Method for predicting corona loss of ultra-high voltage line based on Res-BP neural network

Abstract

The application provides a UHV line corona loss prediction method based on a Res-BP neural network, and comprises the following steps: in step S1, a random forest algorithm RF is used to calculate and sort the importance of weather conditions by taking MSE as Gini impurity, and weather conditions with high importance are selected to construct a feature set dataset; in step S2, the differences between weather conditions in different dates are utilized, and a BIRCH algorithm is used for classification; on this basis, a Res-BP neural network model is established to predict the UHV transmission line corona loss, and a PSO optimization algorithm is used to optimize and adjust the internal parameters of the model; and the application has good accuracy and stability.

Description

Technical Field

[0001] This invention relates to the field of power grid operation technology, and in particular to a method for predicting corona loss in ultra-high voltage lines based on a Res-BP neural network. Background Technology

[0002] With the continuous advancement of the power industry, China has successively built and put into operation numerous ultra-high voltage (UHV) AC transmission lines. Corona discharge is an ionization process triggered by the acceleration of free electrons in the air by an electric field. Under a sufficiently high surface electric field level, electrons gain enough energy to ionize neutral molecules in the air, leading to corona discharge. Under low voltage conditions, transmission lines generally do not reach the corona initiation voltage condition. In previous studies, corona losses in high-voltage power grids were relatively low and were usually ignored or approximated. However, in UHV transmission, the corona phenomenon becomes very common, and corona discharge generates energy consumption. The proportion of corona losses due to corona discharge in the overall transmission line losses is also larger. In conclusion, studying and predicting corona losses in UHV lines is of great significance for the economical and efficient operation of the power grid.

[0003] Currently, there are many methods for obtaining the corona loss of ultra-high voltage (UHV) AC transmission lines, which can be divided into two types. The first is the formula method, which uses relevant experience or calculation formulas to determine the corona loss of UHV AC transmission lines. The formula method has certain limitations, mainly because it does not fully consider weather factors, resulting in lower accuracy and failing to meet accuracy requirements.

[0004] The second type is statistical and machine learning algorithms. With the further improvement of the voltage level of transmission lines, the voltage of ultra-high voltage AC transmission lines has been increased to 1000kV, but there is little research on the prediction of corona loss using statistical and machine learning algorithms. Summary of the Invention

[0005] This invention proposes a method for predicting corona loss in ultra-high voltage (UHV) transmission lines based on a Res-BP neural network, which has good accuracy and stability.

[0006] The present invention adopts the following technical solution.

[0007] A method for predicting corona loss in ultra-high voltage transmission lines based on Res-BP neural networks includes the following steps;

[0008] Step S1: Using the Random Forest algorithm (RF) with MSE as the Gini impurity, calculate and rank the importance of weather conditions, and select the weather conditions with the highest importance to construct a feature set dataset.

[0009] Step S2: Using the differences in weather conditions on different dates in the dataset, classify them using the BIRCH algorithm; based on this, establish a Res-BP neural network model to predict the corona loss of UHV transmission lines, and use the PSO optimization algorithm to optimize and adjust the internal parameters of the model.

[0010] In step S1, the feature set dataset includes independent and dependent variables. The independent variable is weather conditions, and the dependent variable is the corona loss value. Let W... in W is the total input power to the line. out W represents the total output power of the line. L W represents the total line loss. C W represents the corona loss value. I W represents the insulator loss value. R If the resistance loss value is given, then the formula for calculating the corona loss value is:

[0011] W L =W in -W out Formula 17;

[0012] W C =W L -W I -W R Formula 18.

[0013] Step S1 includes the following steps;

[0014] Step A1: Normalize the feature values ​​of the weather data;

[0015] Step A2: Select the feature value from the weather data;

[0016] Step S2 includes the following steps;

[0017] Step A3: Classify the feature set;

[0018] Step A4: Determine the Res-BP neural network structure;

[0019] Step A5: Optimize the number of neurons in the fully connected layers of the Res-BP neural network using the PSO algorithm.

[0020] Step A6: Output the prediction results.

[0021] Step A1 normalizes the feature values ​​of the weather data using the following formula:

[0022]

[0023] Where x' is the normalized value, and x is the original value. max ,xmin These are the maximum and minimum values ​​in the selected dataset, respectively;

[0024] Step A2 involves selecting feature values ​​from the weather data. Specifically, the normalized feature values ​​are fed into a random forest model to calculate the importance of different weather conditions. The features are then sorted according to their importance, and the feature values ​​with higher importance and higher ranking are selected to construct a feature set dataset related to the weather data.

[0025] The random forest algorithm is based on decision trees. It uses the Bagging method to randomly and repeatedly draw samples from the training set to construct k regression trees to build a model. The model is then trained, and the algorithm result is obtained by voting or averaging. In step A2, the Gini coefficient is used as the Gini impurity in the classification task, and the mean squared error (MSE) is used as the Gini impurity in the regression task. The MSE formula is as follows:

[0026]

[0027] In the formula, T i P represents the actual corona loss value. i This represents the predicted corona loss value, and N represents the number of corona loss samples.

[0028] After the RF model is trained, the MSE values ​​for different trees and different feature values ​​are obtained. If a certain feature value appears in i regression trees (i≤k), then the calculated MSE matrix is ​​[MSE1, MSE2, ..., MSE...]. i For i MSE values, the eigenvalue importance is calculated using the following formula:

[0029]

[0030] In the formula, Vim is the feature importance of the feature value, k is the number of trees, and ∑MSE is the sum of all MSEs in the current tree.

[0031] The feature set classification in step A3 is performed using the BIRCH clustering algorithm, with the silhouette coefficient as the metric for judging the quality of classification.

[0032] Step A3 uses the BIRCH clustering algorithm, a hierarchical clustering algorithm that employs bottom-up logic for clustering. It performs clustering analysis on the corona loss feature set through a single scan. The clustering features (CF) and the clustering feature tree (CF-Tree) of the BIRCH clustering algorithm are specifically described as follows:

[0033] The CF is constructed in triplet form, represented as CF=(N,∑ L ,∑ S), where N is the number of D-dimensional data points in the cluster; ∑ L It is the linear sum of N data points, and the formula is:

[0034]

[0035] ∑ S The sum of squares for each data point is given by the formula:

[0036]

[0037] The linear relationship of CF is expressed by the formula:

[0038] CF1+CF2=(N1+N2,∑ L1 +∑ L2 ,∑ S1 +∑ S2 Formula Six;

[0039] CF contains basic information about the corresponding cluster, N, ∑ L Σ S Used to derive the required centroid The formulas for radius ρ and diameter δ are as follows:

[0040]

[0041]

[0042]

[0043] The compactness within a cluster can be determined by the radius ρ and the diameter δ; ρ represents the average distance from each point within the cluster to the centroid, and δ represents the average distance between any two points within the cluster;

[0044] A CF-Tree is a balanced tree that reflects the clustering of corona loss features. It internally stores the features of the hierarchical clusters. The shape of the CF-Tree is determined by three parameters: the first parameter is the maximum number of CFs (BF) in all nodes of the CF Tree, the second parameter is the number of clusters (K), and the third parameter is the maximum sample radius threshold (T) of each CF in the leaf nodes.

[0045] Step A4 determines the Res-BP neural network structure. Through deep learning of the neural network, a precise mapping relationship between weather data and corona loss values ​​is established by mining representative data from weather data. Specifically, the method involves determining the number of fully connected layers, the number of residual blocks, and the number of fully connected layers within each residual block in the Res-BP neural network. The hidden layers of the Res-BP neural network use a structure of one fully connected layer plus two residual blocks, where each residual block consists of three fully connected layers. The Res-BP neural network introduces a convolutional neural network model, ResNets, based on the residual structure. ResNets consists of convolutional layers, multiple residual building blocks, batch normalization (BN) layers, ReLU activation function layers, global average pooling layers, and fully connected layers. Each ResNets residual building block consists of a convolutional layer, a batch normalization (BN) layer, and a ReLU activation function.

[0046] The residual blocks of the Res-BP neural network ensure the existence of gradients during backpropagation by incorporating identity mappings through short cross-layer connections. Let x... l It is the data of the input l-level residual block, W l The parameters of each layer in the l-layer residual block are obtained by passing through three fully connected layers, resulting in the residual data F(x). l W l If the result of the entire residual block is x, then the output of the residual block is x. l+1 =F(x) l W l )+x l Formula 10;

[0047] Where F(x) l W l )=W3σ(W2σ(W1σx)) Formula 11;

[0048] In the formula, represents the activation function, with ELU chosen as the activation function. The ELU activation function combines the sigmoid and ReLU activation functions, exhibiting soft saturation on the left side and no saturation on the right side. The average value of the ELU activation function output is close to 0 and centered at 0. The calculation formula is as follows:

[0049]

[0050] Step A5 involves optimization using the Particle Swarm Optimization (PSO) algorithm. Specifically: First, using the silhouette coefficient as an indicator, optimize the maximum number of CFs (BF) in all nodes of the CF Tree in the BIRCH clustering algorithm, the number of clusters K, and the maximum sample radius threshold T for each CF in the leaf nodes. Finally, using the mean absolute error (MAE) as an indicator, optimize the number of neurons in the fully connected layers of the Res-BP neural network and set the learning rate. The PSO algorithm treats each possible solution as a particle in the entire swarm. Each particle has its unique velocity, position, and fitness value. Velocity represents the speed of particle movement, position represents the direction of particle movement, and fitness value is used to determine the particle's state. Each iteration updates the fitness value. Assuming that in the constructed n-dimensional space, all particles search within the space at a certain velocity, continuously approaching the optimal solution, and that the position vector of the i-th particle in the t-th iteration is X... i,t =(x i,t,1 ,x i,t,2 ,......,x i,t,n The velocity vector is V. i,t =(v i,t,1 ,v i,t,2 ,......,v i,t,n The optimal solution is pbest. i,t =(p i,t,1 ,p i,t,2 ,......,p i,t,n The optimal particle position in the entire swarm is gbest. i,t =(g i,t,1 ,g i,t,2 ,......,g i,t,n When a particle seeks optimization in multidimensional space, it updates its position and velocity vectors in each iteration, as shown in the formula:

[0051] V i,t+1 =ωV i,t +c1r1(pbest i,t -X i,t )+c2r2(gbest i,t -X i,t Formula Thirteen;

[0052] X i,t+1 =V i,t+1 +X i,t Formula Fourteen;

[0053] In the formula, c1 and c2 are acceleration factors, whose values ​​are positive integers. The larger the value, the better for the convergence of the algorithm; r1 and r2 are uniformly distributed random numbers in the range [0,1]; t = 1,2,...,n; i = 1,2,...,m, where m represents the number of particles; ω represents the inertial constant, which is generally taken as ω. max =0.9, ω min =0.4;

[0054] In the optimization of the BIRCH clustering algorithm, the silhouette coefficient is selected as the fitness function, and the formula is:

[0055] In the formula, a i b represents the average distance from a given vector to other samples within the same cluster. i It represents the average distance between a given vector and all samples in its nearest neighboring cluster;

[0056] In the optimization of the Res-BP neural network model, the mean absolute error (MAE) of the corona loss prediction results is selected as the fitness function, and the formula is as follows:

[0057]

[0058] In the formula, T i P represents the actual corona loss value. i This represents the predicted corona loss value, and N represents the number of corona loss samples.

[0059] After completing the model establishment in step S2, the Res-BP neural network model is validated by calculation examples based on historical operating data of UHV transmission lines to evaluate its accuracy and stability.

[0060] The prediction method is based on the principle of corona loss generation and the relationship between weather conditions and corona loss. From an algorithmic perspective, the prediction method first calculates and sorts the importance of feature values ​​using the random forest feature selection method, selects the top 27 feature values ​​to construct a corona loss feature set, then divides the feature set into two classes, A and B, using the BIRCH clustering algorithm with PSO to optimize the internal parameters, and finally feeds them into the Res-BP algorithm with PSO to optimize the internal parameters for training.

[0061] This invention demonstrates excellent stability and accuracy, making it a relatively ideal method for predicting corona loss in ultra-high voltage AC transmission lines.

[0062] This invention proposes a Res-BP neural network-based model for predicting corona loss in ultra-high voltage (UHV) transmission lines using PSO optimization. First, the importance of weather conditions is calculated and ranked using the MSE (Mean Sequence of Es) as the Gini impurity in the RF algorithm. Weather conditions with high importance are selected to construct a feature set. Second, the differences in weather conditions across different dates are used to classify them using the BIRCH algorithm. Based on this, a Res-BP neural network model is established to predict corona loss in UHV transmission lines. The PSO optimization algorithm is then used to optimize and adjust the internal parameters of the model. Finally, a case study is conducted using historical operating data from a UHV transmission line in China to verify the accuracy and stability of the proposed method. Attached Figure Description

[0063] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0064] Appendix Figure 1 This is a flowchart illustrating the present invention;

[0065] Appendix Figure 2 This is a schematic diagram of the regression tree structure of the Random Forest (RF) algorithm of this invention;

[0066] Appendix Figure 3 This is a schematic diagram of the framework of the BIRCH algorithm of this invention;

[0067] Appendix Figure 4 This is a schematic diagram of the residual block structure in the Res-BP neural network of this invention;

[0068] Appendix Figure 5 This is a schematic diagram of the Res-BP neural network structure of the present invention;

[0069] Appendix Figure 6 This is a heatmap illustrating the importance of the random forest algorithm under different weather conditions and regions in the embodiments;

[0070] Appendix Figure 7 This is a schematic diagram of the BIRCH clustering algorithm classifying scatter points in the embodiment. Detailed Implementation

[0071] As shown in the figure, the method for predicting corona loss of UHV transmission lines based on Res-BP neural network includes the following steps;

[0072] Step S1: Using the Random Forest algorithm (RF) with MSE as the Gini impurity, calculate and rank the importance of weather conditions, and select the weather conditions with the highest importance to construct a feature set dataset.

[0073] Step S2: Using the differences in weather conditions on different dates in the dataset, classify them using the BIRCH algorithm; based on this, establish a Res-BP neural network model to predict the corona loss of UHV transmission lines, and use the PSO optimization algorithm to optimize and adjust the internal parameters of the model.

[0074] In step S1, the feature set dataset includes independent and dependent variables. The independent variable is weather conditions, and the dependent variable is the corona loss value. Let W... in W is the total input power to the line. out W represents the total output power of the line. L W represents the total line loss. C W represents the corona loss value. I W represents the insulator loss value. R If the resistance loss value is given, then the formula for calculating the corona loss value is:

[0075] W L =W in -W out Formula 17;

[0076] W C =W L -W I -W R Formula 18.

[0077] Step S1 includes the following steps;

[0078] Step A1: Normalize the feature values ​​of the weather data;

[0079] Step A2: Select the feature value from the weather data;

[0080] Step S2 includes the following steps;

[0081] Step A3: Classify the feature set;

[0082] Step A4: Determine the Res-BP neural network structure;

[0083] Step A5: Optimize the number of neurons in the fully connected layers of the Res-BP neural network using the PSO algorithm.

[0084] Step A6: Output the prediction results.

[0085] Step A1 normalizes the feature values ​​of the weather data using the following formula:

[0086]

[0087] Where x' is the normalized value, and x is the original value. max ,xmin These are the maximum and minimum values ​​in the selected dataset, respectively;

[0088] Step A2 involves selecting feature values ​​from the weather data. Specifically, the normalized feature values ​​are fed into a random forest model to calculate the importance of different weather conditions. The features are then sorted according to their importance, and the feature values ​​with higher importance and higher ranking are selected to construct a feature set dataset related to the weather data.

[0089] The random forest algorithm is based on decision trees. It uses the Bagging method to randomly and repeatedly draw samples from the training set to construct k regression trees to build a model. The model is then trained, and the algorithm result is obtained by voting or averaging. In step A2, the Gini coefficient is used as the Gini impurity in the classification task, and the mean squared error (MSE) is used as the Gini impurity in the regression task. The MSE formula is as follows:

[0090]

[0091] In the formula, T i P represents the actual corona loss value. i This represents the predicted corona loss value, and N represents the number of corona loss samples.

[0092] After the RF model is trained, the MSE values ​​for different trees and different feature values ​​are obtained. If a certain feature value appears in i regression trees (i≤k), then the calculated MSE matrix is ​​[MSE1, MSE2, ..., MSE...]. i For i MSE values, the eigenvalue importance is calculated using the following formula:

[0093]

[0094] In the formula, Vim is the feature importance of the feature value, k is the number of trees, and ΣMSE is the sum of all MSEs in the current tree.

[0095] The feature set classification in step A3 is performed using the BIRCH clustering algorithm, with the silhouette coefficient as the metric for judging the quality of classification.

[0096] Step A3 uses the BIRCH clustering algorithm, a hierarchical clustering algorithm that employs bottom-up logic for clustering. It performs clustering analysis on the corona loss feature set through a single scan. The clustering features (CF) and the clustering feature tree (CF-Tree) of the BIRCH clustering algorithm are specifically described as follows:

[0097] The CF is constructed in triplet form, represented as CF=(N,Σ L ,Σ S), where N is the number of D-dimensional data points in the cluster; Σ L It is the linear sum of N data points, and the formula is:

[0098]

[0099] ∑ S The sum of squares for each data point is given by the formula:

[0100]

[0101] The linear relationship of CF is expressed by the formula:

[0102] CF1+CF2=(N1+N2,∑ L1 +∑ L2 ,∑ S1 +∑ S2 Formula Six;

[0103] CF contains basic information about the corresponding cluster, N, ∑ L ,∑ S Used to derive the required centroid The formulas for radius ρ and diameter δ are as follows:

[0104]

[0105]

[0106]

[0107] The compactness within a cluster can be determined by the radius ρ and the diameter δ; ρ represents the average distance from each point within the cluster to the centroid, and δ represents the average distance between any two points within the cluster;

[0108] A CF-Tree is a balanced tree that reflects the clustering of corona loss features. It internally stores the features of the hierarchical clusters. The shape of the CF-Tree is determined by three parameters: the first parameter is the maximum number of CFs (BF) in all nodes of the CF Tree, the second parameter is the number of clusters (K), and the third parameter is the maximum sample radius threshold (T) of each CF in the leaf nodes.

[0109] Step A4 determines the Res-BP neural network structure. Through deep learning of the neural network, a precise mapping relationship between weather data and corona loss values ​​is established by mining representative data from weather data. Specifically, the method involves determining the number of fully connected layers, the number of residual blocks, and the number of fully connected layers within each residual block in the Res-BP neural network. The hidden layers of the Res-BP neural network use a structure of one fully connected layer plus two residual blocks, where each residual block consists of three fully connected layers. The Res-BP neural network introduces a convolutional neural network model, ResNets, based on the residual structure. ResNets consists of convolutional layers, multiple residual building blocks, batch normalization (BN) layers, ReLU activation function layers, global average pooling layers, and fully connected layers. Each ResNets residual building block consists of a convolutional layer, a batch normalization (BN) layer, and a ReLU activation function.

[0110] like Figure 4 As shown, the residual blocks of the Res-BP neural network ensure the existence of gradients during backpropagation by incorporating identity mappings through short cross-layer connections. Let x... l It is the data of the input l-level residual block, W l The parameters of each layer in the l-layer residual block are obtained by passing through three fully connected layers, resulting in the residual data F(x). l W l If the result of the entire residual block is x, then the output of the residual block is x. l+1 =F(x) l W l )+x l Formula 10;

[0111] Where F(x) l W l )=W3σ(W2σ(W1σx)) Formula 11;

[0112] In the formula, represents the activation function, with ELU chosen as the activation function. The ELU activation function combines the sigmoid and ReLU activation functions, exhibiting soft saturation on the left side and no saturation on the right side. The average value of the ELU activation function output is close to 0 and centered at 0. The calculation formula is as follows:

[0113]

[0114] Step A5 involves optimization using the Particle Swarm Optimization (PSO) algorithm. Specifically: First, using the silhouette coefficient as an indicator, optimize the maximum number of CFs (BF) in all nodes of the CF Tree in the BIRCH clustering algorithm, the number of clusters K, and the maximum sample radius threshold T for each CF in the leaf nodes. Finally, using the mean absolute error (MAE) as an indicator, optimize the number of neurons in the fully connected layers of the Res-BP neural network and set the learning rate. The PSO algorithm treats each possible solution as a particle in the entire swarm. Each particle has its unique velocity, position, and fitness value. Velocity represents the speed of particle movement, position represents the direction of particle movement, and fitness value is used to determine the particle's state. Each iteration updates the fitness value. Assuming that in the constructed n-dimensional space, all particles search within the space at a certain velocity, continuously approaching the optimal solution, and that the position vector of the i-th particle in the t-th iteration is X... i,t =(x i,t,1 ,x i,t,2 ,......,x i,t,n The velocity vector is V. i,t =(v i,t,1 ,v i,t,2 ,......,v i,t,n The optimal solution is pbest. i,t =(p i,t,1 ,p i,t,2 ,......,p i,t,n The optimal particle position in the entire swarm is gbest. i,t =(g i,t,1 ,g i,t,2 ,......,g i,t,n When a particle seeks optimization in multidimensional space, it updates its position and velocity vectors in each iteration, as shown in the formula:

[0115] V i,t+1 =ωV i,t +c1r1(pbest i,t -X i,t )+c2r2(gbest i,t -X i,t Formula Thirteen;

[0116] X i,t+1 =V i,t+1 +X i,t Formula Fourteen;

[0117] In the formula, c1 and c2 are acceleration factors, whose values ​​are positive integers. The larger the value, the better for the convergence of the algorithm; r1 and r2 are uniformly distributed random numbers in the range [0,1]; t = 1,2,...,n; i = 1,2,...,m, where m represents the number of particles; ω represents the inertial constant, which is generally taken as ω. max =0.9, ω min =0.4;

[0118] In the optimization of the BIRCH clustering algorithm, the silhouette coefficient is selected as the fitness function, and the formula is:

[0119]

[0120] In the formula, a i b represents the average distance from a given vector to other samples within the same cluster. i It represents the average distance between a given vector and all samples in its nearest neighboring cluster;

[0121] In the optimization of the Res-BP neural network model, the mean absolute error (MAE) of the corona loss prediction results is selected as the fitness function, and the formula is as follows:

[0122]

[0123] In the formula, T i P represents the actual corona loss value. i This represents the predicted corona loss value, and N represents the number of corona loss samples.

[0124] After completing the model establishment in step S2, the Res-BP neural network model is validated by calculation examples based on historical operating data of UHV transmission lines to evaluate its accuracy and stability.

[0125] The prediction method is based on the principle of corona loss generation and the relationship between weather conditions and corona loss. From an algorithmic perspective, the prediction method first calculates and sorts the importance of feature values ​​using the random forest feature selection method, selects the top 27 feature values ​​to construct a corona loss feature set, then divides the feature set into two classes, A and B, using the BIRCH clustering algorithm with PSO to optimize the internal parameters, and finally feeds them into the Res-BP algorithm with PSO to optimize the internal parameters for training.

[0126] Example:

[0127] The UHV line corona loss prediction method based on PSO optimization and Res-BP neural network in this example can be divided into four stages: screening, classification, training, and prediction.

[0128] To verify the superiority and authenticity of the method proposed in this patent, a corresponding UHV AC transmission line corona loss prediction algorithm model was constructed, taking a UHV AC transmission line in China as an example, and the corona loss was predicted and analyzed.

[0129] 336 sets of data were obtained from the 2020 operational data for algorithmic example analysis. Each set of data was collected on a daily basis. The data contains 60 sets of independent variables and 1 set of dependent variables. The independent variables are weather conditions statistically collected from 6 districts and counties along the route, namely: rainfall, temperature, pressure, relative humidity, specific humidity, evaporation, ultraviolet intensity, sunshine, wind speed (east-west), and wind speed (north-south). The dependent variable is the corona loss value. Table 1 shows the weather conditions in different regions on March 9, 2020, with a corona loss value of 107435.6779 (kW*h) on that day.

[0130] Table 1. Weather conditions in different regions on March 9, 2020

[0131]

[0132] Table 2 Corona loss values ​​for some dates in January 2020

[0133] date Corona loss (kW*h) date Corona loss (kW*h) 20200102 12453.736 20200109 49161.636 20200105 68344.036 20200110 70169.3072 20200106 39512.036 20200111 117212.6502 20200107 25382.536 20200113 153433.216 20200108 38127.636 20200114 69060.45024

[0134] After normalizing the feature values, the first step is to select the feature values ​​with higher importance and sum them into a feature set. Based on the random forest algorithm, the feature values ​​are substituted into formulas two and three to calculate the feature importance, and the results are shown in Table 3. To more intuitively demonstrate the different importance values ​​of the random forest, they are plotted as a heatmap; the higher the value, the darker the color, as shown in Table 3. Figure 6 As shown

[0135] Table 3. Random forest importance under different weather conditions and regions

[0136]

[0137] From Table 3 and Figure 6 The results shown, and based on the principle of importance in random forests, indicate that the features are sorted from largest to smallest, and the top 27 features are summed to form a feature set. The features are, in order: precipitation in Jingning, Lishui, Minhou, Ningde, Shouning, and Zhouning; temperature in Jingning and Minhou; relative humidity in Lishui, Minhou, Ningde, Shouning, and Zhouning; ultraviolet intensity in Jingning, Lishui, Minhou, Shouning, and Zhouning; sunshine duration in Jingning, Lishui, Minhou, Ningde, Shouning, and Zhouning; wind speed (east-west) in Jingning and Lishui; and wind speed (north-south) in Minhou.

[0138] Secondly, the feature set is classified. Before using the BIRCH clustering algorithm for classification, the PSO algorithm is used to optimize its internal parameters. This patent sets the population particle number to 50, the maximum number of iterations to 50, the inertia constant ω = 0.5, BF ∈ [2, 100], K ∈ [2, 6], T ∈ [0.01, 1]. The optimization results are shown in Table 4. The optimized internal parameters are substituted into the BIRCH clustering algorithm for classification. To more intuitively display the classification results, the feature values ​​are reduced to three-dimensional data using the PCA dimensionality reduction algorithm. The resulting classification results are shown in Table 4. Figure 7 As shown, red represents category A, which has 181 data sets; blue represents category B, which has 155 data sets.

[0139] Table 4 BIRCH Clustering Algorithm Parameters

[0140] Model parameters PSO Optimization Results K 2 T 0.89426524 BF 81

[0141] The two feature sets A and B, classified by the BIRCH clustering algorithm, are used to construct corresponding prediction models. In each feature set, 80% of the data is randomly divided into a training set and 20% into a test set.

[0142] To address the parameter optimization problem of the Res-BP neural network, this patent sets the population particle number to 40, the maximum number of iterations to 40, and an inertia constant. The number of neurons in the first fully connected layer is L1∈[1, 1500]; in the first residual block, the number of neurons in the first, second, and third fully connected layers are L2∈[1, 1500], L3∈[1, 1500], and L1, respectively; in the second residual block, the number of neurons in the first, second, and third fully connected layers are L4∈[1, 1500], L5∈[1, 1500], and L1, respectively. All fully connected layers use adaptively adjusted learning rates, thus eliminating the need for optimization. The optimization results are shown in Table 5.

[0143] Table 5 Res-BP Neural Network Parameters

[0144]

[0145] Experiment 1: To verify the effectiveness of feature selection and summation using random forest importance as described above, and the effectiveness of PSO optimization of internal parameters in improving model accuracy, this example builds two Res-BP neural network models. Res-BPⅠ uses the selected and summed feature set with 27 feature values; Res-BPⅡ uses the original feature set with 60 feature values. The comparison results are shown in Table 6, where Ec is the absolute value of the relative error percentage, and E is the mean absolute error, calculated using the same formula as Formula 16.

[0146]

[0147] Table 6 Simulation results of different eigenvalues ​​and methods on the test set.

[0148]

[0149] As shown in Table 6, compared to PS0+Res-BPII, PS0+Res-BPⅠ has only 45% of the number of eigenvalues, but it only slightly increases in the following indicators: Ec≤10% of samples, 10%<Ec≤20% of samples, 20%<Ec≤30% of samples, and mean absolute error. The mean absolute error is particularly high, increasing by only 0.9%. In contrast, PS0+Res-BPⅠ and PS0+Res-BPⅡ outperform Res-BPⅠ and Res-BPⅡ in the Ec≤20% of samples and mean absolute error indicators. The mean absolute error of PS0+Res-BPⅠ is reduced by approximately 6.10%.

[0150] Experiment 2: In verifying the BIRCH clustering algorithm, this patent names the model trained using the A-class feature set as Res-BP-A; the model trained using the B-class feature set as Res-BP-B; the prediction results of the two models are summarized and named PS0+Res-BP-S, and the comparison results are shown in Table 7.

[0151] Table 7. Prediction results of the BIRCH clustering algorithm on the test set.

[0152]

[0153] As shown in Table 7, classifying the feature set after random forest importance selection yields better results in terms of Ec≤10% of samples, mean absolute error, and training time. In particular, it reduces the mean absolute error and training time by 18.18% and 52.68%, respectively. This demonstrates that using the BIRCH clustering algorithm to distinguish feature values ​​of different attributes can significantly improve prediction accuracy, reduce training time, and thus enhance the overall performance of the model.

[0154] Experiment 3: To further verify the stability and accuracy of the method proposed in this patent, a comparative analysis was conducted with other mainstream machine learning algorithms, such as Random Forest, Ridge Regression, and SVM. Four algorithm models were built in this section, with the same feature values ​​as Res-BP-S. The internal parameters of each model were optimized using the PSO algorithm, which set the population particle count to 40 and the maximum number of iterations to 40. The results are shown in Table 8. As shown in Table 8, the PSO+Res-BP-S model significantly outperforms the PSO+SVR, PSO+SVR, and PSO+Random Forest algorithms in terms of Ec≤10% of samples, 20%<Ec≤30% of samples, and mean absolute error. In particular, the PSO+Res-BP-S model reduced the error by 30.46%, 33.85%, and 20.62% respectively, demonstrating the superiority of the method proposed in this patent.

[0155] Table 8. Error Comparison of Four Algorithms

[0156]

[0157] In summary, this paper proposes a corona loss prediction model for UHV lines based on a Res-BP neural network with PSO optimization to address the problem of corona loss prediction in UHV lines.

[0158] This patent analyzes the principle of corona loss generation from a theoretical perspective and studies the relationship between weather conditions and corona loss. From an algorithmic perspective, it first calculates and ranks the importance of feature values ​​using a random forest feature selection method, selecting the top 27 most important feature values ​​to construct a corona loss feature set. Then, it divides the feature set into two classes, A and B, using a BIRCH clustering algorithm with PSO-optimized internal parameters. Finally, it feeds these classes into a Res-BP algorithm with PSO-optimized internal parameters for training. The paper concludes with a comprehensive validation of the proposed method using an example of corona loss in UHV transmission lines. The predicted results outperform other methods proposed in this patent in some indicators, demonstrating good performance in stability and accuracy, making it a relatively ideal method for predicting corona loss in UHV AC transmission lines.

Claims

1. A method for predicting corona loss in ultra-high voltage transmission lines based on Res-BP neural networks, characterized in that: Includes the following steps; Step S1: Using the Random Forest algorithm (RF) with MSE as the Gini impurity, calculate and rank the importance of weather conditions, and select the weather conditions with the highest importance to construct a feature set dataset. Step S2: Using the differences in weather conditions on different dates in the dataset, classify them using the BIRCH algorithm; establish a Res-BP neural network model to predict the corona loss of UHV transmission lines, and use the PSO optimization algorithm to optimize and adjust the internal parameters of the model. In step S1, the feature set dataset includes independent and dependent variables. The independent variable is weather conditions, and the dependent variable is the corona loss value. Input the total power to the line. This represents the total output power of the line. This represents the total line loss. This represents the corona loss value. This represents the insulator loss value. If the resistance loss value is given, then the formula for calculating the corona loss value is: ； ； The feature set classification in step A3 is performed using the BIRCH clustering algorithm, with the silhouette coefficient as the metric for judging the quality of classification. The clustering features (CF) and clustering feature tree (CF-Tree) of the BIRCH clustering algorithm in step A3 are specifically described as follows: The CF is constructed in triplet form, represented as ,in, It is the number of D-dimensional data points in the cluster; yes The linear sum of data points, the formula is: Formula 4; The sum of squares for each data point is given by the formula: Formula 5; The linear relationship of CF is expressed by the formula: Formula Six; The CF contains basic information about the corresponding cluster. , , Used to derive the required centroid ,radius With diameter The formula is Formula 7; Formula 8; Formula Nine; The compactness within a cluster can be determined by its radius. With diameter To judge; It is expressed as the average distance from each point within the cluster to the centroid. It is represented as the average distance between any two points within the cluster; The shape of a CF-Tree is determined by three parameters: the first parameter is the maximum number of CFs (BF) in all nodes of the CF Tree, the second parameter is the number of clusters (K), and the third parameter is the maximum sample radius threshold (T) for each CF in a leaf node. Step S1 includes the following steps; Step A1: Normalize the feature values ​​of the weather data; Step A2: Select the feature value from the weather data; Step A3: Classify the feature set; Step A4: Determine the Res-BP neural network structure; Step A5: Optimize the number of neurons in the fully connected layers of the Res-BP neural network using the PSO algorithm. Step A6: Output the prediction results.

2. The method for predicting corona loss of UHV transmission lines based on Res-BP neural network according to claim 1, characterized in that: Step A1 normalizes the feature values ​​of the weather data using the following formula: Formula 1; in, The value is the normalized value; These are the original values. These are the maximum and minimum values ​​in the selected dataset, respectively; Step A2 involves selecting feature values ​​from the weather data. Specifically, the normalized feature values ​​are fed into a random forest model to calculate the importance of different weather conditions. The feature values ​​are then sorted according to their importance, and the feature values ​​with high importance and high ranking are selected to construct a feature set dataset related to the weather data. The random forest algorithm is based on decision trees. It uses the Bagging method to randomly and repeatedly draw samples from the training set to construct k regression trees to build a model. The model is then trained, and the algorithm result is obtained by voting or averaging. In step A2, the Gini coefficient is used as the Gini impurity in the classification task, and the mean squared error (MSE) is used as the Gini impurity in the regression task. The MSE formula is as follows: Formula 2; In the formula, This represents the actual corona loss value. This indicates the predicted corona loss value. Indicates the number of corona loss samples; After the RF model is trained, the MSE values ​​of different trees and different feature values ​​are obtained; let a certain feature value appear in i regression trees ( Then, the MSE matrix obtained through calculation is: For i MSE values, the eigenvalue importance is calculated using the following formula: Formula 3; In the formula, It is the eigenvalue importance. The number of trees, This is the sum of all MSEs in the current tree.

3. The method for predicting corona loss of UHV transmission lines based on Res-BP neural network according to claim 1, characterized in that: Step A4 determines the Res-BP neural network structure, and through deep learning of the neural network, establishes an accurate mapping relationship between weather data and corona loss values ​​by mining representative data from weather data. The specific method is as follows: The number of fully connected layers, the number of residual blocks, and the number of fully connected layers within each residual block are determined in the Res-BP neural network. The hidden layers of the Res-BP neural network use a structure of one fully connected layer plus two residual blocks, where each residual block consists of three fully connected layers. The Res-BP neural network introduces the ResNets convolutional neural network model based on the residual structure. ResNets consists of convolutional layers, multiple residual building blocks, batch normalization (BN) layers, ReLU activation function layers, global average pooling layers, and fully connected layers. The ResNets residual building blocks consist of convolutional layers, batch normalization (BN) layers, and ReLU activation functions. The residual blocks of the Res-BP neural network ensure the existence of gradients during backpropagation by incorporating identity mappings through short cross-layer connections. Let x... l It is the data of the input l-level residual block, W l The parameters of each layer in the l-layer residual block are obtained by passing through three fully connected layers, resulting in the residual data F(x). l W l If ), then the output of the entire residual block is Formula 10; in Formula 11; In the formula, represents the activation function, and ELU is selected as the activation function. The ELU activation function combines the sigmoid activation function and the ReLU activation function. It has soft saturation on the left side and no saturation on the right side.

4. The method for predicting corona loss of UHV transmission lines based on Res-BP neural network according to claim 1, characterized in that: Step A5 involves optimization using the Particle Swarm Optimization (PSO) algorithm. Specifically, it optimizes the maximum number of Cross-Cluster Nodes (CFs) (BF) in the CF Tree of the BIRCH clustering algorithm, the number of clusters (K), and the maximum sample radius threshold (T) for each CF in the leaf nodes, using the silhouette coefficient as an indicator. Then, it optimizes the number of neurons in the fully connected layers of the Res-BP neural network using the mean absolute error (MAE) as an indicator, and sets the learning rate. The PSO algorithm treats each possible solution as a particle in the entire swarm. Each particle has its unique velocity, position, and fitness value. Velocity represents the speed of particle movement, position represents the direction of particle movement, and fitness value is used to determine the particle's state. Each iteration updates the fitness value. Assuming all particles search within the constructed n-dimensional space, continuously approaching the optimal solution, and assuming the position vector of the i-th particle in the t-th iteration is... The velocity vector is The optimal solution is , The optimal particle position in the entire swarm is When a particle seeks optimization in multidimensional space, it updates its position and velocity vectors in each iteration, as shown in the formula: Formula Thirteen; Formula Fourteen; In the formula, , This is an acceleration factor, and its value is a positive integer. The larger the value, the better it is for the convergence of the algorithm. , It is a uniformly distributed random number in the range [0, 1]; t=1, 2, ..., n; i=1, 2, ..., m, where m represents the number of particles; Denotes the inertial constant, taking , ; In the optimization of the BIRCH clustering algorithm, the silhouette coefficient is selected as the fitness function, and the formula is: Formula 15; In the formula, This represents the average distance from a given vector to other samples within the same cluster. It represents the average distance between a given vector and all samples in its nearest neighboring cluster; In the optimization of the Res-BP neural network model, the mean absolute error (MAE) of the corona loss prediction results is selected as the fitness function, and the formula is as follows: Formula Sixteen; In the formula, This represents the actual corona loss value. This indicates the predicted corona loss value. This indicates the number of corona loss samples.

5. The method for predicting corona loss of UHV transmission lines based on Res-BP neural network according to claim 1, characterized in that: After completing the model establishment in step S2, the Res-BP neural network model is validated by calculation examples based on historical operating data of UHV transmission lines to evaluate its accuracy and stability.

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