Electric power system electromagnetic transient small interference stability analysis method based on multi-dimensional data

Abstract

The invention discloses a power system electromagnetic transient small interference stability analysis method based on multi-dimensional data, and relates to the technical field of power system analysis. According to the method, firstly, multi-source data such as power grid operation, equipment states, environments and user behaviors are collected and fused, and a unified data framework is formed through time synchronization, cleaning preprocessing and a fusion algorithm; secondly, feature value sidelobe information is extracted through wavelet transform and Hilbert transform, and sidelobe intensity, distribution and change trend are analyzed to reveal tiny change of a signal propagation path; and finally, in combination with a chaos polynomial theory, establishing a micro-grid group small signal model, processing a random variable by using a non-parametric kernel density estimation method and an optimal Copula function, and constructing an explicit expression of critical mode damping and the random variable to realize small interference stability evaluation. The method solves the problems of single traditional analysis data, insufficient fusion and the like, can more comprehensively and accurately evaluate the stability of the complex power system containing the distributed energy, and provides reliable guarantee for safe operation of the system.

Description

Technical Field

[0001] This invention relates to the field of power system analysis technology, specifically to a method for electromagnetic transient small-disturbance stability analysis of power systems based on multi-dimensional data, which is particularly suitable for stability assessment and analysis scenarios of complex power systems including distributed energy sources. Background Technology

[0002] With the transformation of the energy structure, a large number of distributed energy sources (such as wind power and photovoltaic power) have been connected to the power system, making the structure and operating characteristics of the power system increasingly complex. Against this backdrop, power system stability analysis faces numerous challenges. Traditional power system stability analysis methods mostly rely on only a single type of data (such as grid operation data), failing to comprehensively reflect the system's true operating state. Because they neglect the influence of various factors such as equipment status, environmental factors, and user behavior, inaccurate assessments often occur when analyzing power systems containing distributed energy sources. For example, when analyzing the system stability after wind turbines and photovoltaic power plants are connected, the random variations in wind speed and solar intensity, as well as the potential impact of equipment failures on system stability, are not considered, leading to the failure to promptly detect small-scale disturbance stability risks under certain operating conditions.

[0003] Existing stability analysis methods lack effective fusion mechanisms when dealing with multi-source data. Data from different sources differ in time scale, data format, and units, making direct comprehensive analysis difficult. This prevents the full exploration of correlations between data points and hinders the provision of comprehensive and accurate information support for stability assessment. For example, grid operation data, equipment status data, environmental data, and user behavior data are stored and analyzed independently, failing to form an organic whole and accurately assess the combined impact of changes in environmental factors (such as the effects of temperature and humidity on equipment performance) and changes in user electricity consumption behavior (such as fluctuations in electric vehicle charging time and frequency) on power system stability.

[0004] In terms of small-disturbance stability assessment indicators, traditional methods typically rely on a single indicator (such as critical mode damping) to judge system stability, failing to comprehensively consider multiple important characteristics of the power system. This single-indicator assessment approach is too one-sided and easily overlooks potential risks in other aspects of the system. For example, when assessing the stability of microgrid groups, focusing only on critical mode damping may neglect key factors such as voltage stability, frequency stability, power balance, and energy reserve margin of the microgrid group, resulting in an inaccurate assessment of system stability and failing to provide reliable guarantees for the safe and stable operation of the power system. Summary of the Invention

[0005] In view of the shortcomings of the prior art, the purpose of this invention is to propose a method for electromagnetic transient small-disturbance stability analysis of power systems based on multi-dimensional data. This method aims to solve the problems of traditional methods relying on single data, insufficient multi-source data fusion methods, and one-sided evaluation indicators. By integrating multi-dimensional data and combining signal processing and chaotic polynomial theory, this invention can achieve accurate evaluation of the small-disturbance stability of complex power systems containing distributed energy sources, and provide more comprehensive information support and reliable guarantee for the safe and stable operation of the system.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for electromagnetic transient small-disturbance stability analysis of power systems based on multi-dimensional data includes the following steps:

[0008] S1. Multi-dimensional data acquisition and fusion: Integrating multi-source data during the operation of the power system, this module collects the data in real time and uses data fusion technology to integrate data from different sources to form a unified data framework.

[0009] S2. Eigenvalue sidelobe extraction and analysis: By preprocessing the multi-source data collected in S1, wavelet transform and Hilbert transform signal processing methods are used to extract eigenvalue sidelobe information from the preprocessed data. By quantitatively analyzing the sidelobe intensity, distribution and changing trend, the subtle changes in the signal propagation path are revealed.

[0010] S3. Using the eigenvalue sidelobe information extracted in S2, combined with chaotic polynomial theory, the stability of the power system is evaluated:

[0011] First, a small-signal analysis model for a microgrid cluster with interconnected back-to-back converters is established, taking correlated factors such as wind speed, light intensity, and load fluctuation as random input variables;

[0012] Subsequently, a probability distribution model for wind turbines, photovoltaics, and loads was established using the nonparametric kernel density estimation method.

[0013] Next, the correlation between random input variables is processed based on the optimal Copula function model, and the chaotic polynomial standard input variables are obtained through inverse cumulative transformation;

[0014] Finally, an explicit expression is established between critical mode damping and random input variables to achieve small-disturbance stability assessment.

[0015] Furthermore, the multi-source data includes power grid operation data, equipment status data, environmental data, and user behavior data.

[0016] The power grid operation data includes time-series data such as voltage, current, and power. This data is acquired through monitoring equipment installed at various nodes of the power grid. These devices record data at regular time intervals, forming a sequence that changes over time. Equipment status data is obtained from the equipment's own control system or monitoring device and is used to reflect the equipment's health status. Environmental data is collected by meteorological monitoring stations or environmental sensors installed near power equipment to understand the impact of environmental factors on the power system. User behavior data is obtained from smart meters or electric vehicle charging management systems and reflects users' electricity consumption patterns.

[0017] Furthermore, the data fusion technology includes:

[0018] S111. Time synchronization: Utilizing the Global Positioning System (GPS) or BeiDou satellite timing system, a precise time reference is provided for all data acquisition devices to ensure consistency of data from different sources in time; when receiving data, the data acquisition terminal adds a time tag to each data sample according to the timing information;

[0019] S112. Data cleaning and preprocessing: Clean the collected data to remove outliers and erroneous data; for continuous data such as voltage and current, detect anomalies by setting threshold ranges; for discrete data such as equipment status, check the rationality and completeness of the data; at the same time, normalize the data to map data of different dimensions to a unified numerical range.

[0020] S113. Data fusion algorithm: Arrange power grid operation data, equipment status data, environmental data, and user behavior data in chronological order to form a multidimensional data matrix X, and calculate the covariance matrix of the data matrix.

[0021]

[0022] In the formula, n is the sample size, and X... T Let X be the transpose of the multidimensional data matrix X, and C be the covariance matrix of the data matrix;

[0023] Perform eigenvalue decomposition on the covariance matrix:

[0024] C=U∧U T ;

[0025] U is the eigenvector matrix; ∧ is the eigenvalue diagonal matrix. The eigenvectors corresponding to the first r largest eigenvalues ​​are selected to form the projection matrix P, which projects the original data onto a new low-dimensional space to obtain the fused data Y = XP, forming a unified data framework.

[0026] Furthermore, the preprocessing step for multi-source data in S2 includes:

[0027] S211. Denoising: Wavelet thresholding is used to denoise the fused data. First, based on the data characteristics, the db4 wavelet is selected to perform wavelet decomposition, decomposing the data into different scale spaces to obtain the corresponding wavelet coefficients. The threshold λ is calculated according to the general threshold formula.

[0028]

[0029] Where σ represents the noise standard deviation, which is estimated through statistical analysis of noisy data; l is the data length;

[0030] A soft thresholding method is used to process the wavelet coefficients. When the absolute value of a wavelet coefficient is less than the threshold, the wavelet system is set to 0; when it is greater than the threshold, the wavelet system is shrunk to:

[0031] sgn(W j′,k′ )(|W j′,k′ |-λ);

[0032] sgn(·) is the sign function, W j′,k′ ...

[0033] After processing, the denoised data is normalized again to ensure the consistency and comparability of the data in subsequent analysis. The processed wavelet coefficients are reconstructed by inverse wavelet transform to obtain the denoised data.

[0034] S212. Normalization: In order to eliminate the influence of different data units and ensure the consistency and comparability of data in subsequent analysis, the same normalization method as in the data acquisition stage is used on the denoised data to map the data to the [0,1] interval.

[0035] Furthermore, in S2, a method for extracting eigenvalue sidelobe information from the preprocessed data using wavelet transform and Hilbert transform signal processing methods is described below.

[0036] S221. Wavelet Transform: Perform Discrete Wavelet Transform (DWT) on the preprocessed data. The discrete wavelet function is defined as follows:

[0037]

[0038] Where, ψ j,k (m) represents the discrete wavelet function; j is the scaling parameter, which determines the scaling degree of the wavelet function; k is the translation parameter, which determines the position of the wavelet function on the time axis; ψ(m) is the basic wavelet function; m is the index of the discrete time series;

[0039] The wavelet coefficients are obtained by performing a DWT transform on the discretized original signal:

[0040]

[0041] x(m) represents the original signal after discretization, which is used as the input signal in the Hilbert transform; N is the data length;

[0042] By analyzing wavelet coefficients at different scales j and positions k, local features of the signal at different frequencies and time resolutions are obtained, highlighting the detailed information of the signal.

[0043] S222. Hilbert Transform: Based on the wavelet transform, the Hilbert transform is applied to the obtained wavelet coefficients. The discrete form of the Hilbert transform is:

[0044]

[0045] H[x(m)] is the result of performing a Hilbert transform on the discretized original signal x(m); s is the variable in the summation operation;

[0046] The discretized original signal x(m) is converted into an analytic signal z(m) by the Hilbert transform, which is expressed as:

[0047] z(m) = x(m) + jH[x(m)];

[0048] The analyzed signal contains the amplitude and phase information of the original signal. By analyzing the analyzed signal, the signal characteristics can be obtained more comprehensively and accurately.

[0049] Furthermore, in step S2, the step of quantitatively analyzing the sidelobe intensity, distribution, and changing trends includes:

[0050] S231. Sidelobe strength calculation: The main lobe amplitude and sidelobe amplitude of the signal are determined by the spectrum analysis method. The spectrum analysis uses the Fast Fourier Transform (FFT) algorithm to convert the time domain signal to the frequency domain for analysis. The sidelobe strength is defined as the ratio of the sidelobe amplitude to the main lobe amplitude. The sidelobe strength can intuitively reflect the relative importance of the sidelobe in the entire signal spectrum. The larger the sidelobe strength, the greater the influence of the sidelobe on the overall characteristics of the signal.

[0051] S232. Sidelobe distribution analysis: The frequency range is divided into multiple sub-intervals, and the number of sidelobes in each sub-interval is counted. Simultaneously, the energy of the sidelobes in each sub-interval is calculated.

[0052]

[0053] Among them, [f i ,f i+1Let A be the i-th subinterval. s (f) is the sidelobe amplitude at frequency f;

[0054] By analyzing the distribution of sidelobe energy in different frequency sub-intervals, we can understand the frequency characteristics and distribution patterns of sidelobes and determine which frequency intervals have a greater impact on the signal.

[0055] S233. Sidelobe variation trend analysis: Using a fixed time interval as the period, continuously calculate the sidelobe intensity and distribution characteristics within each time interval, record the calculated sidelobe intensity and distribution characteristics over time, and plot the corresponding time series curves; by observing the trend of the curves, analyze the variation trend of sidelobe characteristics over time; if the sidelobe intensity or distribution changes significantly over a period of time, it indicates that there are slight changes in the signal propagation path, and these changes are related to the changes in the operating state of the power system.

[0056] Furthermore, in S3, the method for establishing a small-signal analysis model for a microgrid group with back-to-back interconnected converters is as follows:

[0057] S311. Single microgrid modeling: A microgrid group interconnected by back-to-back converters involves multiple microgrids connected via back-to-back converters. For the i-th microgrid, the constructed state equation is:

[0058]

[0059] Among them, X i This is a state variable vector containing the state information of each component within the microgrid, such as the rotor angle and angular velocity of the generator, and the magnitude and phase angle of the node voltage; A i Let A be the state matrix. i Reflects the dynamic coupling relationship between components within a microgrid; B i Given the input matrix, B i Related to the input variable vector, the input variable vector is selected from factors such as wind speed, light intensity, and load fluctuation, which are correlated; U i For the input variable vector;

[0060] S312. Overall modeling of the microgrid group: The overall state equation is obtained by combining the state equations of each microgrid and considering the connection relationship of the converters. The overall state equation is the overall dynamic interaction model of the group, simulating the operating state of the microgrid group under different operating conditions. The overall state equation is expressed as:

[0061]

[0062] h represents the number of microgrids in the microgrid group, which determines the dimensions of the state variable vector, state matrix, input matrix, and input variable vector;

[0063] The eigenvalue sidelobe information extracted from S2 is used to determine whether the parameters in the model have changed. If the eigenvalue sidelobe expands abnormally in a certain frequency range, it means that the parameters of some components in the microgrid have changed, and the model needs to be corrected and adjusted.

[0064] Furthermore, in S3, the method for establishing probability distribution models of wind turbines, photovoltaic systems, and loads using nonparametric kernel density estimation is as follows:

[0065] S321. Data collection and preprocessing: Collect historical data such as wind speed and output power of wind turbines, solar irradiance and output power of photovoltaics, and power changes of loads over time; historical data are obtained from the monitoring systems of wind farms and photovoltaic power plants and the metering devices of the power grid; preprocess the collected data to remove outliers and missing values.

[0066] S322. Kernel function and bandwidth selection: The Gaussian kernel function is selected as the kernel function for probability density function estimation; the Silverman rule is used to initially determine the bandwidth, and then fine-tuning is performed using cross-validation.

[0067] The Gaussian kernel function formula is as follows:

[0068]

[0069] x represents the wind speed, light intensity, or load value for estimating probability density; K(x) represents the kernel function value;

[0070] Bandwidth calculation formula:

[0071]

[0072] σ is the standard deviation of the sample data, M is the number of samples; f represents the bandwidth;

[0073] S323. Probability density function calculation: Calculate the probability density function based on the nonparametric kernel density estimation formula.

[0074] Rate density function:

[0075]

[0076] Based on the feature value sidelobe information extracted in S2, the sample data is filtered. If the feature value sidelobe shows significant changes in certain frequency ranges, it indicates that the range and distribution of the random input variable have changed under these operating conditions. In this case, more sample data under this operating condition should be selected.

[0077] Furthermore, in S3, the correlation between random input variables is processed based on the optimal Copula function model, and the chaotic polynomial standard output is obtained through inverse cumulative transformation.

[0078] Methods for inputting variables:

[0079] S331. Marginal distribution determination: Integrate the established probability distribution models of wind turbines, photovoltaics, and loads to obtain the marginal distribution functions of the random input variables. The marginal distribution functions describe the distribution of each random input variable.

[0080] S332. Copula Function Selection and Parameter Estimation: The Gaussian Copula function is chosen to describe the correlation between random input variables. The Gaussian Copula function is expressed as follows:

[0081] C(u1,u2,…,u η )=Φ ρ (Φ - 1(u1),Φ -1 (u2),…,Φ -1 (u η ));

[0082] u i =F i (x i (i = 1, 2, ..., η);

[0083] Where η represents the number of random variables; u i Let C(u1,u2,…,u) be the random input variables after marginal distribution function transformation; η ) represents the joint distribution of random variables constructed based on the values ​​after marginal distribution function transformation; Φ ρ Φ is an η-dimensional normal distribution function, where ρ is the correlation coefficient matrix, reflecting the correlation between variables. ρ is determined through analysis and fitting of historical data, using methods such as maximum likelihood estimation; -1 It is the inverse function of the standard normal distribution;

[0084] S333. Inverse cumulative transformation: The standard input variables of the chaotic polynomial are obtained through the inverse cumulative transformation. The formula is as follows:

[0085]

[0086] C i z is the i-th component of the Copula function; i F is the standard input variable for the chaotic polynomial. i Let x be the marginal distribution function of the i-th random input variable; i Let z be the sample value of the i-th random input variable; calculate z based on the above. i The value is the standard input variable of the chaotic polynomial; u i These are the random input variables after being transformed by the marginal distribution function.

[0087] Furthermore, in S3, an explicit expression is established between the critical mode damping and the random input variable to realize the small disturbance stability evaluation method:

[0088] S341. Based on chaotic polynomial theory, let the critical mode damping and the standard input variable z of the chaotic polynomial be... i The relationship is represented as:

[0089]

[0090] Where ξ represents critical mode damping; The coefficients of the chaotic polynomials determine the contribution of the combination of the basis functions of the chaotic polynomials to the damping of the critical mode. P is the chaotic polynomial basis function corresponding to the j-th random input variable; j The order of the chaotic polynomial affects its complexity and fitting accuracy.

[0091] It is obtained by using the least squares method and sample data; during the solution process, the sample data is filtered or weighted by combining the eigenvalue sidelobe information in S2.

[0092] S342. Small-disturbance stability assessment: After obtaining the explicit expression between the critical mode damping and the random input variables, the small-disturbance stability of the power system is assessed based on the magnitude of the critical mode damping. A critical mode damping threshold ξ is set. t If the calculated critical mode damping ξ > ξ t If ξ < ξ, then the power system is considered stable under small disturbances; t If the system exhibits abnormal changes in small disturbance stability, then the system faces a risk of instability under small disturbances. Furthermore, by combining the eigenvalue sidelobe information in S2, we can further analyze the changing trend of the system's stability under different operating conditions. When the eigenvalue sidelobe shows abnormal changes in certain frequency ranges, even if the current critical mode damping is greater than the threshold, we still need to pay attention to the potential risks to the system's stability.

[0093] In summary, due to the adoption of the above technical solution, the beneficial technical effects of the invention are as follows:

[0094] Data fusion enhances the completeness and accuracy of information by collecting data on power grid operation, equipment status, environment, and user behavior. Power grid operation data reflects real-time changes in electrical quantities, equipment status data monitors equipment health, environmental data reveals environmental impacts, and user behavior data reflects electricity consumption patterns. Through time synchronization, pre-processing and cleaning, and fusion algorithms, a unified data framework is established, addressing the problems of single data sets and inconsistent formats and times in traditional methods. This provides comprehensive and accurate data for analysis and reduces assessment errors.

[0095] Wavelet and Hilbert transform are used to extract eigenvalue sidelobe information, and the sidelobe intensity, distribution, and variation trends are analyzed. Sidelobe variations reflect changes in signal propagation paths and system operating states, helping to promptly identify potential problems such as equipment anomalies and power fluctuations, providing early warnings for stability assessments, and overcoming the insensitivity of traditional analysis methods to minute changes.

[0096] The model construction enhances the system's description and analysis capabilities. The microgrid cluster model, with back-to-back interconnected converters, considers random input variables such as wind speed, solar intensity, and load fluctuations. Individual microgrid modeling reflects the dynamics of internal components, while the overall modeling simulates the operation of the microgrid cluster. By incorporating eigenvalue sidelobe information to correct model parameters, the model accurately describes the system's dynamic characteristics, making it more realistic than traditional models and improving the reliability of stability assessments.

[0097] A nonparametric kernel density estimation method is used to establish a probability distribution model. An optimal Copula function handles the dependencies between variables, and an inverse cumulative transformation yields the standard input variables for the chaotic polynomial. This reduces variable redundancy, improves the accuracy of the chaotic polynomial model, accurately quantifies the impact of random factors on system stability, and provides reliable theoretical and technical support for stability assessment.

[0098] Stability assessment and optimization decision-making ensure the operation of the system. Based on chaotic polynomial theory, explicit expressions for critical mode damping and random input variables are established, and the system stability is assessed using a critical mode damping threshold. The threshold can be set according to system characteristics and experience to determine the system's stable state. If the critical mode damping is greater than the threshold, the system is stable; otherwise, there is a risk, providing a crucial reference for system operation.

[0099] By combining eigenvalue sidelobe information analysis with stability change trends, potential risks should be considered even if the current critical mode damping meets the standards when sidelobe changes abnormally. Preemptive measures such as adjusting power generation plans, optimizing load allocation, and deploying backup power sources should be taken to ensure the safe and stable operation of the system, reduce the risk of power outages, and improve power supply quality and economic efficiency. Attached Figure Description

[0100] Figure 1 This is a flowchart of a method for electromagnetic transient small-disturbance stability analysis of power systems based on multi-dimensional data. Detailed Implementation

[0101] To make the objectives, technical solutions, and advantages of the invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.

[0102] like Figure 1 As shown, the method for electromagnetic transient small-disturbance stability analysis of power systems based on multi-dimensional data includes the following steps:

[0103] S1. Multi-dimensional data acquisition and fusion: Integrates multi-source data during the operation of the power system, including power grid operation data, equipment status data, environmental data, and user behavior data. Through the data acquisition module, these data are collected in real time, and data fusion technology is used to integrate data from different sources to form a unified data framework.

[0104] S2. Eigenvalue sidelobe extraction and analysis: By preprocessing the multi-source data collected in S1, wavelet transform and Hilbert transform signal processing methods are used to extract eigenvalue sidelobe information from the preprocessed data. Eigenvalue sidelobe includes the sidelobe regions on both sides of the main lobe. By quantitatively analyzing the sidelobe intensity, distribution and change trend, the subtle changes in the signal propagation path are revealed.

[0105] S3. Using the eigenvalue sidelobe information extracted in S2, combined with chaotic polynomial theory, the stability of the power system is evaluated:

[0106] First, a small-signal analysis model for a microgrid cluster with interconnected back-to-back converters is established, taking correlated factors such as wind speed, light intensity, and load fluctuation as random input variables;

[0107] Subsequently, a probability distribution model for wind turbines, photovoltaics, and loads was established using the nonparametric kernel density estimation method.

[0108] Next, the correlation between random input variables is processed based on the optimal Copula function model, and the chaotic polynomial standard input variables are obtained through inverse cumulative transformation;

[0109] Finally, an explicit expression is established between critical mode damping and random input variables to achieve small-disturbance stability assessment.

[0110] The power grid operation data includes time-series data such as voltage, current, and power. This data is acquired through monitoring equipment installed at various nodes of the power grid. These devices record data at specific time intervals (e.g., milliseconds), forming a sequence that changes over time. Equipment status data (equipment operating status, fault records, etc.) is obtained from the equipment's own control system or monitoring devices and is used to reflect the equipment's health status. Environmental data (temperature, humidity, etc.) is collected by meteorological monitoring stations or environmental sensors installed near power equipment to understand the impact of environmental factors on the power system. User behavior data (charging time, charging frequency, etc.) is obtained from smart meters or electric vehicle charging management systems and reflects users' electricity consumption patterns.

[0111] The data fusion technology mentioned includes:

[0112] S111. Time synchronization: Utilizing the Global Positioning System (GPS) or BeiDou satellite timing system, a precise time reference is provided for all data acquisition devices to ensure consistency of data from different sources in time; when receiving data, the data acquisition terminal adds a time tag to each data sample according to the timing information;

[0113] S112. Data cleaning and preprocessing: Clean the collected data to remove outliers and erroneous data; for continuous data such as voltage and current, detect anomalies by setting threshold ranges; for discrete data such as equipment status, check the rationality and completeness of the data; at the same time, normalize the data to map data of different dimensions to a unified numerical range, such as [0,1].

[0114] S113. Data fusion algorithm: Arrange power grid operation data, equipment status data, environmental data, and user behavior data in chronological order to form a multidimensional data matrix X, and calculate the covariance matrix of the data matrix.

[0115]

[0116] In the formula, n is the sample size, and X... T Let X be the transpose of the multidimensional data matrix X, and C be the covariance matrix of the data matrix;

[0117] Perform eigenvalue decomposition on the covariance matrix:

[0118] C=U∧U T ;

[0119] U is the eigenvector matrix; ∧ is the eigenvalue diagonal matrix. The eigenvectors corresponding to the first r largest eigenvalues ​​are selected to form the projection matrix P, which projects the original data onto a new low-dimensional space to obtain the fused data Y = XP, forming a unified data framework.

[0120] The preprocessing steps for multi-source data in S2 include:

[0121] S211. Denoising: Wavelet thresholding is used to denoise the fused data. First, based on the data characteristics, the db4 wavelet is selected to perform wavelet decomposition, decomposing the data into different scale spaces to obtain the corresponding wavelet coefficients. The threshold λ is calculated according to the general threshold formula.

[0122]

[0123] Where σ represents the noise standard deviation, which is estimated through statistical analysis of noisy data; l is the data length;

[0124] A soft thresholding method is used to process the wavelet coefficients. When the absolute value of a wavelet coefficient is less than the threshold, the wavelet system is set to 0; when it is greater than the threshold, the wavelet system is shrunk to:

[0125] sgn(W j′,k′ (W) j′,k′ |-λ);

[0126] sgn(·) is the sign function, W j′,k′ Here, j′ represents the wavelet coefficients; j′ represents the scale, used to identify different scale levels in the wavelet transform; different j′ values ​​correspond to different frequency resolutions. The larger j′ is, the lower the frequency of the signal being analyzed, reflecting the coarser characteristics of the signal; the smaller j′ is, the higher the frequency of the signal being analyzed, reflecting the more detailed characteristics of the signal; k′ represents the position, used to determine the position of the wavelet coefficients on the time axis at a specific scale j′, that is, different k′ values ​​correspond to the characteristics of the signal at different time positions at the same scale;

[0127] After processing, the denoised data is normalized again to ensure the consistency and comparability of the data in subsequent analysis. The processed wavelet coefficients are reconstructed by inverse wavelet transform to obtain the denoised data.

[0128] S212. Normalization: In order to eliminate the influence of different data units and ensure the consistency and comparability of data in subsequent analysis, the same normalization method as in the data acquisition stage is used on the denoised data to map the data to the [0,1] interval.

[0129] In S2, the method of extracting eigenvalue sidelobe information from preprocessed data using wavelet transform and Hilbert transform signal processing methods is as follows:

[0130] S221. Wavelet Transform: Perform Discrete Wavelet Transform (DWT) on the preprocessed data. The discrete wavelet function is defined as follows:

[0131]

[0132] Where, ψ j,k (m) represents the discrete wavelet function; j is the scaling parameter, which determines the scaling degree of the wavelet function; k is the translation parameter, which determines the position of the wavelet function on the time axis; ψ(m) is the basic wavelet function; m is the index of the discrete time series;

[0133] The wavelet coefficients are obtained by performing a DWT transform on the discretized original signal:

[0134]

[0135] x(m) represents the original signal after discretization, which is used as the input signal in the Hilbert transform; N is the data length;

[0136] By analyzing wavelet coefficients at different scales j and positions k, local features of the signal at different frequencies and time resolutions are obtained, highlighting the detailed information of the signal.

[0137] S222. Hilbert Transform: Based on the wavelet transform, the Hilbert transform is applied to the obtained wavelet coefficients. The discrete form of the Hilbert transform is:

[0138]

[0139] H[x(m)] is the result of performing a Hilbert transform on the discretized original signal x(m); s is the variable in the summation operation. s is used to traverse the entire summation interval (-∞, ∞). In the discrete calculation process of the Hilbert transform, the transformation operation of the original signal x(m) is realized by calculating and summing different values ​​of s. It plays the role of traversing the calculation in the summation formula to comprehensively consider the contribution of each sampling point in the original signal sequence to the transformation result.

[0140] The discretized original signal x(m) is converted into an analytic signal z(m) by the Hilbert transform, which is expressed as:

[0141] z(m) = x(m) + jH[x(m)];

[0142] The analyzed signal contains the amplitude and phase information of the original signal. By analyzing the analyzed signal, the signal characteristics can be obtained more comprehensively and accurately.

[0143] In step S2, the steps for quantitatively analyzing the sidelobe intensity, distribution, and changing trends include:

[0144] S231. Sidelobe strength calculation: The main lobe amplitude and sidelobe amplitude of the signal are determined by the spectrum analysis method. The spectrum analysis uses the Fast Fourier Transform (FFT) algorithm to convert the time domain signal to the frequency domain for analysis. The sidelobe strength is defined as the ratio of the sidelobe amplitude to the main lobe amplitude. The sidelobe strength can intuitively reflect the relative importance of the sidelobe in the entire signal spectrum. The larger the sidelobe strength, the greater the influence of the sidelobe on the overall characteristics of the signal.

[0145] S232. Sidelobe distribution analysis: Divide the frequency range into multiple sub-intervals, for example, according to a certain frequency interval, count the number of sidelobes in different sub-intervals, and calculate the energy of the sidelobes in each sub-interval.

[0146]

[0147] Among them, [f i ,f i+1 Let A be the i-th subinterval. s(f) is the sidelobe amplitude at frequency f;

[0148] By analyzing the distribution of sidelobe energy in different frequency sub-intervals, we can understand the frequency characteristics and distribution patterns of sidelobes and determine which frequency intervals have a greater impact on the signal.

[0149] S233. Sidelobe variation trend analysis: Using a fixed time interval (e.g., 1 minute) as the period, continuously calculate the sidelobe intensity and distribution characteristics within each time interval. Record the calculated sidelobe intensity and distribution characteristics over time and plot the corresponding time series curves. By observing the trend of the curves (rising, falling, or fluctuating), analyze the variation trend of the sidelobe characteristics over time. If the sidelobe intensity or distribution changes significantly over a period of time, it indicates that there are slight changes in the signal propagation path, and these changes are related to the changes in the operating state of the power system.

[0150] In S3, the method for establishing a small-signal analysis model for microgrid clusters with back-to-back converter interconnection is as follows:

[0151] S311. Single microgrid modeling: A microgrid group interconnected by back-to-back converters involves multiple microgrids connected via back-to-back converters. For the i-th microgrid, the constructed state equation is:

[0152]

[0153] Among them, X i This is a state variable vector containing the state information of each component within the microgrid, such as the rotor angle and angular velocity of the generator, and the magnitude and phase angle of the node voltage; A i Let A be the state matrix. i Reflects the dynamic coupling relationship between components within a microgrid; B i Given the input matrix, B i Related to the input variable vector, the input variable vector is selected from factors such as wind speed, light intensity, and load fluctuation, which are correlated; U i For the input variable vector;

[0154] S312. Overall modeling of the microgrid group: The overall state equation is obtained by combining the state equations of each microgrid and considering the connection relationship of the converters. The overall state equation is the overall dynamic interaction model of the group, simulating the operating state of the microgrid group under different operating conditions. The overall state equation is expressed as:

[0155]

[0156]

[0157] h represents the number of microgrids in the microgrid group, which determines the dimensions of the state variable vector, state matrix, input matrix, and input variable vector;

[0158] The sidelobe information of the eigenvalues ​​extracted in S2 is used to determine whether the parameters in the model have changed. For example, if the sidelobes of the eigenvalues ​​expand abnormally in a certain frequency range, it means that the parameters of some components in the microgrid have changed, and the model needs to be corrected and adjusted.

[0159] In S3, the method of establishing the probability distribution model of wind turbine, photovoltaic, and load using the nonparametric kernel density estimation method is as follows:

[0160] S321. Data Collection and Preprocessing: Collect historical data such as wind speed and output power of wind turbines, solar irradiance and output power of photovoltaic systems, and load power changes over time. Historical data is obtained from monitoring systems of wind farms and photovoltaic power plants, as well as metering devices in the power grid. The collected data is preprocessed to remove outliers and missing values. For example, for wind speed data, if the wind speed at a certain moment exceeds a certain percentage (e.g., 120%) of the local historical maximum wind speed, it is identified as an outlier and removed. For load data, if the power value is negative and does not conform to the actual situation (e.g., negative power for residential users), it is also processed accordingly.

[0161] S322. Kernel Function and Bandwidth Selection: The Gaussian kernel function is selected as the kernel function for probability density function estimation. The Silverman rule is used to initially determine the bandwidth, and then fine-tuning is performed through cross-validation. Cross-validation involves dividing the sample data into multiple subsets, performing kernel density estimation on different subsets, calculating the error between the estimated value and the true value (such as mean square error), and selecting the bandwidth value that minimizes the error.

[0162] The Gaussian kernel function formula is as follows:

[0163]

[0164] x represents the wind speed, light intensity, or load value for estimating probability density; K(x) represents the kernel function value;

[0165] Bandwidth calculation formula:

[0166]

[0167] σ is the standard deviation of the sample data, M is the number of samples; f represents the bandwidth;

[0168] S323. Calculation of probability density function: Calculate the probability density function according to the nonparametric kernel density estimation formula.

[0169]

[0170] Based on the feature value sidelobe information extracted in S2, the sample data is filtered. If the feature value sidelobe changes significantly in certain frequency ranges, it indicates that the range and distribution of the random input variable may have changed under these operating conditions. In this case, more sample data under this operating condition can be selected.

[0171] In S3, the method for processing the correlation and dependency between random input variables based on the optimal Copula function model, and obtaining the chaotic polynomial standard input variables through inverse cumulative transformation, is as follows:

[0172] S331. Marginal distribution determination: Integrate the established probability distribution models of wind turbines, photovoltaics, and loads to obtain the marginal distribution functions of random input variables (wind speed, solar intensity, load fluctuation, etc.). The marginal distribution functions describe the distribution of each random input variable, providing a foundation for the subsequent construction of joint distributions and handling of the correlation and dependence between variables.

[0173] S332. Copula Function Selection and Parameter Estimation: The Gaussian Copula function is chosen to describe the correlation between random input variables. The Gaussian Copula function is expressed as follows:

[0174] C(u1,u2,…,u η )=Φ ρ (Φ -1 (u1),Φ -1 (u2),…,Φ -1 (u η ));

[0175] u i =F i (x i (i = 1, 2, ..., η);

[0176] Where η represents the number of random variables; u i Let C(u1,u2,…,u) be the random input variables after marginal distribution function transformation; η ) represents the joint distribution of random variables constructed based on the values ​​after marginal distribution function transformation; Φ ρ Φ is an η-dimensional normal distribution function, where ρ is the correlation coefficient matrix, reflecting the correlation between variables. ρ is determined through analysis and fitting of historical data, using methods such as maximum likelihood estimation; -1 It is the inverse function of the standard normal distribution;

[0177] S333. Inverse cumulative transformation: The standard input variables of the chaotic polynomial are obtained through the inverse cumulative transformation. The formula is as follows:

[0178]

[0179] C i z is the i-th component of the Copula function; i F is the standard input variable for the chaotic polynomial. i Let x be the marginal distribution function of the i-th random input variable; i Let z be the sample value of the i-th random input variable; calculate z based on the above. i The value is the standard input variable of the chaotic polynomial; u i These are the random input variables after being transformed by the marginal distribution function;

[0180] In step S3, an explicit expression is established between critical mode damping and random input variables to realize a small-disturbance stability evaluation method:

[0181] S341. Based on chaotic polynomial theory, let the critical mode damping and the standard input variable z of the chaotic polynomial be... i The relationship is represented as:

[0182]

[0183] Where ξ represents critical mode damping; The coefficients of the chaotic polynomials determine the contribution of the combination of the basis functions of the chaotic polynomials to the damping of the critical mode. P is the chaotic polynomial basis function corresponding to the j-th random input variable; j The order of the chaotic polynomial affects its complexity and fitting accuracy. In practical applications, the order of the chaotic polynomial needs to be selected reasonably according to the specific problem and data characteristics in order to balance the accuracy of the model and the computational complexity.

[0184] It is obtained by using the least squares method and sample data. During the solution process, the sample data is filtered or weighted by combining the side lobe information of the eigenvalues ​​in S2. For example, the sample data corresponding to the frequency range with large side lobe intensity and concentrated distribution is given higher weight because these data can better reflect the characteristics of the system under key operating conditions.

[0185] S342. Small-disturbance stability assessment: After obtaining the explicit expression between the critical mode damping and the random input variables, the small-disturbance stability of the power system is assessed based on the magnitude of the critical mode damping. A critical mode damping threshold ξ is set. t (e.g., 0.05-0.1, this threshold can be determined based on the characteristics and operating experience of the actual power system), if the calculated critical mode damping ξ > ξ t If ξ < ξ, then the power system is considered stable under small disturbances; tIf the system exhibits abnormal changes in small disturbance stability, then the system faces a risk of instability under different operating conditions. Furthermore, by combining the eigenvalue sidelobe information in S2, the changing trend of the system's small disturbance stability under different operating conditions can be further analyzed. For example, when the eigenvalue sidelobe shows abnormal changes in certain frequency ranges, even if the current critical mode damping is greater than the threshold, the potential risk to system stability still needs to be considered. This is because abnormal changes in the sidelobe may indicate that certain parameters or operating states within the system are about to change, thus affecting system stability. In this case, corresponding control measures can be taken in advance, such as adjusting the power generation plan, rationally arranging the power output of various power sources based on predicted values ​​of wind speed, solar intensity, and load fluctuations, and optimizing the allocation of power generation resources; optimizing load allocation, using smart grid technology to rationally schedule different regions and different types of loads to balance the system's power demand; and activating backup power sources, promptly starting backup power sources when potential risks to system stability arise to increase the system's power reserves and ensure reliable system operation, thereby ensuring the safe and stable operation of the power system.

[0186] The above description is a preferred embodiment of the invention and is not intended to limit the scope of the invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A method for electromagnetic transient small-disturbance stability analysis of power systems based on multi-dimensional data, characterized in that, Includes the following steps: S1. Multi-dimensional data acquisition and fusion: Integrating multi-source data during the operation of the power system, this module collects the data in real time and uses data fusion technology to integrate data from different sources to form a unified data framework. S2. Eigenvalue sidelobe extraction and analysis: By preprocessing the multi-source data collected in S1, wavelet transform and Hilbert transform signal processing methods are used to extract eigenvalue sidelobe information from the preprocessed data. By quantitatively analyzing the sidelobe intensity, distribution and changing trend, the subtle changes in the signal propagation path are revealed. S3. Using the eigenvalue sidelobe information extracted in S2, combined with chaotic polynomial theory, the stability of the power system is evaluated: First, a small-signal analysis model for a microgrid cluster with interconnected back-to-back converters is established, taking correlated factors such as wind speed, light intensity, and load fluctuation as random input variables; Subsequently, a probability distribution model for wind turbines, photovoltaics, and loads was established using the nonparametric kernel density estimation method. Next, the correlation between random input variables is processed based on the optimal Copula function model, and the chaotic polynomial standard input variables are obtained through inverse cumulative transformation; Finally, an explicit expression is established between critical mode damping and random input variables to achieve small-disturbance stability assessment.

2. The method for electromagnetic transient small-disturbance stability analysis of power systems based on multi-dimensional data according to claim 1, characterized in that, The multi-source data includes power grid operation data, equipment status data, environmental data, and user behavior data. The power grid operation data includes voltage, current, and power time-series data, which are acquired through monitoring equipment installed at various nodes of the power grid. These devices record data at certain time intervals, forming a sequence that changes over time. Equipment status data is obtained from the equipment's own control system or monitoring device and is used to reflect the health status of the equipment. Environmental data is collected by meteorological monitoring stations or environmental sensors installed near power equipment to understand the impact of environmental factors on the power system. User behavior data is obtained from smart meters or electric vehicle charging management systems and reflects users' electricity consumption patterns.

3. The method for electromagnetic transient small-disturbance stability analysis of power systems based on multi-dimensional data according to claim 1, characterized in that, The data fusion technology mentioned includes: S111. Time synchronization: Utilizing the Global Positioning System (GPS) or the BeiDou satellite timing system, a precise time reference is provided for all data acquisition devices to ensure the consistency of data from different sources in time; when receiving data, the data acquisition terminal adds a time tag to each data sample according to the timing information; S112. Data cleaning and preprocessing: Clean the collected data to remove outliers and erroneous data; for continuous voltage and current data, detect anomalies by setting threshold ranges; for discrete data such as equipment status, check the rationality and completeness of the data; at the same time, normalize the data to map data of different dimensions to a unified numerical range. S113. Data fusion algorithm: Arrange power grid operation data, equipment status data, environmental data, and user behavior data in chronological order to form a multidimensional data matrix X, and calculate the covariance matrix of the data matrix. In the formula, n is the sample size, and X... T Let X be the transpose of the multidimensional data matrix X, and C be the covariance matrix of the data matrix; Perform eigenvalue decomposition on the covariance matrix: C=U∧U T ; U is the eigenvector matrix; ∧ is the eigenvalue diagonal matrix. The eigenvectors corresponding to the first r largest eigenvalues ​​are selected to form the projection matrix P, which projects the original data onto a new low-dimensional space to obtain the fused data Y = XP, forming a unified data framework.

4. The method for electromagnetic transient small-disturbance stability analysis of power systems based on multi-dimensional data according to claim 1, characterized in that, The preprocessing steps for multi-source data in S2 include: S211. Denoising: Wavelet thresholding is used to denoise the fused data. First, based on the data characteristics, the db4 wavelet is selected to perform wavelet decomposition, decomposing the data into different scale spaces to obtain the corresponding wavelet coefficients. The threshold λ is then calculated according to the general threshold formula. ： Where σ represents the noise standard deviation, which is estimated through statistical analysis of noisy data; l is the data length; A soft thresholding method is used to process the wavelet coefficients. When the absolute value of a wavelet coefficient is less than the threshold, the wavelet system is set to 0; when it is greater than the threshold, the wavelet system is shrunk to: sgn(W j′,k′ )(|W j′,k′ |-λ); sgn(·) is the sign function, W j′,k′ ... After processing, the denoised data is normalized again to ensure the consistency and comparability of the data in subsequent analysis. The processed wavelet coefficients are reconstructed by inverse wavelet transform to obtain the denoised data. S212. Normalization: In order to eliminate the influence of different data units and ensure the consistency and comparability of data in subsequent analysis, the same normalization method as in the data acquisition stage is used on the denoised data to map the data to the [0,1] interval.

5. The method for electromagnetic transient small-disturbance stability analysis of power systems based on multi-dimensional data according to claim 1, characterized in that, In S2, the method of extracting eigenvalue sidelobe information from preprocessed data using wavelet transform and Hilbert transform signal processing methods is as follows: S221. Wavelet Transform: Perform Discrete Wavelet Transform (DWT) on the preprocessed data. The discrete wavelet function is defined as follows: Where, ψ j,k (m) represents the discrete wavelet function; j is the scaling parameter, which determines the scaling degree of the wavelet function; k is the translation parameter, which determines the position of the wavelet function on the time axis; ψ(m) is the basic wavelet function; m is the index of the discrete time series; The wavelet coefficients are obtained by performing a DWT transform on the discretized original signal: x(m) represents the original signal after discretization, which is used as the input signal in the Hilbert transform; N is the data length; By analyzing wavelet coefficients at different scales j and positions k, local features of the signal at different frequencies and time resolutions are obtained, highlighting the detailed information of the signal. S222. Hilbert Transform: Based on the wavelet transform, the Hilbert transform is applied to the obtained wavelet coefficients. The discrete form of the Hilbert transform is: H[x(m)] is the result of performing a Hilbert transform on the discretized original signal x(m); s is the variable in the summation operation; The discretized original signal x(m) is converted into an analytic signal z(m) by the Hilbert transform, which is expressed as: z(m) = x(m) + jH[x(m)]; The analyzed signal contains the amplitude and phase information of the original signal. By analyzing the analyzed signal, the signal characteristics can be obtained more comprehensively and accurately.

6. The method for electromagnetic transient small-disturbance stability analysis of power systems based on multi-dimensional data according to claim 1, characterized in that, In step S2, the steps for quantitatively analyzing the sidelobe intensity, distribution, and changing trends include: S231. Sidelobe strength calculation: The main lobe amplitude and sidelobe amplitude of the signal are determined by the spectrum analysis method. The spectrum analysis uses the Fast Fourier Transform (FFT) algorithm to convert the time domain signal to the frequency domain for analysis. The sidelobe strength is defined as the ratio of the sidelobe amplitude to the main lobe amplitude. The sidelobe strength can intuitively reflect the relative importance of the sidelobe in the entire signal spectrum. The larger the sidelobe strength, the greater the influence of the sidelobe on the overall characteristics of the signal. S232. Sidelobe distribution analysis: The frequency range is divided into multiple sub-intervals, and the number of sidelobes in each sub-interval is counted. Simultaneously, the energy of the sidelobes in each sub-interval is calculated. Among them, [f i ,f i+1 Let A be the i-th subinterval. s (f) is the sidelobe amplitude at frequency f; By analyzing the distribution of sidelobe energy in different frequency sub-intervals, we can understand the frequency characteristics and distribution patterns of sidelobes and determine which frequency intervals have a greater impact on the signal. S233. Sidelobe variation trend analysis: Using a fixed time interval as the period, continuously calculate the sidelobe intensity and distribution characteristics within each time interval, record the calculated sidelobe intensity and distribution characteristics over time, and plot the corresponding time series curves; by observing the trend of the curves, analyze the variation trend of sidelobe characteristics over time; if the sidelobe intensity or distribution changes significantly over a period of time, it indicates that there are slight changes in the signal propagation path, and these changes are related to the changes in the operating state of the power system.

7. The method for electromagnetic transient small-disturbance stability analysis of power systems based on multi-dimensional data according to claim 1, characterized in that, In S3, the method for establishing a small-signal analysis model for microgrid clusters with back-to-back converter interconnection is as follows: S311. Single microgrid modeling: A microgrid group interconnected by back-to-back converters involves multiple microgrids connected via back-to-back converters. For the i-th microgrid, the constructed state equation is: Among them, X i This is a state variable vector containing the state information of each component within the microgrid, such as the rotor angle and angular velocity of the generator, and the magnitude and phase angle of the node voltage; A i Let A be the state matrix. i Reflects the dynamic coupling relationship between components within a microgrid; B i Given the input matrix, B i Related to the input variable vector, the input variable vector is selected from factors such as wind speed, light intensity, and load fluctuation, which are correlated; U i For the input variable vector; S312. Overall modeling of the microgrid group: The overall state equation is obtained by combining the state equations of each microgrid and considering the connection relationship of the converters. The overall state equation is the overall dynamic interaction model of the group, simulating the operating state of the microgrid group under different operating conditions. The overall state equation is expressed as: h represents the number of microgrids in the microgrid group, which determines the dimensions of the state variable vector, state matrix, input matrix, and input variable vector; The eigenvalue sidelobe information extracted from S2 is used to determine whether the parameters in the model have changed. If the eigenvalue sidelobe expands abnormally in a certain frequency range, it means that the parameters of some components in the microgrid have changed, and the model needs to be corrected and adjusted.

8. The method for electromagnetic transient small-disturbance stability analysis of power systems based on multi-dimensional data according to claim 1, characterized in that, In S3, the method of establishing the probability distribution model of wind turbines, photovoltaics, and load using the nonparametric kernel density estimation method is as follows: S321. Data collection and preprocessing: Collect historical data such as wind speed and output power of wind turbines, solar irradiance and output power of photovoltaics, and power changes of loads over time; historical data are obtained from the monitoring systems of wind farms and photovoltaic power plants and the metering devices of the power grid; preprocess the collected data to remove outliers and missing values. S322. Kernel function and bandwidth selection: The Gaussian kernel function is selected as the kernel function for probability density function estimation; the Silverman rule is used to initially determine the bandwidth, and then fine-tuning is performed using cross-validation. The Gaussian kernel function formula is as follows: x represents the wind speed, light intensity, or load value for estimating probability density; K(x) represents the kernel function value; Bandwidth calculation formula: σ is the standard deviation of the sample data, M is the number of samples; f represents the bandwidth; S323. Calculation of probability density function: Calculate the probability density function according to the nonparametric kernel density estimation formula. Based on the feature value sidelobe information extracted in S2, the sample data is filtered. If the feature value sidelobe shows significant changes in certain frequency ranges, it indicates that the range and distribution of the random input variable have changed under these operating conditions. In this case, more sample data under this operating condition should be selected.

9. The method for electromagnetic transient small-disturbance stability analysis of power systems based on multi-dimensional data according to claim 1, characterized in that, In S3, the method for processing the correlation and dependency between random input variables based on the optimal Copula function model, and obtaining the chaotic polynomial standard input variables through inverse cumulative transformation, is as follows: S331. Marginal distribution determination: Integrate the established probability distribution models of wind turbines, photovoltaics, and loads to obtain the marginal distribution functions of the random input variables. The marginal distribution functions describe the distribution of each random input variable. S332. Copula Function Selection and Parameter Estimation: The Gaussian Copula function is chosen to describe the correlation between random input variables. The Gaussian Copula function is expressed as follows: C(u1,u2,…,u η )=Φ ρ (F -1 (u1),Φ -1 (u2),…,Φ -1 (u η )); u i =F i (x i )(i=1,2,…η); Where η represents the number of random variables; u i Let C(u1,u2,…,u) be the random input variables after marginal distribution function transformation; η ) represents the joint distribution of random variables constructed based on the values ​​after marginal distribution function transformation; Φ ρ ρ is an η-dimensional normal distribution function, and ρ is the correlation coefficient matrix, reflecting the correlation between variables. ρ is determined by analyzing and fitting historical data, using methods such as maximum likelihood estimation; Φ -1 It is the inverse function of the standard normal distribution; S333. Inverse cumulative transformation: The standard input variables of the chaotic polynomial are obtained through the inverse cumulative transformation. The formula is as follows: C i z is the i-th component of the Copula function; i F is the standard input variable for the chaotic polynomial. i Let x be the marginal distribution function of the i-th random input variable; i Let z be the sample value of the i-th random input variable; calculate z based on the above. i The value is the standard input variable of the chaotic polynomial; u i These are the random input variables after being transformed by the marginal distribution function.

10. The method for electromagnetic transient small-disturbance stability analysis of power systems based on multi-dimensional data according to claim 1, characterized in that, In step S3, an explicit expression is established between critical mode damping and random input variables to realize a small-disturbance stability evaluation method: S341. Based on chaotic polynomial theory, let the critical mode damping and the standard input variable z of the chaotic polynomial be... i The relationship is represented as: Where ξ represents critical mode damping; The coefficients of the chaotic polynomials determine the contribution of the combination of the basis functions of the chaotic polynomials to the damping of the critical mode. P is the chaotic polynomial basis function corresponding to the j-th random input variable; j The order of the chaotic polynomial affects its complexity and fitting accuracy. It is obtained by using the least squares method and sample data; during the solution process, the sample data is filtered or weighted by combining the eigenvalue sidelobe information in S2. S342. Small-disturbance stability assessment: After obtaining the explicit expression between the critical mode damping and the random input variables, the small-disturbance stability of the power system is assessed based on the magnitude of the critical mode damping; a critical mode damping threshold ξ is set. t If the calculated critical mode damping ξ > ξ t If ξ < ξ, then the power system is considered stable under small disturbances; t If the system exhibits abnormal changes in small disturbance stability, then the system faces a risk of instability under small disturbances. Furthermore, by combining the eigenvalue sidelobe information in S2, we can further analyze the changing trend of the system's stability under different operating conditions. When the eigenvalue sidelobe shows abnormal changes in certain frequency ranges, even if the current critical mode damping is greater than the threshold, we still need to pay attention to the potential risks to the system's stability.

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