A disturbance source positioning method based on dynamic mode decomposition

Abstract

The application discloses a disturbance source positioning method based on dynamic mode decomposition, belongs to the technical field of power system operation and analysis, and accurately extracts the oscillation mode characteristics of a system by matrix decomposition on measured data; further, a participation factor analysis model fusing time and space characteristics is constructed, the spatial distribution characteristics and time evolution characteristics of the mode are comprehensively considered, and accurate positioning of the oscillation source is realized. Compared with traditional methods, the application has the advantages of not needing to depend on a detailed system model, high positioning accuracy, etc., is completely realized based on measured data calculation, and avoids complex system modeling, and thus has high practical application value and popularization potential.

Description

Technical Field

[0001] This invention belongs to the field of power system operation and analysis technology, and in particular relates to a disturbance source localization technology based on dynamic mode decomposition method, which is used to identify and locate forced disturbance sources in power systems. Background Technology

[0002] In recent years, the development of renewable energy grid integration, communication technology, and smart grids has increased the complexity of power systems, leading to frequent and diverse system disturbances. Accurate identification and location of disturbance sources in power systems are crucial for ensuring stable system operation. Oscillations in power systems are mainly classified into two categories: natural oscillations stemming from the inherent characteristics of the system itself and forced oscillations caused by continuous energy injection from external disturbance sources. While mature solutions exist for natural oscillations, forced oscillations, due to their propagation characteristics and location complexity, are the primary focus of this research. Disturbance source location primarily relies on the analysis of data collected by synchronous phasor measurement units (PMUs), but traditional methods often struggle to accurately distinguish between disturbance sources and disturbance responses when faced with complex disturbances.

[0003] Therefore, developing a new method for effectively identifying and accurately locating disturbance sources in power systems is of great significance. Dynamic mode decomposition (DMD), as an emerging data-driven analysis method, can extract key dynamic features from high-dimensional time-series data without relying on a physical model of the system. Therefore, researching a disturbance source location method based on DMD is crucial for improving power grid security and optimizing control strategies.

[0004] In summary, given the shortcomings of existing technologies, there is an urgent need to develop a high-precision, low-computational-complexity method for identifying and locating disturbance sources in order to effectively address the increasingly complex forced oscillation problem in power systems and improve the stability of system operation. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a disturbance source localization method based on dynamic pattern decomposition, which addresses the problems of low accuracy, high algorithm complexity, and difficulty in adapting to the ever-changing forms of modern power systems in existing disturbance source identification methods.

[0006] A disturbance source localization method based on dynamic pattern decomposition includes the following steps, which are performed sequentially:

[0007] Step 1: Collect power system oscillation data, including active power P, bus voltage V, and frequency f, through synchronous phasor measurement units (PMUs) distributed at the generator locations;

[0008] Step 2: Using power system oscillation data as input, construct a dynamic mode decomposition model;

[0009] Step 3: Perform FFT spectrum analysis on the oscillation modes to identify the main oscillation frequencies of the power system. Based on the phase trajectory characteristics of the modes, they are divided into natural oscillations and forced oscillations.

[0010] Step 4: Calculate the participation factor. Quantify the oscillation mode from the time and space dimensions using the participation factor, and identify the generator unit with the high participation factor value as the oscillation source.

[0011] The dynamic mode decomposition model described in step two is as follows:

[0012] ,

[0013] In the formula, U It is a left singular vector matrix. Y It is the eigenvector matrix. It is a right singular vector matrix. It is the oscillation mode matrix, each column This represents the spatial distribution characteristics of a certain oscillation mode of the system; It is a time-dependent amplitude coefficient matrix. m The number of oscillation modes, For modality j eigenvalues.

[0014] The participation factor calculation method described in step four is as follows:

[0015] ① Calculate the modal time-varying energy:

[0016] ,

[0017] In the formula, For modality j eigenvalues; k For time step; Initial state In the j Projection on each mode;

[0018] ② Constructing participation factors:

[0019] ,

[0020] In the formula, The elements in the right eigenvector matrix correspond to the modes. j In state variables i Spatial components on.

[0021] Through the above design scheme, this invention can bring the following beneficial effects: a disturbance source localization method based on dynamic mode decomposition accurately extracts the oscillation mode characteristics of the system by performing matrix decomposition on measured data; furthermore, it constructs a participation factor analysis model that integrates spatiotemporal characteristics, comprehensively considering the spatial distribution characteristics and temporal evolution characteristics of the modes, to achieve precise localization of the oscillation source. Compared with traditional methods, it has advantages such as not relying on a detailed system model and high localization accuracy, and is entirely based on measurement data calculations, avoiding complex system modeling, thus possessing high practical application value and promotion potential. Attached Figure Description

[0022] The present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0023] Figure 1 This is a schematic flowchart of a disturbance source localization method based on dynamic pattern decomposition according to the present invention.

[0024] Figure 2 This is a topology diagram of the WECC 179-node system in a specific embodiment of the present invention.

[0025] Figure 3 This is a phase trajectory diagram of the forced oscillation mode in a specific embodiment of the present invention.

[0026] Figure 4 This is a thermogram of the participation factors of each oscillation mode of the generator in a specific embodiment of the present invention. Detailed Implementation

[0027] A method for locating forced oscillation disturbance sources based on dynamic mode decomposition, such as Figure 1 As shown: Includes the following steps:

[0028] Step 1: Data Preparation: Synchronous electrical data (including active power) P Bus voltage V ,frequency f It can be generated from oscillation data captured by PMUs distributed at different generator locations.

[0029] Step 2: Using wide-area measurement data under power system oscillation conditions as input, construct a dynamic mode decomposition model:

[0030] ① Measure the data matrix X Divided into two parts: The measurement vector representing the system state at the first N-1 time steps; This represents the measurement vector at the next N-1 time points. The relationship between the two can be expressed as:

[0031]

[0032] in,A It is a high-order complex matrix that can capture the inherent dynamic change characteristics within the measurement information, and its eigenvalues ​​and eigenvectors contain the dynamic oscillation information of the system. r Let be the residual matrix.

[0033] ② Processing matrices using Singular Value Decomposition (SVD) X 1 :

[0034]

[0035] in, U It is a left singular vector matrix; Σ It is a singular value matrix; It is a right singular vector matrix. U and V Both are unitary matrices.

[0036] ③ Construct a low-order approximation matrix F :

[0037]

[0038] in, F The system dynamics matrix after dimensionality reduction. F The eigenvalues ​​and eigenvectors contain the main oscillation information of the system.

[0039] ④ Calculation F Eigenvalues ​​and eigenvectors:

[0040]

[0041] in, Λ It is an eigenvalue matrix. Y It is the eigenvector matrix

[0042] ⑤ Finally, construct the system's dynamic schema expression:

[0043]

[0044] in: It is the oscillation mode matrix, each column This represents the spatial distribution characteristics of a certain oscillation mode of the system; It is a time-dependent amplitude coefficient matrix. m This represents the number of oscillation modes.

[0045] Step 3: Oscillation Characteristics Analysis

[0046] FFT spectral analysis was performed on the extracted oscillation modes to identify the main oscillation frequencies in the system. By analyzing the phase trajectory characteristics of each mode, natural oscillations and forced oscillations were distinguished. Forced oscillation modes exhibit a standard circular closed phase trajectory, while natural oscillation modes show a spiral-shaped inward-curving phase trajectory. The location of disturbance sources is related to forced oscillation modes; therefore, these are used as the object of subsequent oscillation source localization analysis.

[0047] Step 4: Calculate the participation factor;

[0048] ① Calculate the modal time-varying energy:

[0049]

[0050] Where: In the formula, For modality j eigenvalues; k Indicates the time step; Initial state In the j Projection onto each modality.

[0051] ② Constructing participation factors:

[0052]

[0053] in, The elements in the right eigenvector matrix correspond to the modes. j In state variables i Spatial components on.

[0054] By calculating the participation factor, the combined impact of each mode on different state variables of the system can be accurately quantified from both temporal and spatial dimensions, providing a theoretical basis for oscillation source localization. However, its accuracy largely depends on the quality and completeness of the measurement data. In actual power systems, factors such as measurement noise, missing data, and system parameter uncertainties may affect the calculation accuracy of the participation factor. Therefore, in application, it is necessary to combine prior system knowledge and various auxiliary methods for cross-validation to ensure the reliability of oscillation source localization.

[0055] Step 5: Locate the oscillation source;

[0056] By analyzing the participation factor distribution of each generator under forced oscillation mode, the generator unit with the highest participation factor value is identified as the oscillation source. A heatmap can be used to visually represent the participation factor distribution of each generator in the forced oscillation mode, accurately locating the source point causing the system's forced oscillation, thus completing the oscillation source localization.

[0057] This invention utilizes a constructed dynamic mode decomposition and participation factor analysis model to obtain the characteristics of forced oscillation modes and the location of oscillation sources. This step involves analyzing the oscillation characteristics using only measurement data, aiming to avoid modeling the system and achieve data-driven extraction of forced oscillation modes and precise location of oscillation sources.

[0058] The present invention will be further described in detail below with reference to embodiments:

[0059] like Figure 2 The WECC 179-bus system shown has a forced oscillation source located at generator 79, which is modeled using the GENROU model. The remaining generators are modeled using the GENCLS model. The damping parameters of all generators in the system are also shown. D The values ​​are all 4, but the D value of generator No. 79 is 0, and all loads use a constant MVA model. The forced oscillation signal is injected into the excitation system of generator No. 79 in the form of a 0.89Hz sine wave.

[0060] Under forced oscillation conditions, the responses of each node exhibit obvious oscillatory characteristics. To accurately locate the oscillation source, dynamic mode decomposition (DMD) is first used to extract the system's oscillation modes, followed by... Figure 3 As shown, the forced oscillation mode was determined to be mode 4 through phase trajectory analysis. Finally, the participation factor of each node in this mode was calculated to locate the oscillation source. The calculation results are as follows. Figure 4 As shown.

[0061] The precise location results of the forced oscillation source of generator No. 79 further verified the feasibility and effectiveness of the method of the present invention in the location of oscillation sources in power systems.

[0062] according to Figure 4 As shown in the oscillation source localization results, the method proposed in this invention can accurately identify the location of the forced oscillation source, providing effective support for system oscillation suppression and stability control.

Claims

1. A disturbance source localization method based on dynamic mode decomposition, characterized in that: Includes the following steps, And the following steps are performed in sequence: Step 1: Collect power system oscillation data, including active power P, bus voltage V, and frequency f, through synchronous phasor measurement units (PMUs) distributed at the generator locations; Step 2: Using power system oscillation data as input, construct a dynamic mode decomposition model; Step 3: Perform FFT spectrum analysis on the oscillation modes to identify the main oscillation frequencies of the power system. Based on the phase trajectory characteristics of the modes, they are divided into natural oscillations and forced oscillations. Forced oscillations are used as the analysis object for subsequent oscillation source localization. Step 4: Calculate the participation factor. Quantify the oscillation modes from both temporal and spatial dimensions using the participation factor, and identify generator units with high participation factor values ​​as oscillation sources. The dynamic mode decomposition model described in step two is as follows: In the formula, U is the left singular vector matrix, Y is the eigenvector matrix, and V is the eigenvector matrix. * It is a right singular vector matrix, Φ=[φ1,φ2,…φ m ] is the oscillation mode matrix, and each column φ i Γ represents the spatial distribution characteristics of a certain oscillation mode of the system; m (t)=[a1(t),a2(t),…a m (t)] T It is a time-dependent amplitude coefficient matrix, where m is the number of oscillation modes and λ is the amplitude coefficient matrix. j Let Σ be the eigenvalues ​​of mode j, A be a high-order complex matrix capturing the inherent dynamic characteristics within the measurement information, whose eigenvalues ​​and eigenvectors contain the dynamic oscillation information of the system, Σ be the singular value matrix, and Λ be the eigenvalue matrix. This is a dynamic decomposition mode for the system. The participation factor calculation method described in step four is as follows: ① Calculate the modal time-varying energy: In the formula, λ j Let be the eigenvalues ​​of mode j; k is the time step. The projection of the initial state x0 onto the j-th mode; ② Constructing participation factors: P ij |φ ij AND ij | In the formula, φ ij The elements in the right eigenvector matrix represent the spatial components of mode j on state variable i.

Images