A method for high-dimensional uncertainty aggregation modeling of power systems based on Gaussian mixture models

Abstract

This invention discloses a method for high-dimensional uncertainty aggregation modeling of power systems based on Gaussian mixture models (GMMs). The method comprises two stages: characterization of the original uncertainty distribution and GMM aggregation modeling. The GMM aggregation modeling specifically includes three steps: determining the dimension of aggregation variables, calculating aggregation parameters, and integrating aggregation results. This method achieves probability-preserving aggregation of high-dimensional uncertainty variables in power systems while significantly reducing the required sample size, effectively solving the problem of the large sample size required by Monte Carlo sampling when processing high-dimensional data. This invention can be applied to the dimensionality reduction aggregation of high-dimensional variables in uncertain power systems with a high proportion of renewable energy integration, achieving sample space reduction while maintaining probabilistic characteristics, and can be further applied to power system risk assessment, reliability analysis, and operation planning.

Description

Technical Field

[0001] This invention belongs to the field of power system new energy power data aggregation, specifically involving a power system high-dimensional uncertainty aggregation modeling method based on Gaussian mixture model. Background Technology

[0002] With the rapid development of new energy technologies, the penetration rate of new energy sources such as wind power and photovoltaics is constantly increasing. The randomness and volatility of their output have a significant impact on the safe and stable operation of the power grid. At the same time, due to the continuous increase in the number of new energy power plants and units, the dimensionality of their output data has increased significantly. The resulting "high-dimensional uncertainty" problem has brought certain challenges to power system analysis.

[0003] The increased dimensionality of power output and load data due to uncertainties in new energy sources can lead to problems such as the "curse of dimensionality," significantly increasing the difficulty of data processing. Furthermore, high-dimensional data has poor readability, hindering analysis and identification; therefore, dimensionality reduction is typically required. Traditional Monte Carlo sampling can reduce the dimensionality of variables, but it is prone to uneven sampling in high-dimensional spaces and usually requires extensive sampling simulations to ensure accuracy, resulting in relatively low computational efficiency. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a method for high-dimensional uncertainty aggregation modeling of power systems based on Gaussian mixture models, which is used to perform dimensionality reduction aggregation processing on high-dimensional uncertainty variables.

[0005] Technical Solution: The present invention describes a method for high-dimensional uncertainty aggregation modeling of power systems based on Gaussian mixture models (GMMs). This method employs a two-stage approach: original uncertainty distribution representation and GMM-based aggregation. The original uncertainty distribution representation uses power system data as original high-dimensional random variables. A Gaussian mixture model (GMM) is used to fit these original high-dimensional random variables, representing them analytically to obtain the fitted GMM model. The GMM-based aggregation uses the fitted GMM model parameters to calculate the aggregation model parameters based on the required aggregation variable dimension, and then integrates these parameters into the aggregation model result.

[0006] Furthermore, the Gaussian Mixture Model (GMM) is used to fit the original high-dimensional random variables of the power system, and the original high-dimensional random variables of the power system are represented by specific analytical expressions, including:

[0007] Power system data includes renewable energy output or load;

[0008] The original high-dimensional random variable dataset of new energy output or load is X=(x1,x2,...,x d ) TThe GMM was used for fitting, and the model was fitted to a GMM model; x i Let be the i-th dimension of the original high-dimensional random variable of the power system, i = 1, 2, ..., d, where d is the total dimension of the original high-dimensional random variable of the power system, and T is the transpose of the matrix; the fitted GMM model parameters are: the number of Gaussian components k, the weight coefficients ω of each component. k Mean matrix μ k The covariance matrix Σ k The uncertainty distribution of the original high-dimensional random variable dataset of new energy output or load is characterized by a Gaussian mixture model:

[0009]

[0010] Where P(X) is the probability density function of the GMM for the original high-dimensional random variable dataset of new energy output or load, K is the total number of Gaussian components in the GMM model, and N is the total number of Gaussian components in the model. k Let be the probability density of the k-th Gaussian component in the GMM model.

[0011] Furthermore, the parameter estimation of the original high-dimensional random variables of the new energy output or load GMM model is achieved through the expectation-maximization algorithm, and the optimal number of Gaussian components of the GMM model is determined by the elbow method, the profile coefficient method, or the Bayesian information criterion.

[0012] Furthermore, GMM-based variable aggregation includes:

[0013] (1) Determine the required dimension n of the power system aggregate variables and the original high-dimensional random variables contained in each aggregate variable;

[0014] (2) Depending on whether the aggregated variables of new energy output or load in actual power system analysis need to obtain one-dimensional or n-dimensional results, the mean matrix μ of each Gaussian component parameter in the GMM model fitted to the original high-dimensional random variables of new energy output or load is determined. k The covariance matrix Σ k The result μ is transformed into an aggregated result through analytical calculation. k,Y and σ k,Y Or μ k,Y and Σ k,Y μ k,Y The one-dimensional mean matrix of the k-th Gaussian component after aggregating the original high-dimensional random variable dataset of new energy output or load. The variance of the k-th Gaussian component after aggregating the original high-dimensional random variable dataset of new energy output or load; μ k,Y Σ represents the mean matrix of the k-th Gaussian component after aggregating the original high-dimensional random variable dataset of new energy output or load. k,Y Let be the covariance matrix of the k-th Gaussian component after aggregation;

[0015] (3) The aggregated mean and covariance results μ are obtained by... k,Y and σ k,Y Or μ k,Y and Σ k,Y We obtained a joint probability distribution model of the aggregated variables of the power system after dimensionality reduction and aggregation.

[0016] Furthermore, in step (2), if the required power system aggregation variable dimension is one dimension, the mean and variance of the k-th Gaussian component of the aggregation variable are expressed as follows:

[0017]

[0018] Where, μ k,Y μ is the one-dimensional mean matrix of the k-th Gaussian component after aggregating the original high-dimensional random variable dataset of new energy output or load. k,i For the k-th Gaussian component x i The mean, x i Let Σ be the original high-dimensional random variable of the power system with dimension i, and d be the total dimension of the original high-dimensional random variable of the power system; k,ij For the k-th Gaussian component x i With x j covariance, x j Let x be the original high-dimensional random variable of the power system with dimension j. If i = j, then x is the random variable. i Its own variance, i.e., ∑ k,ii For the k-th Gaussian component x i The variance of the variable itself, where i and j are indices of the dimensions of the original high-dimensional random variables of the power system; The variance of the k-th Gaussian component after aggregating the original high-dimensional random variable dataset of new energy output or load.

[0019] Furthermore, in step (2), if the required power system aggregate variable dimension is n-dimensional, for the k-th Gaussian component of the aggregate variable, each element in its mean column vector is the sum of the means of several random variables corresponding to that aggregate variable; the calculation of the covariance matrix includes the following steps:

[0020] (21) Solving for the mean matrix: Each element in the mean matrix is ​​the sum of the means of the original high-dimensional random variables corresponding to the aggregate variable;

[0021] If the m-dimensional power system data is evenly distributed among n-dimensional aggregate variables, its mean matrix is ​​represented as follows:

[0022]

[0023] Where, μ k,Yμ represents the mean matrix of the k-th Gaussian component after aggregating the original high-dimensional random variable dataset of new energy output or load. k,i For the original variable x in the k-th Gaussian component i The mean;

[0024] (22) Solving for the variance of the aggregate variable y: For the k-th Gaussian component, the variance of the i-th aggregate variable y i The variance is expressed as:

[0025]

[0026] in, For the i-th aggregate variable y i The variance of the k-th Gaussian component, c ij For 0-1 variables, the meaning is: if the aggregate variable y i It contains a random variable x j Then the y i x below j The corresponding coefficient c ij The value is 1 if it is not 0 otherwise, c il Similarly; Cov(x) k,j ,x k,l ) represents the original high-dimensional random variable x in the k-th Gaussian component. j With x l The covariance between them, where j and l are indices of the dimensions of the original high-dimensional random variables of the power system;

[0027] (23) The correlation coefficient ρ between every two aggregate variables in the kth Gaussian component k,ab for:

[0028]

[0029] Where, ρ k,ab Represents the aggregate variable y in the k-th Gaussian component a With y b The correlation coefficient between them, Cov(y) k,a ,y k,b ) represents the aggregate variable y in the k-th Gaussian component. a With y b The covariance between For the a-th aggregate variable y a The variance of the k-th Gaussian component in the equation. For the b-th aggregate variable y b The variance of the k-th Gaussian component, c aj With c bl Both are 0-1 variables, with the same meaning as c. ij Similarly;

[0030] (24) Solving for the covariance matrix: Combine the variance and correlation coefficient obtained in the above steps to obtain the covariance matrix corresponding to the k-th Gaussian component:

[0031]

[0032] Where, Σ k,Y Let be the covariance matrix of the k-th Gaussian component after aggregation. Let be the variance of the k-th Gaussian element in the first aggregate variable y1. Let y2 be the variance of the k-th Gaussian element. For the nth aggregate variable y n The variance of the k-th Gaussian element, σ k,1 Let σ be the standard deviation of the k-th Gaussian element in the first aggregate variable y1. k,2 Let σ be the standard deviation of the k-th Gaussian element in the second aggregate variable y2. k,n For the nth aggregate variable y n The standard deviation of the k-th Gaussian element, ρ k,12 Let ρ be the correlation coefficient between aggregate variables y1 and y2 in the k-th Gaussian component. k,1n For the aggregate variables y1 and y2 in the k-th Gaussian component n The correlation coefficient between them.

[0033] Furthermore, the joint probability distribution model of the aggregated variables of the power system after dimensionality reduction and aggregation is as follows:

[0034]

[0035] Where P(Y) is the GMM probability density function of the aggregated variables of the power system data after dimensionality reduction and aggregation.

[0036] The system corresponding to the above method includes two stages: characterization of the original uncertainty distribution and aggregation based on GMM, wherein:

[0037] The original uncertainty distribution representation unit is used to fit the original high-dimensional random variables of the power system using GMM. It represents the original high-dimensional random variables of the power system through a specific analytical form to obtain the fitted GMM model.

[0038] The GMM-based aggregation unit is used to calculate the aggregation model parameters based on the required aggregation variable dimension using the fitted GMM model parameters, and then integrate them into the aggregation model result.

[0039] An electronic device for storing and executing the method, the device comprising:

[0040] Memory containing executable program code;

[0041] A processor coupled to the memory;

[0042] The processor calls the executable program code stored in the memory to execute the steps of the method for high-dimensional uncertainty aggregation modeling of power systems based on Gaussian mixture models.

[0043] A computer-readable storage medium for storing and executing the method, the computer-readable storage medium storing computer instructions, which, when invoked, are used to execute the steps of the high-dimensional uncertainty aggregation modeling of the power system based on the Gaussian mixture model.

[0044] Beneficial effects: Compared with the prior art, the significant technical effect of the present invention is that it realizes the dimensionality reduction and aggregation of the original high-dimensional random variables through two stages: original uncertainty distribution representation and GMM-based aggregation. Compared with the traditional Monte Carlo simulation method, it has higher accuracy and efficiency, thereby achieving the goal of saving sample number and computing resources in high-dimensional uncertainty probability preservation dimensionality reduction. Attached Figure Description

[0045] Figure 1 is a flow chart of the method of the present invention;

[0046] Figure 2 The images show a comparison of two marginal distributions of the aggregation method proposed in this embodiment of the invention and the Monte Carlo method with different sampling times. (a) and (b) are comparisons of the marginal distribution y1 of the aggregation results obtained by the GMM aggregation method and the Monte Carlo method with 100 and 1000 sampling times, respectively; (c) and (d) are comparisons of the marginal distribution y2 of the aggregation results obtained by the GMM aggregation method and the Monte Carlo method with 100 and 1000 sampling times, respectively.

[0047] Figure 3 The above are comparison diagrams of the voltage amplitude and phase angle of a node obtained by substituting the original data into the aggregation result obtained by the aggregation method proposed in this embodiment of the invention and the voltage phase angle of a certain node obtained by probabilistic power flow calculation; wherein, (a) is a comparison diagram of the voltage amplitude of the node and (b) is a comparison diagram of the voltage phase angle of the node. Detailed Implementation

[0048] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention.

[0049] To address the problem of dimensionality reduction and aggregation of high-dimensional data in uncertain power systems, this invention proposes a high-dimensional uncertainty aggregation modeling method for power systems based on Gaussian mixture models (GMMs). This method achieves probability-preserving dimensionality reduction of high-dimensional variables while maintaining a certain level of accuracy and efficiency. It employs a two-stage approach: original uncertainty distribution representation and GMM-based aggregation. The original uncertainty distribution representation uses a GMM to fit the original high-dimensional random variables of the power system, such as renewable energy output and load, representing these random variables through specific analytical expressions. The GMM-based aggregation calculates the aggregation model parameters based on the required aggregation variable dimension using the fitted GMM model parameters and integrates them into the aggregation model result. Figure 1 As shown, the main steps include:

[0050] S1. First, the uncertainty distribution of the raw power system data is characterized. The power system data consists of raw high-dimensional random variables, including renewable energy output and load, etc. The raw high-dimensional random variable dataset of renewable energy output or load is X = (x1, x2, ..., x...). d ) T The GMM was used for fitting, and the model was fitted to a GMM model; x i Let be the i-th dimension of the original high-dimensional random variable of the power system, i.e., the i-th dimension of the original high-dimensional random variable of the new energy output or load, i = 1, 2, ..., d, where d is the total dimension of the original high-dimensional random variable of the power system, and T is the transpose of the matrix; the fitted GMM model parameters are: the number of Gaussian components k, the weight coefficient ω of each Gaussian component. k Mean matrix μ k The covariance matrix Σ k The uncertainty distribution of the original high-dimensional random variable dataset of new energy output or load is characterized by a Gaussian mixture model:

[0051]

[0052] Where P(X) is the probability density function of the GMM for the original high-dimensional random variable dataset of new energy output or load, K is the total number of Gaussian components in the GMM model, and N is the total number of Gaussian components in the model. k Let be the probability density of the k-th Gaussian component in the GMM model.

[0053] The parameter estimation of the GMM model of the original high-dimensional random variable dataset of the power system, such as the output of new energy sources and the load, can be achieved by the expectation-maximization algorithm, while the optimal number of Gaussian components can be determined by the elbow method, the profile coefficient method, or the Bayesian information criterion.

[0054] S2. Based on the actual power system's network architecture, generator locations, and variable correlations, and in conjunction with the actual power system analysis needs, determine the required aggregate variable dimension n and the original high-dimensional random variables contained in each aggregate variable.

[0055] S3. Depending on whether the power system data aggregation variables require one-dimensional or n-dimensional results, for each Gaussian component, the original GMM model parameters μ... k and Σ k The result μ is transformed into an aggregated result through analytical calculation. k,Y and σ k,Y Or μ k,Y and Σ k,Y Specifically, it includes the following steps:

[0056] S31. If the required aggregation variable dimension is one dimension, the mean and variance of the k-th Gaussian component are expressed as follows:

[0057]

[0058] Where, μ k,Y μ is the one-dimensional mean matrix of the k-th Gaussian component after aggregating the original high-dimensional random variable dataset of new energy output or load. k,i For the k-th Gaussian component x i The mean; Σ k,ij For the k-th Gaussian component x i With x j covariance, x j Let x be the original high-dimensional random variable of the power system with dimension j. If i = j, then x is the random variable. i Its own variance, i.e., ∑ k,ii For the k-th Gaussian component x i The variance of the variable itself, where i and j are indices of the dimensions of the original high-dimensional random variables of the power system; The variance of the k-th Gaussian component after aggregating the original high-dimensional random variable dataset of new energy output or load.

[0059] S32. If the required power system data aggregation variables have an n-dimensional dimension, the calculation of the mean matrix and covariance matrix for the k-th Gaussian component includes the following steps:

[0060] S321. Solving for the mean matrix: Each element in the mean matrix is ​​the sum of the means of the original high-dimensional random variables corresponding to the aggregate variable;

[0061] If the m-dimensional power system data (new energy output or load) is evenly distributed among n-dimensional aggregate variables, its mean matrix is ​​represented as follows:

[0062]

[0063] Where, μ k,Y μ represents the mean matrix of the k-th Gaussian component after aggregating the original high-dimensional random variable dataset of new energy output or load.k,i For the original variable x in the k-th Gaussian component i The mean.

[0064] In this embodiment, 9-dimensional wind farm output data is used as an example. If the 9-dimensional wind farm output data is evenly distributed into 3-dimensional aggregate variables, its mean matrix is ​​represented as follows:

[0065]

[0066] Where, μ k,Y，9-3 μ represents the 3D mean matrix of the k-th Gaussian component after the 9-dimensional wind field power output data is aggregated into 3D. k,i For the original variable x in the k-th Gaussian component i The mean.

[0067] S322, The variance σ of the aggregate variable y 2 Solution: For the k-th Gaussian component, the i-th aggregate variable y i The variance can be expressed as:

[0068]

[0069] in, For the i-th aggregate variable y i The variance of the k-th Gaussian component, c ij For 0-1 variables, the meaning is: if the aggregate variable y i It contains a random variable x j Then the y i x below j The corresponding coefficient c ij The value is 1 if it is not 0 otherwise, c il Similarly; Cov(x) k,j ,x k,l ) represents the original high-dimensional random variable x in the k-th Gaussian component. j With x l The covariance between them, where j and l are indices of the dimensions of the original high-dimensional random variables of the power system.

[0070] S323, the correlation coefficient ρ between every two aggregate variables in the k-th Gaussian component. k,ab for:

[0071]

[0072] Where, ρ k,ab Represents the aggregate variable y in the k-th Gaussian component a With y b The correlation coefficient between them, Cov(y) k,a ,y k,b ) represents the aggregate variable y in the k-th Gaussian component.a With y b The covariance between For the a-th aggregate variable y a The variance of the k-th Gaussian component in the equation. For the b-th aggregate variable y b The variance of the k-th Gaussian component, c aj With c bl Both are 0-1 variables, with the same meaning as c. ij Similarly.

[0073] S324. Solving for the covariance matrix: Combine the variance and correlation coefficient obtained in the above steps to obtain the covariance matrix corresponding to the k-th Gaussian component:

[0074]

[0075] Where, Σ k,Y Let be the covariance matrix of the k-th Gaussian component after aggregation. Let be the variance of the k-th Gaussian element in the first aggregate variable y1. Let y2 be the variance of the k-th Gaussian element. For the nth aggregate variable y n The variance of the k-th Gaussian element, σ k,1 Let σ be the standard deviation of the k-th Gaussian element in the first aggregate variable y1. k,2 Let σ be the standard deviation of the k-th Gaussian element in the second aggregate variable y2. k,n For the nth aggregate variable y n The standard deviation of the k-th Gaussian element, ρ k,12 Let ρ be the correlation coefficient between aggregate variables y1 and y2 in the k-th Gaussian component. k,1n For the aggregate variables y1 and y2 in the k-th Gaussian component n The correlation coefficient between them.

[0076] S4. The obtained aggregated mean and covariance results μ k,Y and Σ k,Y The aggregated variable Y = (y1, y2, ..., y3) is obtained from the original high-dimensional random variables of new energy output or load after dimensionality reduction and aggregation. n ) T The joint probability distribution model is as follows:

[0077]

[0078] Wherein, P(Y) is the GMM probability density function of the aggregated variable of the original high-dimensional random variables of new energy output or load after dimensionality reduction and aggregation.

[0079] This invention also provides a high-dimensional uncertainty aggregation modeling system for power systems based on Gaussian mixture models, comprising two stages: representation of the original uncertainty distribution and aggregation based on Gaussian mixture models, wherein:

[0080] The original uncertainty distribution representation unit is used to fit the original high-dimensional random variables of the power system using GMM. It represents the original high-dimensional random variables of the power system through a specific analytical form to obtain the fitted GMM model.

[0081] The GMM-based aggregation unit is used to calculate the aggregation model parameters based on the required aggregation variable dimension using the fitted GMM model parameters, and then integrate them into the aggregation model result.

[0082] The present invention also provides an electronic device for storing and executing the method, the device comprising:

[0083] Memory containing executable program code;

[0084] A processor coupled to the memory;

[0085] The processor calls the executable program code stored in the memory to execute the steps of the method for high-dimensional uncertainty aggregation modeling of power systems based on Gaussian mixture models.

[0086] The present invention also provides a computer-readable storage medium for storing and executing the method, the computer-readable storage medium storing computer instructions, which, when invoked, are used to execute the steps of the high-dimensional uncertainty aggregation modeling of power systems based on Gaussian mixture models.

[0087] Taking the IEEE 39-bus system as an example, five traditional generating units were replaced with renewable energy units. The measured power output data from the 20-dimensional wind farm was reduced to 5-dimensional data and substituted into the five renewable energy units for system probabilistic power flow analysis. First, the GMM aggregation results were compared with the Monte Carlo method to verify the accuracy of the GMM method. Figure 2 Figures (a) to (d) show a comparison of the probability density curves of the GMM aggregation results and the Monte Carlo (MC) sampling results of different sampling orders. It can be observed that the Monte Carlo method increasingly approximates the results obtained by the GMM method as the number of sampling orders increases, thus ensuring the accuracy and precision of the GMM method. The GMM aggregation results are then substituted into the system probabilistic power flow calculation and compared with the power flow results obtained from the original data. Figure 3 Figures (a) and (b) show the probabilistic results of node voltage and phase angle for a certain node under two data sources. It can be seen that the GMM aggregation method also has extremely high accuracy in system probabilistic power flow analysis.

[0088] The technical means disclosed in this invention are not limited to those disclosed in the above embodiments, but also include technical solutions composed of any combination of the above technical features. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications are also considered within the scope of protection of this invention.

Claims

1. A method for high-dimensional uncertainty aggregation modeling of power systems based on Gaussian mixture models, characterized in that, The method employs a two-stage approach: original uncertainty distribution representation and GMM-based aggregation. The original uncertainty distribution representation involves using power system data as original high-dimensional random variables. A GMM is used to fit these original high-dimensional random variables, representing them through a specific analytical expression to obtain the fitted GMM model. The GMM-based aggregation involves using the fitted GMM model parameters to calculate the aggregation model parameters based on the required aggregation variable dimension, and then integrating these parameters into the aggregation model result. GMM-based variable aggregation includes: (1) Determine the required dimension n of the power system aggregate variables and the original high-dimensional random variables contained in each aggregate variable; (2) Depending on whether the aggregated variables of new energy output or load in actual power system analysis need to obtain one-dimensional or n-dimensional results, the mean matrix μ of each Gaussian component parameter in the GMM model fitted to the original high-dimensional random variables of new energy output or load is determined. k The covariance matrix Σ k The result μ is transformed into an aggregated result through analytical calculation. k,Y and σ k,Y Or μ k,Y and Σ k,Y μ k,Y The one-dimensional mean matrix of the k-th Gaussian component after aggregating the original high-dimensional random variable dataset of new energy output or load. The variance of the k-th Gaussian component after aggregating the original high-dimensional random variable dataset of new energy output or load; μ k,Y Σ represents the mean matrix of the k-th Gaussian component after aggregating the original high-dimensional random variable dataset of new energy output or load. k,Y Let be the covariance matrix of the k-th Gaussian component after aggregation; If the required power system aggregation variable dimension is one-dimensional, the mean and variance of the k-th Gaussian component of the aggregation variable are expressed as follows: Where, μ k,Y μ is the one-dimensional mean matrix of the k-th Gaussian component after aggregating the original high-dimensional random variable dataset of new energy output or load. k,i For the k-th Gaussian component x i The mean, x i Let ∑ be the original high-dimensional random variable of the power system in dimension i, and d be the total dimension of the original high-dimensional random variable of the power system; k,ij For the k-th Gaussian component x i With x j covariance, x j Let x be the original high-dimensional random variable of the power system with dimension j. If i = j, then x is the random variable. i Its own variance, i.e., ∑ k,ii For the k-th Gaussian component x i The variance of the variable itself, where i and j are indices of the dimensions of the original high-dimensional random variables of the power system; The variance of the k-th Gaussian component after aggregating the original high-dimensional random variable dataset of new energy output or load; (3) The aggregated mean and covariance results μ are obtained by... k,Y and σ k,Y Or μ k,Y and Σ k,Y We obtained a joint probability distribution model of the aggregated variables of the power system after dimensionality reduction and aggregation.

2. The method for high-dimensional uncertainty aggregation modeling of power systems based on Gaussian mixture models according to claim 1, characterized in that, The Gaussian Mixture Model (GMM) is used to fit the original high-dimensional random variables of the power system, and the original high-dimensional random variables of the power system are represented by specific analytical expressions, including: Power system data includes renewable energy output or load; The original high-dimensional random variable dataset of new energy output or load is X=(x1,x2,...,x d ) T The GMM was used for fitting, and the model was fitted to a GMM model; x i Let be the i-th dimension of the original high-dimensional random variable of the power system, i = 1, 2, ..., d, where d is the total dimension of the original high-dimensional random variable of the power system, and T is the transpose of the matrix; the fitted GMM model parameters are: the number of Gaussian components k, the weight coefficients ω of each component. k Mean matrix μ k The covariance matrix Σ k The uncertainty distribution of the original high-dimensional random variable dataset of new energy output or load is characterized by a Gaussian mixture model: Where P(X) is the probability density function of the GMM for the original high-dimensional random variable dataset of new energy output or load, K is the total number of Gaussian components in the GMM model, and N is the total number of Gaussian components in the model. k Let be the probability density of the k-th Gaussian component in the GMM model.

3. The method for high-dimensional uncertainty aggregation modeling of power systems based on Gaussian mixture models according to claim 2, characterized in that, The parameter estimation of the original high-dimensional random variables of the new energy output or load GMM model is achieved by the expectation-maximization algorithm, and the optimal number of Gaussian components of the GMM model is determined by the elbow method, the profile coefficient method or the Bayesian information criterion.

4. The method for high-dimensional uncertainty aggregation modeling of power systems based on Gaussian mixture models according to claim 1, characterized in that, In step (2), if the required power system aggregate variable dimension is n-dimensional, for the k-th Gaussian component of the aggregate variable, each element in its mean column vector is the sum of the means of several random variables corresponding to that aggregate variable; the calculation of the covariance matrix includes the following steps: (21) Solving for the mean matrix: Each element in the mean matrix is ​​the sum of the means of the original high-dimensional random variables corresponding to the aggregate variable; If the m-dimensional power system data is evenly distributed among n-dimensional aggregate variables, its mean matrix is ​​represented as follows: Where, μ k,Y μ represents the mean matrix of the k-th Gaussian component after aggregating the original high-dimensional random variable dataset of new energy output or load. k,i For the original variable x in the k-th Gaussian component i The mean; (22) Solving for the variance of the aggregate variable y: For the k-th Gaussian component, the variance of the i-th aggregate variable y i The variance is expressed as: in, For the i-th aggregate variable y i The variance of the k-th Gaussian component, c ij For 0-1 variables, the meaning is: if the aggregate variable y i It contains a random variable x j Then the y i x below j The corresponding coefficient c ij The value is 1 if it is not 0 otherwise, c il Similarly; Cov(x) k,j ,x k,l ) represents the original high-dimensional random variable x in the k-th Gaussian component. j With x l The covariance between them, where j and l are indices of the dimensions of the original high-dimensional random variables of the power system; (23) The correlation coefficient ρ between every two aggregate variables in the kth Gaussian component k,ab for: Where, ρ k,ab Represents the aggregate variable y in the k-th Gaussian component a With y b The correlation coefficient between them, Cov(y) k,a ,y k,b ) represents the aggregate variable y in the k-th Gaussian component. a With y b The covariance between For the a-th aggregate variable y a The variance of the k-th Gaussian component in the equation. For the b-th aggregate variable y b The variance of the k-th Gaussian component, c aj With c bl Both are 0-1 variables, with the same meaning as c. ij Similarly; (24) Solving for the covariance matrix: Combine the variance and correlation coefficient obtained in the above steps to obtain the covariance matrix corresponding to the k-th Gaussian component: Where, Σ k,Y Let be the covariance matrix of the k-th Gaussian component after aggregation. Let be the variance of the k-th Gaussian element in the first aggregate variable y1. Let y2 be the variance of the k-th Gaussian element. For the nth aggregate variable y n The variance of the k-th Gaussian element, σ k,1 Let σ be the standard deviation of the k-th Gaussian element in the first aggregate variable y1. k,2 Let σ be the standard deviation of the k-th Gaussian element in the second aggregate variable y2. k,n For the nth aggregate variable y n The standard deviation of the k-th Gaussian element, ρ k,12 Let ρ be the correlation coefficient between aggregate variables y1 and y2 in the k-th Gaussian component. k,1n For the aggregate variables y1 and y2 in the k-th Gaussian component n The correlation coefficient between them.

5. The method for high-dimensional uncertainty aggregation modeling of power systems based on Gaussian mixture models according to claim 1, characterized in that, The joint probability distribution model of the aggregated variables of the power system after dimensionality reduction and aggregation is as follows: Where P(Y) is the GMM probability density function of the aggregated variables of the power system data after dimensionality reduction and aggregation.

6. A high-dimensional uncertainty aggregation modeling system for power systems based on Gaussian mixture models, characterized in that, It includes two stages: characterization of the original uncertainty distribution and aggregation based on GMM, wherein: The original uncertainty distribution representation unit is used to fit the original high-dimensional random variables of the power system using GMM. It represents the original high-dimensional random variables of the power system through a specific analytical form to obtain the fitted GMM model. The GMM-based aggregation unit is used to calculate the aggregation model parameters based on the required aggregation variable dimension using the fitted GMM model parameters, and integrate them into the aggregation model result. GMM-based variable aggregation includes: (1) Determine the required dimension n of the power system aggregate variables and the original high-dimensional random variables contained in each aggregate variable; (2) Depending on whether the aggregated variables of new energy output or load in actual power system analysis need to obtain one-dimensional or n-dimensional results, the mean matrix μ of each Gaussian component parameter in the GMM model fitted to the original high-dimensional random variables of new energy output or load is determined. k The covariance matrix Σ k The result μ is transformed into an aggregated result through analytical calculation. k,Y and σ k,Y Or μ k,Y and Σ k,Y μ k,Y The one-dimensional mean matrix of the k-th Gaussian component after aggregating the original high-dimensional random variable dataset of new energy output or load. The variance of the k-th Gaussian component after aggregating the original high-dimensional random variable dataset of new energy output or load; μ k,Y Σ represents the mean matrix of the k-th Gaussian component after aggregating the original high-dimensional random variable dataset of new energy output or load. k,Y Let be the covariance matrix of the k-th Gaussian component after aggregation; If the required power system aggregation variable dimension is one-dimensional, the mean and variance of the k-th Gaussian component of the aggregation variable are expressed as follows: Where, μ k,Y μ is the one-dimensional mean matrix of the k-th Gaussian component after aggregating the original high-dimensional random variable dataset of new energy output or load. k,i For the k-th Gaussian component x i The mean, x i Let Σ be the original high-dimensional random variable of the power system with dimension i, and d be the total dimension of the original high-dimensional random variable of the power system; k,ij For the k-th Gaussian component x i With x j covariance, x j Let x be the original high-dimensional random variable of the power system with dimension j. If i = j, then x is the random variable. i Its own variance, i.e., Σ k,ii For the k-th Gaussian component x i The variance of the variable itself, where i and j are indices of the dimensions of the original high-dimensional random variables of the power system; The variance of the k-th Gaussian component after aggregating the original high-dimensional random variable dataset of new energy output or load; (3) The aggregated mean and covariance results μ are obtained by... k,Y and σ k,Y Or μ k,Y and Σ k,Y We obtained a joint probability distribution model of the aggregated variables of the power system after dimensionality reduction and aggregation.

7. An electronic device, characterized in that, The device includes: Memory containing executable program code; A processor coupled to the memory; The processor calls the executable program code stored in the memory to execute the steps of the high-dimensional uncertainty aggregation modeling method for power systems based on Gaussian mixture models as described in any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions, which, when invoked, are used to perform the steps of high-dimensional uncertainty aggregation modeling of power systems based on Gaussian mixture models as described in any one of claims 1-5.

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