Novel power system node inertia estimation method based on CKAN model

Abstract

The invention discloses a novel power system node inertia estimation method based on a CKAN model, and the method comprises the following steps: firstly, collecting the electrical data at a node when a novel power system is subjected to active disturbance, constructing an original data set, carrying out the preprocessing of the original data set, and constructing a feature data set; then, designing a CNN (convolutional neural network) feature extraction module and a KAN (Kolmogorov-Arnodean network) module based on a wavelet basis function, and constructing a CKAN (convolutional Kolmogorov-Arnodean network) model through series fusion; and finally, optimizing the hyper-parameters of the CKAN model by using a Bayesian optimization algorithm to improve the estimation precision of the CKAN model. According to the CKAN model provided by the invention, the local features of the input data can be extracted through the CNN feature extraction module, and then the KAN module performs wavelet transform on the local features and excavates core information, so that the inertia of each node of the novel power system can be quickly and accurately estimated.

Description

Technical Field

[0001] The present invention relates to the field of research on the stability of new power systems, and specifically relates to a new method for estimating the inertia of power system nodes based on the CKAN (Convolutional Kolmogorov-Arnold Network) model. Background Art

[0002] Inertia is an important indicator for measuring the ability of a power system to resist active power disturbances and maintain frequency stability. In traditional power systems, the inertia remains basically constant, which plays an important role in maintaining power stability. However, with the increasing proportion of new energy, synchronous generators, which are the main source of inertia, are gradually replaced. New energy power generation equipment usually does not have the inertia characteristics of synchronous generators, resulting in a decline in the overall inertia level of the system and a decrease in the system stability margin. At the same time, the regional differences in the distribution of natural scenery resources have broken the originally relatively balanced pattern of inertia resources. The areas with concentrated access to new energy show low inertia characteristics, in sharp contrast to the high inertia in areas rich in synchronous generators. This difference limits the system's ability to accommodate new energy. Therefore, for new power systems with a high proportion of new energy, the research on inertia assessment not only needs to focus on the overall inertia level of the system but also needs to pay attention to the spatial distribution of inertia at the node level in order to identify weak inertia nodes and optimize the inertia distribution. For this purpose, the present invention proposes a new method for estimating the inertia of power system nodes based on the CKAN model, providing technical guidance for the access layout of new energy by accurately estimating the node inertia. Summary of the Invention

[0003] To achieve the above object, the technical solution provided by the present invention is as follows:

[0004] S1: When an active power disturbance occurs in the new power system, collect the electrical data at the nodes, construct an original data set, and preprocess the original data set to construct a feature data set;

[0005] S1-1: When an active power disturbance occurs in the new power system, collect the frequency change data at each node accessing the virtual synchronous machine in real time to construct a frequency change data set. The specific form of the frequency change data set F n,m at the nth node during the mth active power disturbance is:

[0006] F n,m =[F n,m,1 ,F n,m,2 ,…,F n,m,t ,…,F n,m,T (1)

[0007] In formula (1), F n,m,tIt represents the frequency value of the nth node at the tth sampling moment during the mth active power disturbance, where n = 1, 2, …, N, N represents the total number of nodes connected to the virtual synchronous machine, m = 1, 2, …, M, M represents the total number of active power disturbances, and t = 1, 2, …, T, T represents the total number of samplings during the active power disturbance;

[0008] S1-2: When an active power disturbance occurs in the system, record the true inertia value of the virtual synchronous machine at the node as the inertia data set. For the inertia data set H at the nth node n The specific form is:

[0009] H n =[H n,1 ,H n,2 ,…,H n,m ,…,H n,M (2)

[0010] In formula (2), H n,m represents the true inertia value of the virtual synchronous machine at the nth node during the mth active power disturbance;

[0011] S1-3: According to the frequency change data set F n,m obtained in step S1-1, construct the original data set X ori , and its specific form is:

[0012]

[0013] In formula (3), X n represents the original data set corresponding to the nth node, which includes the frequency change data at the node after M active power disturbances. The specific form of X n is:

[0014]

[0015] S1-4: Normalize the original data set X ori in step S1-3, and merge it with the inertia data set H n in step S1-2 to obtain the feature data set D nd The specific form is:

[0016]

[0017] In formula (5), D n represents the feature data set corresponding to the nth node, and its specific form is:

[0018]

[0019] In formula (6), represents the normalized frequency change data set;

[0020] S1-5: feature data set D of step S1-4 nd Divide the dataset into 70% as training set and 30% as validation set.

[0021] S2: Design a CNN (convolutional neural network) feature extraction module and a KAN (Kolmogorov-Arnold network) module based on wavelet basis functions, and construct a CKAN model through serial fusion;

[0022] S2-1: The CNN feature extraction module includes three one-dimensional convolutional layers, three batch normalization layers, and three maximum pooling layers. The convolutional layer performs convolution operations on the input data and extracts local features of the input data layer by layer. The batch normalization layer is responsible for normalizing each batch of input data and adjusting the distribution of the input data to a standard distribution with a mean close to 0 and a variance close to 1. The maximum pooling layer takes the maximum value of the local area of ​​the extracted features through a sliding window to reduce the feature dimension and highlight important features.

[0023] S2-2: The KAN module contains five layers of wavelet KAN linear layers. The number of nodes in the five layers of wavelet KAN linear layers are 1472, 512, 128, 32 and 1 respectively. Each layer transforms the input data using a combination of basis weights and wavelet basis functions. The basis weights extract the global features of the input data through linear transformation, and the wavelet basis functions capture the local features of the input data such as peak values ​​and fluctuations through wavelet transformation. By reducing the number of nodes layer by layer, the KAN module gradually extracts the core information of the input data.

[0024] S2-3: The CNN feature extraction module of step S2-1 and the KAN module of step S2-2 are connected in series to build a CKAN model. The CKAN model can extract local features of the input frequency change data through the CNN feature extraction module, and then combine the global and local features through the KAN module to establish a mapping relationship between the frequency change data and the inertia data, and finally output the inertia estimation value;

[0025] S3: Use the Bayesian optimization algorithm to optimize the hyperparameters of the CKAN model to improve the estimation accuracy of the CKAN model;

[0026] S3-1: Use the Bayesian optimization algorithm to optimize the learning rate and batch size of the CKAN model and establish the parameter space P:

[0027]

[0028] In formula (7), learning_rate represents the learning rate to be optimized, (10 -5 ,10 -2) is the range of the learning rate, batch_size represents the batch size to be optimized, and (32, 256) is the range of the batch size;

[0029] S3-2: To improve the estimation accuracy of the CKAN model, the mean square error of the validation set is designed to be minimized as the objective function f(p):

[0030]

[0031] In Equation (8), c is the number of samples in the validation set, y (i) is the true value of the i-th sample, is the estimated value of the CKAN model for the i-th sample, i = 1, 2,... c, and p represents a set of hyperparameter combinations in the parameter space P;

[0032] S3-3: According to the parameter space P and the objective function f(p), define the Gaussian process model:

[0033] f(p) ~ GP(μ(p), κ(p, p')) (9)

[0034] In Equation (9), GP is the Gaussian process model, μ(p) is the mean function, representing the current estimate of the target, κ(p, p′) is the covariance function, representing the correlation between p and p′, and p′ represents another set of hyperparameter combinations in the parameter space P;

[0035] S3-4: Randomly sample J sets of hyperparameter combinations from the parameter space P as training points, and calculate the objective function value for each set of hyperparameter combinations as the observed value to construct the dataset S:

[0036] S = {(p1, q1), (p2, q2),...(p j , q j ),...(p J , q J )} (10)

[0037] In Equation (10), p j is the j-th training point in the dataset S, j = 1, 2,... J, q j is the observed value corresponding to the training point p j in the dataset S, q j = f(p j ) + ε, where ε is the noise;

[0038] S3-5: Use the Gaussian process model to calculate the predicted mean and predicted variance of the new point p*:

[0039]

[0040] In Equation (11), μ(p*) is the predicted mean of the new point p*, and κ * is the vector of kernel function values between the new point p* and all training points, is the transpose of the vector of kernel function values between the new point p* and all training points, K is the kernel matrix, representing the kernel function values between all training points, σ n 2 is the noise variance, I is the identity matrix, q is the vector of observations of all training points, σ p 2 (p*) is the predicted variance of the new point p*, and κ ** is the kernel function value of the new point p* with itself;

[0041] S3-6: Select the expected improvement function EI(p*) as the acquisition function:

[0042] EI(p*) = (μ(p*) - f + - ξ)Φ(Z) + σ p (p*)φ(Z) (12)

[0043] In Equation (12), f + is the currently known best observation value, ξ is the exploration factor, Φ(Z) is the cumulative distribution function of the standard normal distribution, σ p (p*) is the predicted standard deviation of the new point p*, and φ(Z) is the probability density function of the standard normal distribution;

[0044] S3-7: By maximizing the acquisition function EI(p*), select the new training point p next :

[0045] p next = argmaxEI(p*) (13)

[0046] In Equation (13), argmax is an operator, indicating finding the p* value that maximizes the acquisition function EI(p*);

[0047] S3-8: Calculate the observation value q next of the new training point p next :

[0048] q next = f(p next ) + ε (14)

[0049] S3-9: Add the new data point (p next , q next ) to the dataset S to form the updated dataset S new :

[0050] S new = S ∪ {(p next,q next )} (15)

[0051] In formula (15), ∪ is the union operator;

[0052] S3-10: Repeat steps S3-5 to S3-9 until the maximum number of set iterations is completed, and obtain the parameter combination that minimizes the mean square error of the validation set, which is the optimal learning rate and batch size of the CKAN model;

[0053] S3-11: Set the CKAN model according to the optimal learning rate and batch size obtained in step S3-10, train and debug the CKAN model using the training set and the validation set, and output the accurate estimation result of the inertia of the new power system nodes.

[0054] Compared with the prior art, the principle and advantages of this solution are as follows:

[0055] The present invention discloses a method for estimating the inertia of new power system nodes based on the CKAN model, including the following steps: First, when there is an active power disturbance in the new power system, collect the electrical data at the nodes, construct an original data set, and preprocess the original data set to construct a feature data set; Then, design a CNN feature extraction module and a KAN module based on wavelet basis functions, and construct a CKAN model through cascade fusion; Finally, use the Bayesian optimization algorithm to optimize the hyperparameters of the CKAN model to improve the estimation accuracy of the CKAN model; The CKAN model proposed by the present invention can extract the local features of the input data through the CNN feature extraction module, and then perform wavelet transform on the local features by the KAN module to mine the core information, so as to quickly and accurately estimate the inertia at each node of the new power system. Brief Description of the Drawings

[0056] Figure 1 It is a flowchart of the method for estimating the inertia of new power system nodes based on the CKAN model in the embodiment of the present invention;

[0057] Figure 2 It is a structural diagram of the CKAN model in the embodiment of the present invention;

[0058] Figure 3 It is the topology structure of the IEEE10-machine 39-node new power system model in the embodiment of the present invention;

[0059] Figure 4 It is a scatter plot of the true value and the estimated value when estimating the inertia of new power system nodes using the traditional CNN model in the embodiment of the present invention;

[0060] Figure 5 It is a residual plot when estimating the inertia of new power system nodes using the traditional CNN model in the embodiment of the present invention;

[0061] Figure 6 This is the scatter plot of the true value and the estimated value when the unoptimized CKAN model is used to estimate the inertia of the new power system nodes in the embodiments of the present invention;

[0062] Figure 7 This is the residual plot when the unoptimized CKAN model is used to estimate the inertia of the new power system nodes in the embodiments of the present invention;

[0063] Figure 8 This is the scatter plot of the true value and the estimated value when the optimized CKAN model is used to estimate the inertia of the new power system nodes in the embodiments of the present invention;

[0064] Figure 9 This is the residual plot when the optimized CKAN model is used to estimate the inertia of the new power system nodes in the embodiments of the present invention. Detailed implementation manners

[0065] The present invention will be further described below in conjunction with specific embodiments:

[0066] Figure 1 Shown is the flow chart of the method for estimating the inertia of the new power system nodes based on the CKAN model, Figure 2 Shown is the structure diagram of the constructed CKAN model.

[0067] The specific steps of step S1 are as follows:

[0068] S1-1: When there is an active power disturbance in the new power system, collect the frequency change data at each node accessing the virtual synchronous machine in real time to construct a frequency change data set. The frequency change data set F n,m in the nth node at the mth active power disturbance has the following specific form:

[0069] F n,m =[F n,m,1 , F n,m,2 , …, F n,m,t , …, F n,m,T (16)

[0070] In formula (16), F n,m,t represents the frequency value at the tth sampling moment in the mth active power disturbance of the nth node. n = 1, 2, … N, where N represents the total number of nodes accessing the virtual synchronous machine, m = 1, 2, … M, where M represents the total number of active power disturbances, and t = 1, 2, … T, where T represents the total number of samplings during the active power disturbance;

[0071] S1-2: When there is an active power disturbance in the system, record the true inertia value of the virtual synchronous machine at the node as the inertia data set. For the inertia data set H nThe specific form is as follows:

[0072] H n = [H n,1 , H n,2 , …, H n,m , …, H n,M (17)

[0073] In formula (17), H n,m represents the true inertia value of the virtual synchronous machine at the nth node during the mth active power disturbance;

[0074] S1-3: According to the frequency change data set F n,m obtained in step S1-1, construct the original data set X ori , and its specific form is as follows:

[0075]

[0076] In formula (18), X n represents the original data set corresponding to the nth node, and it includes the frequency change data at the node after M active power disturbances. The specific form of X n is as follows:

[0077]

[0078] S1-4: Normalize the original data set X ori in step S1-3, and merge it with the inertia data set H n in step S1-2 to obtain the feature data set D nd whose specific form is as follows:

[0079]

[0080] In formula (20), D n represents the feature data set corresponding to the nth node, and its specific form is as follows:

[0081]

[0082] In formula (21), represents the normalized frequency change data set;

[0083] S1-5: Divide the feature data set D nd in step S1-4, where 70% is used as the training set and 30% is used as the validation set;

[0084] The specific steps of step S2 are as follows:

[0085] S2-1: The CNN feature extraction module consists of three one-dimensional convolutional layers, three batch normalization layers, and three max pooling layers. The convolutional layers perform convolutional operations on the input data to extract local features of the input data layer by layer. The batch normalization layers are responsible for normalizing each batch of input data, adjusting the distribution of the input data to a standard distribution with a mean close to 0 and a variance close to 1. The max pooling layers take the maximum value of the local regions of the extracted features through a sliding window, reducing the feature dimension and highlighting important features;

[0086] S2-2: The KAN module consists of five wavelet KAN linear layers. The number of nodes in the five wavelet KAN linear layers are 1472, 512, 128, 32, and 1 respectively. Each layer uses a combination of base weights and wavelet basis functions to transform the input data. Among them, the base weights extract the global features of the input data through linear transformation, and the wavelet basis functions capture local features such as peaks and fluctuations of the input data through wavelet transformation. By gradually reducing the number of nodes layer by layer, the KAN module gradually extracts the core information of the input data;

[0087] S2-3: Connect the CNN feature extraction module in step S2-1 and the KAN module in step S2-2 in series for fusion to construct the CKAN model. The CKAN model can extract the local features of the input frequency change data through the CNN feature extraction module, and then combine the global and local features through the KAN module to establish the mapping relationship between the frequency change data and the inertia data, and finally output the inertia estimation value;

[0088] The specific steps of step S3 are as follows:

[0089] S3-1: Use the Bayesian optimization algorithm to optimize the learning rate and batch size of the CKAN model, and establish the parameter space P:

[0090]

[0091] In formula (22), learning_rate represents the learning rate to be optimized, (10 -5 , 10 -2 ) is the value range of the learning rate, batch_size represents the batch size to be optimized, and (32, 256) is the value range of the batch size;

[0092] S3-2: In order to improve the estimation accuracy of the CKAN model, design the minimum mean square error of the validation set as the objective function f(p):

[0093]

[0094] In formula (23), c is the number of samples in the validation set, y (i) is the true value of the i-th sample, is the estimated value of the CKAN model for the i-th sample, where i = 1, 2, … c, and p represents a set of hyperparameter combinations in the parameter space P;

[0095] S3-3: Define the Gaussian process model according to the parameter space P and the objective function f(p):

[0096] f(p) ∼ GP(μ(p), κ(p, p')) (24)

[0097] In equation (24), GP is the Gaussian process model, μ(p) is the mean function representing the current estimate of the objective, κ(p, p′) is the covariance function representing the correlation between p and p′, and p′ represents another set of hyperparameter combinations in the parameter space P;

[0098] S3-4: Randomly sample J sets of hyperparameter combinations from the parameter space P as training points, and calculate the objective function values for each set of hyperparameter combinations as observed values to construct the dataset S:

[0099] S = {(p1, q1), (p2, q2),...(p j , q j ),...(p J , q J )} (25)

[0100] In equation (25), p j is the j-th training point in the dataset S, where j = 1, 2, … J, q j is the observed value corresponding to the training point p j in the dataset S, q j = f(p j ) + ε, where ε is the noise;

[0101] S3-5: Use the Gaussian process model to calculate the predicted mean and predicted variance of the new point p*:

[0102]

[0103] In equation (26), μ(p*) is the predicted mean of the new point p*, κ * is the vector of kernel function values between the new point p* and all training points, is the transpose of the vector of kernel function values between the new point p* and all training points, K is the kernel matrix representing the kernel function values between all training points, σ n 2 is the noise variance, I is the identity matrix, q is the vector of observed values of all training points, σ p 2 (p*) is the predicted variance of the new point p*, κ ** is the kernel function value of the new point p* with itself;

[0104] S3-6: Select the expected improvement function EI(p*) as the acquisition function:

[0105] EI(p*) = (μ(p*) - f + - ξ)Φ(Z) + σ p (p*)φ(Z) (27)

[0106] In Equation (27), f + is the currently known best observation value, ξ is the exploration factor, Φ(Z) is the cumulative distribution function of the standard normal distribution, and σ p (p*) is the predicted standard deviation of the new point p*, and φ(Z) is the probability density function of the standard normal distribution;

[0107] S3-7: Select the new training point p next by maximizing the acquisition function EI(p*):

[0108] p next = argmaxEI(p*) (28)

[0109] In Equation (28), argmax is an operator indicating finding the p* value that maximizes the acquisition function EI(p*);

[0111] S3-8: Calculate the observation value q next of the new training point p next :

[0112] q next = f(p next ) + ε (29)

[0113] S3-9: Add the new data point (p next , q next ) to the dataset S to form the updated dataset S new :

[0114] S new = S ∪ {(p next , q next )} (30)

[0115] In Equation (30), ∪ is the union operator;

[0116] S3-10: Repeat steps S3-5 to S3-9 until the maximum number of iterations set is completed, and obtain the parameter combination that minimizes the mean square error of the validation set, which is the optimal learning rate and batch size of the CKAN model;

[0117] S3-11: Set the CKAN model according to the optimal learning rate and batch size obtained in step S3-10, train and debug the CKAN model using the training set and the validation set, and output the accurate estimation result of the inertia of the new power system nodes.

[0118] To verify the effectiveness of the proposed method, a new power system model of IEEE 10-machine 39-bus is built on the MATLAB software, and its topological structure is as Figure 3 shown. Virtual synchronous machines are connected at buses 30-39. By setting random power disturbances with amplitudes of ±5% of the rated power under steady-state operating conditions, the load fluctuations in the actual system are simulated, and the frequency change data at the buses where 10 virtual synchronous machines are connected are collected. The collected data are respectively input into the traditional CNN model, the unoptimized CKAN model, and the optimized CKAN model for node inertia estimation, and the estimation effects of each model are compared.

[0119] Figure 4 、 Figure 5 Shown in

[0120] Figure 6 、 Figure 7 is the effect of using the traditional CNN model to estimate the inertia of the new power system nodes. The overall estimation mean square error is 16.18%, the root mean square error is 40.23%, and the model goodness of fit is 0.99980.

[0121] Figure 8 、 Figure 9 Shown in

[0122] is the effect of using the unoptimized CKAN model to estimate the inertia of the new power system nodes. The overall estimation mean square error is 2.19%, the root mean square error is 14.80%, and the model goodness of fit is 0.99997.

[0123] Shown in

[0122] is the effect of using the optimized CKAN model to estimate the inertia of the new power system nodes. The overall estimation mean square error is 0.43%, the root mean square error is 6.55%, and the model goodness of fit is 0.99999. Compared with the traditional CNN model, the optimized CKAN model has improved the mean square error by 97.34% and the root mean square error by 83.72% in terms of estimation accuracy. Compared with the unoptimized CKAN model, the optimized CKAN model has improved the mean square error by 80.37% and the root mean square error by 55.74% in terms of estimation accuracy.

[0123] As can be seen from the above analysis, the method for estimating the inertia of the new power system nodes based on the CKAN model proposed by the present invention can more accurately capture the complex nonlinear relationship of the inertia of the power system nodes, achieve high-precision inertia estimation, and provide more reliable technical support for the stable operation of the power system.

[0123] The above-described embodiments are only the preferred embodiments of the present invention, and do not limit the scope of implementation of the present invention. Therefore, any changes made according to the shape and principle of the present invention should be covered within the protection scope of the present invention.

Claims

1. A novel method for estimating the inertia of nodes in a power system based on the CKAN model, characterized in that It includes the following steps: S1: When there is an active power disturbance in the new power system, collect the electrical data at the nodes, construct the original data set, and preprocess the original data set to construct the feature data set; S1-1: When there is an active power disturbance in the new power system, collect the frequency change data at each node accessing the virtual synchronous machine in real time to construct a frequency change data set. The specific form of the frequency change data set F n,m at the nth node during the mth active power disturbance is as follows: F n,m = [F n,m,1 , F n,m,2 , …, F n,m,t , …, F n,m,T (1) In formula (1), F n,m,t represents the frequency value of the nth node at the tth sampling moment during the mth active power disturbance, where n = 1, 2, … N, N represents the total number of nodes connected to the virtual synchronous machine, m = 1, 2, … M, M represents the total number of active power disturbances, and t = 1, 2, … T, T represents the total number of samplings during the active power disturbance; S1-2: When there is an active power disturbance in the system, record the true inertia value of the virtual synchronous machine at the node as the inertia data set. For the inertia data set H at the nth node n The specific form is as follows: H n = [H n,1 , H n,2 , …, H n,m , …, H n,M (2) In Equation (2), H n,m represents the true inertia value of the virtual synchronous machine at the nth node during the mth active power disturbance; S1-3: Construct the original dataset X based on the frequency change dataset F obtained in step S1-1 n,m , where the specific form is as follows: ori : In formula (3), X n represents the original data set corresponding to the nth node, which includes the frequency change data at the node after M active power disturbances. The specific form of X n is as follows: S1-4: Normalize the original dataset X obtained in step S1-3 ori and merge it with the inertia dataset H obtained in step S1-2 n to obtain the feature dataset D nd The specific form is as follows: In formula (5), D n represents the feature data set corresponding to the nth node, and its specific form is: In formula (6), represents the normalized frequency change data set; S1-5: Divide the feature dataset D in step S1-4 nd such that 70% is used as the training set and 30% is used as the validation set; S2: Design a CNN (Convolutional Neural Network) feature extraction module and a KAN (Kolmogorov - Arnold Network) module based on wavelet basis functions, and construct a CKAN (Convolutional Kolmogorov - Arnold Network) model through cascaded fusion; S2 - 1: The CNN feature extraction module includes three layers of one - dimensional convolutional layers, three layers of batch normalization layers, and three layers of max - pooling layers. The convolutional layers perform convolutional operations on the input data to extract the local features of the input data layer by layer. The batch normalization layers are responsible for normalizing each batch of input data, adjusting the distribution of the input data to a standard distribution with a mean close to 0 and a variance close to 1. The max - pooling layers take the maximum value of the local area of the extracted features through a sliding window, reduce the feature dimension, and highlight the important features; S2 - 2: The KAN module includes five layers of wavelet KAN linear layers. The number of nodes in the five layers of wavelet KAN linear layers are 1472, 512, 128, 32, and 1 respectively. Each layer uses a combination of base weights and wavelet basis functions to transform the input data. Among them, the base weights extract the global features of the input data through linear transformation, and the wavelet basis functions capture the local features such as peaks and fluctuations of the input data through wavelet transformation. By gradually reducing the number of nodes layer by layer, the KAN module gradually extracts the core information of the input data; S2 - 3: Cascade - fuse the CNN feature extraction module in step S2 - 1 and the KAN module in step S2 - 2 to construct a CKAN model. The CKAN model can extract the local features of the input frequency change data through the CNN feature extraction module, and then combine the global and local features through the KAN module to establish the mapping relationship between the frequency change data and the inertia data, and finally output the inertia estimation value; S3: Use the Bayesian optimization algorithm to optimize the hyperparameters of the CKAN model to improve the estimation accuracy of the CKAN model; S3 - 1: Use the Bayesian optimization algorithm to optimize the learning rate and batch size of the CKAN model, and establish the parameter space P: In Equation (7), learning_rate represents the learning rate to be optimized, and (10 -5 , 10 -2 ) is the value range of the learning rate. batch_size represents the batch size to be optimized, and (32, 256) is the value range of the batch size; S3 - 2: To improve the estimation accuracy of the CKAN model, design the minimum mean square error of the validation set as the objective function f(p): In Equation (8), c is the number of samples in the validation set, y (i) is the true value of the i-th sample, is the estimated value of the CKAN model for the i-th sample, i = 1, 2, … c, and p represents a set of hyperparameter combinations in the parameter space P; S3 - 3: According to the parameter space P and the objective function f(p), define the Gaussian process model: f(p)~GP(μ(p),κ(p,p')) (9) In formula (9), GP is the Gaussian process model, μ(p) is the mean function, representing the current estimate of the target, κ(p,p′) is the covariance function, representing the correlation between p and p′, and p′ represents another set of hyperparameter combinations in the parameter space P; S3 - 4: Randomly sample J groups of hyperparameter combinations from the parameter space P as training points, and calculate the objective function values for each group of hyperparameter combinations as observation values to construct the data set S: S = {(p1, q1), (p2, q2),...(p j , q j ),...(p J , q J )} (10) In Equation (10), p j is the j-th training point in the data set S, where j = 1, 2, …, J, and q j is the observation corresponding to the training point p j in the data set S, and q j = f(p j ) + ε, where ε is the noise; S3 - 5: Use the Gaussian process model to calculate the predicted mean and predicted variance of the new point p*: In Equation (11), μ(p*) is the predicted mean of the new point p*, and κ * is the vector of kernel function values between the new point p* and all training points, is the transpose of the vector of kernel function values between the new point p* and all training points, K is the kernel matrix representing the kernel function values between all training points, σ n 2 is the noise variance, I is the identity matrix, q is the vector of observations of all training points, σ p 2 σ(p*) is the predicted variance of the new point p*, and κ ** is the kernel function value of the new point p* with itself; S3 - 6: Select the expected improvement function EI(p*) as the acquisition function: EI(p*) = (μ(p*) - f + - ξ)Φ(Z) + σ p (p*)φ(Z) (12) In formula (12), f + is the currently known best observed value, ξ is the exploration factor, Φ(Z) is the cumulative distribution function of the standard normal distribution, σ p (p*) is the predicted standard deviation of the new point p*, and φ(Z) is the probability density function of the standard normal distribution; S3-7: Select a new training point p by maximizing the acquisition function EI(p*) next : p next = argmaxEI(p*) (13) In Equation (13), argmax is an operator, indicating finding the p* value that maximizes the acquisition function EI(p*); S3-8: Calculate the observation value q of the new training point p next next :​ q next = f(p next ) + ε (14) S3-9: Add the new data point (p next , q next ) to the data set S to form the updated data set S new : S new = S ∪ {(p next , q next )} (15) In Equation (15), ∪ is the union operator; S3-10: Repeat steps S3-5 to S3-9 until the set maximum number of iterations is completed, and obtain the parameter combination that minimizes the mean squared error of the validation set, which is the optimal learning rate and batch size of the CKAN model; S3-11: Set the CKAN model according to the optimal learning rate and batch size obtained in step S3-10, train and debug the CKAN model using the training set and the validation set, and output the accurate estimation result of the inertia of the new power system nodes.

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