A data-driven engagement factor calculation method

Abstract

The present application belongs to the technical field of power system dynamic analysis, and particularly relates to a data-driven participation factor calculation method, which extracts modal information directly from the dynamic response data of a power system based on dynamic mode decomposition, avoids the dependence of traditional methods on the mathematical model of the power system, significantly reduces the calculation complexity, and is suitable for real-time analysis of large-scale power systems; through the combination of singular value decomposition and DMD, the high-dimensional data of the power system is processed by dimension reduction, low-dimensional modal information is extracted, the calculation efficiency and analysis accuracy are improved, the participation factor is redefined, the dynamic characteristics of the power system evolving with space and time are combined, the participation degree of the mode can be more comprehensively quantified, and the dominant mode and key nodes in the power system can be accurately identified. The method has strong adaptability, can process the dynamic behavior of a nonlinear power system, is suitable for various operating states, and provides strong support for the dynamic stability analysis and real-time monitoring of the power system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of power system dynamic analysis, and particularly relates to a data-driven participation factor calculation method, a participation factor extraction method based on dynamic mode decomposition (DMD), and a mode analysis and participation factor calculation method for power system dynamic behavior. BACKGROUND

[0002] With the continuous expansion of the scale of the power system and the high proportion of renewable energy connected to the grid, the dynamic characteristics of the power system are becoming increasingly complex. How to extract effective features from the dynamic response data of the power system and realize power system fault detection is still a challenging problem. Although traditional modal analysis methods such as wavelet transform and variational mode decomposition have been widely used in power system dynamic analysis, these methods usually rely on experience to select thresholds and are prone to modal aliasing and noise sensitivity, which makes it difficult to meet the analysis needs of modern power systems. In addition, traditional participation factor calculation methods are usually based on the state matrix of the power system, and the calculation process is complex and time-consuming, which makes it difficult to be quickly applied in large-scale power systems.

[0003] As a data-driven method, dynamic mode decomposition (DMD) can extract modal information of the power system from the dynamic response data of the power system, extract low-dimensional dynamic modes from high-dimensional data, and reveal the internal evolution law of the power system, providing a new idea for power system disturbance analysis. In addition, the DMD method has been widely used in the field of fluid mechanics, but its application in power system dynamic analysis is still relatively rare. Therefore, there is an urgent need for a participation factor extraction method based on DMD to simplify the analysis process of power system dynamic behavior and improve the calculation efficiency. SUMMARY

[0004] To solve the technical problems mentioned in the background that the dynamic characteristics of the power system are becoming increasingly complex, the traditional modal analysis method usually relies on experience to select thresholds and is prone to modal aliasing and noise sensitivity, and the calculation process is complex and time-consuming, the application provides a data-driven participation factor calculation method for simplifying the mode analysis and participation factor calculation of power system dynamic behavior, improving the calculation efficiency, and meeting the real-time analysis needs of modern power systems.

[0005] The technical scheme provided by the application is as follows: a data-driven participation factor calculation method, which comprises the following steps:

[0006] Step 1: Constructing a Hankel matrix using the dynamic response data of the power system;

[0007] The acquired dynamic response data of the power system is taken as input, and a Hankel matrix is constructed from the discrete dynamic response data of the power system as follows:

[0008] (1);

[0009] In formula (1): represents the data sampled at the sampling point at the moment; represents a vector composed of all observable sampling values at the moment;

[0010] Step two, linear mapping approximation is performed on the discrete sampling measurement data.

[0011] The discrete sampling measurement data can be approximated by linear mapping as follows:

[0012] (2);

[0013] In formula (2): is a high-order complex matrix that can capture the inherent dynamic change characteristics of the measurement information, and the eigenvalues and eigenvectors thereof contain dynamic oscillation information of the power system;

[0014] The Krylov subspace sequence is obtained and is represented as

[0015] (3);

[0016] (4);

[0017] (5);

[0018] From formulas (3)-(5), the following can be obtained:

[0019] (6);

[0020] Step three, low-dimensional modal information is extracted by DMD decomposition.

[0021] The original data matrix is decomposed by orthogonal projection as follows:

[0022] (7);

[0023] In formula (7): represents a low-dimensional approximation matrix similar to , but discarding irrelevant features; is a left singular vector matrix of the matrix , which is a left singular vector matrix of singular value decomposition (SVD) as shown in the following formula, i.e.

[0024] (8);

[0025] In formula (8), matrix U and matrix V are left and right singular value vectors respectively, and are both unitary matrices; is a singular value diagonal matrix;

[0026] By synthesizing the above formula, the low-dimensional approximate matrix of the power system can be obtained as The calculation formula of the low-dimensional approximate matrix is

[0027] (9);

[0028] Eigenvalue decomposition is performed on the low-dimensional approximate matrix

[0029] (10);

[0030] In formula (10), λ is an eigenvalue matrix, is a non-zero eigenvalue corresponding to an oscillation mode, is an eigenvector matrix, , indicates a mode in the low-dimensional space, is the number of oscillation modes;

[0031] From the above, it can be obtained that:

[0032] (11);

[0033] Step four, establishing an oscillation mode matrix and an amplitude coefficient matrix;

[0034] According to the SVD definition of the data matrix:

[0035] (12);

[0036] (13);

[0037] (14);

[0038] In formula (12), is an oscillation mode matrix, each column indicates the relative oscillation trend of a certain oscillation mode in the power system, reflecting the spatial distribution characteristics of the power system under different modes;

[0039] In formula (14), is a time-dependent amplitude coefficient matrix, describing the evolution of the amplitude of each mode over time;

[0040] Step five, extracting an oscillation mode participation factor;​​

[0041] estimated data sequence , which can be expressed as:

[0042] (15) ;

[0043] Equation (15) decomposes the dynamic behavior of the power system into the superposition of multiple modes, each of which is determined by its spatial characteristics , temporal characteristics and amplitude evolution respectively; each dynamic mode is weighted by the product of each Ritz mode value and the corresponding energy extracted from each time-varying mode, i.e. (16) ;

[0044] The state-mode relationship is defined as:

[0045] (17) ;

[0046] In equation (17), a measure of the mode participation in the power system state is provided;

[0047] The participation factor matrix is established by summing up each row vector of the above equation, which is used to correlate the power system state and the mode:

[0048] (18) ;

[0049] (19) ;

[0050] where, is the participation factor, which is directly related to the spatial distribution and temporal characteristics of the mode, and at the same time, it can describe the contribution of the mode at both local and global levels.

[0051] The technical scheme provided by the embodiments of the present application has at least the following beneficial effects:

[0052] The application is based on a dynamic mode decomposition (DMD) method, extracts modal information directly from dynamic response data of a power system, avoids dependence on a mathematical model of the power system in a traditional method, significantly reduces calculation complexity, and is suitable for real-time analysis of a large-scale power system. Through combination of singular value decomposition and DMD, high-dimensional data of the power system is processed in a dimension reduction manner, low-dimensional modal information is extracted, and calculation efficiency and analysis accuracy are improved. In addition, the application proposes a new participation factor definition method, combines dynamic characteristics of the power system with space-time evolution, can more comprehensively quantify the participation degree of a mode, and accurately identifies a dominant mode and a key node in the power system. The method has strong adaptability, can process dynamic behaviors of a nonlinear power system, is suitable for various operating states, provides strong support for dynamic stability analysis and real-time monitoring of the power system, and has high practical application value. BRIEF DESCRIPTION OF DRAWINGS

[0053] In order to more clearly illustrate the technical solutions in the embodiments of the application, the following will briefly introduce the drawings needed to be used in the embodiment description. Obviously, the drawings in the following description only some embodiments of the application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0054] Figure 1 A data-driven participation factor calculation method flowchart in the embodiment of the application;

[0055] Figure 2 A time curve graph of dynamic response data of the 10kV resonance grounding power system in the embodiment of the application, in which the measuring device collects transient zero sequence currents of each line;

[0056] Figure 3 A participation factor calculation result graph of the data-driven participation factor calculation method in the embodiment of the application. DETAILED DESCRIPTION

[0057] The technical solutions in the application will be described below with reference to the drawings.

[0058] In the embodiments of the application, the words such as "example", "for example" and the like are used to represent an example, illustration or description. Any embodiment or design scheme described as "example" in the application should not be interpreted as more preferred or more advantageous than other embodiments or design schemes. Rather, the word "example" is intended to present a concept in a specific manner. In addition, in the embodiments of the application, the meaning expressed by "and / or" can be both, or can be one of the two.

[0059] In the embodiments of the present application, "image" and "picture" can be used interchangeably, and it should be pointed out that the meanings expressed are consistent when the distinction is not emphasized. "Of", "corresponding" and "corresponding" can be used interchangeably, and it should be pointed out that the meanings expressed are consistent when the distinction is not emphasized.

[0060] In the embodiments of the present application, sometimes the subscript such as W1 can be written in the form of non-subscript such as W1, and the meanings expressed are consistent when the distinction is not emphasized.

[0061] In order to make the technical problems, technical solutions and advantages to be solved by the present application more clear, the following will be described in detail with reference to the drawings and specific embodiments.

[0062] Figure 1 For the flow chart of the data-driven participation factor calculation method in the present application, the present application provides a data-driven participation factor calculation method, which refers to Figure 1 , comprising the following steps, and the following steps are performed in sequence,

[0063] Step 1, constructing a Hankel matrix using dynamic response data of a power system, the specific process is:

[0064] Dynamic mode decomposition algorithm: obtaining dynamic response data of a power system based on time domain simulation or PMU measurement:

[0065] (20);

[0066] In formula (20), is the sampling value of the dynamic response of the power system at time , and is a sampling interval.

[0067] Discrete dynamic response data of the power system is used to construct the following Hankel matrix:

[0068] (1);

[0069] In formula (1), represents the sampling data at sampling point at time ; represents a vector composed of all observable sampling values at time ;

[0070] Step 2, linearly mapping and approximating the discrete sampling measurement data, the specific process is:

[0071] The discrete sampled measurement data can be approximately represented by a linear mapping as

[0072] (2);

[0073] In formula (2), is a high-order complex matrix that can capture the dynamic variation characteristics inherent in the measurement information, and the eigenvalues and eigenvectors thereof contain the dynamic oscillation information of the power system;

[0074] The Krylov subspace sequence is obtained and represented as

[0075] (3);

[0076] (4);

[0077] (5);

[0078] From formulas (3)-(5), we can obtain

[0079] (6);

[0080] Step three, low-dimensional modal information is extracted by DMD decomposition, and the specific process is as follows:

[0081] The original data matrix is orthogonally projected and decomposed as

[0082] (7);

[0083] In formula (7), represents a low-dimensional approximation matrix similar to , but discards irrelevant features; is the matrix is the left singular vector matrix of singular value decomposition (SVD) as shown in the following formula, that is,

[0084] (8);

[0085] In formula (8), the matrices U and V are left and right singular value vectors, respectively, and are both unitary matrices; is a singular value diagonal matrix;

[0086] By combining the above formulas, the calculation formula of the low-dimensional approximation matrix of the power system can be obtained as

[0087] (9);

[0088] The eigenvalue decomposition of the low-dimensional approximation matrix is performed:

[0089] (10);

[0090] In formula (10), is the eigenvalue matrix, is the non-zero eigenvalue corresponding to the oscillation mode, is the eigenvector matrix, , represents the mode in the low-dimensional space, is the number of oscillation modes;

[0091] From the above, it is obtained that:

[0092] (11);

[0093] Step four, establish the oscillation mode matrix and the amplitude coefficient matrix, the specific process is:

[0094] According to the SVD definition of the data matrix:

[0095] (12);

[0096] (13);

[0097] (14);

[0098] In formula (12), is the oscillation mode matrix, each column represents the relative oscillation trend of a certain oscillation mode in the power system, reflecting the spatial distribution characteristics of the power system under different modes;

[0099] In formula (14), is the time-dependent amplitude coefficient matrix, describing the evolution of the amplitude of each mode over time;

[0100] Step five, extract the oscillation mode participation factor;

[0101] The estimated data sequence can be expressed as:

[0102] (15);

[0103] Formula (15) decomposes the dynamic behavior of the power system into the superposition of multiple modes, each mode being determined by its spatial characteristics , time characteristics and amplitude evolution ; each dynamic mode is weighted by the product of each Ritz mode value and the corresponding energy extracted from each time-varying mode, that is (16);

[0104] Estimation of the relationship between the state and the mode of the power system is a key step to understand the contribution of each mode to the overall power system dynamics. The participation factor proposed by the traditional method assesses this relationship through the product of the right eigenvector and the left eigenvector. This method has the advantage of not depending on the unit and dimension of the state variable, and provides a robust analysis tool for the state-mode association of the power system. However, in the present invention, we propose a new participation degree definition method, which directly introduces the dynamic characteristics of the power system evolving in space and time, thus more comprehensively quantifying the participation degree of the mode.

[0105] Therefore, we define the state-mode relationship as:

[0106] (17);

[0107] In formula (17), The mode provides a measure of the participation of the state of the power system;

[0108] The participation factor matrix is established, which is calculated by adding each row vector of the above formula, and is used to associate the state and the mode of the power system:

[0109] (18);

[0110] (19);

[0111] Wherein, The participation factor is directly related to the spatial distribution and temporal characteristics of the mode, and at the same time it can describe the contribution of the mode at both local and global levels.

[0112] The data-driven participation factor calculation method proposed in the present invention extracts the participation factor based on dynamic mode decomposition, extracts the mode information of the power system in a data-driven manner, analyzes the dynamic behavior of the power system according to the extracted mode information and participation factor, and identifies the dominant mode and key node in the power system, which provides a basis for dynamic stability analysis and control of the power system. Avoid the dependence on the mathematical model of the power system in the traditional method, simplify the calculation process, improve the calculation efficiency. Compared with the traditional method, the present invention has high practical application value and can adapt to the real-time analysis needs of modern power systems.

[0113] The present invention will be further described in detail below in conjunction with examples:

[0114] The method is verified on a 10kV resonant grounding power system simulation model built by PSCAD / EMTDC electromagnetic simulation software, and the model includes 5 lines. Assuming that single-phase grounding fault occurs in line L3, the fault transition resistance is 10Ω, the initial phase angle of fault is 90°, the model sampling frequency is 20kHz, and the fundamental frequency is 50Hz. The transient zero sequence current of each line is collected by the measuring device as the dynamic response data input of the 10kV resonant grounding power system, and the dynamic response data of the 10kV resonant grounding power system is as shown in Figure 2 The data-driven participation factor calculation method proposed in the application is used to identify the dynamic response data of the 10kV resonant grounding power system, and the participation factor and the participation degree of each modal participation factor As shown in Figure 3 .

[0115] In the above example, the two groups of dominant oscillation frequencies identified by the DMD method are 50.15Hz and 370.56Hz, which are basically consistent with the dominant oscillation frequencies of the power system identified by FFT, i.e. 49.94Hz and 374.53Hz. And Figure 3 It can be seen that the participation degree of mode 3 to the whole power system is significantly higher than that of other modes, and the participation degree formula introduced in the theory of the application can be derived that mode 3 has a great dynamic influence on the power system fault, which is consistent with the energy concentration of the fault characteristic signal on a specific frequency and a specific line. This mode can be used as a dominant characteristic mode to identify the fault line. At the same time, the adaptability of the algorithm is analyzed by setting different conditions, and the results are shown in Table 1,

[0116] Table 1 Participation factor extraction effect of the method

[0117] Fault line Transition resistance Signal-to-noise ratio Fault distance Initial phase angle P ki ]]> Extraction result L1 20 0 3 30° [[[[ 200.80 51.98 54.85 70.41 35.59]]]> Correct L1 20 0 8 30° <![CDATA[[ 193.17 53.16 50.84 66.48 34.09]]]> Correct L2 10 5 15 0° [[30.15 199.14 32.36 48.87 21.64]]]> Correct L2 10 20 15 0° [[54.26 172.25 55.67 81.26 37.17]]]> Correct L4 500 0 5 30° [[30.51 37.55 40.43 99.11 26.76]]]> Correct L4 2000 0 5 30° [[16.61 18.10 19.31 40.01 12.76]]]> Correct L5 15 5 10 30° [29.30 30.15 30.49 36.71 1 61.27 ]]]> Correct L5 15 5 10 60° [[19.07 20.12 20.99 25.27 1 34.79 ]]]> Correct

[0118] The above analysis can verify that the modal information extracted by the DMD method is used to calculate the participation factor of the power system, analyze the dynamic behavior of the power system according to the calculation results of the participation factor, identify the dominant mode and key node in the power system, provide a basis for dynamic stability analysis and control of the power system, and has good robustness. Through the above embodiments, the feasibility and effectiveness of the method in the analysis of the dynamic behavior of the power system are verified.

[0119] The software program involved in the application is programmed according to mobile communication, network and computer processing technology, and the software program involved in the application is a technology familiar to those skilled in the art.

[0120] The above-described embodiments can be implemented in whole or in part by software, hardware (such as a circuit), firmware, or any combination thereof. When implemented in software, the above-described embodiments can be implemented in the form of a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, the processes or functions described in the embodiments of the present application are wholly or partially generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions can be stored in a computer-readable storage medium or transferred from one computer-readable storage medium to another computer-readable storage medium, for example, the computer instructions can be transferred from one website, computer, server, or data center to another website, computer, server, or data center through a wired (such as infrared, wireless, microwave, etc.) manner. The computer-readable storage medium can be any available medium accessible by a computer or a data storage device such as a server, data center, etc. containing one or more available medium collections. The available medium can be a magnetic medium (such as a floppy disk, a hard disk, a magnetic tape), an optical medium (such as a DVD), or a semiconductor medium. The semiconductor medium can be a solid-state disk.

[0121] It should be understood that the term "and / or" herein merely describes an association relationship of associated objects, which means that there can be three relationships, for example, A and / or B can represent three cases of A alone, A and B together, and B alone, where A and B can be singular or plural. In addition, the character " / " herein generally represents that the associated objects before and after are an "or" relationship, but can also represent an "and / or" relationship, which can be understood according to the context before and after.

[0122] In the present application, "at least one" means one or more, and "multiple" means two or more. "At least one of the following" or the like means any combination of the items, including any combination of single or multiple items. For example, at least one of a, b, or c can represent a, b, c, a-b, a-c, b-c, or a-b-c, where a, b, and c can be single or multiple.

[0123] It should be understood that in various embodiments of the present application, the size of the sequence number of the above-described processes does not mean the order of execution, and the execution order of the processes should be determined according to their functions and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0124] Those skilled in the art can clearly understand that the units and algorithm steps of each example described in combination with the embodiments disclosed herein can be realized by electronic hardware or a combination of computer software and electronic hardware. Whether the functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the present application.

[0125] Those skilled in the art can clearly understand that, for the convenience and brevity of the description, the specific working processes of the devices, apparatuses and units described above can refer to the corresponding processes in the foregoing method embodiments, which will not be repeated here.

[0126] In several embodiments provided by the present application, it should be understood that the disclosed devices, apparatuses and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely schematic, for example, the division of the units is only a logical function division, and actual implementation can have another division manner, for example, multiple units or components can be combined or integrated into another device, or some features can be ignored or not executed. In addition, the coupling or direct coupling or communication connection between the units shown or discussed can be indirect coupling or communication connection through some interfaces, devices or units, which can be electrical, mechanical or other forms.

[0127] The units described as separate components can or can not be physically separated, and the components shown as units can or can not be physical units, that is, they can be located in one place, or can be distributed on multiple network units. Part or all of the units can be selected according to actual needs to achieve the purpose of the embodiment scheme.

[0128] In addition, each functional unit in each embodiment of the present application can be integrated into a processing unit, or each unit can exist physically independently, or two or more units can be integrated into one unit.

[0129] If the functions are realized in the form of software function units and sold or used as independent products, they can be stored in a computer readable storage medium. Based on this understanding, the technical solutions of the present application or the parts of the present application that essentially contribute to the prior art or the parts of the technical solutions can be embodied in the form of software products. The computer software product is stored in a storage medium and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in the various embodiments of the present application. The aforementioned storage medium includes a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, and various media that can store program codes.

[0130] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art can easily think of changes or replacements within the technical scope disclosed by the present application, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A data-driven engagement factor calculation method, characterized in that, Comprising the following steps: Step one, using the dynamic response data of power system to construct Hankel matrix; The acquired dynamic response data of power system is taken as input, and a matrix is constructed with the discrete dynamic response data of power system; Step two, linear mapping approximation is performed on the discrete sampling measurement data; Step three, low-dimensional modal information is extracted by DMD decomposition; Step four, an oscillation modal matrix and an amplitude coefficient matrix are established; Step five, an oscillation mode participation factor is extracted: the dynamic behavior of the power system is decomposed into the superposition of multiple modes, each mode is determined by its spatial characteristics, time characteristics and amplitude evolution; a state-mode relationship is defined to represent the measure of the participation of the mode to the power system state; A participation factor matrix is established to associate the power system state and the mode, the participation factor is directly related to the spatial distribution and time characteristics of the mode, and it can describe the contribution of the mode at both local and global levels; In step three, the low-dimensional modal information is extracted by DMD decomposition: By orthogonal projection decomposition of the raw data matrix : （7）； In formula (7): denotes similar features, but a low-dimensional approximation matrix of irrelevant features is discarded; denotes similar features, but a low-dimensional approximation matrix of irrelevant features is discarded; is a matrix is a left singular vector matrix of singular value decomposition (SVD) shown as follows: （8）； In formula (8), the matrix U and the matrix V are left and right singular value vectors respectively, and are both unitary matrices; is a singular value diagonal matrix; From the above equations, the low-dimensional approximation matrix of the power system can be obtained The calculation formula is （9） ； Low-dimensional approximate matrices Eigenvalue decomposition is performed: （10）； In formula (10): is an eigenvalue matrix, is a non-zero eigenvalue corresponding to an oscillation mode, is an eigenvector matrix, denotes a mode in a low-dimensional space, is the number of oscillation modes; From the above arrangement: （11）； In step five, the process of extracting the oscillation mode participation factor is: estimated data sequence may be expressed as: （15）； Equation (15) decomposes the dynamic behavior of the power system into a superposition of multiple modes, each of which is determined by its spatial characteristics , temporal characteristics , and amplitude evolution , respectively; each dynamic mode is weighted by the product of each Ritz mode value and the corresponding energy extracted from each time-varying mode, i.e. (16); Define the state-mode relationship: （17）； In formula (17), A measure of the mode's participation in the power system state is provided; A participation factor matrix is established, which is calculated by adding each row vector of the above formula, and is used to associate the power system state and the mode: （18）； （19）； wherein, is a participation factor, directly related to the spatial distribution and temporal characteristics of the modalities, while it can describe the contribution of the modalities at both local and global levels.

2. The data-driven participation factor calculation method according to claim 1, characterized in that, In step one, the acquired dynamic response data of power system is taken as input, and the following Hankel matrix is constructed with the discrete dynamic response data of power system: （1）； In formula (1): express At the sampling point Sampling data; Indicates the first A vector consisting of all observable sampled values ​​at any given time.

3. The data-driven participation factor calculation method of claim 2, wherein, In step two, the discrete sampling measurement data can be represented by linear mapping approximation as: （2）； In formula (2): is a high-order complex matrix that can capture the dynamic variation characteristics inherent in the measurement information, and the eigenvalues and eigenvectors thereof contain dynamic oscillation information of the power system; Get the Krylov subspace sequence, denoted as （3）； （4）； （5）； From formula (3)-(5), we can get: （6）。 4. The data-driven participation factor calculation method of claim 3, wherein, In step four, the process of establishing the oscillation modal matrix and the amplitude coefficient matrix is: According to the SVD of the data matrix: （12）； （13）； （14）； In formula (12), is an oscillation mode matrix, each column represents the relative oscillation trend of a certain oscillation mode in the power system, reflecting the spatial distribution characteristics of the power system under different modes; In formula (14), is a time-dependent amplitude coefficient matrix, describing the evolution of the amplitude of each mode over time.

5. The data-driven participation factor calculation method of claim 1, wherein, In step one, the dynamic response data of power system is acquired by time domain simulation or PMU.

6. The data-driven participation factor calculation method of claim 5, wherein, Based on time domain simulation or PMU measurement, the dynamic response data of power system is acquired: （20）； In equation (20), For dynamic response of power systems The sampled value at time 10:

00. The sampling interval is denoted as .

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