings have been disclosed for illustrative purposes, those skilled in the art will appreciate that: various substitutions, changes and modifications are possible without departing from the spirit and scope of the invention and the appended claims, and therefore the scope of the invention is not limited to the embodiments and the disclosure of the drawings.
Claims (4)
1. A new energy power distribution network harmonic and transient oscillation power quality composite disturbance parameter extraction method is characterized by comprising the following steps of: the method comprises the following steps:
s1, acquiring current signals containing harmonic waves and transient oscillation disturbance in a power distribution network based on the power distribution network, and adopting a noise reduction method based on singular value decomposition to perform noise reduction processing on the current signals containing noise in the power distribution network and reconstruct a sampling signal sequence;
s2, analyzing the reconstructed signal sequence by using an effective rank calculation method based on a second derivative theory, calculating sequence points with a fitting function second derivative function of 0, and determining the order of a Prony algorithm model;
and S3, extracting harmonic characteristics by adopting a Prony algorithm, acquiring the amplitude and the frequency of a harmonic signal in the power distribution network, and simultaneously extracting the amplitude, the frequency and the attenuation factor of transient harmonic oscillation.
2. The method for extracting the harmonic and transient oscillation power quality composite disturbance parameters of the new energy power distribution network according to claim 1, which is characterized by comprising the following steps: the S1 specifically comprises the following steps:
the method comprises the steps of dividing a sampling signal vector space in a power distribution network into a noise signal space and an effective signal space, wherein the noise signal space and the effective signal space are mutually orthogonal, and aiming at discrete signals x= [ x ] acquired at sampling points of the power distribution network 1 ,x 2 ,…,x N ]The structure of Han is as followsThe matrix of the kel-shape,
wherein: if the number of sampling points N is odd, n= (n+1)/2, m= (n+1)/2, if N is even, n=n/2, m=n/2+1;
then, singular value decomposition is carried out on the matrix X to obtain the following formula:
wherein: the matrix U is an orthogonal matrix in m x m dimensions;
the matrix Σ is an n×n-dimensional matrix;
Δ q×q is a diagonal matrix, and the elements on the diagonal are singular values of matrix X;
the V matrix is an n×n-dimensional reversible orthogonal matrix;
according to the singular value decomposition theory, if k-dimensional effective signal space exists, the diagonal matrix delta q×q The k singular values corresponding to the k singular values are necessarily existed, the remaining q-k singular values are the dimension numbers corresponding to the noise signal space, and k is the order corresponding to the effective signal space;
diagonal matrix delta q×q The elements on the diagonal are singular value sequences corresponding to the matrix X, and the singular value sequences are sequentially arranged according to the absolute values of the singular value elements, which can be simply described as: sigma (sigma) 11 ，σ 22 ，…，σ kk ,σ (k+1)(k+1) ,…,σ nn ；
Wherein: sequence sigma 11 ，σ 22 ，…，σ kk The element value is larger and the variation amplitude of the value is relatively smaller, and the k+1th singular value sigma (k+1)(k+1) The numerical value is higher than the kth singular value sigma kk A substantial drop will occur, followed by sequence sigma (k+1)(k+1) ,σ (k+2)(k+2) …,σ nn The numerical variation will again tend to be smooth without significant fluctuations;
by setting a threshold value, the effective order of the matrix is obtained,
selecting the minimum k value corresponding to the function v (k) larger than the threshold value, namely the effective order;
then for the blocking matrix delta in the matrix sigma q×q Processing, namely setting the q-k order diagonal elements to be zero, and marking the corrected matrix as sigma k Then, the obtained product is transformed to obtain:
using the reconstructed Hankel matrixAnd regenerating a sampling signal sequence to complete the filtering process.
3. The method for extracting the harmonic and transient oscillation power quality composite disturbance parameters of the new energy power distribution network according to claim 1, which is characterized by comprising the following steps: the step S2 is specifically as follows:
the singular values of the sampling sample matrix R are ordered according to the order of magnitude, and then the sequence is as follows:
σ 1 ≥σ 2 ≥…≥σ p ≥σ p+1 ≈…≈σ pe
sigma due to the presence of noise in the actual electrical signal p+1 And the singular value is not 0, is a series of values tending to 0, generates a function by fitting discrete singular value data points, then calculates the second derivative of the function, if the following formula is satisfied, that is, the critical point with the second derivative of 0 exists,
the method indicates that the singular values of the matrix are mutated before and after the point, the point is the demarcation point of the effective rank, and the sequence number corresponding to the critical point indicates the effective rank order p.
4. The method for extracting the harmonic and transient oscillation power quality composite disturbance parameters of the new energy power distribution network according to claim 1, which is characterized by comprising the following steps: the step S3 is specifically as follows:
assuming that the sampling signal function is x (N), then x (0), x (1), …, x (N-1) are fit by the following equation, denoted as
Wherein: p is the order of the model, and N is the number of signal adoption points;
b i and z i The essence is complex number, and the corresponding calculation formula is:
to ensure that the fitted signal is as close as possible to the actual sampled signal, it is necessary to use the sum of squares of the errors as the optimization objective, its corresponding objective function, as follows:
the sampled signal function x (n) is then processed as follows:
wherein: p is p e The order of the sampling sample matrix R is connected, the sampling sample matrix R is constructed according to the above, and the elements and structures in the matrix are as follows:
carrying out singular value decomposition or least square estimation on the matrix R, and solving an effective rank p, wherein the size of the effective rank p depends on the number of signal disturbance quantities, and when the signal is free of noise, the physical meaning of the effective rank p is the number of non-zero elements in the singular value matrix after the singular value of the sample matrix R is decomposed;
and (3) retaining partial elements of the matrix R corresponding to the effective rank order p, and solving the following formula:
1+a 1 z -1 +…+a p z -p ＝0
get its corresponding root z i Then z i Carry-in typeAnd performs the following transformation to obtain the following matrix equation:
wherein: the leftmost matrix is an N x p-dimensional vandermonde matrix, which is full-rank and invertible, and if the leftmost matrix is denoted as matrix V, and matrix V is invertible, the following transformation can be performed:
finally, calculating the characteristic parameters of the mixed disturbance signal, mainly including the amplitude A of transient oscillation i Frequency f i Attenuation factor alpha i And phase theta i The method comprises the steps of carrying out a first treatment on the surface of the Frequency f of harmonic signal i Amplitude parameter A i In parameter calculation, the harmonic signal can be regarded as attenuation factor alpha i Oscillation parameters of =0,
wherein: i=1, 2, …, n, representing the number of disturbance signal components.
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