Method and device for identifying low-frequency oscillation mode of power system and computer equipment

Abstract

The method for identifying the low-frequency oscillation mode of the power system provided by the invention comprises the following steps: when low-frequency oscillation of the power system is detected, performing multi-signal prony analysis on a real-time oscillation signal to obtain a measurement result of the low-frequency oscillation, the measurement result comprising a measurement mode and a measurement vibration mode thereof; obtaining a state matrix according to a mathematical model constructed when the power system operates at the balance point; displacement-inverse transformation is adopted to preprocess the state matrix disturbed by the low-frequency oscillation, an Arnoldi iterative algorithm is combined to solve a candidate result of the low-frequency oscillation, and the candidate result comprises a candidate mode and a candidate vibration mode; and matching the measurement result with the candidate result, and determining the low-frequency oscillation mode of the power system according to the matching result. Therefore, online, rapid and accurate identification of the excited mode in the large-scale AC / DC hybrid power system is realized.

Description

Technical Field

[0001] The present application relates to the technical field of power systems, and in particular to a method, device, and computer equipment for identifying low-frequency oscillation patterns in power systems. Background Art

[0002] With the widespread integration of renewable energy generation and its associated power electronic equipment into power systems, their inherent volatility makes the system prone to operating in a critically stable state. The resulting AC / DC hybrid characteristics exacerbate the system's low-frequency oscillations, posing a severe challenge to the stable operation of large-scale power systems. Traditionally, low-frequency oscillation patterns are identified by establishing a mathematical model of the power system and then identifying theoretical patterns after feature analysis. However, as the scale of power grids continues to expand, this method frequently suffers from the "curse of dimensionality," resulting in complex modeling, high computational effort, and difficulty meeting the requirements for real-time identification of oscillation patterns, limiting its application in dynamic control.

[0003] In recent years, the rapid development of wide-area measurement systems (WAMS) has opened up new avenues for analyzing low-frequency oscillations. By measuring the real-time dynamic behavior of power systems using WAMS, data-driven methods such as the Prony algorithm and the matrix bundle algorithm can be used to identify key power system modes. However, these methods generally lack support for the physical model of the power system, making it difficult to obtain theoretical modal information about the system. Even if the corresponding measurement patterns are obtained, in large-scale power systems, the extremely dense distribution of eigenvalues ​​makes it difficult to accurately match the excited theoretical modes based solely on eigenvalues, resulting in a lack of accuracy and interpretability in the identification results. Therefore, existing WAMS-based identification algorithms have limited effectiveness in locating and controlling actual oscillation modes and are unable to support efficient identification and dynamic response to complex power grid oscillation behavior.

[0004] In summary, there is an urgent need for a low-frequency oscillation mode identification method that has both real-time perception capabilities and the ability to integrate power system physical model information, so as to achieve online, rapid and accurate identification of excited modes in large-scale AC / DC hybrid power systems, address the shortcomings of existing methods in terms of identification accuracy, real-time performance and physical interpretability, and provide reliable support for dynamic monitoring and oscillation control of power systems. Summary of the Invention

[0005] The purpose of this application is to solve at least one of the above technical deficiencies, especially the technical deficiency in the prior art of how to quickly identify the key modes of real-time oscillations.

[0006] In a first aspect, the present application provides a method for identifying low-frequency oscillation patterns in a power system, the method comprising:

[0007] When low-frequency oscillation is detected in the power system, multi-signal prony analysis is performed on the real-time oscillation signal to obtain the measurement results of the low-frequency oscillation, which include the measurement mode and its measurement vibration shape;

[0008] According to the mathematical model constructed when the power system operates at the equilibrium point, the state matrix is ​​obtained;

[0009] The displacement-inverse transform is used to pre-process the state matrix after being disturbed by the low-frequency oscillation, and the candidate results of the low-frequency oscillation are solved by combining the Arnoldi iteration algorithm. The candidate results include candidate modes and candidate vibration shapes.

[0010] The measurement results are matched with the candidate results, and the low-frequency oscillation mode of the power system is determined based on the matching results.

[0011] In one embodiment, the step of performing multi-signal prony analysis on the real-time oscillation signal to obtain a measurement result of the low-frequency oscillation includes:

[0012] According to the real-time oscillation signal, a matrix equation is constructed, where the matrix equation is used to represent the real-time oscillation signal as a linear combination of different oscillation modes;

[0013] Constructing a polynomial characteristic equation according to the matrix equation, solving the characteristic roots of the polynomial characteristic equation to obtain an estimated mode of low-frequency oscillation, and solving the matrix equation to obtain an amplitude matrix;

[0014] A linear regression model is constructed according to the estimated pattern and amplitude matrix, and the stepwise regression method is applied to the linear regression model to obtain the measurement results of low-frequency oscillation.

[0015] In one embodiment, the step of constructing a polynomial characteristic equation according to the matrix equation includes:

[0016] The expression of the polynomial characteristic equation is:

[0017]

[0018] in, The variable representing the characteristic root, represents the order of the multi-order form, Represents the coefficients of the polynomial, constructed by the matrix equation Obtained by multiplying the order phasors.

[0019] In one embodiment, the step of constructing a linear regression model based on the estimated mode and the amplitude matrix includes:

[0020] Compute explanatory terms based on the estimated mode and magnitude matrices;

[0021] After normalizing the explanatory terms, a linear regression model is constructed in combination with the real-time oscillation signal.

[0022] In one embodiment, the step of obtaining a state matrix based on a mathematical model constructed when the power system operates at a balance point includes:

[0023] After obtaining the dynamic network and network parameters, dynamic component model and model parameters of the power system, linearization is performed at the equilibrium point to obtain a mathematical model, and the mathematical model is simplified to obtain a state matrix.

[0024] In one embodiment, the step of preprocessing the state matrix after being disturbed by the low-frequency oscillation by using the shift-inverse transform includes:

[0025] Performing LU decomposition on the state matrix after being disturbed by the low-frequency oscillation to obtain a first upper triangular matrix and a first lower triangular matrix, and calculating a first intermediate variable based on the first upper triangular matrix and the first lower triangular matrix;

[0026] Perform LU decomposition on the first intermediate variable to obtain a second upper triangular matrix and a second lower triangular matrix, and calculate the second intermediate variable based on the first upper triangular matrix and the first lower triangular matrix;

[0027] An auxiliary vector is calculated according to the second upper triangular matrix, the second lower triangular matrix and the second intermediate variable, and a preprocessed state matrix is ​​obtained according to the first upper triangular matrix, the first lower triangular matrix and the auxiliary vector.

[0028] In one embodiment, the step of matching the measurement result with the candidate result and determining the low frequency oscillation mode of the power system according to the matching result includes:

[0029] Construct a fitting factor phasor, and combine the fitting factor phasor with the candidate vibration shape to establish a matching relationship with the measured vibration shape;

[0030] Solve the matching relationship to obtain the best fitting factor, and match the best fitting factor with the candidate matrix to obtain the matching result;

[0031] The error between the matching result and the measurement matrix is ​​calculated. When the error is less than a preset threshold, the candidate mode corresponding to the candidate vibration shape is taken as the low-frequency oscillation mode of the power system.

[0032] In a second aspect, the present application provides a device for identifying low-frequency oscillation patterns in a power system, the device comprising:

[0033] The measurement result determination module is used to perform multi-signal prony analysis on the real-time oscillation signal when low-frequency oscillation is detected in the power system to obtain the measurement result of the low-frequency oscillation, and the measurement result includes the measurement mode and its measurement vibration shape;

[0034] a state matrix determination module for obtaining a state matrix based on a mathematical model constructed when the power system operates at a balance point;

[0035] The candidate result determination module is used to pre-process the state matrix after being disturbed by the low-frequency oscillation by using the displacement-inverse transformation, and to solve the candidate results of the low-frequency oscillation by combining the Arnoldi iteration algorithm. The candidate results include candidate modes and candidate vibration shapes;

[0036] The low-frequency oscillation mode determination module is used to match the measurement results with the candidate results and determine the low-frequency oscillation mode of the power system according to the matching results.

[0037] In a third aspect, the present application provides a storage medium: the storage medium stores computer-readable instructions, and when the computer-readable instructions are executed by one or more processors, the one or more processors execute the steps of the power system low-frequency oscillation pattern recognition method as described in any of the above embodiments.

[0038] In a fourth aspect, the present application provides a computer device, comprising: one or more processors, and a memory;

[0039] The memory stores computer-readable instructions, and when the computer-readable instructions are executed by one or more processors, the steps of the method for identifying a low-frequency oscillation pattern of a power system in any one of the above embodiments are performed.

[0040] It can be seen from the above technical solutions that the embodiments of the present application have the following advantages:

[0041] The method for identifying low-frequency oscillation patterns in power systems provided in this application combines the advantages of real-time measurement and physical modeling. Upon detecting a low-frequency oscillation in the power system, this method first extracts the measurement mode and vibration mode of the oscillation signal through multi-signal Prony analysis, enabling rapid perception of real-time oscillation behavior. Subsequently, based on a mathematical model constructed at the system equilibrium point, the method combines the inverse shift transform and the Arnoldi iteration algorithm to efficiently extract the system's theoretical modal information and generate candidate modes and vibration modes with physical interpretability. By matching the measurement results with the candidate results, the excited theoretical modes can be accurately identified in large-scale AC / DC hybrid systems with dense modal eigenvalues, effectively improving the accuracy and interpretability of the identification. This method not only overcomes the computational complexity and poor real-time performance of traditional modeling methods, but also addresses the lack of physical information in data-driven methods. It enables online, rapid, and accurate identification of key oscillation modes, providing reliable technical support for dynamic monitoring and oscillation control of power systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0043] Figure 1 A flow chart of a method for identifying low-frequency oscillation patterns in a power system according to an embodiment of the present application;

[0044] Figure 2 A flow chart of a hybrid algorithm based on pattern matching provided in an embodiment of the present application;

[0045] Figure 3 A block diagram of a four-machine, two-area system provided in an embodiment of the present application;

[0046] Figure 4 The feature analysis and multi-signal Prony algorithm pattern analysis results provided in the embodiments of this application;

[0047] Figure 5 Comparison of the multi-signal Prony analysis mode shape and the characteristic analysis mode shape provided in the embodiments of this application;

[0048] Figure 6 A schematic diagram of the structure of a low-frequency oscillation pattern recognition device for a power system according to an embodiment of the present application;

[0049] Figure 7 A schematic diagram of the internal structure of a computer device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0050] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0051] This application provides a method for identifying low-frequency oscillation patterns in power systems. The following embodiments are described using the method applied to a computer device as an example. It is understood that the computer device can be any device with data processing capabilities, including but not limited to a single server, a server cluster, a personal laptop computer, a desktop computer, etc. Figure 1 As shown, the method may include the following steps:

[0052] S101: When low-frequency oscillation is detected in the power system, a multi-signal prony analysis is performed on the real-time oscillation signal to obtain a measurement result of the low-frequency oscillation, where the measurement result includes a measurement mode and a measurement vibration shape.

[0053] Low-frequency oscillations refer to oscillations in power systems with frequencies below 1 Hz. These oscillations are typically caused by energy exchange between generators, loads, and their control systems, and are characterized by long duration and wide impact. Real-time oscillation signals refer to time-series data collected by wide-area measurement systems (WAMS) that reflect the current dynamic operating state of the power system, such as voltage amplitude, frequency, and phase angle. Multi-signal Prony analysis is a signal processing algorithm based on time series data that extracts oscillation mode parameters, including frequency, damping ratio, and mode shape, from oscillation signals at multiple measurement points. Measurement results are structured output data generated by multi-signal Prony analysis, which characterize the current oscillation behavior. A measurement mode is a representative oscillation mode extracted from the measurement results, containing characteristic parameters such as oscillation frequency and damping ratio. A measurement mode shape refers to the amplitude and phase information of the signal oscillation at each measurement node within the corresponding measurement mode, reflecting the propagation path and impact range of the oscillation in the power system.

[0054] The computer must first continuously receive real-time dynamic data from the wide-area measurement system. Connected to multiple synchronized measurement devices via an interface module, it continuously collects key electrical parameters such as voltage phasors, frequency, and power. It then buffers, time-calibrates, and pre-processes the collected data to ensure the timeliness and consistency of the data required for analysis.

[0055] After completing real-time data acquisition, the computer activates the multi-signal Prony analysis module to jointly model the synchronized data streams from multiple measurement points. During this analysis, the computer constructs a least-squares estimation model for each measurement signal, identifying multiple exponential signal components in the data. It then extracts the oscillation frequency, damping ratio, amplitude, and initial phase angle of each component, thereby constructing multiple current measurement modes for the power system. Multi-signal Prony analysis outperforms single-signal analysis, improving identification robustness and modal separation accuracy. It is particularly suitable for complex scenarios with strong inter-node coupling and significant electrical interference.

[0056] The computer then classifies the extracted measurement patterns and identifies the propagation path of the mode within the power grid by calculating the amplitude distribution and phase angle differences of the vibration modes. For example, if a mode exhibits anti-phase characteristics at multiple nodes and its amplitude is concentrated in a certain area, it can be preliminarily determined to be an inter-regional vibration mode.

[0057] In a specific embodiment, the identification process can be executed by a processing unit embedded in a dispatching master station, a smart power station controller, or an edge computing terminal. The calculation process can be run periodically or immediately after detecting abnormal frequency fluctuations, sudden changes in spectrum characteristics, or power event triggering, to ensure that key patterns can be identified in the early stages of grid oscillation.

[0058] By performing multi-signal Prony analysis on real-time oscillation signals, the frequency, damping ratio, and mode shape of system oscillations can be rapidly extracted without relying on physical models, enabling accurate perception and quantitative modeling of actual oscillation behavior. This approach not only improves the speed and robustness of oscillation pattern recognition, overcoming the difficulties of large-scale power grid modeling and the high-dimensional computational bottleneck, but also captures key modal features at an early stage, effectively supporting matching with theoretical modes, thereby improving the accuracy and interpretability of modal identification.

[0059] S102: Obtain a state matrix according to a mathematical model constructed when the power system operates at a balance point.

[0060] The equilibrium point of a power system refers to a stable operating state in which the output of each generator matches the load power, the system frequency is stable, and the voltage distribution is reasonable. A mathematical model is a system dynamics model that expresses the relationships between various components in the power system in the form of differential or algebraic equations. It is typically linearized at the equilibrium point. The state matrix is ​​one of the core parameter matrices in a linearized power system model. It characterizes the dynamic coupling relationship between the system's state variables, and its eigenvalues ​​can be used to analyze system stability and oscillation characteristics.

[0061] First, the computer equipment needs to collect network topology data, generator model parameters (such as rotational inertia, excitation system parameters, etc.), load modeling methods, and power flow distribution information at static operating points when the power system is operating under stable conditions. This information is usually provided in real time by the power grid dispatching center, EMS (energy management system) or SCADA system and input into the computer equipment in the form of structured data.

[0062] After acquiring the input data, the computer activates the model building module to mathematically model the power system. This modeling process involves establishing a set of nonlinear differential-algebraic equations to describe the relationships between generators, voltage control, load dynamics, and network coupling. Jacobian linearization of this nonlinear system near the equilibrium point is then performed based on the power flow solution. This linearization is automatically performed in the computational module through numerical or analytical derivation, generating a set of state-space equations describing the system state evolution, the central component of which is the state matrix.

[0063] Furthermore, the state matrix solution process can be integrated into a modular software framework that supports adjustable parameters and flexible switching of model types. For example, the state matrix generation module can support different types of generator models, such as second-order, fourth-order, and sixth-order models, and different load modeling schemes, such as fixed-resistance, ZIP, or dynamic load models. After the calculation is completed, the state matrix is ​​saved, formatted, and post-processed, such as calculating eigenvalues, participation factors, and modal vibration shapes, providing analytical basis for subsequent modal identification or oscillation mode matching.

[0064] By constructing a mathematical model at the equilibrium point of the power system and deriving the state matrix based on it, the computer equipment can characterize the system's dynamic characteristics with a simplified linear structure, significantly reducing the complexity of the model solution while retaining the ability to express the system's key modal information. This execution method not only enables the accurate implementation of subsequent modal analysis, damping assessment, and oscillation identification, but also provides a quantitative basis for control parameter tuning and system structure optimization, improving the automation level, response speed, and computational efficiency of power grid operation analysis. This enables efficient modeling and intelligent assessment of the dynamic stability of the power system, enhancing the power system's ability to perceive and respond to abnormal disturbances.

[0065] S103: Preprocessing the state matrix after being disturbed by the low-frequency oscillation by using a displacement-inverse transformation, and solving the candidate results of the low-frequency oscillation by combining the Arnoldi iteration algorithm, the candidate results including the candidate mode and its candidate vibration shape.

[0066] Low-frequency oscillation disturbances refer to dynamic oscillations in the 0.1-2 Hz range caused by small disturbances in the power system. The inverse shift transform is a mathematical transformation method that shifts the target eigenvalue region toward the center of the spectrum to accelerate eigenvalue extraction. The Arnoldi iteration algorithm is a subspace projection algorithm suitable for sparse matrices that can effectively extract some eigenvalues ​​and eigenvectors of the matrix for the extraction of specific modes. Candidate results refer to the oscillation modes and their corresponding vibration shapes initially identified by the algorithm, which can then be further compared and verified with the measurement results.

[0067] After a low-frequency oscillation event occurs in the power system, computing equipment can extract eigenmodes from the state matrix under the oscillation disturbance to assist in determining the system oscillation mode. First, the stability analysis module or oscillation identification module acquires the post-perturbation system state matrix in real time. This matrix can be derived from an online model update system, historical simulation data, or a fitting of field measurement data. Since the goal is to identify low-frequency eigenmodes, this matrix requires preprocessing to focus on the frequency domain.

[0068] Subsequently, the computer device calls the shift-inverse transform processing module to perform a transform operation on the state matrix. In this transform step, a target frequency range is preset, such as 0.2~1Hz, and a shift factor σ is constructed so that the state matrix is ​​in the form Perform matrix transformation. This process makes low-frequency eigenvalues ​​more prominent in the spectrum, facilitating focused extraction by subsequent algorithms. During preprocessing, the computer must perform matrix inversion or solve a system of linear equations, which can be achieved through LU decomposition or a sparse solver. The transformed matrix is ​​then cached in memory for subsequent iterations.

[0069] After preprocessing is completed, the computer device starts the Arnoldi iterative solution module, which uses the Krylov subspace method to iteratively extract a specific number of eigenpairs, namely eigenvalues ​​and eigenvectors, from the transformed state matrix to obtain candidate oscillation modes in the low-frequency range. To improve accuracy and computational efficiency, the module can set the number of iterations, restart mechanism and convergence threshold, and automatically evaluate the degree of match between the current eigenpair and the target frequency in each round of iteration. Ultimately, the output candidate results include a set of complex eigenvalues, namely candidate modes, and their corresponding eigenvectors, namely candidate vibration shapes. These results can be used for subsequent comparison with measured modes to identify whether there is an actual risk of low-frequency oscillation.

[0070] By preprocessing the state matrix after low-frequency oscillation disturbances using a shift-inverse transform, the eigenvalue spectrum structure of the target frequency region can be transformed into the main feature region, significantly improving the Arnoldi iteration algorithm's ability to focus on and extract the target low-frequency modes. Combined with the Arnoldi iteration algorithm for solution, a small number of key low-frequency candidate modes and their vibration shapes can be efficiently extracted from the large-scale, sparse state matrix. This approach not only improves the accuracy and computational performance of modal extraction, but also enhances the early warning capability and response speed of system oscillation risks, avoids the resource waste associated with full-spectrum calculations, and facilitates rapid and intelligent identification of low-frequency dynamic behavior in power systems.

[0071] S104: Match the measurement result with the candidate result, and determine the low-frequency oscillation mode of the power system according to the matching result.

[0072] A matching result is a correspondence between the measured result and the candidate result based on similarity in frequency, damping, mode shape, and other dimensions. A low-frequency oscillation pattern is a confirmed, real low-frequency oscillation phenomenon in the system, including its frequency, damping characteristics, and mode shape structure. It serves as an important basis for power system stability analysis and control decisions.

[0073] During power system operation, the effective identification of low-frequency oscillations is crucial for ensuring the system's dynamic stability. Computer equipment simultaneously acquires two key data sources after an oscillation signal occurs. First, it performs real-time Prony analysis on dynamic signals such as voltage and current collected on-site to extract the observed oscillation mode and generate measurement results. Second, it uses the Arnoldi iteration method based on the perturbation state matrix to extract theoretical candidate oscillation modes and generate candidate results. The two types of data are highly similar in structure, providing a foundation for subsequent comparison and confirmation.

[0074] To effectively match the two types of data, the computer equipment is equipped with a modal matching analysis module. This module takes the measurement results and candidate results as input sets and performs item-by-item comparison by setting multiple similarity indicators. For example, a frequency difference threshold matching method can be used to screen candidate modes with a frequency error within 0.01Hz. This is then combined with damping ratio consistency and mode shape similarity to perform gradual fine-sieving, such as cosine similarity or principal component angle, to ultimately obtain a set of highly matched results. The matching process can use a weighted scoring mechanism, dynamically adjusting the weights based on the credibility of different indicators to ensure that the matching results are statistically and physically consistent.

[0075] In practice, all candidate modalities are sequentially traversed for each measurement modality, sorted by matching score, and the highest-scoring candidate is selected as the corresponding match. To avoid false matches, a minimum score threshold can be set; measurement modalities that do not meet the threshold are considered invalid or new. Furthermore, to support large-scale online processing, the matching process can be accelerated through matrix operations or optimized through parallel processing.

[0076] Ultimately, the matching analysis module outputs a set of verified matching pairs. Based on these matching relationships, it extracts the corresponding actual oscillation patterns, forming a set of low-frequency oscillation patterns currently present in the power system. This set of patterns can be further provided to the system control module for dynamic stability analysis, generator damping adjustment recommendations, or event alarm triggering.

[0077] By matching measurement results with candidate results, the computer equipment can effectively integrate the dual information sources of the measured signal and the theoretical model, improving the accuracy of low-frequency oscillation identification. This comparison method can achieve robustness against interference factors and reduce the error rate. Furthermore, determining the low-frequency oscillation mode based on the matching results not only ensures that the identified mode actually exists in the current system, but also helps to eliminate false modes with no practical impact in the mathematical model, achieving accurate analysis and response to power system oscillation risks. Through this execution method, oscillation modes can be quickly and reliably identified, thereby improving the safety and intelligence level of power grid operation.

[0078] The above-described embodiment combines the advantages of real-time measurement and physical modeling. When a low-frequency oscillation in the power system is detected, this method first extracts the measured mode and mode shape of the oscillation signal through multi-signal Prony analysis, enabling rapid perception of real-time oscillation behavior. Subsequently, based on a mathematical model constructed at the system equilibrium point, the method combines the inverse shift transform and the Arnoldi iteration algorithm to efficiently extract theoretical modal information about the system, generating candidate modes and mode shapes with physical interpretability. By matching the measured results with the candidate results, the excited theoretical modes can be accurately identified in large-scale AC / DC hybrid systems with dense modal eigenvalues, effectively improving identification accuracy and interpretability. This method not only overcomes the computational complexity and poor real-time performance of traditional modeling methods, but also addresses the lack of physical information in data-driven approaches. It enables online, rapid, and accurate identification of key oscillation modes, providing reliable technical support for dynamic monitoring and oscillation control of power systems.

[0079] In one embodiment, the step of performing multi-signal prony analysis on the real-time oscillation signal to obtain a measurement result of the low-frequency oscillation includes:

[0080] According to the real-time oscillation signal, a matrix equation is constructed, where the matrix equation is used to represent the real-time oscillation signal as a linear combination of different oscillation modes;

[0081] Constructing a polynomial characteristic equation according to the matrix equation, solving the characteristic roots of the polynomial characteristic equation to obtain an estimated mode of low-frequency oscillation, and solving the matrix equation to obtain an amplitude matrix;

[0082] A linear regression model is constructed according to the estimated pattern and amplitude matrix, and the stepwise regression method is applied to the linear regression model to obtain the measurement results of low-frequency oscillation.

[0083] The matrix equation is a mathematical form that expands the dynamic signal across multiple hypothetical oscillation modes, reflecting that the original signal can be represented as a linear combination of multiple oscillation modes. The polynomial characteristic equation converts the modal information implicit in the matrix equation into a standard polynomial form to solve for the characteristic roots, thereby identifying the system's oscillation frequency and damping characteristics. The characteristic roots represent the frequency and attenuation characteristics of low-frequency oscillation modes and are an important basis for determining system stability. The estimated mode refers to the frequency and damping characteristics of each low-frequency oscillation mode obtained by modeling the real-time oscillation signal and solving the characteristic equation. The amplitude matrix is ​​a coefficient matrix that represents the intensity and phase of each oscillation mode in the actual measured signal. The linear regression model is a mathematical model used to fit the relationship between the actual signal and the theoretical oscillation mode. The stepwise regression method is a regression modeling technique that selects influencing factors one by one, automatically screening out the most significant oscillation modes.

[0084] To effectively extract low-frequency oscillation information from power systems, computing equipment must first construct a structured representation of the acquired real-time oscillation signal. This system constructs a matrix equation to convert the continuous time series signal into a weighted linear combination of multiple hypothetical oscillation modes at different times. This matrix equation, typically constructed based on the Prony method or subspace identification principles, accurately reflects the relationship between the system's modal response and the input signal.

[0085] After obtaining the matrix equation, it is further converted into a polynomial characteristic equation. By constructing a determinant expression related to the matrix, the characteristic polynomial is formed. Numerical calculation methods such as QR decomposition or eigenvalue decomposition are used to solve all the characteristic roots of the characteristic equation. Each characteristic root corresponds to a possible low-frequency oscillation mode, including its frequency and damping ratio. This process lays the foundation for identifying potential unstable modes of the system.

[0086] Next, with the known eigenvalues, we back-substitute the matrix equation and solve for the unknown coefficients, yielding the corresponding amplitude matrix. Each column in the amplitude matrix represents the contribution of a different mode to the original signal and its relative phase, quantifying the actual contribution of each mode to the system's oscillations.

[0087] To further enhance the reliability of the results, a computer system constructs a linear regression model based on the estimated modal information and amplitude matrix to analyze signal reconstruction errors. In this model, the independent variable is the characteristic function of the estimated mode, the dependent variable is the actual sampled signal sequence, and the fitting error is used to evaluate the model's accuracy. Based on this, a stepwise regression method is used to automatically select the set of modes that most significantly improve the fitting accuracy from the numerous estimated modes, eliminating redundant or misclassified modes to ensure that the final output modes have physical interpretability and statistical significance.

[0088] Ultimately, the output is a set of authentic and reliable low-frequency oscillation modal characteristics. As measurement results, it not only includes the oscillation frequency and damping ratio, but also further provides the relative amplitude and vibration shape information of each mode, which can be used for stability adjustment of the control system and formulation of oscillation warning strategies.

[0089] In one example, in power system signal analysis, after the system is linearized, it can be described using a linear state-space model. In this case, the general solution of the system can be expressed as the sum of a set of decaying sinusoidal signals:

[0090] For the case of m groups of signals and N sampling points, the general solution of the system is written as:

[0091]

[0092] These relationships can be further expressed in matrix form:

[0093]

[0094] To simplify the representation, it is further simplified as a matrix equation:

[0095]

[0096] Among them, the matrix Z stores the exponential terms of different frequencies, C contains the amplitude coefficient, and Y records the observation values ​​of each sampling point.

[0097] In this embodiment, by constructing a matrix equation and solving its characteristic roots, theoretical modeling of the potential oscillation modes in the system can be achieved, providing a solid foundation for subsequent oscillation identification. Solving the amplitude matrix can further quantify the modal influence and enhance the explanatory power of the identification results. The introduction of linear regression modeling and stepwise regression algorithms can eliminate redundant noise terms from the numerous estimated modes, retaining only the most representative modal information, and effectively improving the model's fitting accuracy and anti-interference ability. Therefore, through this step-by-step processing method, computer equipment can achieve high-precision extraction, robust modeling, and dynamic screening of low-frequency oscillation modes in the power system without relying on prior model parameters, thereby improving the reliability, timeliness, and engineering application value of oscillation detection results.

[0098] In one embodiment, the step of constructing a polynomial characteristic equation according to the matrix equation includes:

[0099] The expression of the polynomial characteristic equation is:

[0100]

[0101] in, The variable representing the characteristic root, represents the order of the multi-order form, Represents the coefficients of the polynomial, constructed by the matrix equation Obtained by multiplying the order phasors.

[0102] In the signal analysis of power systems, the key features of the signal can be effectively extracted by constructing a polynomial characteristic equation. This equation is constructed based on the product relationship between the matrix equation and the phasor. This directly corresponds to the signal's decaying sinusoidal pattern, reflecting the signal's frequency and attenuation characteristics. This allows complex signals to be decomposed into a superposition of multiple simple harmonics, clearly demonstrating the signal's inherent structure and dynamic characteristics while reducing noise interference and improving the accuracy and reliability of signal analysis.

[0103] In one example, in power system signal analysis, for the constructed phasor , the following relationship can be derived:

[0104]

[0105] For any set of measured values ​​in the m signal , the following relationship exists:

[0106]

[0107] in, , , .

[0108] Combining the equations corresponding to all m groups of data in sequence, we can get:

[0109]

[0110] in, , .

[0111] According to the principle of Prony analysis, the elements in the matrix Z are the roots of the following nth-order polynomial:

[0112]

[0113] To reduce the influence of noise and signal offset, the number of equations is usually chosen to be By solving the equations by the least squares method, we can obtain the polynomial coefficient vector θ. Then, solving the polynomial can obtain the pattern Finally, the least squares method is used again to solve the original equations to obtain the amplitude matrix C. This process realizes the effective analysis and feature extraction of power system signals.

[0114] In one embodiment, the step of constructing a linear regression model based on the estimated pattern and the amplitude matrix includes:

[0115] Compute explanatory terms based on the estimated mode and magnitude matrices;

[0116] After normalizing the explanatory terms, a linear regression model is constructed in combination with the real-time oscillation signal.

[0117] The explanatory terms are a set of fitted variables that can be used to explain changes in the original signal, formed by combining the estimated pattern with the amplitude matrix. They are the independent variables in regression modeling. Normalization is the process of converting explanatory terms of different dimensions or scales to a uniform magnitude range to eliminate the interference of scale differences between variables on modeling accuracy.

[0118] First, based on the existing estimated modes and amplitude matrix, the theoretical contribution of each mode to the original oscillation signal is calculated, generating a set of explanatory terms for fitting. Specifically, the estimated modes can be constructed as complex exponential or sinusoidal functions, and then multiplied by the corresponding elements in the amplitude matrix to generate multiple sequences of modal component functions. These components together form the set of explanatory terms.

[0119] To improve the stability and convergence of subsequent modeling, the generated explanatory item set is normalized. Standard deviation normalization or minimum and maximum value normalization can be used to ensure that all explanatory items are in the same numerical range, such as [0, 1], or with a mean of 0 and a standard deviation of 1. This prevents certain modes from gaining undue dominance in the regression process due to excessively large values. This normalization process can be performed in parallel using batch matrix operations to improve processing efficiency.

[0120] After normalization, these processed explanatory terms are used as independent variables, along with the real-time oscillation signal obtained from the actual power system as the dependent variable, to construct a linear regression model. The regression model can be solved using the least squares method, and regularization techniques such as ridge regression can also be introduced to improve robustness in the presence of noise. This model will be used to fit the component structure of the signal, thereby identifying the most likely low-frequency oscillation modes in the actual system.

[0121] This regression modeling can also be expanded to variable selection algorithms such as stepwise regression or LASSO, which automatically selects a set of modes that best fit the system signal from the normalized explanatory terms, thereby eliminating false detection interference and further improving the accuracy and physical rationality of the results.

[0122] In one example, when estimating a pattern from measurement data and magnitude matrix Next, we use the stepwise regression method for each set of data to select the measurement patterns contained in the real-time oscillation data. The specific steps are as follows:

[0123] For each real mode , and the calculation formula of its explanation term is:

[0124]

[0125] For each pair of complex modes corresponding to the mode components , and the calculation formula of its explanation term is:

[0126]

[0127] The real and complex mode interpretation terms are then normalized so that each interpretation term is consistent with the measured signal data. Have the same standard deviation:

[0128]

[0129] Among them, the column vector is the mode component The corresponding explanation item is normalized.

[0130] Next, construct the following linear regression model:

[0131]

[0132] in, is a real number that needs to be estimated using the least squares method, and is the noise vector.

[0133] Finally, the regression model was subjected to stepwise regression, using two-sided Test, from each explanatory term not in the model The most significant explanatory terms are selected and added to the model, and the least significant explanatory terms are removed from the model. This step is repeated until no explanatory terms need to be added or removed from the model.

[0134] By repeating the above steps for each set of data, the measurement modes contained in the signal and their corresponding vibration shapes can be obtained. This process helps to accurately identify and extract key dynamic features in the signal, providing an important basis for real-time monitoring and fault diagnosis of power systems.

[0135] In this embodiment, calculating the explanatory term is the prerequisite for establishing a mathematical mapping between the estimated modal characteristics and the actual signal, which helps to convert the theoretical mode into a quantifiable model input; normalization processing can significantly eliminate the differences in the numerical scales of different modal explanatory terms, improving the stability, numerical conditions, and convergence speed of linear regression modeling; constructing a linear regression model establishes a direct relationship between the normalized explanatory term and the actual oscillation signal, which can effectively identify the most matching modal characteristics. Therefore, by sequentially performing the operations of calculating the explanatory term, normalization, and regression modeling, not only can the accuracy and noise resistance of modal identification be improved, but the generalization ability of the model and the engineering interpretability of the results can also be enhanced, thus having significant practical value in the actual operation monitoring and oscillation early warning of power systems.

[0136] In one embodiment, the step of obtaining a state matrix based on a mathematical model constructed when the power system operates at a balance point includes:

[0137] After obtaining the dynamic network and network parameters, dynamic component model and model parameters of the power system, linearization is performed at the equilibrium point to obtain a mathematical model, and the mathematical model is simplified to obtain a state matrix.

[0138] The dynamic network refers to the time-varying topology and node connectivity of the power system, reflecting the dynamic interconnectedness of generators, loads, transformers, and other equipment. Network parameters are the electrical properties of each line, reactor, and other power component in the dynamic network, such as impedance, conductance, and susceptance. The dynamic component model is a mathematical description of the operating behavior of each dynamic component in the system, formed by differential equation modeling. Model parameters refer to the specific numerical settings in these dynamic component models, such as inertia constant, damping coefficient, and time constant.

[0139] First, it's necessary to obtain the dynamic network structure and parameters, as well as the dynamic component models and corresponding model parameters. In practical applications, this can be accomplished by accessing the power grid SCADA system, EMS system, or stability analysis database to automatically collect information on the current system topology, device connectivity, and electrical component parameters. Furthermore, by accessing the power grid device model library, the computer can match the dynamic mathematical models of various components and load their configuration parameters, such as the excitation system time constant and synchronous reactance.

[0140] After acquiring the aforementioned basic data, the computer linearizes the system at the equilibrium point based on the system's current operating conditions. This equilibrium point is typically determined based on the steady-state solution from power flow calculations. The computer then performs a Taylor expansion on the nonlinear differential-algebraic equations, ignoring higher-order terms, to construct a linearized mathematical model. This process can involve automatically differentiating the equations using a symbolic computation module, or by constructing the Jacobian matrix through numerical perturbation methods to achieve linearization.

[0141] After the linearized mathematical model is formed, the computer further simplifies the model structure. Specifically, this can be done by employing time-domain order reduction methods, modal preservation techniques, or ignoring state variables with minimal impact on system dynamics, thereby reducing the model dimensionality while preserving the system's key dynamic characteristics. This simplification is intended to improve the efficiency of subsequent processing, particularly in large-scale power grids, where the simplified model can significantly reduce the computational resources required for modal analysis and oscillation identification.

[0142] Finally, based on the simplified linear differential equations, a state-space expression is generated and the state matrix is ​​extracted. This state matrix, as the core representation of the system's dynamic behavior, can be used in subsequent functional modules such as eigenvalue calculation, modal analysis, and oscillation source location. Each element of the state matrix is ​​determined by the dynamic model parameters and the network structure, ensuring physical interpretability and traceability.

[0143] In one example, by By linearizing around , we can build a linear state space model of the system. The specific linearization process is as follows:

[0144] The nonlinear equations of the power system are transformed into equilibrium points. Performing Taylor expansion at , and ignoring high-order small terms, we get the linearized form of the system:

[0145]

[0146] Among them, the matrix 、 、 and They represent the Jacobian matrix of the system state equation, which is defined as:

[0147] , , , .

[0148] In order to study the influence of state variables on the system, the above linearized equations are simplified to obtain the state matrix of the system: :

[0149]

[0150] This process linearizes the power system and converts the complex nonlinear system into a linear state space model, which facilitates subsequent dynamic analysis and controller design. It describes the dynamic relationship between system state variables and is an important basis for analyzing system stability and designing control strategies.

[0151] In this embodiment, the dynamic network, network parameters, and component model parameters of the power system are acquired through computer equipment, enabling accurate modeling of the current system operating state. Linearization at the equilibrium point simplifies the original complex nonlinear system into an easily manageable linear model, thereby reducing computational complexity. Simplifying the mathematical model reduces the amount of computation while preserving the system's primary dynamic behavior, improving processing efficiency. Generating a state matrix provides a unified, standardized data structure for subsequent oscillation modal analysis, stability assessment, and other tasks. Consequently, this approach effectively improves system modeling accuracy, accelerates subsequent analysis, and enhances the model's scalability and engineering practicality, ultimately enabling rapid identification and precise location of power system oscillation behavior.

[0152] In one embodiment, the step of preprocessing the state matrix after being disturbed by the low-frequency oscillation by using the shift-inverse transform includes:

[0153] Performing LU decomposition on the state matrix after being disturbed by the low-frequency oscillation to obtain a first upper triangular matrix and a first lower triangular matrix, and calculating a first intermediate variable based on the first upper triangular matrix and the first lower triangular matrix;

[0154] Perform LU decomposition on the first intermediate variable to obtain a second upper triangular matrix and a second lower triangular matrix, and calculate the second intermediate variable based on the first upper triangular matrix and the first lower triangular matrix;

[0155] An auxiliary vector is calculated according to the second upper triangular matrix, the second lower triangular matrix and the second intermediate variable, and a preprocessed state matrix is ​​obtained according to the first upper triangular matrix, the first lower triangular matrix and the auxiliary vector.

[0156] LU decomposition decomposes a square matrix into the product of a lower triangular matrix (L) and an upper triangular matrix (U) to simplify linear algebra operations. The first upper triangular matrix and the first lower triangular matrix represent the U and L matrices, respectively, obtained by LU decomposition of the state matrix after the first shift. The first intermediate variable is a transitional vector or matrix calculated based on the results of the first LU decomposition and participates in subsequent iterative operations. The second upper triangular matrix and the second lower triangular matrix are the results of further LU decomposition of the first intermediate variable. The second intermediate variable is the result of further intermediate calculations obtained by combining the second set of upper and lower triangular matrices. The auxiliary vector is a numerical quantity used to construct the final preprocessing matrix based on the second intermediate variable. The preprocessed state matrix is ​​a numerically preprocessed and optimized version of the original state matrix, combining all the above decomposition and calculation results.

[0157] To improve the efficiency of solving the state matrix during the low-frequency oscillation analysis of the power system, the computer device first performs a displacement process on the state matrix after being disturbed by the low-frequency oscillation. Specifically, this operation can add a certain displacement factor to the original state matrix to enhance numerical stability and shift the matrix eigenvalues ​​to the target area, so that subsequent calculations are more stable. Next, the computer device performs an LU decomposition operation on the displaced state matrix to obtain the first upper triangular matrix and the first lower triangular matrix. This process decomposes the large-scale sparse state matrix into upper and lower triangular forms by calling the matrix calculation module, which facilitates the subsequent solution of the linear equation system. It is particularly suitable for scenarios where frequent matrix inversion calls are required in frequency domain feature analysis. Subsequently, the above-mentioned triangular matrix is ​​used to calculate the first intermediate variable. This operation can be completed through forward substitution and back substitution operations. This intermediate variable is usually a vector or a low-dimensional matrix, which is used to characterize the propagation behavior of the disturbance under the current system.

[0158] In order to further extract high-order interference information, the computer device continues to perform a second LU decomposition on the first intermediate variable to obtain a second upper triangular matrix and a second lower triangular matrix, and calculates the second intermediate variable based on this. This process is essentially a recursive numerical decomposition operation on the intermediate variable. This hierarchical analysis is completed through nested decomposition modules, thereby improving the step-by-step approximation accuracy of the matrix solution. Based on the result of the second decomposition, the auxiliary vector is calculated. This vector can be regarded as the result of the disturbance response feature extraction after two layers of LU transformation, representing the deep response characteristics of the system under the influence of oscillatory disturbances. Finally, combining the auxiliary vector with the first set of LU decomposition results, the computer device constructs and outputs the preprocessed state matrix. This matrix can be directly used for tasks such as modal identification, frequency feature extraction, and damping factor analysis, and has higher numerical stability and structural sparsity.

[0159] In one example, a preprocessing method based on matrix decomposition and linear solution is used to efficiently calculate candidate modes and their corresponding vibration shapes. The specific process is as follows:

[0160] First, by solving the linear system, the intermediate variables are calculated ,Right now:

[0161]

[0162] in, is the eigenvalue, is the system state matrix, is the input vector.

[0163] Next, the matrix Perform LU decomposition and get:

[0164]

[0165] At the same time, the matrix is ​​calculated The update form:

[0166]

[0167] Then, the updated matrix Perform LU decomposition:

[0168]

[0169] and calculate the intermediate variables :

[0170]

[0171] Next, solve the linear system , and finally get:

[0172]

[0173] The above preprocessing method effectively simplifies the subsequent eigenvalue calculation process. Subsequently, the Arnoldi iteration algorithm is used to solve for the corresponding candidate modes and further obtain their corresponding vibration shapes. This process not only improves computational efficiency but also enhances the numerical stability of the eigenvalue problem.

[0174] In this embodiment, shifting the state matrix helps change its eigenvalue distribution, making subsequent numerical processing more centralized and controllable. Through layer-by-layer LU decomposition and iterative calculation of intermediate variables, the computer equipment can realize the conversion of high-dimensional sparse matrices into stable and solvable structures, thereby reducing the computational complexity in processes such as matrix inversion and modal calculation. The resulting preprocessed state matrix has good numerical conditions, which helps to improve the accuracy and stability of subsequent modal analysis or fault location algorithms. Therefore, it can significantly improve the reliability and computational efficiency of system oscillation modeling and response analysis, and is an indispensable basic step in realizing dynamic diagnosis of complex power systems.

[0175] In one embodiment, the step of matching the measurement result with the candidate result and determining the low frequency oscillation mode of the power system according to the matching result includes:

[0176] Construct a fitting factor phasor, and combine the fitting factor phasor with the candidate vibration shape to establish a matching relationship with the measured vibration shape;

[0177] Solve the matching relationship to obtain the best fitting factor, and match the best fitting factor with the candidate matrix to obtain the matching result;

[0178] The error between the matching result and the measurement matrix is ​​calculated. When the error is less than a preset threshold, the candidate mode corresponding to the candidate vibration shape is taken as the low-frequency oscillation mode of the power system.

[0179] The fitting factor phasor is a set of complex weighting factors used to adjust or scale the candidate vibration modes to be closest to the measured vibration modes. It is usually expressed as a complex vector and is used to minimize the difference between the candidate vibration modes and the actual measurement results. The matching relationship refers to the mathematical fitting model established between the measured vibration modes and the weighted candidate vibration modes, which is generally expressed as a least squares optimization problem. The best fitting factor is the optimal complex coefficient vector solved under this matching relationship to minimize the error. The matching result is an estimate of the measured vibration mode after applying the best fitting factor to the candidate matrix. The error is the difference between the matching result and the actual measured vibration mode. The preset threshold is a pre-set error tolerance limit.

[0180] First, the fitting factor phasor must be constructed. Specifically, a set of candidate mode shape matrices and a vector of measured mode shapes are received. By invoking the complex linear algebra computation module, the required fitting factor phasor is constructed as a complex vector variable using the least squares criterion. This factor, when applied to the candidate mode shapes, closely approximates the measured mode shapes, thus forming a matching model.

[0181] After constructing the matching model, the computer performs a matching relationship solution operation. A solver, such as one based on QR decomposition or pseudo-inverse operations, is called to solve the constructed linear fitting equations to obtain the best fit factor. This factor theoretically represents a set of complex coefficients that is optimized to minimize the error between the measured mode shape and the candidate linear combination mode shape. Subsequently, the candidate matrix is ​​matched based on this best fit factor, performing a matrix multiplication operation to obtain a matching result that is closest to the measured mode shape.

[0182] After obtaining the matching results, the error analysis phase begins. The final error value is obtained by subtracting the matching result from the measured mode shape and calculating the norm. This error value is then compared with a pre-set error threshold. If the error is less than the threshold, it indicates that the candidate mode shape can accurately reconstruct the measured mode shape after fitting, and the candidate mode corresponding to the candidate mode shape is confirmed to be an actual low-frequency oscillation mode in the system.

[0183] In one example, suppose that candidate modes, and their corresponding vibration shapes form a matrix The vibration mode obtained by multi-signal Prony analysis is used Indicates that the fitting factors form a vector The relationship between the three is as follows:

[0184]

[0185] The least squares method is used to solve the above equation and the fitting factor is obtained. . The matching results are:

[0186]

[0187] Define the error as If the error is less than a given threshold , the pattern matching is considered successful. This process effectively evaluates the matching degree between the candidate pattern and the actual vibration shape through the least squares method and error analysis, thus ensuring the accuracy and reliability of pattern recognition.

[0188] In this embodiment, by constructing a fitting factor phasor and combining it with the candidate vibration mode, the measured vibration mode can be accurately reconstructed, thereby establishing an effective mapping relationship between the candidate and the actual vibration mode. Furthermore, by solving this matching relationship to obtain the best fitting factor and matching it with the candidate matrix, the oscillation form closest to the actual measurement can be selected from multiple candidates, effectively avoiding ambiguity and misjudgment in vibration mode identification. Furthermore, by calculating the error and comparing it with the preset threshold, the credibility of the identification result can be verified in a quantitative manner, thereby achieving high-reliability and high-precision low-frequency oscillation mode identification. Therefore, the execution of this series of actions not only improves the degree of automation of the calculation, but also ensures the accuracy, robustness and engineering availability of the power system modal identification results.

[0189] To facilitate understanding of the solutions of this application, specific examples are provided below for illustration.

[0190] like Figure 2 As shown, the system begins with an initial modal analysis to identify weakly damped modes within the system and analyze their strongly correlated state variables to determine the observed objects. Subsequently, when the system oscillates, the oscillation waveforms of these observed objects are measured. Next, a determination is made as to whether low-frequency oscillations are occurring. If not, the oscillation is considered to have disappeared, and the system has returned to steady state. If low-frequency oscillations occur, Prony analysis using multi-signal processing is performed to extract the measured oscillation mode and its mode shape. Theoretical modes are calculated using the mathematical model of the power system and a characteristic analysis algorithm, and candidate modes that meet the requirements are selected. The success of the mode matching is then checked. If unsuccessful, the mode matching is repeated. If successful, mode shape matching is further performed, and the excited mode is determined by the contribution coefficient, ultimately completing the entire process.

[0191] In order to verify the accuracy and effectiveness of the low-frequency oscillation pattern recognition method proposed in this paper, it was verified on a classic four-machine two-area system. The node topology of the four-machine two-area system is shown in the figure below. Figure 3 As shown in the figure, a weak tie line connects two regions of roughly similar size and structure to form a synchronous grid. Each region is equipped with two similar generator sets, whose rated capacities and transient and steady-state parameters are consistent with commonly used data. Assuming the rated voltage and capacity are baseline values, the per-unit generator parameters are shown in the table.

[0192]

[0193] In order to ensure that the length of the sampling window is greater than the period of the low-frequency oscillation, and when the decay oscillation just occurs, too many high-damping modes are activated, and these modes are not of concern during analysis, the measurement signal is analyzed 20 cycles after the decay oscillation occurs. The results are similar to the results of the characteristic analysis mode as shown in Figure 4 As shown. Figure 4It can be seen that there is only one candidate mode near the multi-signal Prony analysis result, so the corresponding vibration mode is compared with the corresponding vibration mode, and the results are as follows: Figure 5 As shown. Figure 5 It can be seen that the corresponding vibration modes of the two are almost completely consistent, and the error is . Therefore, this method meets the accuracy requirements in pattern recognition.

[0194] The following describes the power system low frequency oscillation pattern recognition device provided by the embodiment of the present application. The power system low frequency oscillation pattern recognition device described below and the power system low frequency oscillation pattern recognition method described above can be referred to each other. Figure 6 As shown, the present application provides a device for identifying low-frequency oscillation patterns in a power system, the device comprising:

[0195] The measurement result determination module 201 is used to perform multi-signal prony analysis on the real-time oscillation signal when a low-frequency oscillation is detected in the power system to obtain the measurement result of the low-frequency oscillation, which includes the measurement mode and its measurement vibration shape;

[0196] A state matrix determination module 202 is configured to obtain a state matrix based on a mathematical model constructed when the power system is operating at a balance point;

[0197] The candidate result determination module 203 is used to pre-process the state matrix after being disturbed by the low-frequency oscillation by using a displacement-inverse transform, and solve the candidate results of the low-frequency oscillation in combination with the Arnoldi iteration algorithm. The candidate results include candidate modes and candidate vibration shapes;

[0198] The low frequency oscillation mode determination module 204 is configured to match the measurement result with the candidate result and determine the low frequency oscillation mode of the power system according to the matching result.

[0199] In one embodiment, the measurement result determination module 201 includes:

[0200] A matrix equation construction unit is used to construct a matrix equation according to the real-time oscillation signal, wherein the matrix equation is used to represent the real-time oscillation signal as a linear combination of different oscillation modes;

[0201] a polynomial characteristic equation construction unit, configured to construct a polynomial characteristic equation based on a matrix equation, and solve the characteristic roots of the polynomial characteristic equation to obtain an estimated mode of low-frequency oscillation, and solve the matrix equation to obtain an amplitude matrix;

[0202] The measurement result determination unit is used to construct a linear regression model according to the estimated mode and the amplitude matrix, and apply a stepwise regression method to the linear regression model to obtain the measurement result of the low-frequency oscillation.

[0203] In one embodiment, the polynomial characteristic equation construction unit includes:

[0204] The polynomial characteristic equation constructs a subunit, and the expression for the polynomial characteristic equation is:

[0205]

[0206] in, The variable representing the characteristic root, represents the order of the multi-order form, Represents the coefficients of the polynomial, constructed by the matrix equation Obtained by multiplying the order phasors.

[0207] In one embodiment, the measurement result determination unit includes:

[0208] an explanatory term calculation subunit, for calculating the explanatory term based on the estimated mode and the magnitude matrix;

[0209] The linear regression module constructs a sub-unit, which is used to normalize the explanatory terms and then combine them with the real-time oscillation signal to build a linear regression model.

[0210] In one embodiment, the state matrix determination module 202 includes:

[0211] The state matrix determination unit is used to obtain the dynamic network and network parameters, dynamic component model and model parameters of the power system, linearize at the equilibrium point to obtain a mathematical model, and simplify the mathematical model to obtain a state matrix.

[0212] In one embodiment, the candidate result determination module 203 includes:

[0213] a first intermediate variable calculation unit, configured to perform LU decomposition on the state matrix after the state matrix is ​​shifted by the low-frequency oscillation disturbance to obtain a first upper triangular matrix and a first lower triangular matrix, and calculate a first intermediate variable based on the first upper triangular matrix and the first lower triangular matrix;

[0214] A second intermediate variable calculation unit is configured to perform LU decomposition on the first intermediate variable to obtain a second upper triangular matrix and a second lower triangular matrix, and calculate the second intermediate variable based on the first upper triangular matrix and the first lower triangular matrix;

[0215] The auxiliary vector calculation unit is used to calculate the auxiliary vector according to the second upper triangular matrix, the second lower triangular matrix and the second intermediate variable, and obtain the preprocessed state matrix according to the first upper triangular matrix, the first lower triangular matrix and the auxiliary vector.

[0216] In one embodiment, the low frequency oscillation mode determination module 204 includes:

[0217] A matching relationship establishing unit is used to construct a fitting factor phasor and combine the fitting factor phasor with the candidate vibration shape to establish a matching relationship with the measured vibration shape;

[0218] A matching result determination unit is used to solve the matching relationship, obtain the best fitting factor, and match the best fitting factor with the candidate matrix to obtain the matching result;

[0219] The low-frequency oscillation mode determination unit is used to calculate the error between the matching result and the measurement matrix. When the error is less than a preset threshold, the candidate mode corresponding to the candidate vibration shape is used as the low-frequency oscillation mode of the power system.

[0220] In one embodiment, the present application also provides a storage medium storing computer-readable instructions. When the computer-readable instructions are executed by one or more processors, the one or more processors execute the steps of the method for identifying low-frequency oscillation patterns of power systems as described in any of the above embodiments.

[0221] In one embodiment, the present application also provides a computer device having computer-readable instructions stored therein. When the computer-readable instructions are executed by one or more processors, the one or more processors execute the steps of the method for identifying low-frequency oscillation patterns of power systems as described in any of the above embodiments.

[0222] Schematically, as Figure 7 As shown, Figure 7 This is a schematic diagram of the internal structure of a computer device provided in an embodiment of the present application. The computer device 300 can be provided as a server. Figure 7 Computer device 300 includes a processing component 302, which further includes one or more processors, and memory resources represented by memory 301 for storing instructions executable by processing component 302, such as application programs. The application programs stored in memory 301 may include one or more modules, each corresponding to a set of instructions. Furthermore, processing component 302 is configured to execute the instructions to perform the method for identifying low-frequency oscillation patterns in a power system according to any of the aforementioned embodiments.

[0223] The computer device 300 may further include a power supply component 303 configured to perform power management of the computer device 300, a wired or wireless network interface 304 configured to connect the computer device 300 to a network, and an input / output (I / O) interface 305. The computer device 300 may operate based on an operating system stored in the memory 301, such as Windows Server™, Mac OS X™, Unix™, Linux™, Free BSD™, or the like.

[0224] Those skilled in the art will understand that Figure 7 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement.

[0225] Finally, it should be noted that, in this article, relational terms such as first and second are merely used to distinguish one entity or operation from another, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprise," "include," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. Without further restriction, an element defined by the phrase "comprising a..." does not exclude the presence of other identical elements in the process, method, article, or device comprising the element. Herein, "one," "said," "the," and "its" may also include plural forms unless the context clearly indicates otherwise. A plurality refers to at least two, such as 2, 3, 5, or 8. "And / or" includes any and all combinations of the relevant listed items.

[0226] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The various embodiments can be combined as needed, and the same or similar parts can be referenced to each other.

[0227] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present application. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application is not limited to the embodiments shown herein, but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for identifying low-frequency oscillation patterns in a power system, characterized in that: The method comprises: When low-frequency oscillation is detected in the power system, multi-signal prony analysis is performed on the real-time oscillation signal to obtain a measurement result of the low-frequency oscillation, the measurement result including a measurement mode and a measurement vibration shape; Obtaining a state matrix according to a mathematical model constructed when the power system operates at a balance point; Using a displacement-inverse transform to pre-process the state matrix after being disturbed by the low-frequency oscillation, and combining it with an Arnoldi iteration algorithm to solve the candidate results of the low-frequency oscillation, the candidate results including the candidate mode and its candidate vibration shape; The measurement result is matched with the candidate result, and a low-frequency oscillation mode of the power system is determined according to the matching result.

2. The method for identifying low-frequency oscillation patterns in a power system according to claim 1, wherein: The step of performing multi-signal prony analysis on the real-time oscillation signal to obtain a measurement result of the low-frequency oscillation includes: constructing a matrix equation based on the real-time oscillation signal, wherein the matrix equation is used to represent the real-time oscillation signal as a linear combination of different oscillation modes; Constructing a polynomial characteristic equation according to the matrix equation, solving the characteristic roots of the polynomial characteristic equation to obtain an estimated mode of low-frequency oscillation, and solving the matrix equation to obtain an amplitude matrix; A linear regression model is constructed according to the estimation mode and the amplitude matrix, and a stepwise regression method is applied to the linear regression model to obtain a measurement result of the low-frequency oscillation.

3. The method for identifying low-frequency oscillation patterns in a power system according to claim 2, wherein: The step of constructing a polynomial characteristic equation according to the matrix equation comprises: The expression of the polynomial characteristic equation is: in, The variable representing the characteristic root, represents the order of the multi-order form, Represents the coefficients of the polynomial, constructed by the matrix equation and Obtained by multiplying the order phasors.

4. The method for identifying low-frequency oscillation patterns in a power system according to claim 2, wherein: The step of constructing a linear regression model according to the estimation mode and the amplitude matrix includes: calculating an explanatory term based on the estimated mode and the magnitude matrix; After normalizing the explanatory terms, the linear regression model is constructed in combination with the real-time oscillation signal.

5. The method for identifying low-frequency oscillation patterns in a power system according to claim 1, wherein: The step of obtaining a state matrix according to a mathematical model constructed when the power system is operating at a balance point includes: After obtaining the dynamic network and network parameters, dynamic component model and model parameters of the power system, linearization is performed at the equilibrium point to obtain the mathematical model, and the mathematical model is simplified to obtain the state matrix.

6. The method for identifying low-frequency oscillation patterns in a power system according to claim 1, wherein: The step of preprocessing the state matrix disturbed by the low-frequency oscillation by using the shift-inverse transform includes: Performing LU decomposition on the state matrix after being disturbed by the low-frequency oscillation after shifting to obtain a first upper triangular matrix and a first lower triangular matrix, and calculating a first intermediate variable based on the first upper triangular matrix and the first lower triangular matrix; Performing LU decomposition on the first intermediate variable to obtain a second upper triangular matrix and a second lower triangular matrix, and calculating a second intermediate variable based on the first upper triangular matrix and the first lower triangular matrix; An auxiliary vector is calculated according to the second upper triangular matrix, the second lower triangular matrix and the second intermediate variable, and a preprocessed state matrix is ​​obtained according to the first upper triangular matrix, the first lower triangular matrix and the auxiliary vector.

7. The method for identifying low-frequency oscillation patterns in a power system according to claim 1, wherein: The step of matching the measurement result with the candidate result and determining the low-frequency oscillation mode of the power system according to the matching result includes: Constructing a fitting factor phasor, and combining the fitting factor phasor with the candidate vibration shape to establish a matching relationship with the measured vibration shape; Solving the matching relationship to obtain a best fit factor, and matching the best fit factor with the candidate matrix to obtain a matching result; An error between the matching result and the measurement matrix is ​​calculated, and when the error is less than a preset threshold, a candidate mode corresponding to the candidate vibration shape is used as a low-frequency oscillation mode of the power system.

8. A device for identifying low-frequency oscillation patterns in a power system, characterized in that: The device comprises: A measurement result determination module is used to perform multi-signal prony analysis on the real-time oscillation signal when a low-frequency oscillation is detected in the power system to obtain a measurement result of the low-frequency oscillation, wherein the measurement result includes a measurement mode and a measurement vibration shape; a state matrix determination module, configured to obtain a state matrix based on a mathematical model constructed when the power system operates at a balance point; a candidate result determination module, configured to pre-process the state matrix after being disturbed by the low-frequency oscillation using a displacement-inverse transform, and solve the candidate results of the low-frequency oscillation using an Arnoldi iterative algorithm, wherein the candidate results include candidate modes and candidate vibration shapes; The low-frequency oscillation mode determination module is configured to match the measurement result with the candidate result, and determine the low-frequency oscillation mode of the power system according to the matching result.

9. A storage medium, characterized in that: The storage medium stores computer-readable instructions, which, when executed by one or more processors, enable the one or more processors to perform the steps of the method for identifying low-frequency oscillation patterns in a power system as claimed in any one of claims 1 to 7.

10. A computer device, characterized in that: include: one or more processors, and memory; The memory stores computer-readable instructions, which, when executed by the one or more processors, execute the steps of the method for identifying low-frequency oscillation patterns of a power system according to any one of claims 1 to 7.

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