Frequency analysis method and system based on multi-collinearity subduction generative adversarial network

Abstract

The invention discloses a frequency analysis method and system based on a multi-collinearity subduction generative adversarial network, and relates to the field of power system source and load scene generation. Comprising the following steps: acquiring historical source and load random scene data, performing spatio-temporal conjoint analysis and progressive statistical analysis on the historical source and load random scene data, generating a historical data set matrix, and performing dimension reduction processing; performing multi-collinearity diagnosis on the source and load random scene data after dimension reduction processing, and eliminating collinearity greater than a preset value; bayesian prior distribution and variation inference are introduced into the generative adversarial network model to optimize a network structure, and a multi-collinearity subduction generative adversarial network model is obtained; and generating diversified source and load scene data, inputting the diversified source and load scene data into the power system frequency response model for simulation analysis, and evaluating the frequency response characteristics of the power system in different source and load fluctuation scenes. The method effectively improves the precision of the model and the stability of the system, and is suitable for generating diversified frequency analysis scenes.

Description

Technical Field

[0001] The present invention relates to the field of power system source and load scenario generation, and in particular to a frequency analysis method and system based on a multicollinearity elimination generative adversarial network. Background Art

[0002] With the rapid development of renewable energy (such as wind power and photovoltaics), the randomness and uncertainty of sources and loads in the power system have increased significantly. This uncertainty is not only reflected in the time dimension, but also involves the correlation of the spatial dimension, especially between photovoltaic power stations, wind farms and load demands in different geographical locations. Traditional frequency analysis methods face the challenges of low accuracy and weak adaptability when dealing with these complex source and load fluctuation scenarios. Existing technologies mostly rely on historical data or statistical models for disturbance frequency analysis, which has many limitations.

[0003] Source and load data usually have multicollinearity problems, that is, there is a high degree of linear correlation between multiple variables, which leads to inaccurate estimation of model parameters, thus affecting the accuracy and effectiveness of frequency analysis. Traditional methods often ignore this problem, resulting in insufficient accuracy of system frequency analysis. In addition, source and load data have significant spatiotemporal correlation, and simple time series modeling cannot fully reflect its complexity. At the same time, due to the volatility of wind power and photovoltaics, the data samples of system operation scenarios are limited. Existing methods show limitations in dealing with data scarcity and uncertainty, and it is difficult to improve modeling accuracy. On the other hand, the source and load scenario data generated by the frequency analysis method based on historical data lacks diversity, which limits the comprehensiveness of frequency analysis. This not only leads to blind spots in frequency stability assessment and risk analysis, but also makes the system unable to effectively cover a wide range of operating scenarios. Therefore, there is an urgent need for more diverse scenario generation methods to improve the coverage and accuracy of frequency analysis.

[0004] In recent years, generative adversarial networks have made significant progress in the field of data generation and can generate realistic simulation data by learning data distribution. Therefore, generative adversarial networks have been widely introduced into the modeling and data analysis of power systems, especially in generating source and load random scenario data and improving the diversity of data samples, showing great potential. However, generative adversarial networks still face the challenge of multicollinearity when dealing with source and load scenarios. Multicollinearity in source and load data will lead to redundancy in the data generated by the model and fail to accurately capture the nonlinear relationship between variables, which not only reduces the diversity of the generated data, but also affects its authenticity. Therefore, the source and load scenario data generated by the generative adversarial network often have deviations when simulating complex scenarios, and it is difficult to fully meet the requirements for high precision and diversified scenarios in power system frequency analysis.

[0005] In view of this, this application is hereby filed. Summary of the invention

[0006] The technical problem to be solved by the present invention is that the source and load scenario data generated by the prior art generative adversarial network often have deviations when simulating complex scenarios, and it is difficult to fully meet the requirements for high precision and diversified scenarios in power system frequency analysis. The purpose of the present invention is to provide a frequency analysis method and system based on a generative adversarial network with multicollinearity reduction. The method integrates multicollinearity reduction into a generative adversarial network for optimal frequency analysis of power systems under uncertainty on both the source and load sides, thereby effectively improving the accuracy of the model and the stability of the system. The present invention is suitable for generating diversified frequency analysis scenarios.

[0007] The present invention is achieved through the following technical solutions:

[0008] In a first aspect, the present invention provides a frequency analysis method based on a multicollinearity reduction generative adversarial network, the method comprising:

[0009] Obtain historical source and load-random scene data, conduct spatiotemporal joint analysis and progressive statistical analysis on the historical source and load-random scene data, and generate a historical data set matrix; use dimensionality reduction technology to reduce the dimension of the historical data set matrix to obtain processed source and load-random scene data;

[0010] Perform multicollinearity diagnosis on the processed source and load random scene data, eliminate the collinearity greater than the preset value, and obtain the data after eliminating the collinearity;

[0011] Based on the data after eliminating collinearity, a generative adversarial network model is constructed; and Bayesian prior distribution and variational inference are introduced into the generative adversarial network model to optimize the network structure, thus obtaining a multicollinearity-eliminating generative adversarial network model;

[0012] Based on the multicollinearity elimination generative adversarial network model, diversified source and load scenario data are generated, and the diversified source and load scenario data are input into the power system frequency response model for simulation analysis to evaluate the frequency response characteristics of the power system under different source and load fluctuation scenarios.

[0013] The above technical solution, the present invention accurately captures the data characteristics of source and load random variables through spatiotemporal characteristic analysis combined with progressive statistical analysis and dimensionality reduction technology. Then, the multicollinearity reduction technology is integrated into the generative adversarial network to generate more diverse and realistic source and load fluctuation scenario data by eliminating multicollinearity in the data, providing high-quality scenario data support for power system frequency analysis under uncertainty on both sides of the source and load, thereby effectively improving the accuracy of the model and the stability of the system.

[0014] Furthermore, the historical source and load random scenario data include historical data of photovoltaic power plants and wind farms and historical data of load demand;

[0015] The historical data of photovoltaic power plants and wind farms include hourly sampling values ​​of power generation;

[0016] The historical data of load demand includes hourly sampling values ​​of power consumption;

[0017] Among them, the historical data of photovoltaic power stations and wind farms, and the historical data of load demand all contain geographic location coordinates.

[0018] Furthermore, the historical source and load random scene data are subjected to spatiotemporal joint analysis and progressive statistical analysis to generate a historical data set matrix. The historical data set matrix is ​​subjected to dimensionality reduction processing using dimensionality reduction technology to obtain processed source and load random scene data, including:

[0019] Combining time dimension analysis and space dimension analysis, the historical source and load random scene data are analyzed in a time-by-hour manner to obtain the first data;

[0020] Using a progressive statistical analysis method, statistically analyzing the first data on a quarterly and daily basis to obtain second data;

[0021] Based on the second data, a historical data set matrix is ​​generated; the historical data set matrix is ​​a source and load random variable set with high temporal correlation and high spatial correlation;

[0022] The principal component analysis (PCA) dimensionality reduction technique is used to reduce the dimension of the historical data set matrix to obtain the processed source and load random scene data.

[0023] Furthermore, the expression of the historical data set matrix is:

[0024]

[0025] In the formula, X is the historical data set matrix, N is the number of days, T is the number of daily time sampling points, and for each day’s data x i , its expanded form is: in, represents the source and load data at the tth time point on the i-th day, and K is the number of different types of source and load random scenarios (such as photovoltaic, wind power, and load).

[0026] Furthermore, multicollinearity diagnosis is performed on the processed source and load random scene data to eliminate collinearity greater than a preset value, and obtain data after collinearity elimination, including:

[0027] Performing data standardization on the processed source and load random scene data to obtain standardized data;

[0028] Calculate the covariance matrix of the standardized data and perform multicollinearity diagnosis based on the covariance matrix;

[0029] The strength of collinearity in the data is diagnosed by using the variance inflation factor, and the eigenvalue decomposition is performed using the covariance matrix to eliminate collinearity greater than a preset value;

[0030] The eigenvalue decomposition results are processed by data dimension reduction, projection and recovery to obtain the data after eliminating collinearity.

[0031] Furthermore, the Bayesian prior distribution and variational inference are introduced into the generative adversarial network model to optimize the network structure, and a multicollinearity reduction generative adversarial network model is obtained, including:

[0032] Introduce Bayesian prior distribution into the generative adversarial network model, assume that the hidden variable θ of the generator obeys the standard Gaussian distribution, and define the likelihood function of the generative adversarial network model;

[0033] Using variational inference techniques, we approximate the true posterior distribution through a parameterized approximate distribution;

[0034] The KL divergence is introduced to measure the difference between the approximate distribution and the true posterior distribution, and the parameters of the generator are optimized by minimizing the KL divergence;

[0035] Combining the loss of the generative adversarial network model with the loss term predetermined by multicollinearity, the minimization of the loss function is used as the objective function of the generator;

[0036] By minimizing the objective function, the generator can continuously optimize its own hidden variable θ under the feedback of the discriminator, and obtain a multicollinearity reduction generative adversarial network model.

[0037] Furthermore, the expression of the KL divergence is:

[0038]

[0039] The loss function The expression is:

[0040]

[0041] Where θ is the parameter of the model; φ is the variational parameter; KL() is the divergence function to measure the difference between the two distributions; logq(θ|x; φ) is the logarithmic probability density function of the approximate distribution, and logp(θ|x) is the logarithmic probability density function of the true distribution. is the expectation under the approximate distribution, q(θ|x; φ) is the approximate posterior distribution, and p(θ|x) is the true posterior distribution.

[0042] Furthermore, based on the multicollinearity reduction generative adversarial network model, a variety of source and load scenario data are generated, and the diverse source and load scenario data are input into the power system frequency response model for simulation analysis to evaluate the frequency response characteristics of the power system under different source and load fluctuation scenarios, including:

[0043] A set of random noise vectors are input into the generator of the multicollinearity reduction generative adversarial network model to generate diverse source and load scenario data;

[0044] Input diverse source and load scenario data into the power system frequency response model for simulation;

[0045] The Euler method in numerical methods is used to solve the differential equations of the power system frequency response model and simulate the frequency changes of the power system under different source and load fluctuation scenarios;

[0046] By simulating frequency response, the frequency variation curve and key indicators of the power system under different source and load fluctuation scenarios are obtained; and the frequency response characteristics of the power system under various scenarios are analyzed based on key indicators.

[0047] In a second aspect, the present invention further provides a frequency analysis system based on a multicollinearity reduction generative adversarial network, the system comprising:

[0048] A data acquisition unit, used to acquire historical source and load random scene data;

[0049] The first analysis unit is used to perform spatiotemporal joint analysis and progressive statistical analysis on the historical source and load random scene data to generate a historical data set matrix;

[0050] A dimensionality reduction processing unit, used to perform dimensionality reduction processing on the historical data set matrix by using dimensionality reduction technology to obtain processed source and load random scene data;

[0051] A multicollinearity diagnosis and elimination unit is used to perform multicollinearity diagnosis on the processed source and load random scene data, eliminate collinearity greater than a preset value, and obtain data after collinearity elimination;

[0052] A generative adversarial network construction unit, used to construct a generative adversarial network model based on the data after eliminating collinearity;

[0053] The network model optimization unit is used to introduce Bayesian prior distribution and variational inference into the generative adversarial network model to optimize the network structure and obtain a multicollinearity-reducing generative adversarial network model;

[0054] The second analysis unit is used to generate diversified source and load scenario data based on the multicollinearity reduction generative adversarial network model, input the diversified source and load scenario data into the power system frequency response model for simulation analysis, and evaluate the frequency response characteristics of the power system under different source and load fluctuation scenarios.

[0055] Furthermore, the multicollinearity diagnosis and elimination unit includes:

[0056] A standardization processing subunit is used to perform data standardization processing on the processed source and load random scene data to obtain standardized data;

[0057] A covariance matrix calculation subunit, used to calculate the covariance matrix of the standardized data;

[0058] A diagnosis and elimination subunit is used to perform multicollinearity diagnosis based on the covariance matrix, diagnose the collinearity strength in the data through the variance inflation factor, and perform eigenvalue decomposition using the covariance matrix to eliminate collinearity greater than a preset value;

[0059] The result processing subunit is used to perform data dimension reduction, projection and recovery processing on the eigenvalue decomposition results to obtain data after eliminating collinearity.

[0060] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0061] 1. The frequency analysis method and system of the present invention based on the multicollinearity reduction generative adversarial network, through in-depth analysis of the spatiotemporal characteristics of source and load random variables, through progressive statistical analysis and spatiotemporal correlation modeling, effectively improves the accuracy of source and load uncertainty modeling, can fully capture the potential correlation and trend in the data, and ensure that the frequency analysis can cover a variety of complex operation scenarios;

[0062] 2. The frequency analysis method and system of the present invention based on the multicollinearity reduction generative adversarial network, the present invention eliminates the linear correlation in the data through the multicollinearity reduction technology, ensures that the generated data is more independent and diversified, enhances the training stability and generalization ability of the frequency analysis model, and thus improves the accuracy and effectiveness of the frequency analysis scenario;

[0063] 3. The present invention is based on a frequency analysis method and system for a generative adversarial network with multicollinearity reduction. The present invention integrates multicollinearity reduction technology into a generative adversarial network model, and by introducing Bayesian statistics and variational inference, improves the model's ability to capture data distribution characteristics, generates high-quality simulation data for power system frequency analysis, and solves the problem of modeling errors caused by insufficient data in the prior art. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of this application, and do not constitute a limitation of the embodiments of the present invention. In the drawings:

[0065] Figure 1 This is a flow chart of a frequency analysis method based on a multicollinearity reduction generative adversarial network according to the present invention;

[0066] Figure 2 A framework diagram of a generative adversarial network model for multicollinearity reduction of the present invention;

[0067] Figure 3 A frequency analysis flow chart for generating an adversarial network for multicollinearity reduction of the present invention;

[0068] Figure 4 A comparison diagram of the actual scenario of the method of the present invention and the scenario generated by the multicollinearity reduction generative adversarial network;

[0069] Figure 5 This is a structural block diagram of the frequency analysis system of the present invention based on the multicollinearity reduction generative adversarial network. DETAILED DESCRIPTION

[0070] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with embodiments and drawings. The exemplary embodiments of the present invention and their description are only used to explain the present invention and are not intended to limit the present invention.

[0071] Figure 2It is a framework diagram of the generative adversarial network model for multicollinearity reduction of the method of the present invention. First, by comprehensively collecting historical data of photovoltaic power stations, wind farms and historical data of load demand, a detailed analysis is carried out in combination with the time dimension and spatial dimension of each hour and each season to accurately identify the potential multicollinearity characteristics in the source and load data. In this process, the hourly analysis can capture the changing trend in different time periods, and the quarterly analysis can reflect the long-term trend with seasonal changes. These analyses ensure a clear understanding of the spatiotemporal characteristics of the source and load random variables, thereby providing a data basis for subsequent modeling. After the data preprocessing is completed, the multicollinearity problem in the data is systematically diagnosed and eliminated through the calculation of the covariance matrix and eigenvalue decomposition. The covariance matrix reflects the correlation between different source and load variables, and the eigenvalue decomposition helps to identify and remove redundant correlations, thereby ensuring that the generative adversarial network model can better capture the nonlinear relationship between the source and load random variables in subsequent processing. The fine processing of this step ensures that the data has independence and diversity in the model, avoiding model distortion caused by collinearity problems. Finally, the data after multicollinearity reduction is integrated into the generative adversarial network model. In the training process of the generative adversarial network model, a Bayesian statistical model is introduced to capture the uncertainty in the data distribution, and the training process of the generator is optimized through variational inference technology. Bayesian statistics can provide a reasonable prior distribution for the generator, while variational inference further improves the quality and diversity of the generated data by approximating the posterior distribution. Through this optimization process, the generator can dynamically learn and continuously improve, and ultimately generate diverse and realistic frequency analysis scene data.

[0072] Figure 3 The figure is a frequency analysis flow chart of the multicollinearity reduction generative adversarial network model of the method of the present invention. First, a variety of source and load scenario data are generated by the multicollinearity reduction generative adversarial network to better simulate the complex dynamic characteristics of photovoltaic power generation, wind power generation and load demand in the power system. On this basis, a frequency response model of the power system is constructed. The model describes the dynamic frequency response of the system under different source and load scenarios through differential equations, and comprehensively considers key parameters such as the inertia, frequency modulation characteristics and load characteristics of the system. Next, through statistical analysis of the frequency response simulation results, key indicators such as frequency deviation and recovery time under different scenarios are evaluated. By generating probability distribution functions and cumulative distribution functions, the frequency stability of the system under various scenarios is comprehensively analyzed, and the risk of the system exceeding the allowable frequency deviation range under different conditions is evaluated. Finally, a parameter sensitivity analysis is performed to study the influence of parameters such as the inertia constant of the system on the frequency response of the system by changing them. This analysis helps to identify key parameters that affect system stability and provides a reference for optimizing system frequency stability to ensure the safe and reliable operation of the power system under diverse scenarios.

[0073] Example 1

[0074] like Figure 1 As shown, Figure 1 The present invention is a flow chart of a frequency analysis method based on a multicollinearity reduction generative adversarial network; the present invention is a frequency analysis method based on a multicollinearity reduction generative adversarial network, the method comprising:

[0075] Step 1, obtain historical source and load random scene data, perform spatiotemporal joint analysis and progressive statistical analysis on the historical source and load random scene data, and generate a historical data set matrix; use dimensionality reduction technology to reduce the dimension of the historical data set matrix to obtain processed source and load random scene data;

[0076] Step 2, performing multicollinearity diagnosis on the processed source and load random scene data, eliminating collinearity greater than a preset value, and obtaining data after collinearity elimination;

[0077] Step 3, constructing a generative adversarial network model based on the data after eliminating collinearity; and introducing Bayesian prior distribution and variational inference to optimize the network structure in the generative adversarial network model to obtain a multicollinearity-reduced generative adversarial network model;

[0078] Step 4: Generate diversified source and load scenario data based on the multicollinearity reduction generative adversarial network model, input the diversified source and load scenario data into the power system frequency response model for simulation analysis, and evaluate the frequency response characteristics of the power system under different source and load fluctuation scenarios.

[0079] The above technical solution, the present invention accurately captures the data characteristics of source and load random variables through spatiotemporal characteristic analysis combined with progressive statistical analysis and dimensionality reduction technology. Then, the multicollinearity reduction technology is integrated into the generative adversarial network to generate more diverse and realistic source and load fluctuation scenario data by eliminating multicollinearity in the data, providing high-quality scenario data support for power system frequency analysis under uncertainty on both sides of the source and load, thereby effectively improving the accuracy of the model and the stability of the system.

[0080] In this embodiment, step 1 identifies the multicollinearity characteristics in the source and load data through detailed spatiotemporal characteristics analysis, and uses progressive statistical analysis and dimensionality reduction technology to effectively model the data. This analysis process can accurately capture the dynamic characteristics of the source and load random variables, laying the foundation for the subsequent multicollinearity reduction steps.

[0081] Specifically, the historical source and load random scenario data include historical data of photovoltaic power plants and wind farms and historical data of load demand;

[0082] The historical data of photovoltaic power plants and wind farms include hourly sampling values ​​of power generation;

[0083] The historical data of load demand includes hourly sampling values ​​of power consumption;

[0084] The historical data of photovoltaic power stations and wind farms, as well as the historical data of load demand, all contain geographic location coordinates to analyze spatial correlation. The frequency of data collection is at least once an hour to ensure accurate capture of spatiotemporal characteristics. The time span of data collection should cover multiple quarters or years to analyze changes in different seasons and climate conditions.

[0085] Specifically, the historical source and load random scene data are subjected to spatiotemporal joint analysis and progressive statistical analysis to generate a historical data set matrix; the historical data set matrix is ​​subjected to dimensionality reduction processing using dimensionality reduction technology to obtain processed source and load random scene data, including:

[0086] Step 11, combining time dimension analysis and space dimension analysis, performing spatiotemporal joint analysis on the historical source and load random scene data in an hourly manner to obtain first data;

[0087] Step 11 specifically includes:

[0088] (1) Time dimension analysis

[0089] In order to better understand the time series variation of the source and load random variables, we first analyze the data hour by hour. Through this expansion, we can better capture the time series variation characteristics within each day. Specifically, for each day’s data X i (t), expanded into an hourly matrix:

[0090]

[0091] Among them, X i represents the source and load data of the i-th day; is the source and load data at the tth time point on the i-th day; T is the number of time sampling points in a day (such as T=24 means hourly sampling).

[0092] (2) Spatial dimension analysis

[0093] Based on the similarity of geographical locations, it can be found that adjacent or close photovoltaic power stations, wind farms and load demands show a certain positive correlation. In order to quantify this spatial correlation, the spatial correlation coefficient r is used. ij To measure the data correlation between two different positions i and j:

[0094]

[0095] Among them, μ i and μ jare the average output or load value at positions i and j, respectively, r ij The closer it is to 1, the stronger the correlation between the two positions.

[0096] (3) Spatiotemporal joint analysis

[0097] Combine time dimension analysis with space dimension analysis to identify highly correlated source and load variables. For example, under similar climate conditions, the output trends of adjacent photovoltaic power stations and wind farms at the same time may be very similar, showing a high positive correlation. For these source and load variables with time and space correlation, overall modeling is performed to avoid the deviation caused by independent analysis.

[0098]

[0099] The overall modeling can reflect these spatiotemporal correlations and provide data support for subsequent multicollinearity reduction and frequency analysis scenario generation.

[0100] Step 12, using a progressive statistical analysis method, statistically analyzing the first data on a quarterly and daily basis to obtain second data;

[0101] Step 12 specifically includes:

[0102] In order to better understand the seasonal trends of source and load data, we analyze the average source and load data through statistics of quarterly changes to identify the trend of changes. We perform statistical analysis on hourly data every day to capture peaks and valleys and optimize the modeling of daily changes.

[0103]

[0104] Among them, X * Represents the average source and load data for each hour of each day.

[0105] Step 13, based on the second data, generate a historical data set matrix; the historical data set matrix is ​​a source and load random variable set with high temporal correlation and high spatial correlation;

[0106] After the progressive statistical analysis method is completed, the historical data set is defined as follows:

[0107]

[0108] The historical data set is organized into a matrix form, that is, the expression of the historical data set matrix is:

[0109]

[0110] In the formula, X is the historical data set matrix, N is the number of days, T is the number of daily time sampling points, and for each day’s data xi , its expanded form is: in, represents the source and load data at the tth time point on the i-th day, and K is the number of different types of source and load random scenarios (such as photovoltaic, wind power, and load).

[0111] Step 14, using principal component analysis (PCA) dimensionality reduction technology to reduce the dimension of the historical data set matrix to obtain processed source and load random scene data.

[0112] In order to further reduce the dimension of the data and extract the most representative information, principal component analysis (PCA) dimensionality reduction technology is used to reduce the dimension of each day's data and then build a model to reduce unnecessary noise and redundant information:

[0113] X reduced = PCA(X) (7);

[0114] By extracting the principal components, the temporal and spatial characteristics of the data can be more effectively represented and the model calculation can be simplified.

[0115] In this embodiment, step 2 systematically eliminates the multicollinearity problem in the source and load data through multicollinearity diagnosis and reduction. First, the collinearity strength in the data is diagnosed, and then the eigenvalue decomposition of the covariance matrix is ​​used for dimensionality reduction and projection, and finally it is verified whether the collinearity is significantly eliminated. After eliminating multicollinearity, the linear correlation of the data is weakened, ensuring that the subsequent generative adversarial network model can better capture the nonlinear relationship between the source and load random variables, thereby generating more diverse and realistic frequency analysis scenario data. The specific process is as follows:

[0116] Step 21, performing data standardization processing on the processed source and load random scene data to obtain standardized data;

[0117] In order to ensure the dimensional consistency of different source and load random variables and avoid the value range of some features being too large or too small to affect model training, it is necessary to standardize the source and load random scene data processed in step 1. Convert the feature data of each source and load variable into a standard normal distribution with a mean of 0 and a standard deviation of 1:

[0118]

[0119] in, is the data at the tth time point on the i-th day; μ is the mean of the data; σ is the standard deviation of the data.

[0120] This normalization process ensures that the data is not affected by dimensional differences and that each feature has a similar scale range in the model.

[0121] Step 22, calculating the covariance matrix of the standardized data, and performing multicollinearity diagnosis based on the covariance matrix;

[0122] Multicollinearity can be detected by the covariance matrix. The covariance matrix C reflects the correlation between the source and the load random variable. Calculate the covariance matrix C of the standardized data:

[0123]

[0124] Where N is the number of sample days; T is the number of time sampling points per day; It is the standardized data; is the transposed data after standardization;

[0125] The diagonal elements of the covariance matrix represent the variance of each source and load variable, while the off-diagonal elements represent the correlation between different variables. The larger the off-diagonal elements of the covariance matrix, the stronger the multicollinearity between the variables.

[0126] Step 23, diagnosing the collinearity strength in the data through the variance inflation factor, and performing eigenvalue decomposition using the covariance matrix to eliminate collinearity greater than a preset value;

[0127] In order to quantify the strength of multicollinearity, the variance inflation factor (VIF) is used to diagnose whether there is multicollinearity in the data. VIF can measure whether a variable is linearly predicted by other variables, thereby determining the severity of collinearity.

[0128] For each variable x j , calculate its VIF:

[0129]

[0130] in, is the variable x in the regression analysis j The coefficient of determination predicted by other variables. VIF(x j ) is larger, indicating that the collinearity between the variable and other variables is stronger. It is generally believed that when VIF(x j ))>10, the variable has serious multicollinearity problems and the data needs to be eliminated.

[0131] After diagnosing multicollinearity, in order to effectively eliminate collinearity, eigenvalue decomposition is performed on the covariance matrix C. Through eigenvalue decomposition, the main relevant dimensions can be found, and redundant correlations can be removed, thereby reducing collinearity.

[0132] Perform eigenvalue decomposition on the covariance matrix C:

[0133]

[0134] Among them, U is the eigenvector matrix, which represents the principal component direction of the data; is the transpose of the eigenvector matrix; Λ is the diagonal matrix of eigenvalues, and the eigenvalues ​​represent the size of the variance in each direction. The directions with larger eigenvalues ​​(eigenvectors) represent the directions with important information in the data, while the directions with eigenvalues ​​close to 0 represent the directions of multicollinearity.

[0135] Step 24, and perform data dimension reduction, projection and recovery processing on the eigenvalue decomposition results to obtain data after eliminating collinearity.

[0136] By decomposing the results of eigenvalues, the data can be projected onto the principal component direction with larger eigenvalues ​​to eliminate redundant collinearity. In this way, the multicollinearity in the original data is effectively eliminated and the most representative feature information is retained.

[0137] Data projection, retaining the main eigenvectors (Eigenvectors corresponding to larger eigenvalues), projecting the standardized data onto these principal component directions:

[0138]

[0139] in, is the transposed matrix of the retained main eigenvectors, is the projected data.

[0140] Data recovery, the projected data can still be restored to the original space through inverse transformation, and the data after eliminating collinearity is:

[0141]

[0142] In this embodiment, after eliminating the multicollinearity problem in the source and load data, step 3 constructs a multicollinearity reduction generative adversarial network model for subsequent generation of diversified frequency analysis scenarios. Step 3 integrates the multicollinearity reduction technology in step 2 into the generative adversarial network to ensure that the generated data can better reflect the nonlinear relationship between the source and load random variables, and improve the quality and diversity of the generated scenarios. By introducing Bayesian statistics and variational inference into the generative adversarial network model, the structure and training method of the generative network are further optimized, so that it can generate high-quality frequency analysis scenario data that conforms to the target distribution on the basis of collinearity reduction. The specific process is as follows:

[0143] Step 31: Introduction of Bayesian prior distribution

[0144] By introducing the Bayesian prior distribution into the generative adversarial network model, the generator can better adapt to the distribution of source and load random variables and improve the diversity of generated data. In order to capture the uncertainty in the input data characteristics, it is assumed that the hidden variable θ of the generator has a standard Gaussian distribution (prior distribution):

[0145]

[0146] in, is the Gaussian distribution function, and I is the identity matrix.

[0147] Step 32, likelihood function definition

[0148] The output G(θ) of the generator should be close to the target source and load data distribution, so the likelihood function of the generative adversarial network model is defined as:

[0149]

[0150] where Λ is the precision matrix (i.e., the inverse of the covariance matrix) and is used to capture residual collinearity in the data.

[0151] Step 33, variational inference

[0152] Using variational inference technology, the generator can effectively learn the distribution of generated data by optimizing the parameters θ of the approximate distribution. Since it is too complicated to directly calculate the posterior distribution p(θ|x) of the generator, variational inference technology is used to approximate the true posterior distribution through the parameterized approximate distribution q(θ|x; φ);

[0153] q(θ|x;φ)≈p(θ|x) (16).

[0154] Step 34: Divergence and objective function optimization

[0155] In order to ensure that the data distribution generated by the generator is as close as possible to the real data distribution, the present invention introduces KL divergence to measure the difference between the approximate distribution and the real posterior distribution, and optimizes the parameters of the generator by minimizing the KL divergence; the smaller the KL divergence, the closer the data generated by the generator is to the real data.

[0156] The expression of KL divergence is:

[0157]

[0158] To further optimize the generator, the loss of the generative adversarial network model is combined with the loss term specific to multicollinearity. The goal of the generator is to minimize the following loss function

[0159]

[0160] Where θ is the parameter of the model; φ is the variational parameter; KL() is the divergence function to measure the difference between the two distributions; logq(θ|x; φ) is the logarithmic probability density function of the approximate distribution, and logp(θ|x) is the logarithmic probability density function of the true distribution. is the expectation under the approximate distribution, q(θ|x; φ) is the approximate posterior distribution, and p(θ|x) is the true posterior distribution.

[0161] By minimizing the objective function, the generator can continuously optimize its own hidden variable θ under the feedback of the discriminator, and obtain a multicollinearity reduction generative adversarial network model.

[0162] In this embodiment, step 4 elaborates on how to generate the source and load scenario data required for frequency analysis through the multicollinearity reduction generative adversarial network, and use these data to perform frequency response analysis of the system to ensure the diversity and authenticity of the scenarios and the comprehensiveness of the system frequency evaluation. Specifically, it includes:

[0163] Step 41: Generate diverse source and load scenario data

[0164] A set of random noise vectors z is input into the generator of the multicollinearity reduction generative adversarial network model to generate diverse source and load scenario data; the noise vector usually follows a standard normal distribution The generator converts the noise input z into simulated source and load scene data Generate diverse source and load scenario data including time series data of photovoltaic, wind power generation and load demand, which have similar statistical characteristics to historical data.

[0165] Step 42: Build a frequency analysis model

[0166] In order to evaluate the frequency response of the power system under different source and load scenarios, it is necessary to first build a frequency dynamic response model of the power system. The model should take into account factors such as system inertia, frequency regulation characteristics, and load characteristics.

[0167] The frequency dynamic response model of the power system is usually described by the following differential equation:

[0168]

[0169] Where M is the system inertia constant, that is, the rotational inertia of the power system; D is the damping coefficient of the power system, that is, the damping capacity of the power system to frequency changes; ΔP m is the mechanical power variation, mainly the active power regulation part of the generator; ΔP e is the variation of electrical power, including fluctuations in load and renewable energy output; Δf is the frequency deviation of the power system;

[0170] The active power imbalance in the system mainly comes from the output changes of load and renewable energy:

[0171] ΔP e =△P L -△P G (20);

[0173] Among them, ΔP L is the power change required by the load; ΔP G It is the power change of the generator set, including the output change of renewable energy such as wind power and photovoltaic power.

[0174] Combine diverse sources and load scenario data Input the frequency response model of the power system for simulation; use the Euler method in the numerical method to solve the differential equation of the power system frequency response model, and simulate the frequency change of the power system under different source and load fluctuation scenarios;

[0175]

[0176] Wherein, Δf(t) is the frequency deviation at time t; Δf(t+Δt) is the frequency deviation at time t+Δt, indicating the frequency change after a time step Δt.

[0177] Step 43, Statistical Analysis and Evaluation

[0178] By simulating frequency response, the frequency variation curve and key indicators of the power system under different source and load fluctuation scenarios are obtained; and the frequency response characteristics of the power system under various scenarios are analyzed based on key indicators.

[0179] Statistical analysis: Statistics are performed on indicators such as frequency deviation and recovery time in different scenarios to obtain probability distribution functions and cumulative distribution functions, which are used to analyze the frequency response characteristics of the system in various scenarios.

[0180] For example, the probability distribution of frequency deviation:

[0181] P(Δf)=Probability(Δf=b) (22);

[0182] Wherein, Probability (Δf=b) represents the probability that the frequency deviation Δf is equal to the frequency threshold b.

[0183] Cumulative distribution function:

[0184] F(Δf)=∫Probability(Δf≤b) (23);

[0185] Among them, ∫Probability(Δf≤x) is the integral of the probability distribution function, which represents the cumulative probability that the frequency deviation is less than or equal to the frequency threshold b.

[0186] Risk assessment, based on the generated frequency deviation distribution, evaluates the risk of the system exceeding the allowable frequency deviation range and calculates the probability of frequency exceeding the limit:

[0187] P 超限 =Probability(|Δf|>b) (24);

[0188] Here, Probability (|Δf|>b) represents the probability that the absolute value of the frequency deviation |Δf| exceeds the frequency threshold b.

[0189] If the probability of exceeding the limit is high, it means that the frequency stability of the system under the current source and load scenario is poor, and measures need to be taken to enhance the frequency stability of the system.

[0190] Step 44: Parameter sensitivity analysis

[0191] In order to further understand the frequency stability of the system, parameter sensitivity analysis is performed. By changing the system inertia constant M, the changes in the system frequency response are observed, and parameter sensitivity analysis provides guidance for system optimization. Calculate the impact of parameter changes on frequency deviation:

[0192]

[0193] Figure 4 It is a comparison diagram between the actual scenario of the method of the present invention and the scenario generated by the multicollinearity reduction generative adversarial network model. In order to verify the effectiveness of the multicollinearity reduction generative adversarial network model in extracting spatiotemporal correlation features, nine-dimensional data of three loads, three photovoltaics and three wind power are analyzed. By comparing the correlation coefficients of the real sample data and the generated sample data in each dimension, and drawing the correlation coefficient diagram between the scenarios, the degree of correlation between different dimensions is represented by the numerical value. The results show that the sample data generated by the multicollinearity reduction generative adversarial network model is highly consistent with the real data in terms of correlation.

[0194] Example 2

[0195] like Figure 5 As shown, Figure 5 : This is a structural block diagram of a frequency analysis system based on a multicollinearity-reducing generative adversarial network of the present invention; the difference between this embodiment and embodiment 1 is that this embodiment provides a frequency analysis system based on a multicollinearity-reducing generative adversarial network, and the system corresponds to the frequency analysis method based on a multicollinearity-reducing generative adversarial network of embodiment 1 in a one-to-one manner; the system includes:

[0196] A data acquisition unit, used to acquire historical source and load random scene data;

[0197] The first analysis unit is used to perform spatiotemporal joint analysis and progressive statistical analysis on the historical source and load random scene data to generate a historical data set matrix;

[0198] A dimensionality reduction processing unit, used to perform dimensionality reduction processing on the historical data set matrix by using dimensionality reduction technology to obtain processed source and load random scene data;

[0199] A multicollinearity diagnosis and elimination unit is used to perform multicollinearity diagnosis on the processed source and load random scene data, eliminate collinearity greater than a preset value, and obtain data after collinearity elimination;

[0200] A generative adversarial network construction unit, used to construct a generative adversarial network model based on the data after eliminating collinearity;

[0201] The network model optimization unit is used to introduce Bayesian prior distribution and variational inference into the generative adversarial network model to optimize the network structure and obtain a multicollinearity-reducing generative adversarial network model;

[0202] The second analysis unit is used to generate diversified source and load scenario data based on the multicollinearity reduction generative adversarial network model, input the diversified source and load scenario data into the power system frequency response model for simulation analysis, and evaluate the frequency response characteristics of the power system under different source and load fluctuation scenarios.

[0203] As a further implementation, the multicollinearity diagnosis and elimination unit includes:

[0204] A standardization processing subunit is used to perform data standardization processing on the processed source and load random scene data to obtain standardized data;

[0205] A covariance matrix calculation subunit, used to calculate the covariance matrix of the standardized data;

[0206] A diagnosis and elimination subunit is used to perform multicollinearity diagnosis based on the covariance matrix, diagnose the collinearity strength in the data through the variance inflation factor, and perform eigenvalue decomposition using the covariance matrix to eliminate collinearity greater than a preset value;

[0207] The result processing subunit is used to perform data dimension reduction, projection and recovery processing on the eigenvalue decomposition results to obtain data after eliminating collinearity.

[0208] Among them, the execution process of each unit can be executed according to the process steps of the frequency analysis method based on multicollinearity reduction generative adversarial network in Example 1, and will not be repeated one by one in this embodiment.

[0209] The present invention first analyzes the spatiotemporal characteristics of source and load random variables, and combines progressive statistical analysis and dimensionality reduction technology to accurately capture the temporal and spatial correlation of the data. Secondly, the multicollinearity diagnostic technology is used to effectively eliminate the multicollinearity problem in the data to ensure that the model can effectively extract nonlinear features. Then, the multicollinearity reduction technology is integrated into the generative adversarial network model, and the training process of the generative network is optimized through Bayesian statistics and variational inference to generate diverse and representative source and load random scenario data. Finally, the generated source and load scenario data is applied to the simulation analysis of the power system frequency response model to evaluate the frequency response characteristics of the system under different source and load fluctuation scenarios. This method solves the problems of insufficient disturbance scenario data and low accuracy of source and load uncertainty modeling faced in the power system frequency response analysis, improves the model's learning ability for data randomness, and provides reliable scenario data support for the optimal frequency analysis of the power system under source and load bilateral uncertainty.

[0210] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0211] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0212] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0213] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0214] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A frequency analysis method based on multicollinearity reduction generative adversarial network, characterized in that: The method includes: Acquire historical source and load-random scene data, perform spatiotemporal joint analysis and progressive statistical analysis on the historical source and load-random scene data, and generate a historical data set matrix; perform dimensionality reduction processing on the historical data set matrix using dimensionality reduction technology to obtain processed source and load-random scene data; Perform multicollinearity diagnosis on the processed source and load random scene data, eliminate the collinearity greater than the preset value, and obtain the data after eliminating the collinearity; A generative adversarial network model is constructed based on the data after collinearity elimination; and a Bayesian prior distribution and variational inference are introduced into the generative adversarial network model to optimize the network structure, so as to obtain a multicollinearity elimination generative adversarial network model; Based on the multicollinearity elimination generative adversarial network model, diversified source and load scenario data are generated, and the diversified source and load scenario data are input into the power system frequency response model for simulation analysis to evaluate the frequency response characteristics of the power system under different source and load fluctuation scenarios.

2. The frequency analysis method based on multicollinearity reduction generative adversarial network according to claim 1 is characterized in that: The historical source and load random scene data include historical data of photovoltaic power stations and wind farms and historical data of load demand; The historical data of the photovoltaic power station and the wind farm include hourly sampling values ​​of power generation; The historical data of load demand includes hourly sampling values ​​of power consumption; Among them, the historical data of photovoltaic power stations and wind farms, and the historical data of load demand all contain geographic location coordinates.

3. The frequency analysis method based on multicollinearity reduction generative adversarial network according to claim 1 is characterized in that: Performing spatiotemporal joint analysis and progressive statistical analysis on the historical source and load random scene data to generate a historical data set matrix; using dimensionality reduction technology to perform dimensionality reduction processing on the historical data set matrix to obtain processed source and load random scene data, including: Combining time dimension analysis and space dimension analysis, performing a spatiotemporal joint analysis on the historical source and load random scene data in an hourly manner to obtain first data; Using a progressive statistical analysis method, statistically analyzing the first data on a quarterly and daily basis to obtain second data; Based on the second data, a historical data set matrix is ​​generated; the historical data set matrix is ​​a source and load random variable set with high temporal correlation and high spatial correlation; The principal component analysis dimensionality reduction technique is used to reduce the dimension of the historical data set matrix to obtain processed source and load random scene data.

4. The frequency analysis method based on multicollinearity reduction generative adversarial network according to claim 3 is characterized in that: The expression of the historical data set matrix is: In the formula, X is the historical data set matrix, N is the number of days, T is the number of daily time sampling points, and for each day’s data x i , its expanded form is: in, represents the source and load data at the t-th time point on the i-th day, and K is the number of different types of source and load random scenarios.

5. The frequency analysis method based on multicollinearity reduction generative adversarial network according to claim 1 is characterized in that: Perform multicollinearity diagnosis on the processed source and load random scene data, eliminate collinearity greater than the preset value, and obtain data after eliminating collinearity, including: Performing data standardization on the processed source and load random scene data to obtain standardized data; Calculating a covariance matrix for the standardized data, and performing multicollinearity diagnosis based on the covariance matrix; The strength of collinearity in the data is diagnosed by using the variance inflation factor, and the eigenvalue decomposition is performed using the covariance matrix to eliminate collinearity greater than a preset value; The eigenvalue decomposition results are processed by data dimension reduction, projection and recovery to obtain the data after eliminating collinearity.

6. The frequency analysis method based on multicollinearity reduction generative adversarial network according to claim 1 is characterized in that: Introducing Bayesian prior distribution and variational inference to optimize the network structure into the generative adversarial network model, a multicollinearity reduction generative adversarial network model is obtained, including: Introducing a Bayesian prior distribution into the generative adversarial network model, assuming that the latent variable θ of the generator obeys a standard Gaussian distribution, and defining a likelihood function of the generative adversarial network model; Using variational inference techniques, we approximate the true posterior distribution through a parameterized approximate distribution; The KL divergence is introduced to measure the difference between the approximate distribution and the true posterior distribution, and the parameters of the generator are optimized by minimizing the KL divergence; Combining the loss of the generative adversarial network model with the loss term predetermined by multicollinearity, minimizing the loss function is used as the objective function of the generator; By minimizing the objective function, the generator continuously optimizes its own hidden variable θ under the feedback of the discriminator, and obtains a multicollinearity reduction generative adversarial network model.

7. The frequency analysis method based on multicollinearity reduction generative adversarial network according to claim 6 is characterized in that: The expression of the KL divergence is: The loss function The expression is: Where θ is the parameter of the model; φ is the variational parameter; KL() is the divergence function to measure the difference between the two distributions; logq(θ|x; φ) is the logarithmic probability density function of the approximate distribution, and logp(θ|x) is the logarithmic probability density function of the true distribution. is the expectation under the approximate distribution, q(θ|x; φ) is the approximate posterior distribution, and p(θ|x) is the true posterior distribution.

8. The frequency analysis method based on multicollinearity reduction generative adversarial network according to claim 1 is characterized in that: Based on the multicollinearity reduction generative adversarial network model, a variety of source and load scenario data are generated, and the diverse source and load scenario data are input into the power system frequency response model for simulation analysis to evaluate the frequency response characteristics of the power system under different source and load fluctuation scenarios, including: Inputting a set of random noise vectors into the generator of the multicollinearity reduction generative adversarial network model to generate diversified source and load scenario data; Input diverse source and load scenario data into the power system frequency response model for simulation; The Euler method in numerical methods is used to solve the differential equations of the power system frequency response model and simulate the frequency changes of the power system under different source and load fluctuation scenarios; By simulating the frequency response, the frequency variation curve and key indicators of the power system under different source and load fluctuation scenarios are obtained; and based on the key indicators, the frequency response characteristics of the power system under various scenarios are analyzed.

9. A frequency analysis system based on a multicollinearity reduction generative adversarial network, characterized in that: The system includes: A data acquisition unit, used to acquire historical source and load random scene data; A first analysis unit is used to perform spatiotemporal joint analysis and progressive statistical analysis on the historical source and load random scene data to generate a historical data set matrix; A dimensionality reduction processing unit, used to perform dimensionality reduction processing on the historical data set matrix using a dimensionality reduction technique to obtain processed source and load random scene data; A multicollinearity diagnosis and elimination unit is used to perform multicollinearity diagnosis on the processed source and load random scene data, eliminate collinearity greater than a preset value, and obtain data after collinearity elimination; A generative adversarial network construction unit, used to construct a generative adversarial network model based on the data after eliminating collinearity; A network model optimization unit, used for introducing Bayesian prior distribution and variational inference to optimize the network structure in the generative adversarial network model to obtain a multicollinearity reduction generative adversarial network model; The second analysis unit is used to generate diversified source and load scenario data based on the multicollinearity reduction generative adversarial network model, input the diversified source and load scenario data into the power system frequency response model for simulation analysis, and evaluate the frequency response characteristics of the power system under different source and load fluctuation scenarios.

10. The frequency analysis system based on multicollinearity reduction generative adversarial network according to claim 9, characterized in that: The multicollinearity diagnosis and elimination unit comprises: A standardization processing subunit is used to perform data standardization processing on the processed source and load random scene data to obtain standardized data; A covariance matrix calculation subunit, used for calculating the covariance matrix of the standardized data; A diagnosis and elimination subunit, configured to perform multicollinearity diagnosis based on the covariance matrix, diagnose the collinearity strength in the data by using a variance inflation factor, and perform eigenvalue decomposition using the covariance matrix to eliminate collinearity greater than a preset value; The result processing subunit is used to perform data dimension reduction, projection and recovery processing on the eigenvalue decomposition results to obtain data after eliminating collinearity.

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