Subsynchronous oscillation parameter identification method and system based on feature system implementation algorithm

Abstract

The application discloses a method and system for identifying subsynchronous oscillation parameters based on a feature system, and relates to the fields of wide-area monitoring of power systems and subsynchronous oscillation technology.The technical scheme is as follows: a real number domain Hankel matrix is constructed, a real number domain system matrix is constructed based on the real number domain Hankel matrix, and the eigenvalue of the system matrix is solved.The obtained eigenvalue can satisfy the conjugate constraint of the angular frequency of two modes of a fundamental component and the conjugate constraint of the angular frequency of two modes of an oscillation component.In addition, a real part Hankel matrix is constructed according to the real part of a data sequence of a synchronous phasor, and an imaginary part Hankel matrix is constructed according to the imaginary part of the data sequence of the synchronous phasor.The real part Hankel matrix and the imaginary part Hankel matrix are spliced to obtain the real number domain Hankel matrix, which can completely retain the information of the complex number domain synchronous phasor and can accurately identify the subsynchronous oscillation parameters under an ultra-short data window.

Description

Technical Field

[0001] This invention relates to the field of wide-area monitoring and subsynchronous oscillation technology in power systems, and more specifically, to a method and system for identifying subsynchronous oscillation parameters based on a feature-based system implementation algorithm. Background Technology

[0002] In modern power systems, subsynchronous oscillations are mainly caused by resonance between large-scale renewable energy generation units and transmission lines. Subsynchronous oscillations can significantly reduce system transmission capacity, jeopardize system safety, and even lead to system instability. Therefore, close monitoring of the dynamic process of subsynchronous oscillations in power systems is necessary. While wide-area measurement systems and synchronization phasor measurement terminals can effectively monitor subsynchronous oscillation events in power systems, the fundamental, subsynchronous, and supersynchronous components (frequency deviations from the rated frequency) appear in the synchronization phasor data through spectral leakage, making it difficult to accurately obtain the frequency, amplitude, and phase of each component in the subsynchronous oscillation.

[0003] Previous studies have shown that the synchronization phasor under subsynchronous oscillation is a modal model composed of a linear combination of four modes. Therefore, some scholars have proposed using the eigenvalue system realization algorithm (ERA) to solve for the subsynchronous oscillation parameters. ERA is a classic modal parameter extraction algorithm. By constructing the Hankel matrix and the system matrix, the modal parameter extraction problem is transformed into a matrix factorization problem, which can directly obtain the angular frequencies and coefficients of each mode. It is simple to solve and has low computational cost. However, since the synchronization phasor is in the complex domain, there is an angular frequency conjugate constraint between the two modes of its fundamental component, and there is also an angular frequency conjugate constraint between the two modes of its oscillation component. The ERA method, which directly solves for the eigenvalues ​​of the complex domain system matrix, cannot consider the above-mentioned angular frequency conjugate constraints, resulting in a large identification error of the subsynchronous oscillation parameters under noisy conditions.

[0004] Therefore, how to research and design a subsynchronous oscillation parameter identification method and system based on feature system implementation algorithm that can overcome the above-mentioned defects is an urgent problem that we need to solve. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for identifying subsynchronous oscillation parameters based on a feature-based system implementation algorithm. This method can completely preserve the information of the complex domain synchronization phasor and accurately identify subsynchronous oscillation parameters under ultra-short data windows.

[0006] The above-mentioned technical objective of the present invention is achieved through the following technical solution:

[0007] Firstly, a method for identifying subsynchronous oscillation parameters based on a feature-based system implementation algorithm is provided, including the following steps:

[0008] The data sequence of the synchronization phasor under subsynchronous oscillation is obtained. The synchronization phasor under subsynchronous oscillation is a modal model composed of a linear combination of four complex exponents and four constant parameters. The four complex exponents include the angular frequency of the fundamental positive frequency component, the angular frequency of the fundamental negative frequency component, the angular frequency of the oscillation positive frequency component, and the angular frequency of the oscillation negative frequency component.

[0009] Construct the real part Hankel matrix and the imaginary part Hankel matrix based on the real part and imaginary part of the data sequence of the synchronization phasor, respectively;

[0010] The real part Hankel matrix is ​​concatenated with the imaginary part Hankel matrix to obtain the first real field Hankel matrix;

[0011] By shifting each element of the first real-field Hankel matrix forward by one unit time, we obtain the second real-field Hankel matrix.

[0012] Singular value decomposition is performed on the first real-field Hankel matrix to obtain the left singular matrix, the right singular matrix, and the eigenvalue matrix;

[0013] Based on the number of modes of the synchronization phasor, the left singular matrix, the right singular matrix, and the eigenvalue matrix are truncated.

[0014] The system matrix is ​​determined based on the truncated left singular matrix, right singular matrix, eigenvalue matrix, and the second real-field Hankel matrix;

[0015] Solve for the eigenvalues ​​of the system matrix, and calculate the four complex exponents and the four constant parameters based on the eigenvalues ​​of the system matrix;

[0016] Based on the four complex exponents and the four constant parameters, the frequency, amplitude, and phase of the fundamental component, subsynchronous component, and supersynchronous component are determined.

[0017] Furthermore, the expression for the modal model is specifically as follows:

[0018]

[0019]

[0020] w1=jα, w2=-jα, w3=jβ, w4=-jβ;

[0021]

[0022] in, Let R1, R2, R3, and R4 be the k-th synchronization phasor, and R4 be four constant parameters. w1 is the angular frequency of the fundamental positive frequency component, w2 is the angular frequency of the fundamental negative frequency component, w3 is the angular frequency of the oscillation positive frequency component, and w4 is the angular frequency of the fundamental negative frequency component. f0, x0, and φ0 represent the frequency, amplitude, and phase of the fundamental component, respectively. sub φ sub f sub x represents the amplitude, phase, and frequency of the subsynchronous component, respectively. sup φ sup f sup These represent the amplitude, phase, and frequency of the supersynchronous component, respectively; * indicates the complex conjugate; N is the number of data points used to calculate the synchronization phasor from the instantaneous values; f N f is the rated frequency of the power system. s The value of l is ±1, which is the frequency for uploading synchronous phasor data.

[0023] Furthermore, the expressions for the real Hankel matrix and the imaginary Hankel matrix are as follows:

[0024]

[0025]

[0026] Among them, Re(H) rs (k-1)) is the real part of the Hankel matrix, Im(H) rs (k-1)) is the imaginary Hankel matrix, r and s are the number of rows and columns of the Hankel matrix, respectively, Re represents the real part, and Im represents the imaginary part. Let k be the kth synchronization phasor.

[0027] Furthermore, the expression for the first real-field Hankel matrix is ​​as follows:

[0028]

[0029] Where H(k-1) is the first real field Hankel matrix, Re(H rs (k-1)) is the real part of the Hankel matrix, Im(H) rs (k-1) is the imaginary Hankel matrix.

[0030] Furthermore, the specific expression for performing singular value decomposition on the first real-field Hankel matrix is ​​as follows:

[0031] H(0) = UDV H ;

[0032] Where H(0) is the first real field Hankel matrix when k=1, U is the left singular matrix, V is the right singular matrix, D is the eigenvalue matrix, and the superscript H indicates the conjugate transpose.

[0033] Furthermore, the expression for truncating the left singular matrix, the right singular matrix, and the eigenvalue matrix is ​​specifically as follows:

[0034] U r =U(:,1:4)

[0035] D r =D(1:4,1:4);

[0036] V r =V(:,1:4)

[0037] Among them, U r V is the truncated left singular matrix. r D is the truncated right singular matrix. r This is the truncated eigenvalue matrix.

[0038] Furthermore, the expression for the system matrix is ​​specifically as follows:

[0039]

[0040] Where A is the system matrix and H(1) is the second real field Hankel matrix when k=2.

[0041] Secondly, a subsynchronous oscillation parameter identification system based on a feature system implementation algorithm is provided, including:

[0042] The data acquisition module is used to obtain the data sequence of the synchronization phasor under subsynchronous oscillation. The synchronization phasor under subsynchronous oscillation is a modal model composed of a linear combination of four complex exponents and four constant parameters. The four complex exponents include the angular frequency of the fundamental positive frequency component, the angular frequency of the fundamental negative frequency component, the angular frequency of the oscillation positive frequency component, and the angular frequency of the oscillation negative frequency component.

[0043] A matrix construction module is used to construct a real Hankel matrix and an imaginary Hankel matrix based on the real and imaginary parts of the data sequence of the synchronization phasor, respectively.

[0044] A matrix concatenation module is used to concatenate the real part Hankel matrix with the imaginary part Hankel matrix to obtain a first real field Hankel matrix.

[0045] The matrix shifting module is used to shift each element of the first real-field Hankel matrix forward by a unit time to obtain the second real-field Hankel matrix.

[0046] The matrix decomposition module is used to perform singular value decomposition on the first real field Hankel matrix to obtain the left singular matrix, the right singular matrix, and the eigenvalue matrix.

[0047] The truncation processing module is used to truncate the left singular matrix, the right singular matrix, and the eigenvalue matrix according to the number of modes of the synchronization phasor;

[0048] The matrix determination module is used to determine the system matrix based on the truncated left singular matrix, right singular matrix, eigenvalue matrix, and the second real-field Hankel matrix;

[0049] The matrix solving module is used to solve for the eigenvalues ​​of the system matrix and to calculate the four complex exponents and the four constant parameters based on the eigenvalues ​​of the system matrix.

[0050] The parameter solving module is used to determine the frequency, amplitude, and phase of the fundamental component, subsynchronous component, and supersynchronous component based on the four complex exponents and the four constant parameters.

[0051] Thirdly, a computer terminal is provided, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, it implements the subsynchronous oscillation parameter identification method based on the feature system implementation algorithm as described in any one of the first aspects.

[0052] Fourthly, a computer-readable medium is provided having a computer program stored thereon, the computer program being executed by a processor to implement the subsynchronous oscillation parameter identification method based on the feature system implementation algorithm as described in any one of the first aspects.

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] The subsynchronous oscillation parameter identification method based on the feature system implementation algorithm provided by this invention constructs a real-domain Hankel matrix, builds a real-domain system matrix based on the real-domain Hankel matrix, and solves for the eigenvalues ​​of the system matrix. The obtained eigenvalues ​​can satisfy the angular frequency conjugate constraints of the two modes of the fundamental component and the angular frequency conjugate constraints of the two modes of the oscillation component, solving the problem of large errors caused by directly obtaining the eigenvalues ​​of the complex-domain system matrix in traditional ERA. In addition, a real-part Hankel matrix is ​​constructed based on the real part of the data sequence of the synchronization phasor, and an imaginary-part Hankel matrix is ​​constructed based on the imaginary part of the data sequence of the synchronization phasor. The real-part Hankel matrix and the imaginary-part Hankel matrix are concatenated to obtain the real-domain Hankel matrix, which can completely preserve the information of the complex-domain synchronization phasor and accurately identify the subsynchronous oscillation parameters under ultra-short data windows. Attached Figure Description

[0055] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:

[0056] Figure 1 This is a flowchart from Embodiment 1 of the present invention;

[0057] Figure 2 This is a system block diagram in Embodiment 2 of the present invention. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0059] Example 1: A subsynchronous oscillation parameter identification method based on feature system implementation algorithm, such as Figure 1 As shown, it includes the following steps:

[0060] Step 101: Obtain the data sequence of the synchronization phasor under subsynchronous oscillation, wherein the synchronization phasor under subsynchronous oscillation is a modal model composed of a linear combination of 4 complex exponents and 4 constant parameters. The 4 complex exponents include: the angular frequency of the fundamental positive frequency component, the angular frequency of the fundamental negative frequency component, the angular frequency of the oscillation positive frequency component, and the exponent corresponding to the angular frequency of the oscillation negative frequency component.

[0061] Step 102: Construct the real part Hankel matrix based on the real part of the data sequence of the synchronization phasors, and construct the imaginary part Hankel matrix based on the imaginary part of the data sequence of the synchronization phasors;

[0062] Step 103: Concatenate the real part Hankel matrix with the imaginary part Hankel matrix to obtain the first real field Hankel matrix;

[0063] Step 104: Shift each element of the first real-field Hankel matrix forward by one unit time to obtain the second real-field Hankel matrix;

[0064] Step 105: Perform singular value decomposition on the Hankel matrix in the first real field to obtain the left singular matrix, the right singular matrix, and the eigenvalue matrix;

[0065] Step 106: Based on the number of modes of the synchronizing phasors, truncate the left singular matrix, right singular matrix, and eigenvalue matrix;

[0066] Step 107: Determine the system matrix based on the truncated left singular matrix, right singular matrix, eigenvalue matrix, and the second real field Hankel matrix;

[0067] Step 108: Solve for the eigenvalues ​​of the system matrix, and calculate the four complex exponents and the four constant parameters based on the eigenvalues ​​of the system matrix;

[0068] Step 109: Determine the frequency, amplitude, and phase of the fundamental component, subsynchronous component, and supersynchronous component based on the four complex exponents and four constant parameters.

[0069] In one embodiment, in step 101, the modal model of the synchronization phasor under subsynchronous oscillation is expressed by the following formula:

[0070]

[0071] in:

[0072]

[0073] w1=jα, w2=-jα, w3=jβ, w4=-jβ (3)

[0074]

[0075] In the formula, Let R1, R2, R3, and R4 be the k-th synchronization phasor, and R4 be four constant parameters. w1 is the angular frequency of the fundamental positive frequency component, w2 is the angular frequency of the fundamental negative frequency component, w3 is the angular frequency of the oscillation positive frequency component, and w4 is the angular frequency of the fundamental negative frequency component. f0, x0, and φ0 represent the frequency, amplitude, and phase of the fundamental component, respectively. sub φ sub f sub x represents the amplitude, phase, and frequency of the subsynchronous component, respectively. sup φ sup f sup These represent the amplitude, phase, and frequency of the supersynchronous component, respectively; * indicates the complex conjugate; N is the number of data points used to calculate the synchronization phasor from the instantaneous values; f N f is the rated frequency of the power system. s To synchronize the phasor data upload frequency.

[0076] In practice, the process of establishing the synchronous phasor model will be introduced first.

[0077] Establish an instantaneous signal model for the power system, as shown in Equation (5), which includes a fundamental component with a possible frequency shift, a pair of frequency-coupled subsynchronous components, and a supersynchronous component.

[0078] x(t) = x0 cos(2πf0t + φ0) + x sub cos(2πf sub t+φ sub )+xsup cos(2πf sup t+φ sup (5)

[0079] In the formula, x(t) is the instantaneous signal.

[0080] The synchronous phasor sequence corresponding to the instantaneous signal x(t) This can be obtained by performing a Discrete Fourier Transform (DFT) on equation (5). Since the Discrete Fourier Transform is a linear transform, we have:

[0081]

[0082] In the formula, and These are the fundamental component, subsynchronous component, and supersynchronous component of the synchronizing phasor, respectively.

[0083] According to the theory of discrete Fourier transform, From the fundamental positive frequency component and fundamental negative frequency component It consists of two parts. The corresponding angular frequency is The corresponding angular frequency is Without loss of generality, we can first assume f0 < f N And based on the subsequent calculation results, the final result is determined to be f0 < f N Or f0 > f N That is, assuming α is a positive angular frequency and -α is a negative angular frequency.

[0084] From the positive frequency component of the subsynchronous and subsynchronous negative frequency components It consists of two parts, taking into account Corresponding positive angle frequency Corresponding negative angular frequency Similarly, From the supersynchronous positive frequency component and supersynchronous negative frequency components It consists of two parts. Corresponding positive angle frequency Corresponding negative angular frequency Based on the above derivation, the subsynchronous positive frequency component and supersynchronous negative frequency components Synthesized into positive frequency components of oscillation Subsynchronous negative frequency component and supersynchronous positive frequency components Synthesized into oscillating negative frequency components

[0085] The mathematical model of the power system synchronization phasor is as follows:

[0086]

[0087] in,

[0088]

[0089]

[0090]

[0091] In the formula, and These are the fundamental positive frequency component and the fundamental negative frequency component, respectively. and These represent the positive and negative frequency components of the oscillation, respectively. Q(f,l) is a function in the synchronous phasor calculation process, where f can take the values ​​f0, f1, f2, and f3. sub f sup , j is the imaginary part of the complex number, and l can take ±1.

[0092] By defining the mathematical model (7) of the synchronizing phasor as shown in Equations (2) and (3), the synchronizing phasor can be rewritten as a modal model consisting of a linear combination of four modes, where two modes correspond to the fundamental component and two modes correspond to the oscillation component, as shown in Equation (1).

[0093] In one embodiment, step 102, constructing a real Hankel matrix based on the real part of the data sequence of the synchronization phasors and constructing an imaginary Hankel matrix based on the imaginary part of the data sequence of the synchronization phasors, may include: constructing the real Hankel matrix and the imaginary Hankel matrix in the following manner:

[0094]

[0095]

[0096] In the formula, Re(Η) rs (k-1)) is the real part of the Hankel matrix, Im(H) rs (k-1) is the imaginary Hankel matrix, r and s are the number of rows and columns of the Hankel matrix, respectively, Re represents the real part and Im represents the imaginary part.

[0097] In one embodiment, step 103, concatenating the real part Hankel matrix with the imaginary part Hankel matrix to obtain the first real-field Hankel matrix, may include determining the first real-field Hankel matrix as follows:

[0098]

[0099] Where H(k-1) is the first real field Hankel matrix.

[0100] In specific implementation, in step 104, we can let k = 1 in equation (10) to obtain the first real field Hankel matrix H(0), and move each element of the first real field Hankel matrix forward by one unit time to obtain the second real field Hankel matrix. That is, let k = 2 to obtain the second real field Hankel matrix H(1).

[0101] In one embodiment, step 105, performing singular value decomposition on the first real-field Hankel matrix to obtain a left singular matrix, a right singular matrix, and an eigenvalue matrix, may include: performing singular value decomposition on the first real-field Hankel matrix in the following manner:

[0102] H(0) = UDV H (11)

[0103] In the formula, H(0) is the first real field Hankel matrix, U is the left singular matrix, V is the right singular matrix, D is the eigenvalue matrix, and the superscript H indicates the conjugate transpose.

[0104] In one embodiment, step 106, truncating the left singular matrix, right singular matrix, and eigenvalue matrix according to the number of modes of the synchronization phasors, may include truncating the left singular matrix, right singular matrix, and eigenvalue matrix in the following manner:

[0105]

[0106] In the formula, U r V is the truncated left singular matrix. r D is the truncated right singular matrix. r This is the truncated eigenvalue matrix.

[0107] In practice, since the number of modes of the synchronization phasor is 4, the left singular matrix, right singular matrix and eigenvalue matrix can be truncated according to this number of modes.

[0108] In one embodiment, step 107, determining the system matrix based on the truncated left singular matrix, right singular matrix, eigenvalue matrix, and the second real-field Hankel matrix, may include determining the system matrix in the following manner:

[0109]

[0110] In the formula, A is the system matrix and H(1) is the second real field Hankel matrix.

[0111] In practice, existing ERA methods directly construct the Hankel matrix based on the synchronization phasors in the complex field, and then construct the complex field system matrix. By solving for the eigenvalues ​​of the system matrix, w1, w2, w3, and w4 can be obtained, and R1, R2, R3, and R4 can be solved using the least squares method. This method can solve accurately under ideal conditions, but under noisy conditions, directly solving for the eigenvalues ​​of the system matrix A yields... and Not satisfied with e jα and e -jα The conjugate relationship, and Similarly, it does not satisfy e. jβ and e -jβ The conjugate relationship makes it impossible to accurately solve for α and β, leading to significant errors in parameter identification for each component. The main reason for this problem is that the existing ERA constructs a matrix in the complex domain, so under the influence of measurement noise, the four eigenvalues ​​obtained are not pairwise conjugates. Theoretically, constructing a real-domain Hankel matrix could solve the problem of angular frequency conjugate constraints. To retain all information of the complex-domain synchronization phasor while constructing the real-domain Hankel matrix, this embodiment of the invention combines the real and imaginary parts of the synchronization phasor to construct a real-domain Hankel matrix.

[0112] Since the Hankel matrices H(0) and H(1) constructed in this embodiment of the invention are both in the real number field, the resulting system matrix A is also in the real number field. In step 108, by solving the eigenvalues ​​of the real number field system matrix, w1, w2, w3, and w4 can be obtained, and the obtained... and Satisfy e jα and e -jα The conjugate relationship, and It also satisfies e jβ and e -jβ By establishing the conjugate relationship, the angular frequency α of the fundamental component and the angular frequency β of the oscillation component can be accurately solved. Therefore, the advantages of this embodiment are that, on the one hand, by constructing a real-domain Hankel matrix, the problem that the angular frequencies obtained by directly obtaining the eigenvalues ​​of the complex-domain system matrix in the existing ERA do not satisfy the conjugate constraints of ±jα and ±jβ is solved. On the other hand, by combining the real and imaginary parts of the synchronization phasor to construct the Hankel matrix, the information of the synchronization phasor can be completely preserved, effectively improving the identification accuracy of the fundamental parameters, subsynchronous oscillation parameters and supersynchronous components.

[0113] In step 108, the four constants can be solved as follows:

[0114]

[0115] In the formula, K is the number of synchronous phasors.

[0116] In specific implementation, in step 109, the fundamental positive frequency component can first be determined according to formula (7) based on the angular frequency of the fundamental component, the angular frequency of the oscillation component, and the four constant parameters in the modal model. Fundamental negative frequency component Oscillating positive frequency component and oscillating negative frequency components The calculated value is:

[0117]

[0118] Then, based on the fundamental positive frequency component Calculated values ​​of fundamental negative frequency components Determine the frequency, amplitude, and phase of the fundamental component; based on the positive frequency component of the oscillation. and oscillating negative frequency components The calculated values ​​are used to determine the frequency, amplitude, and phase of the subsynchronous component, as well as the frequency, amplitude, and phase of the supersynchronous component.

[0119] In step 109, the frequency, amplitude, and phase of the fundamental component can be determined as follows;

[0120]

[0121]

[0122] In step 109, the frequency, amplitude, and phase of the subsynchronous component, as well as the frequency, amplitude, and phase of the supersynchronous component, can be determined as follows:

[0123]

[0124] f sup =2f N -f sub (19)

[0125]

[0126] The following is a specific example to demonstrate how the invention can be implemented.

[0127] To verify the correctness and effectiveness of the proposed power system oscillation parameter identification method based on synchronous phasor data, a verification study was conducted using simulated PMU (Phasor Measurement Unit) data with known parameters. The instantaneous value signal for generating the simulated PMU data is shown in formula (5), and the specific parameters are set as follows: system rated frequency f N With a frequency of 50Hz, the fundamental amplitude x0 and phase φ0 are fixed at 100rad and 0rad respectively. The phase φ of the subsynchronous / supersynchronous oscillation component in the subsynchronous oscillation... sub and φ sup Taking values ​​of 0.5 rad and 0.75 rad respectively, the amplitude x sub and x sup To study the parameter identification accuracy characteristics of the embodiments of the present invention under the influence of noise, zero-mean white noise was added to the instantaneous value signal, and a 40dB SNR (signal-to-noise ratio) condition was used, with values ​​of 20 and 10 respectively.

[0128] The performance of the improved algorithm (hereinafter referred to as "Improved ERA") proposed in this embodiment of the invention was compared with that of the original ERA. The comparison results are shown in Table 1. sub Take the four sets of data shown in Table 1 respectively, and use a data window of 200ms for both methods.

[0129] Table 1 Comparison of parameter identification errors between the improved ERA and the original ERA

[0130]

[0131] As shown in Table 1, due to the influence of noise, the original ERA algorithm has a relatively large error in identifying the parameters of each component. Especially in the third and fourth groups of experiments, when the fundamental frequency deviates significantly from the power frequency, the two eigenvalues ​​corresponding to the fundamental component obtained by the solution do not satisfy the conjugate constraint, making it difficult to accurately identify the fundamental frequency. This results in a large error in the identification results of the fundamental amplitude and other component parameters. Compared with the original ERA algorithm, the improved ERA algorithm proposed in this embodiment can identify the parameters of each component more accurately.

[0132] Example 2: A subsynchronous oscillation parameter identification system based on a feature system implementation algorithm. This system is used to implement the subsynchronous oscillation parameter identification method based on a feature system implementation algorithm described in Example 1, such as... Figure 2 As shown, it includes a data acquisition module, a matrix construction module, a matrix splicing module, a matrix forward shifting module, a matrix decomposition module, a truncation processing module, a matrix determination module, a matrix solving module, and a parameter solving module.

[0133] The system includes the following modules: a data acquisition module for obtaining the data sequence of the synchronization phasor under subsynchronous oscillation, where the synchronization phasor is a modal model composed of a linear combination of four complex exponents and four constant parameters, wherein the four complex exponents include the angular frequencies of the fundamental positive frequency component, the fundamental negative frequency component, the angular frequencies of the oscillation positive frequency component, and the angular frequencies of the oscillation negative frequency component; a matrix construction module for constructing a real Hankel matrix and an imaginary Hankel matrix based on the real and imaginary parts of the synchronization phasor data sequence; a matrix splicing module for splicing the real Hankel matrix and the imaginary Hankel matrix to obtain a first real-field Hankel matrix; and a matrix forward shifting module for shifting each element of the first real-field Hankel matrix forward by a unit time step to obtain a second real-field Hankel matrix. The system consists of a Hankel matrix; a matrix decomposition module for performing singular value decomposition on the first real-field Hankel matrix to obtain a left singular matrix, a right singular matrix, and an eigenvalue matrix; a truncation module for truncating the left singular matrix, the right singular matrix, and the eigenvalue matrix according to the number of modes of the synchronization phasor; a matrix determination module for determining the system matrix based on the truncated left singular matrix, right singular matrix, eigenvalue matrix, and the second real-field Hankel matrix; a matrix solving module for solving the eigenvalues ​​of the system matrix and calculating the four complex exponents and the four constant parameters based on the eigenvalues ​​of the system matrix; and a parameter solving module for determining the frequency, amplitude, and phase of the fundamental component, the subsynchronous component, and the supersynchronous component based on the four complex exponents and the four constant parameters.

[0134] Working Principle: This invention constructs a real-domain Hankel matrix, builds a real-domain system matrix based on the real-domain Hankel matrix, and solves for the eigenvalues ​​of the system matrix. The obtained eigenvalues ​​can satisfy the angular frequency conjugate constraints of the two modes of the fundamental component and the angular frequency conjugate constraints of the two modes of the oscillation component. This solves the problem of large errors caused by directly obtaining the eigenvalues ​​of the complex-domain system matrix in traditional ERA. In addition, a real-part Hankel matrix is ​​constructed based on the real part of the data sequence of the synchronization phasor, and an imaginary Hankel matrix is ​​constructed based on the imaginary part of the data sequence of the synchronization phasor. The real-part Hankel matrix and the imaginary Hankel matrix are concatenated to obtain the real-domain Hankel matrix, which can completely preserve the information of the complex-domain synchronization phasor and can accurately identify the subsynchronous oscillation parameters under ultra-short data windows.

[0135] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0136] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0137] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0138] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0139] The above specific embodiments further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A subsynchronous oscillation parameter identification method based on feature system implementation algorithm, characterized in that, Includes the following steps: The data sequence of the synchronization phasor under subsynchronous oscillation is obtained. The synchronization phasor under subsynchronous oscillation is a modal model composed of a linear combination of four complex exponents and four constant parameters. The four complex exponents include the angular frequency of the fundamental positive frequency component, the angular frequency of the fundamental negative frequency component, the angular frequency of the oscillation positive frequency component, and the angular frequency of the oscillation negative frequency component. Construct the real part Hankel matrix and the imaginary part Hankel matrix based on the real part and imaginary part of the data sequence of the synchronization phasor, respectively; The real part Hankel matrix is ​​concatenated with the imaginary part Hankel matrix to obtain the first real field Hankel matrix; By shifting each element of the first real-field Hankel matrix forward by one unit time, we obtain the second real-field Hankel matrix. Singular value decomposition is performed on the first real-field Hankel matrix to obtain the left singular matrix, the right singular matrix, and the eigenvalue matrix; Based on the number of modes of the synchronization phasor, the left singular matrix, the right singular matrix, and the eigenvalue matrix are truncated. The system matrix is ​​determined based on the truncated left singular matrix, right singular matrix, eigenvalue matrix, and the second real-field Hankel matrix; Solve for the eigenvalues ​​of the system matrix, and calculate the four complex exponents and the four constant parameters based on the eigenvalues ​​of the system matrix; Based on the four complex exponents and the four constant parameters, the frequency, amplitude, and phase of the fundamental component, subsynchronous component, and supersynchronous component are determined.

2. The subsynchronous oscillation parameter identification method based on the feature system implementation algorithm according to claim 1, characterized in that, The specific expression of the modal model is as follows: w1=jα, w2=-jα, w3=jβ, w4=-jβ; in, Let R1, R2, R3, and R4 be the k-th synchronization phasor, and R4 be four constant parameters. w1 is the angular frequency of the fundamental positive frequency component, w2 is the angular frequency of the fundamental negative frequency component, w3 is the angular frequency of the oscillation positive frequency component, and w4 is the angular frequency of the fundamental negative frequency component. f0, x0, and φ0 represent the frequency, amplitude, and phase of the fundamental component, respectively. sub φ sub f sub x represents the amplitude, phase, and frequency of the subsynchronous component, respectively. sup φ sup f sup These represent the amplitude, phase, and frequency of the supersynchronous component, respectively; * indicates the complex conjugate; N is the number of data points used to calculate the synchronization phasor from the instantaneous values; f N f is the rated frequency of the power system. s The value of l is ±1, which is the frequency for uploading synchronous phasor data.

3. The subsynchronous oscillation parameter identification method based on the feature system implementation algorithm according to claim 1, characterized in that, The expressions for the real Hankel matrix and the imaginary Hankel matrix are as follows: Among them, Re(H) rs (k-1)) is the real part of the Hankel matrix, Im(H) rs (k-1)) is the imaginary Hankel matrix, r and s are the number of rows and columns of the Hankel matrix, respectively, Re represents the real part, and Im represents the imaginary part. Let k be the kth synchronization phasor.

4. The subsynchronous oscillation parameter identification method based on the feature system implementation algorithm according to claim 3, characterized in that, The expression for the first real-field Hankel matrix is ​​as follows: Where H(k-1) is the first real field Hankel matrix, Re(H rs (k-1)) is the real part of the Hankel matrix, Im(H) rs (k-1) is the imaginary Hankel matrix.

5. The subsynchronous oscillation parameter identification method based on the feature system implementation algorithm according to claim 4, characterized in that, The specific expression for singular value decomposition of the first real-field Hankel matrix is ​​as follows: H(0)=UDV H ; Where H(0) is the first real field Hankel matrix when k=1, U is the left singular matrix, V is the right singular matrix, D is the eigenvalue matrix, and the superscript H indicates the conjugate transpose.

6. The subsynchronous oscillation parameter identification method based on the feature system implementation algorithm according to claim 5, characterized in that, The expression for truncating the left singular matrix, the right singular matrix, and the eigenvalue matrix is ​​as follows: Among them, U r V is the truncated left singular matrix. r D is the truncated right singular matrix. r This is the truncated eigenvalue matrix.

7. The subsynchronous oscillation parameter identification method based on the feature system implementation algorithm according to claim 6, characterized in that, The specific expression for the system matrix is ​​as follows: Where A is the system matrix and H(1) is the second real field Hankel matrix when k=2.

8. A subsynchronous oscillation parameter identification system based on a feature system implementation algorithm, characterized by including: The data acquisition module is used to obtain the data sequence of the synchronization phasor under subsynchronous oscillation. The synchronization phasor under subsynchronous oscillation is a modal model composed of a linear combination of four complex exponents and four constant parameters. The four complex exponents include the angular frequency of the fundamental positive frequency component, the angular frequency of the fundamental negative frequency component, the angular frequency of the oscillation positive frequency component, and the angular frequency of the oscillation negative frequency component. A matrix construction module is used to construct a real Hankel matrix and an imaginary Hankel matrix based on the real and imaginary parts of the data sequence of the synchronization phasor, respectively. A matrix concatenation module is used to concatenate the real part Hankel matrix with the imaginary part Hankel matrix to obtain a first real field Hankel matrix. The matrix shifting module is used to shift each element of the first real-field Hankel matrix forward by a unit time to obtain the second real-field Hankel matrix. The matrix decomposition module is used to perform singular value decomposition on the first real field Hankel matrix to obtain the left singular matrix, the right singular matrix, and the eigenvalue matrix. The truncation processing module is used to truncate the left singular matrix, the right singular matrix, and the eigenvalue matrix according to the number of modes of the synchronization phasor; The matrix determination module is used to determine the system matrix based on the truncated left singular matrix, right singular matrix, eigenvalue matrix, and the second real-field Hankel matrix; The matrix solving module is used to solve for the eigenvalues ​​of the system matrix and to calculate the four complex exponents and the four constant parameters based on the eigenvalues ​​of the system matrix. The parameter solving module is used to determine the frequency, amplitude, and phase of the fundamental component, subsynchronous component, and supersynchronous component based on the four complex exponents and the four constant parameters.

9. A computer terminal comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the subsynchronous oscillation parameter identification method based on the feature system implementation algorithm as described in any one of claims 1-7.

10. A computer-readable medium having a computer program stored thereon, characterized in that, The computer program, when executed by a processor, can implement the subsynchronous oscillation parameter identification method based on the feature system implementation algorithm as described in any one of claims 1-7.

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