CN113036780A - Electromechanical oscillation parameter identification method based on subspace dynamic mode decomposition - Google Patents
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- H—ELECTRICITY
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- H—ELECTRICITY
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Abstract
The invention relates to an electromechanical oscillation parameter identification method based on subspace dynamic mode decomposition, which belongs to the technical field of nonlinear random power systems.
Description
Technical Field
The invention belongs to the technical field of nonlinear stochastic power systems, and particularly relates to an electromechanical oscillation parameter identification method based on subspace dynamic mode decomposition.
Background
In a modern power system, various random disturbances are more and more common due to the year-by-year expansion of a large-scale interconnected power grid structure, and the power system often causes electromechanical oscillation due to lack of damping, so that the power transmission of a power line is influenced, and the stable operation of the system is threatened.
At present, the analysis method of the electromechanical oscillation of the power system mainly comprises an analysis method based on a system mathematical model and an analysis method based on a system actual measurement signal. Analysis methods based on system mathematical models are often used for off-line analysis and are not suitable for complex high-dimensional system on-line calculation. The core of the analysis method based on the system actual measurement signals is that the mode identification is carried out from a high-dimensional nonlinear system by utilizing the spectrum analysis and the oscillation information is obtained, so that the method is easily influenced by noise, the order determination is complex, and the method has great limitation when the nonlinear system is processed.
The random data of the power system is a response signal with small fluctuation similar to noise, and contains a large amount of real-time dynamic characteristics of the system. The method has an irreplaceable effect on the operation control of the power system by using the random signal to perform the small-interference online stability evaluation. A Subspace Dynamic Mode Decomposition (SDMD) method is used for carrying out oscillation mode extraction on random data of a nonlinear power system, the ill-conditioned problem and the mode mixing problem that an electromechanical oscillation mode is submerged in Dynamic response possibly caused by the traditional Dynamic Mode Decomposition (DMD) method are solved, and the stability of continuous identification can be enhanced when electromechanical oscillation parameters are extracted from random response data by combining with a Subspace algorithm. The single subspace identification method is mainly used for a linear time invariant system, and the subspace dynamic mode decomposition method effectively solves the problem of modal deviation caused by the subspace method when the nonlinear system is processed.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method for identifying the electromechanical oscillation parameters based on the subspace dynamic mode decomposition is provided, combines the dynamic characteristics of the system random response, not only solves the problems of dimension disaster and mode mixing, but also has good stability of continuous identification of random data, can effectively adapt to the time-varying characteristic of a power system affected by small interference, and has higher practical application value.
A method for identifying electromechanical oscillation parameters based on subspace dynamic mode decomposition is characterized by comprising the following steps: comprises the following steps which are sequentially carried out,
step one, constructing a matrix Y according to the measured data of the wide area monitoring systemt，
Yt＝[yt,yt+1,…,yt+m-1]
In the formula: t is time, m is total number of data, ytMeasured data at time t, yt+1Measured data at time t +1, yt+m-1Measuring data at the time of t + m < -1 >;
according to matrix YtA Hankel matrix is constructed and,
Yp＝[Y0 T Y1 T]T
Yf＝[Y2 T Y3 T]T
in the formula: y is0、Y1、Y2And Y3Are all matrices constructed by the measured data,Trepresenting the transpose of the matrix, YpRepresenting past output line space, YfRepresenting a future input line space;
mixing Y in Hankel matrixfOrthogonal projection to YpSo as to obtain the projection matrix O,
in the formula: p is an orthogonal projection operation symbol;
the projection matrix O is subjected to truncated singular value decomposition,
in the formula: u shapeqIs a unitary matrix, SqExcept for the main diagonal, the other elements are all 0, VqIs a unitary matrix of the matrix,Hrepresents a conjugate transpose;
will unitary matrix UqThe first n rows of (A) are taken as Uq1Unitary matrix UqLast n rows of (1) as Uq2To U, to Uq1The truncated singular value decomposition is carried out,
Uq1＝USVH
in the formula: u is a unitary matrix, the other elements of the matrix S except the main diagonal are 0, and V is the unitary matrix;
according to unitary matrix U, Uq2V and a diagonal matrix S, constructing a system low-dimensional approximate state matrix,
in the formula:
for a low-dimensional approximation of the state matrix of the system, S-1Is the inverse of the s matrix;
step two, the low-dimensional approximate state matrix of the system obtained in the step one
The decomposition of the characteristic value is carried out,
in the formula:
is a state matrix
Is determined by the feature vector of (a),
is composed of
The matrix is an inverse matrix of the matrix, wherein Λ is a main diagonal matrix, the main diagonal is the Ritz generalized eigenvalue of the system, and the other elements except the main diagonal are all 0;
acquiring electromechanical oscillation information of the system;
step three, according to the relation between the discrete system and the continuous system,
in the formula: lambdacIs an eigenvalue matrix of the continuous system, the main pair line elements are the eigenvalues of the continuous system, the other elements are all 0, delta t is the sampling interval of the measured data, the unit is second, lambda1Is Λ c1 characteristic value of (a) < lambda >2Is ΛcOf the 2 nd characteristic value, λnIs ΛcThe value of the n-th characteristic value of (c),
converting the characteristic matrix of the discrete system into a characteristic value matrix of the continuous system;
step four, obtaining the oscillation frequency and the oscillation damping ratio according to the eigenvalue matrix of the continuous system obtained in the step three,
in the formula: f. of1,f2,…,fnRespectively, 1 st, 2 nd, … th, n oscillation frequencies, | lambda of the system1|,|λ2|,…,|λnI is the 1 st, 2 nd, … th of the system, the modulus of the n characteristic values, xi1,ξ2,…,ξnRespectively, 1 st, 2 nd, … th, n oscillation damping ratios, real (lambda) of the system1),real(λ2),…,real(λn) The real parts of the 1 st, 2 nd, … th, n eigenvalues of the system, respectively;
judging the damping state of the system according to the obtained oscillation damping ratio, and identifying the low-frequency oscillation mode of the system by combining the obtained oscillation frequency;
so far, the electromechanical oscillation parameter identification based on the subspace dynamic mode decomposition is completed.
Through the design scheme, the invention can bring the following beneficial effects: a method for identifying electromechanical oscillation parameters based on subspace dynamic mode decomposition is characterized in that a nonlinear power system is modeled, electromechanical oscillation parameters of the system are identified by adopting the subspace dynamic mode decomposition method based on measured data of a wide-area monitoring system, the dynamic characteristic of system random response is considered, the problems of dimension disaster and mode mixing are solved, the stability of continuous identification of random data is good, the time-varying characteristic of a power system affected by small interference can be effectively adapted, and the method has high practical application value.
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The invention is further described with reference to the following figures and detailed description:
fig. 1 is an electrical wiring diagram of a machine 2 area system in an embodiment 4 of a method for identifying electromechanical oscillation parameters based on subspace dynamic mode decomposition according to the present invention.
FIG. 2 is a Ritz generalized eigenvalue distribution graph obtained in step two of the electromechanical oscillation parameter identification method based on subspace dynamic mode decomposition according to the present invention.
Fig. 3 is a probability density chart i of an electromechanical oscillation characteristic parameter according to an embodiment of the electromechanical oscillation parameter identification method based on subspace dynamic mode decomposition.
FIG. 4 is a probability density chart II of the characteristic parameters of the electromechanical oscillation according to the embodiment of the method for identifying the electromechanical oscillation parameters based on the subspace dynamic mode decomposition.
Detailed Description
A method for identifying electromechanical oscillation parameters based on subspace dynamic mode decomposition comprises the following steps:
firstly, a low-dimensional approximate state matrix of the system covers main dynamic characteristics of the system and can meet actual engineering requirements, and in order to obtain the low-dimensional approximate state matrix of the system, firstly, a matrix Y is constructed according to measured data of a wide area monitoring systemtOf the formulaShown in the figure:
Yt＝[yt,yt+1,…,yt+m-1]
in the formula: t is time, m is total number of data, ytMeasured data at time t, yt+1Measured data at time t +1, yt+m-1Measuring data at the time of t + m < -1 >;
according to the formula matrix YtConstructing a Hankel matrix:
Yp＝[Y0 T Y1 T]T
Yf＝[Y2 T Y3 T]T
in the formula: y is0、Y1、Y2And Y3Are all matrices constructed by the measured data,Trepresenting the transpose of the matrix, YpRepresenting the "past" output line space, YfRepresents the "future" input line space;
mixing Y in Hankel matrixfOrthogonal projection to YpThe projection matrix O is obtained as shown in the following formula:
in the formula: o is a projection matrix, and P is an orthogonal projection operation symbol;
performing truncated singular value decomposition on the projection matrix O, as shown in the following formula:
in the formula: u shapeqIs a unitary matrix, SqExcept for the main diagonal, the other elements are all 0, VqIs a unitary matrix of the matrix,Hrepresents a conjugate transpose;
will UqThe first n rows of (A) are taken as Uq1，UqLast n rows of (1) as Uq2To U, to Uq1Truncated singular value decomposition is performed as shown in the following equation:
Uq1＝USVH
in the formula: u is a unitary matrix, S is all 0 except for the main diagonal, V is a unitary matrix,
constructing a system low-dimensional approximate state matrix as shown in a formula (15):
according to unitary matrix U, Uq2V and a diagonal matrix S, constructing a system low-dimensional approximate state matrix,
in the formula:
for a low-dimensional approximation of the state matrix of the system, S-1Is the inverse of the S matrix;
step two, after small disturbance occurs, the characteristic value of the system contains the information of electromechanical oscillation of the system, so that the low-dimensional approximate state matrix of the system is obtained
And (3) carrying out characteristic value decomposition, as shown in formula (16):
in the formula:
is a state matrix
Is determined by the feature vector of (a),
is composed of
Inverse matrix of matrix, Λ being main diagonal matrix, main diagonal being systematicRitz generalized eigenvalue, the other elements except the main diagonal are all 0;
and step three, further converting the characteristic matrix of the discrete system into a characteristic value matrix of the continuous system according to the relationship between the discrete system and the continuous system, wherein the characteristic value matrix is shown as the following formula:
in the formula: lambdacIs an eigenvalue matrix of the continuous system, the main pair line elements are the eigenvalues of the continuous system, the other elements are all 0, delta t is the sampling interval of the measured data, the unit is second, lambda1Is Λ c1 characteristic value of (a) < lambda >2Is ΛcOf the 2 nd characteristic value, λnIs ΛcThe nth characteristic value of (a);
and step four, finally obtaining the oscillation frequency and the damping ratio of the system, judging whether the system is in an underdamping state according to the damping ratio as shown in the following formula, and identifying the low-frequency oscillation mode of the system by combining the oscillation frequency.
In the formula: f. of1,f2,…,fnRespectively, the 1 st, 2 nd, … th, n oscillation frequencies,
|λ1|,|λ2|,…,|λnl is the system's 1 st, 2 nd, … th, modulo n characteristic values,
ξ1,ξ2,…,ξnrespectively, the 1 st, 2 nd, … th, n oscillation damping ratios,
real(λ1),real(λ2),…,real(λn) The real part of the n eigenvalues of the system 1, 2, …, respectively.
The method disclosed by the invention has the advantages that the nonlinear power system is modeled, the electromechanical oscillation parameters of the system are identified by adopting a subspace dynamic mode decomposition method based on the measured data of the wide area monitoring system, the dynamic characteristic of the random response of the system is considered, the problems of dimension disaster and mode mixing are solved, the stability of continuous identification of random data is good, the time-varying characteristic of the power system influenced by small interference can be effectively adapted, and the method has higher practical application value.
The process of the invention is described in detail below with reference to specific examples:
fig. 1 is an electrical wiring diagram of a 4-machine 2-area system, in the diagram, G1, G2, G3 and G4 are all generators, and random response data of the system in the operation mode is obtained by Small Signal Analysis (SSAT) software in consideration of that the load at the node 4 and the node 14 in the system is randomly fluctuated by 3% of a basic operation value as an environmental stimulus.
FIG. 2 is a graph of Ritz's generalized eigenvalue spread within the unit circle and near the circle boundary representing the system in steady state oscillation. The Ritz characteristic values obtained by single calculation of the SDMD and DMD are given in the figure, the oscillation frequency and the damping ratio of the system are further obtained through calculation, and as shown in the table 1, compared with the traditional dynamic mode decomposition method, the method provided by the invention improves the accuracy of identification of the electromechanical oscillation frequency and the damping ratio of the power system, and particularly greatly improves the accuracy of identification of the damping ratio of the system.
TABLE 1 electromechanical oscillation parameter identification results
Fig. 3 and 4 are probability density diagrams of characteristic parameters of electromechanical oscillation. In order to measure the overall effect of the method of the invention on the continuous identification of the random response data, continuous data with the length of 1000 seconds (sampling interval of 0.01 second, 100000 data in total) in the random response data is selected for analysis, the data length of a sliding calculation window is 20 seconds (2000 data in total), the interval of each sliding of the window is 0.1 second, namely, electromechanical oscillation parameter identification is carried out once every 0.1 second, and electromechanical oscillation parameter identification is carried out 981 times in total. In fig. 3, the mean value of the frequency of the electromechanical oscillation is 0.6062Hz, the mean value of the damping ratio is 3.87%, and the data in the graph are concentrated near the mean value and have small divergence, so that the identification stability is very high, and the adaptability of the invention for improving the stable operation of the power system and preventing the low-frequency oscillation is demonstrated.
Claims (1)
1. A method for identifying electromechanical oscillation parameters based on subspace dynamic mode decomposition is characterized by comprising the following steps: comprises the following steps which are sequentially carried out,
step one, constructing a matrix Y according to the measured data of the wide area monitoring systemt，
Yt＝[yt,yt+1,…,yt+m-1]
In the formula: t is time, m is total number of data, ytMeasured data at time t, yt+1Measured data at time t +1, yt+m-1Measuring data at the time of t + m < -1 >;
according to matrix YtA Hankel matrix is constructed and,
Yp＝[Y0 T Y1 T]T
Yf＝[Y2 T Y3 T]T
in the formula: y is0、Y1、Y2And Y3All being matrices constructed from measured data, T representing the transpose of the matrix, YpRepresenting past output line space, YfRepresenting a future input line space;
mixing Y in Hankel matrixfOrthogonal projection to YpSo as to obtain the projection matrix O,
in the formula: p is an orthogonal projection operation symbol;
the projection matrix O is subjected to truncated singular value decomposition,
in the formula: u shapeqIs a unitary matrix, SqExcept for the main diagonal, the other elements are all 0, VqIs a unitary matrix, H stands for conjugate transpose;
will unitary matrix UqThe first n rows of (A) are taken as Uq1Unitary matrix UqLast n rows of (1) as Uq2To U, to Uq1The truncated singular value decomposition is carried out,
Uq1＝USVH
in the formula: u is a unitary matrix, the other elements of the matrix S except the main diagonal are 0, and V is the unitary matrix;
according to unitary matrix U, Uq2V and a diagonal matrix S, constructing a system low-dimensional approximate state matrix,
in the formula:
for a low-dimensional approximation of the state matrix of the system, S-1Is the inverse of the S matrix;
step two, the low-dimensional approximate state matrix of the system obtained in the step one
The decomposition of the characteristic value is carried out,
in the formula:
is a state matrix
Is determined by the feature vector of (a),
is composed of
The matrix is an inverse matrix of the matrix, wherein Λ is a main diagonal matrix, the main diagonal is the Ritz generalized eigenvalue of the system, and the other elements except the main diagonal are all 0;
acquiring electromechanical oscillation information of the system;
step three, according to the relation between the discrete system and the continuous system,
in the formula: lambdacIs an eigenvalue matrix of the continuous system, the main pair line elements are the eigenvalues of the continuous system, the other elements are all 0, delta t is the sampling interval of the measured data, the unit is second, lambda1Is Λc1 characteristic value of (a) < lambda >2Is ΛcOf the 2 nd characteristic value, λnIs ΛcThe value of the n-th characteristic value of (c),
converting the characteristic matrix of the discrete system into a characteristic value matrix of the continuous system;
step four, obtaining the oscillation frequency and the oscillation damping ratio according to the eigenvalue matrix of the continuous system obtained in the step three,
in the formula: f. of1,f2,…,fnRespectively, 1 st, 2 nd, … th, n oscillation frequencies, | lambda of the system1|,|λ2|,…,|λnI is the 1 st, 2 nd, … th of the system, the modulus of the n characteristic values, xi1,ξ2,…,ξnRespectively, 1 st, 2 nd, … th, n oscillation damping ratios, real (lambda) of the system1),real(λ2),…,real(λn) The real parts of the 1 st, 2 nd, … th, n eigenvalues of the system, respectively;
judging the damping state of the system according to the obtained oscillation damping ratio, and identifying the low-frequency oscillation mode of the system by combining the obtained oscillation frequency;
so far, the electromechanical oscillation parameter identification based on the subspace dynamic mode decomposition is completed.
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Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104993480A (en) * | 2015-07-22 | 2015-10-21 | 福州大学 | Power system low-frequency oscillation online identification method based on recursive stochastic subspace |
| CN109753689A (en) * | 2018-12-10 | 2019-05-14 | 东北电力大学 | A kind of online identifying approach of electric system electromechanical oscillations modal characteristics parameter |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104993480A (en) * | 2015-07-22 | 2015-10-21 | 福州大学 | Power system low-frequency oscillation online identification method based on recursive stochastic subspace |
| CN109753689A (en) * | 2018-12-10 | 2019-05-14 | 东北电力大学 | A kind of online identifying approach of electric system electromechanical oscillations modal characteristics parameter |
Non-Patent Citations (2)
| Title |
|---|
| 杨德友等: "一种随机数据驱动下基于SDMD的机电振荡参数辨识", 《电网分析与研究》 * |
| 杨德友等: "基于动态响应的机电振荡特征识别与能控型评估方法", 《电力自动化设备》 * |
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