Power system node inertia estimation method based on ckam model

Abstract

The application discloses a power system node inertia estimation method based on a CKAN model, and comprises the following steps: firstly, when active disturbance occurs in a power system, electrical data at a node is collected, an original data set is constructed, and the original data set is preprocessed to construct a feature data set; then, a CNN (convolutional neural network) feature extraction module and a KAN (Kolmogorov-Arnold network) module based on a wavelet base function are designed, a CKAN (convolutional Kolmogorov-Arnold network) model is constructed by being connected in series and fused, and finally, a Bayesian optimization algorithm is used to optimize CKAN model hyperparameters, so that the estimation accuracy of the CKAN model is improved; the CKAN model provided by the application can extract local features of input data through the CNN feature extraction module, and then the KAN module can perform wavelet transform on the local features to mine core information, so that the inertia at each node of the power system can be quickly and accurately estimated.

Description

Technical Field

[0001] The present invention relates to the field of power system stability research, and in particular to a power system node inertia estimation method based on a 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 disturbances and maintain frequency stability. In traditional power systems, inertia remains basically constant, which plays an important role in maintaining power stability. However, with the increase in the 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. The overall inertia level of the system decreases, resulting in a decrease in the system stability margin. At the same time, the regional differences in the distribution of natural wind and solar resources have broken the original relatively balanced pattern of inertia resources. The areas where new energy is concentrated have low inertia characteristics, which is in sharp contrast to the high inertia in areas rich in synchronous generators. This difference limits the system's ability to absorb new energy. Therefore, for power systems with a high proportion of new energy, the research work on inertia assessment needs to focus not only on the overall inertia level of the system, but also on the spatial distribution of inertia at the node level, so as to find weak inertia nodes and optimize the inertia distribution. To this end, the present invention proposes a power system node inertia estimation method based on the CKAN model, which provides technical guidance for the access layout of new energy by accurately estimating node inertia. Summary of the Invention

[0003] To achieve the above objectives, the technical solutions provided by the present invention are:

[0004] S1: When an active disturbance occurs in the power system, electrical data at the node is collected to construct a raw data set, which is then preprocessed to construct a feature data set.

[0005] S1-1: When active disturbance occurs in the power system, frequency change data of each node connected to the virtual synchronous machine is collected in real time to build a frequency change data set, where the frequency change data set F of the nth node at the mth active disturbance is n,m The specific form 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,trepresents the frequency value of the nth node at the tth sampling time during the mth active power disturbance, n = 1, 2, ... N, N represents the total number of nodes connected to the virtual synchronizer, m = 1, 2, ... M, M represents the total number of active power disturbances, t = 1, 2, ... T, T represents the total number of samples during the active power disturbance;

[0008] S1-2: When active disturbance occurs in the system, the real inertia value of the virtual synchronous machine at the node is recorded 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 It represents the real inertia value of the virtual synchronous machine at the nth node when the mth active disturbance occurs;

[0011] S1-3: Frequency change data set F obtained according to step S1-1 n,m , construct the original data set X ori , 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 disturbances. n The specific form is:

[0014]

[0015] S1-4: The original data set X in step S1-3 ori Normalize and compare with the inertia data set H in step S1-2 n Merge to get feature dataset 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 dataset;

[0020] S1-5: Feature dataset 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 Kolmogorov-Arnold network (KAN) module based on wavelet basis functions, and construct a CKAN model through serial fusion.

[0022] S2-1: The CNN feature extraction module consists of three one-dimensional convolutional layers, three batch normalization layers, and three maximum pooling layers. The convolutional layers perform convolution operations on the input data, extracting 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 maximum pooling layer uses a sliding window to maximize the local area of ​​the extracted features, reducing the feature dimension and highlighting important features.

[0023] S2-2: The KAN module consists of five wavelet-KAN linear layers, with the number of nodes in the five wavelet-KAN linear layers being 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, while the wavelet basis functions capture local features such as peaks and fluctuations in the input data 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 serially integrated to construct 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 CKAN model hyperparameters 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 learning rate, batch_size represents the batch size to be optimized, (32,256) is the range of batch size;

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

[0030]

[0031] In formula (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: Based on 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 formula (9), GP is a Gaussian process model, μ(p) is the mean function, which represents the current estimate of the target, κ(p, p′) is the covariance function, which represents 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 observation value to construct the data set S:

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

[0037] In formula (10), p j is the jth training point in the dataset S, j = 1, 2, ... J, q j is the corresponding training point p in the dataset S j The observed value, q j =f(p j )+ε, ε is noise;

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

[0039]

[0040] In formula (11), μ(p * ) is the new point p * The predicted mean, κ * It is a new point p * and the kernel function value vector between all training points, It is a new point p * The transpose of the kernel function value vector between all training points, K is the kernel matrix, which represents the kernel function value between all training points, σ n 2 is the noise variance, I is the identity matrix, q is the vector of all training point observations, σ p 2 (p * ) is the new point p * The prediction variance, κ ** It is a new point p * and its own kernel function value;

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

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

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

[0046] In formula (13), argmax is an operator, which means finding the acquisition function EI(p * )The largest p * value;

[0047] S3-8: Calculate new training point p next The observed value q next :

[0048] q next =f(p next )+ε(14)S3-9: The new data point (p next ,q next ) is added to the dataset S to form the updated dataset S new :

[0049] S new =S∪{(p next ,q next )}(15)

[0050] In formula (15), ∪ is the union operator;

[0051] S3-10: Repeat steps S3-5 to S3-9 until the maximum number of iterations is reached, and obtain the parameter combination that minimizes the mean square error of the validation set, which is the optimal learning rate and batch size for the CKAN model;

[0052] 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 validation set, and output accurate estimation results of the power system node inertia.

[0053] Compared with the existing technology, the principles and advantages of this solution are as follows:

[0054] The present invention discloses a method for estimating the inertia of power system nodes based on a CKAN model. The method comprises the following steps: first, when an active disturbance occurs in the power system, electrical data at the node is collected to construct an original data set, and the original data set is preprocessed to construct a feature data set; then, a CNN feature extraction module and a KAN module based on a wavelet basis function are designed, and the CKAN model is constructed by serial fusion; finally, a Bayesian optimization algorithm is used to optimize the hyperparameters of the CKAN model to improve the estimation accuracy of the CKAN model; the CKAN model proposed in the present invention can extract local features of input data through the CNN feature extraction module, and then the KAN module performs wavelet transform on the local features to mine core information, thereby realizing rapid and accurate estimation of the inertia at each node of the power system. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 Flowchart of a method for estimating node inertia of a power system based on a CKAN model in an embodiment of the present invention;

[0056] Figure 2 : is a structural diagram of the CKAN model in an embodiment of the present invention;

[0057] Figure 3 The IEEE 10-machine 39-node power system model topology in an embodiment of the present invention;

[0058] Figure 4 A scatter plot of the true value and the estimated value when estimating the node inertia of the power system using the traditional CNN model in an embodiment of the present invention;

[0059] Figure 5 This is a residual graph of estimating the node inertia of the power system using the traditional CNN model in an embodiment of the present invention;

[0060] Figure 6 A scatter plot of true and estimated values ​​when estimating power system node inertia using an unoptimized CKAN in an embodiment of the present invention;

[0061] Figure 7 This is a residual graph of estimating the node inertia of the power system using the unoptimized CKAN model in an embodiment of the present invention;

[0062] Figure 8 A scatter plot of true and estimated values ​​when estimating the node inertia of a power system using the optimized CKAN model in an embodiment of the present invention;

[0063] Figure 9 This is a residual graph of estimating the node inertia of the power system using the optimized CKAN model in an embodiment of the present invention. DETAILED DESCRIPTION

[0064] The present invention will be further described below in conjunction with specific embodiments:

[0065] Figure 1 The figure shows a flow chart of the power system node inertia estimation method based on the CKAN model. Figure 2 Shown is the structural diagram of the constructed CKAN model.

[0066] The step S1 is specifically as follows:

[0067] S1-1: When active disturbance occurs in the power system, frequency change data of each node connected to the virtual synchronous machine is collected in real time to build a frequency change data set, where the frequency change data set F of the nth node at the mth active disturbance is n,m The specific form is:

[0068] F n,m =[F n,m,1 ,F n,m,2 ,…,F n,m,t ,…,F n,m,T ](16)

[0069] In formula (16), F n,m,trepresents the frequency value of the nth node at the tth sampling time during the mth active power disturbance, n = 1, 2, ... N, N represents the total number of nodes connected to the virtual synchronizer, m = 1, 2, ... M, M represents the total number of active power disturbances, t = 1, 2, ... T, T represents the total number of samples during the active power disturbance;

[0070] S1-2: When active disturbance occurs in the system, the real inertia value of the virtual synchronous machine at the node is recorded as the inertia data set. For the inertia data set H at the nth node n The specific form is:

[0071] H n =[H n,1 ,H n,2 ,…,H n,m ,…,H n,M ](17)

[0072] In formula (17), H n,m It represents the real inertia value of the virtual synchronous machine at the nth node when the mth active disturbance occurs;

[0073] S1-3: Frequency change data set F obtained according to step S1-1 n,m , construct the original data set X ori , its specific form is:

[0074]

[0075] In formula (18), X n represents the original data set corresponding to the nth node, which includes the frequency change data at the node after M active disturbances. n The specific form is:

[0076]

[0077] S1-4: The original data set X in step S1-3 ori Normalize and compare with the inertia data set H in step S1-2 n Merge to get feature dataset D nd The specific form is:

[0078]

[0079] In formula (20), D n Represents the feature data set corresponding to the nth node, and its specific form is:

[0080]

[0081] In formula (21), represents the normalized frequency change dataset;

[0082] S1-5: Feature dataset D of step S1-4 nd Divide the dataset into 70% as training set and 30% as validation set;

[0083] The step S2 is specifically as follows:

[0084] S2-1: The CNN feature extraction module consists of three one-dimensional convolutional layers, three batch normalization layers, and three maximum pooling layers. The convolutional layers perform convolution operations on the input data, extracting 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 maximum pooling layer uses a sliding window to maximize the local area of ​​the extracted features, reducing the feature dimension and highlighting important features.

[0085] S2-2: The KAN module consists of five wavelet-KAN linear layers, with the number of nodes in the five wavelet-KAN linear layers being 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, while the wavelet basis functions capture local features such as peaks and fluctuations in the input data through wavelet transformation. By reducing the number of nodes layer by layer, the KAN module gradually extracts the core information of the input data.

[0086] S2-3: The CNN feature extraction module of step S2-1 and the KAN module of step S2-2 are serially integrated to construct 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;

[0087] The step S3 is specifically as follows:

[0088] 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:

[0089]

[0090] In formula (22), learning_rate represents the learning rate to be optimized, (10 -5 ,10 -2 ) is the range of learning rate, batch_size represents the batch size to be optimized, (32,256) is the range of batch size;

[0091] S3-2: In order to improve the estimation accuracy of the CKAN model, the minimum mean square error of the validation set is designed as the objective function f(p):

[0092]

[0093] 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, i = 1, 2, ... c, and p represents a set of hyperparameter combinations in the parameter space P;

[0094] S3-3: Based on the parameter space P and the objective function f(p), define the Gaussian process model:

[0095] f(p)~GP(μ(p),κ(p,p')) (24)

[0096] In formula (24), GP is a Gaussian process model, μ(p) is the mean function, which represents the current estimate of the target, κ(p, p′) is the covariance function, which represents the correlation between p and p′, and p′ represents another set of hyperparameter combinations in the parameter space P;

[0097] 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 observation value to construct the data set S:

[0098] S={(p1,q1),(p2,q2),...(p j ,q j ),...(p J ,q J )} (25)

[0099] In formula (25), p j is the jth training point in the dataset S, j = 1, 2, ... J, q j is the corresponding training point p in the dataset S j The observed value, q j =f(p j )+ε, ε is noise;

[0100] S3-5: Use the Gaussian process model to calculate the new point p * The predicted mean and predicted variance of :

[0101]

[0102] In formula (26), μ(p * ) is the new point p * The predicted mean, κ * It is a new point p *and the kernel function value vector between all training points, It is a new point p * The transpose of the kernel function value vector between all training points, K is the kernel matrix, which represents the kernel function value between all training points, σ n 2 is the noise variance, I is the identity matrix, q is the vector of all training point observations, σ p 2 (p * ) is the new point p * The prediction variance, κ ** It is a new point p * and its own kernel function value;

[0103] S3-6: Select the expected improvement function EI(p * ) as the acquisition function:

[0104] EI(p * )=(μ(p * )-f + -ξ)Φ(Z)+σ p (p * )φ(Z) (27)

[0105] In formula (27), f + is the best known observation value, ξ is the exploration factor, Φ(Z) is the cumulative distribution function of the standard normal distribution, σ p (p * ) is the new point p * The predicted standard deviation of , φ(Z) is the probability density function of the standard normal distribution;

[0106] S3-7: By maximizing the acquisition function EI(p * ), select a new training point p next :

[0107] p next =argmaxEI(p * ) (28)

[0108] In formula (28), argmax is an operator, which means finding the acquisition function EI(p * )The largest p * value;

[0109] S3-8: Calculate new training point p next The observed value q next :

[0110] q next =f(p next )+ε (29)S3-9: The new data point (p next ,qnext ) is added to the dataset S to form the updated dataset S new :

[0111] S new =S∪{(p next ,q next )} (30)

[0112] In formula (30), ∪ is the union operator;

[0113] S3-10: Repeat steps S3-5 to S3-9 until the maximum number of iterations is reached, and obtain the parameter combination that minimizes the mean square error of the validation set, which is the optimal learning rate and batch size for the CKAN model;

[0114] 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 validation set, and output accurate estimation results of the power system node inertia.

[0115] In order to verify the effectiveness of the proposed method, an IEEE 10-machine 39-bus power system model was built on MATLAB software. Its topology is as follows: Figure 3 As shown in the figure, virtual synchronous generators were connected at nodes 30-39. A random power perturbation with an amplitude of ±5% of rated power was set under steady-state operating conditions to simulate load fluctuations in the actual system. Frequency variation data was collected at the nodes where the 10 virtual synchronous generators were connected. This collected data was then fed into a traditional CNN model, an unoptimized CKAN model, and an optimized CKAN model for node inertia estimation, and the estimation performance of each model was compared.

[0116] Figure 4 、 Figure 5 The figure shows the effect of using the traditional CNN model to estimate the node inertia of the power system. The overall estimation mean square error is 16.18%, the root mean square error is 40.23%, and the model fit goodness is 0.99980.

[0117] Figure 6 、 Figure 7 The figure shows the effect of using the unoptimized CKAN model to estimate the node inertia of the power system. The overall estimation mean square error is 2.19%, the root mean square error is 14.80%, and the model fit goodness of fit is 0.99997.

[0118] Figure 8 、 Figure 9The results show the effectiveness of the optimized CKAN model in estimating power system node inertia. The overall estimation mean square error (MSE) is 0.43%, the root mean square error (RMS) is 6.55%, and the model goodness of fit is 0.99999. Compared with the traditional CNN model, the optimized CKAN model improves estimation accuracy by 97.34% in MSE and 83.72% in RMSE. Compared with the unoptimized CKAN model, the optimized CKAN model improves estimation accuracy by 80.37% in MSE and 55.74% in RMSE.

[0119] From the above analysis, it can be seen that the power system node inertia estimation method based on the CKAN model proposed in this invention can more accurately capture the complex nonlinear relationship of the power system node inertia, achieve high-precision inertia estimation, and provide more reliable technical support for the stable operation of the power system.

[0120] The embodiments described above are only preferred embodiments of the present invention and are not intended to limit the scope of implementation of the present invention. Therefore, any changes made based on the shape and principle of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for estimating node inertia of a power system based on the CKAN model, characterized in that: The following steps are involved: S1: When an active disturbance occurs in the power system, electrical data at the node is collected to construct a raw data set, which is then preprocessed to construct a feature data 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 serial fusion; S2-1: The CNN feature extraction module consists of three one-dimensional convolutional layers, three batch normalization layers, and three maximum pooling layers. The convolutional layers perform convolution operations on the input data, extracting local features of the input data layer by layer. The batch normalization layers are responsible for normalizing each batch of input data. The maximum pooling layer uses a sliding window to maximize the local area of ​​the extracted features, reducing the feature dimension and highlighting important features. S2-2: The KAN module consists of five wavelet KAN linear layers. 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, while the wavelet basis functions capture the peak and fluctuation local features of the input data through wavelet transformation. S2-3: The CNN feature extraction module of step S2-1 and the KAN module of step S2-2 are serially integrated to construct 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; S3: Use the Bayesian optimization algorithm to optimize the hyperparameters of the CKAN model, design the minimum mean square error of the validation set as the objective function, and obtain the parameter combination that minimizes the mean square error of the validation set.

2. The method for estimating node inertia of a power system based on the CKAN model according to claim 1, characterized in that: The step S1 comprises: S1-1: When active disturbance occurs in the power system, frequency change data of each node connected to the virtual synchronous machine is collected in real time to build a frequency change data set, where the frequency change data set F of the nth node at the mth active disturbance is n,m The specific form is: 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 time during the mth active power disturbance, n = 1, 2, ... N, N represents the total number of nodes connected to the virtual synchronizer, m = 1, 2, ... M, M represents the total number of active power disturbances, t = 1, 2, ... T, T represents the total number of samples during the active power disturbance; S1-2: When active disturbance occurs in the system, the real inertia value of the virtual synchronous machine at the node is recorded as the inertia data set. For the inertia data set H at the nth node n The specific form is: H n =[H n,1 ,H n,2 ,…,H n,m ,…,H n,M ] (2) In formula (2), H n,m It represents the real inertia value of the virtual synchronous machine at the nth node when the mth active power disturbance occurs; S1-3: Frequency change data set F obtained according to step S1-1 n,m , construct the original data set X ori , its specific form is: 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 disturbances. n The specific form is: S1-4: The original data set X in step S1-3 ori Normalize and compare with the inertia data set H in step S1-2 n Merge to get feature dataset D nd The specific form is: 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 dataset; S1-5: Feature dataset D of step S1-4 nd The dataset is divided into 70% as training set and 30% as validation set.

3. The method for estimating power system node inertia based on the CKAN model according to claim 1, characterized in that: The step S3 comprises: 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 formula (7), learning_rate represents the learning rate to be optimized, (10 -5 ,10 -2 ) is the range of learning rate, batch_size represents the batch size to be optimized, (32,256) is the range of batch size; S3-2: Design the validation set with the minimum mean square error as the objective function f(p): In formula (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: Based on 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 a Gaussian process model, μ(p) is the mean function, which represents the current estimate of the target, κ(p, p′) is the covariance function, which represents the correlation between p and p′, and p′ represents another set of hyperparameter combinations in the parameter space P; 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 observation value to construct the data set S: S={(p1,q1),(p2,q2),...(p j ,q j ),...(p J ,q J )} (10) In formula (10), p j is the jth training point in the dataset S, j = 1, 2, ... J, q j is the corresponding training point p in the dataset S j The observed value, q j =f(p j )+ε, ε is noise; S3-5: Using the Gaussian process model, calculate the predicted mean and predicted variance of the new point p*: In formula (11), μ(p*) is the predicted mean of the new point p*, κ * is the kernel function value vector between the new point p* and all training points, is the transpose of the kernel function value vector between the new point p* and all training points, K is the kernel matrix, which represents the kernel function value between all training points, σ n 2 is the noise variance, I is the identity matrix, q is the vector of all training point observations, σ p 2 (p*) is the prediction variance of the new point p*, κ ** is the kernel function value of the new point p* and 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 best known 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*, 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 formula (13), argmax is an operator, which means finding the p* that maximizes the acquisition function EI(p*) value; S3-8: Calculate new training point p next The observed value q next : what next =f(p next )+ε (14) S3-9: The new data point (p next ,q next ) is added to the dataset S to form the updated dataset S new : S new =S∪{(p next ,q next )} (15) In formula (15), ∪ is the union operator; S3-10: Repeat steps S3-5 to S3-9 until the maximum number of iterations is reached, and obtain the parameter combination that minimizes the mean square error of the validation set, which is the optimal learning rate and batch size for 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 validation set, and output accurate estimation results of the power system node inertia.

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