Line dynamic current-carrying capacity prediction method based on WOA optimized VMD and double attention mechanism-time-varying integrated model

Abstract

The invention discloses a line dynamic current-carrying capacity prediction method based on WOA optimization VMD and a double attention mechanism-time-varying integrated model, and the method effectively solves a common problem of existing research through the deep fusion of a feature attention mechanism, WOA optimization VMD and a time-varying integrated model. And an innovative solution is provided for high-precision prediction of the dynamic current-carrying capacity of the line. The method has breakthrough development in the aspects of nonlinear relation modeling, signal decomposition optimization and multi-model collaborative prediction, has important theoretical value and wide engineering application prospect, and injects new vitality for intelligent development of a power grid.

Description

Technical Field

[0001] The present invention relates to the technical field of overhead transmission line current carrying capacity prediction, and in particular to a line dynamic current carrying capacity prediction method based on WOA optimized VMD and a dual attention mechanism-time-varying integrated model. Background Art

[0002] With the continuous growth of electricity demand and the expansion of the power grid, predicting the current carrying capacity of overhead transmission lines has become a key technology for ensuring the safe and stable operation of the power grid. Accurate line current carrying capacity prediction not only optimizes grid scheduling but also effectively prevents failures caused by line overloads, improving the reliability and economic efficiency of the power system.

[0003] At present, the research progress on the current carrying capacity prediction of overhead transmission lines is as follows:

[0004] (1) Chinese patent: "Method and device for predicting the current carrying capacity interval of overhead transmission lines based on LSSVM model" (Announcement No.: CN117096860A) mainly uses the processed sample data set and LSSVM model to obtain the current carrying capacity of overhead transmission lines in the future time period. However, the prediction scheme mentioned in this invention patent has two problems: ①: The hyperparameters required by the model need to be manually selected, which leads to weak generalization and low robustness of the model, and difficulty in processing large amounts of nonlinear sample data. ②: The influencing factors of the conductor current carrying capacity involve meteorological data with high randomness such as wind speed and wind direction angle. It is difficult to guarantee the accuracy of the prediction by directly predicting the data.

[0005] (2) Chinese patent: "A method for predicting the dynamic current carrying capacity of overhead transmission lines based on an RNN model" (Announcement No. CN117592591A), predicts the current carrying capacity data of overhead transmission lines in future time periods based on a sample data set and an RNN model. However, the prediction method mentioned in this invention patent has the following problems: ①: The influencing factors of the conductor current carrying capacity include long-term time series data such as wind speed. Due to the characteristics of parameter sharing and multiple multiplication, a single RNN prediction model is prone to gradient explosion and other problems. ②: The hyperparameters required by the model need to be manually extracted, which leads to weak generalization ability of the model.

[0006] (3) Chinese patent: "A method, system, equipment and medium for predicting the medium- and long-term current carrying capacity of overhead lines" (Announcement No. CN117096859A). This invention analyzes and optimizes the meteorological data near the overhead lines, optimizes the data set by using the particle swarm algorithm to optimize the extreme learning machine, and then establishes a medium- and long-term prediction based on the Prophet model, thereby improving the accuracy of the current carrying capacity prediction of overhead lines. However, the prediction method improved by this invention patent has the following problems: ①: The local optimality problem of the particle swarm algorithm: Although the particle swarm algorithm has strong global search capabilities, it is easy to fall into local optimality in high-dimensional parameter space, resulting in the failure to fully optimize the parameters of the prediction model. ②: The generalization ability of the prediction model is insufficient. The performance of the extreme learning machine is highly dependent on the random initialization of the initial weights and biases, which may lead to unstable generalization ability of the model on different line dynamic current carrying capacity data sets.

[0007] (4) Chinese patent: "A method and system for predicting the current carrying capacity of a transmission line" (Announcement No. CN117096858A). This method uses differential evolution to improve the gray wolf algorithm to optimize the preset parameters in the support vector machine regression; and inputs the current carrying capacity and meteorological data of the transmission line at the current M consecutive time points into the prediction regression model, and finally obtains the current carrying capacity prediction data for the M consecutive time points after the current M consecutive time points. However, the prediction method mentioned in this invention patent has the following problems: ①: The relationship between meteorological factors and the dynamic current carrying capacity of the line has been proven to be nonlinear and high-dimensional. The traditional support vector machine model is difficult to fully capture the high-order interactions between multiple variables due to its insufficient model complexity. ②: Meteorological conditions (such as wind speed, temperature, and sunshine intensity) are highly dynamic and random, and a single meteorological data analysis may be difficult to capture their complex changing patterns.

[0008] In summary, with the rapid development of artificial intelligence and big data technologies in recent years, data-driven prediction methods have gradually become a research hotspot in the field of line dynamic current carrying capacity. However, current research often has the following common problems: 1. Although existing studies have taken into account the regression relationship with different weights between various meteorological factors and line dynamic current carrying capacity, existing studies often use linear regression methods such as the Pearson coefficient method to quantify their regression relationship, which makes it difficult to fully capture the nonlinear relationship between various meteorological factors and line dynamic current carrying capacity. 2. The prediction models used in existing studies do not adequately handle the randomness of meteorological conditions that affect line dynamic current carrying capacity, resulting in room for improvement in the prediction accuracy of the model. 3. The prediction models used in existing studies are mostly single models or combined models with insufficient model complexity, resulting in the model's generalization ability on different line dynamic current carrying capacity data sets being not stable enough. Summary of the Invention

[0009] The purpose of the present invention is to overcome the above-mentioned shortcomings and provide a line dynamic current carrying capacity prediction method based on WOA optimized VMD and dual attention mechanism-time-varying integrated model to solve the problems raised in the background technology.

[0010] To solve the above technical problems, the technical solution adopted by the present invention is: a method for predicting line dynamic current carrying capacity based on WOA optimized VMD and dual attention mechanism-time-varying integrated model, which includes the following steps:

[0011] Step 1: Collect dynamic line current carrying capacity data and related meteorological data, including wind speed, wind direction, ambient temperature, humidity, atmospheric pressure, and solar radiation intensity;

[0012] Step 2: Use a feature attention mechanism to quantify the importance of the collected data, strengthen features that are highly correlated with the line's dynamic current carrying capacity, and weaken features with poor correlation. The quantified data is then cleaned to handle missing values ​​and outliers to ensure data quality.

[0013] Step 3: Scale the cleaned data to the same scale to eliminate dimensional differences and divide the data into training and test sets;

[0014] Step 4: Construct the fitness function of the WOA algorithm based on the data characteristics and decomposition requirements of the line dynamic current carrying capacity;

[0015] Step 5: Use the WOA algorithm to adaptively and iteratively optimize the hyperparameters of the VMD algorithm to determine the optimal hyperparameter combination for the VMD algorithm to decompose the dynamic current carrying capacity of the line;

[0016] Step 6: Use the optimized VMD algorithm to decompose the line dynamic current carrying capacity data in the training set to obtain a series of components with different center frequencies but local stability;

[0017] Step 7: Use the sample entropy algorithm to cluster and superimpose the decomposed components into trend components, periodic components, and random components;

[0018] Step 8: Use the time-varying ensemble model to predict each cluster component. The model consists of three single prediction models: LSTM-Attention, TCN, and LSSVM.

[0019] Step 9: For the prediction results of multiple single models, a prediction evaluation index matrix is ​​formed according to the prediction evaluation criteria, and the grey correlation coefficient time-varying weight combination method is used to assign weights point by point;

[0020] Step 10: Multiply the assigned weights by the prediction results of the three single models to obtain the final comprehensive prediction result;

[0021] Step 11: Use multiple evaluation indicators to evaluate the comprehensive prediction results of the line dynamic current carrying capacity to verify the accuracy and stability of the method.

[0022] Preferably, step 4 specifically includes the following process:

[0023] Step 4.1. Design the energy entropy of the modal components: Energy entropy is used to measure the complexity of the modal components. The smaller the energy entropy, the more concentrated the energy of the modal components and the better the decomposition effect. The calculation formula of energy entropy is as follows:

[0024]

[0025] in:

[0026] Where: u j (i) is the value of the jth modal component at the i-th moment; N is the data length; E j is the total energy entropy; p j (i) is the partial energy entropy value of the jth modal component;

[0027] Step 4.2: Design the correlation of modal components: Correlation is used to measure the similarity between the modal components and the original signal. The higher the correlation, the more the modal components can reflect the characteristics of the original signal. The correlation calculation formula is as follows:

[0028]

[0029] Where: cov(u j ,Y) covariance between the modal component uj and the original signal Y; and σ Y are the standard deviations of the modal components and the original signal, respectively;

[0030] Step 4.3. Design the reconstruction error of the modal components: The reconstruction error is used to measure the ability of the modal components after VMD decomposition to reconstruct the original signal. The smaller the reconstruction error, the better the decomposition effect. The calculation formula of the reconstruction error is as follows:

[0031]

[0032] Where: K is the number of modal components; ||·||2 represents the L2 norm; RE represents the reconstruction error of the modal component; Y represents the original signal; uj represents the jth modal component;

[0033] Step 4.3: Based on the above indicators, the fitness function is designed as follows:

[0034]

[0035] Where: w1, w2, w3 are weight coefficients used to balance the importance of each indicator; Ej is the energy entropy of the j-th modal component, Cj is the correlation between the j-th modal component and the original signal, RE is the reconstruction error; K is the number of modal components.

[0036] Preferably, the process of adaptively iteratively optimizing the hyperparameters of the VMD algorithm using the WOA algorithm in step 5 is as follows:

[0037] Step 5.1, initialize WOA parameters: artificially set the WOA population size to N and the maximum number of iterations to T max ;

[0038] Step 5.2, VMD decomposition: In each iteration, VMD decomposition is performed using the parameters generated by WOA (modal number K and penalty factor α);

[0039] Step 5.3, calculate the fitness value: calculate the fitness value of the current decomposition result according to the fitness function;

[0040] Step 5.4, update the optimal solution: update the optimal solution of WOA according to the fitness value;

[0041] Step 5.5, iterative optimization: Repeat the above steps until the maximum number of iterations is reached or convergence occurs.

[0042] Preferably, the specific calculation formula of the WOA algorithm is as follows:

[0043] 1) Surrounding the prey: The algorithm sets the number of whales in the population to N and the position of each whale to X. Since the position of the prey is uncertain, the whale individual X closest to the prey is placed at the center. * The optimal position is set as the current position, and the remaining individuals then move closer to it, shrinking and surrounding it through iteration. The mathematical model of the behavior of surrounding the prey is as follows:

[0044]

[0045] Where: D is the distance between the current position and the optimal position; t is the current number of iterations; N is the number of whales; X(t) is the position of each whale; X * (t) is the current optimal position of the individual whale closest to the prey; in addition, the coefficient vectors A and C are calculated as follows:

[0046]

[0047] Where: r1, r2∈[0,1], are random parameters; aa is a linear parameter, which decreases linearly from 2 to 0; T max is the maximum number of iterations; t is the current number of iterations;

[0048] 2) Hunting behavior: Whales swim towards their prey in a spiral motion. The mathematical model is as follows:

[0049] X(t+1)=X * (t)+D p e bl cos(2πl)

[0050] Where: D p =|X * (t)-X(t)|,D p Indicates the distance between the whale and its prey; X * (t) is the optimal position of the individual whale after t iterations; the constant b is used to determine the spiral shape; the random number l∈[-1,1];

[0051] Assume that the probability of surrounding the prey is P i , then the probability of spiral contraction behavior is 1-P i , the mathematical model of whale position update is as follows:

[0052]

[0053] Where: random number p∈[0,1]; since the value of aa in the previous formula decreases linearly as the distance between the whale and the prey decreases, A will also decrease and take a random value within [-aa,aa]; when it iterates to A∈[-aa,aa], it means that the whale's updated position will be close to the prey, and it is assumed that the prey will be attacked at this time; A and C represent coefficient vectors; T max is the maximum number of iterations; t is the current number of iterations; the constant b is used to determine the spiral shape; D p represents the distance between the whale and its prey; X(t) is the position of each whale; X * (t) is the current optimal position of the individual whale closest to the prey;

[0054] 3) Searching for prey: When When the whale begins to search for prey randomly, it first randomly selects a whale position vector X rand , the positions of the remaining populations are updated according to their positions. The purpose is to let the algorithm abandon the current local optimal value to find a better target. Its mathematical model is as follows:

[0055] D=|CX rand -X(t)|

[0056] X(t+1)=X rand -AD

[0057] Where: A, C and D represent coefficient vectors; X randRepresents a randomly selected whale position vector; X(t) and X(t+1) represent the current iteration number and the next iteration number, respectively.

[0058] Preferably, step 6 specifically includes the following process:

[0059] Step 6.1: To avoid frequency aliasing between the dynamic current carrying components of each line, a constrained variational equation system is constructed with the goal of minimizing the sum of the data bandwidths of each component:

[0060]

[0061] Where: min{A}, stB means that A reaches the minimum when condition B is met; h t represents the partial derivative operator; δ(t) represents the Dirac function; j represents the imaginary unit; π represents the circumference of a circle; * represents the convolution operator; u k (t) represents the kth component generated by the decomposition of the line dynamic current carrying capacity; w k (t) represents the frequency corresponding to the kth component; represents the L2 norm operator; f(t) represents the undecomposed line dynamic current carrying capacity;

[0062] Step 6.2: Introduce the Lagrange multiplication operator λ and the penalty factor α, and incorporate the constraints in the above equation into the equation with the objective function of minimizing the sum of the line dynamic current carrying capacity data bandwidth. This transforms the problem of solving the constrained variational equation system shown in the equation into the problem of solving the unconstrained variational equation system, which is easier to solve:

[0063]

[0064] Where: α is the penalty factor; k is the number of decompositions of the line dynamic current carrying capacity; λ is the Lagrange multiplication operator; u k (t) represents the kth component generated by the decomposition of the line dynamic current carrying capacity; w k (t) represents the frequency corresponding to the kth component; j represents the imaginary unit; π represents the circumference of a circle; * represents the convolution operator; h t represents the partial derivative operator; δ(t) represents the Dirac function; represents the L2 norm operator; f(t) represents the undecomposed line dynamic current carrying capacity;

[0065] Step 6.3: Iteratively update u using the alternating direction multiplication method k (t), w k (t), find the "saddle point" of the above equation, that is, the optimal solution of the constrained variational equation; u k (t), w k The update formulas for (t) are:

[0066]

[0067] Where: n represents the number of iterations; and Respectively represent f(t),u k The Fourier transform of (t) and λ(t); α is the penalty factor.

[0068] Preferably, step 7 specifically includes the following process:

[0069] First, assume that u(i) is a time series of length N, where 1, 2, and N;

[0070] For each i, construct a vector x(i) = [u(i), u(i+1), ... u(i+k-1)] of length K;

[0071] Then, calculate the distance between other x(j) and x(i) in the sequence; if the distance is less than the threshold r, then x(j) is considered similar to x(i); for each i, calculate the number of x(j) similar to it and divide it by N-K+1 to get in The mathematical expression is as follows:

[0072]

[0073] Then, calculate all the averages with the following formula:

[0074]

[0075] Finally, increase the dimension k to k+1 and repeat the above steps to get the final result B (k+1) ;

[0076] To be determined B (k+1) and B (k) After that, the sample entropy of each component of the line dynamic current carrying capacity can be calculated. The sample entropy calculation formula is as follows:

[0077]

[0078] Where: ZZ is the length of the pattern; r is the similarity threshold, which is taken as a percentage of the standard deviation; N is the length of the time series;

[0079] If the value of sample entropy is smaller, it means that the pattern in the time series is more regular and predictable; on the contrary, the larger the value of sample entropy is, the more complex and random the time series is.

[0080] The sample entropy of trend classification is generally small, the sample entropy of periodic component is moderate, and the sample entropy of random component is large. By setting appropriate sample entropy thresholds S1 and S2, the decomposed modal components are divided into the following three categories:

[0081] When SampEn(ZZ,r) is less than or equal to S1, the modal component is the trend component;

[0082] When SampEn(ZZ,r) is greater than S1 and less than or equal to S2, the modal component is a trend component;

[0083] When SampEn(ZZ,r) is greater than S2, the modal component is a random component.

[0084] Preferably, in step 8, the LSTM-Attention model in the time-varying integrated model combines the long short-term memory network and the attention mechanism to capture the long-term dependencies in the time series; the TCN model in the time-varying integrated model adopts a temporal convolutional network to extract local features and long-term dependencies in the time series; the LSSVM model in the time-varying integrated model adopts a least squares support vector machine to process nonlinear regression problems and improve prediction accuracy.

[0085] Preferably, step 9 specifically includes the following process:

[0086] Step 9.1: Formation of the prediction evaluation index matrix: Each model gives prediction results for N sample points and uses multiple evaluation indicators for evaluation;

[0087] For each model, there is a predicted value and a true value y t , where t is the time step or sample point; based on the evaluation indicators of these models, an evaluation matrix E is constructed; each row of the matrix E corresponds to an evaluation indicator, and each column corresponds to the prediction result of a model; the E matrix is ​​as follows:

[0088]

[0089] Where: e ij represents the score of model j under the i-th evaluation index, indicating the performance of the model, where i = 1, 2, 3, j = 1, 2, 3;

[0090] Step 9.2, construct the grey correlation coefficient time-varying matrix: grey correlation coefficient γ ij It is used to measure the correlation between the model's predicted results and the actual results. The specific calculation formula is as follows:

[0091]

[0092] Where: is the predicted value of model j for time node t; y t is the actual value; ρ refers to the resolution coefficient;

[0093] The time-varying coefficient of the matrix can be calculated using the grey correlation coefficient obtained above. The weight calculation formula is as follows:

[0094]

[0095] where n ij represents the weight of model j at time node t; γ ij It is the result obtained by calculating the grey correlation coefficient;

[0096] Step 9.3, get the weighted combination prediction result: Combining the prediction results of each model and the corresponding time-varying weights, the prediction results of the three models can be weighted combined; assuming that the prediction result of each model at time point t is for:

[0097]

[0098] In the formula: is the final prediction result, n ij Refers to the weight of model j at time node t; The predicted value of model j at time node t.

[0099] Preferably, step 10 specifically includes the following process: multiplying the prediction results of the three models by their corresponding time-varying weights and summing them to obtain a final comprehensive prediction result:

[0100]

[0101] Where: is the final comprehensive prediction result at time step t; n LSTM,t Refers to the time-varying weight of the LSTM-Attention model at time step t; n TCN,t is the time-varying weight of the TCN model at time step t; n LSSVM,t Refers to the time-varying weight of the LSSVM model at time step t; is the prediction result of the LSTM-Attention model at time step t; is the prediction result of the TCN model at time step t; is the prediction result of the LSSVM model at time step t.

[0102] Preferably, in step 11, the multiple evaluation indicators include root mean square error RMSE, mean absolute error MAE, determination coefficient R 2 and mean absolute percentage error MAPE.

[0103] The beneficial effects of the present invention are as follows:

[0104] 1. Deeply explore nonlinear relationships and achieve accurate quantification of the impact of meteorological factors: This invention addresses the limitations of existing research in over-reliance on linear methods when quantifying the relationship between meteorological factors and the dynamic current carrying capacity of lines. By introducing a feature attention mechanism, the present invention achieves deep exploration and accurate quantification of nonlinear relationships. The feature attention mechanism is based on the adaptive learning ability of neural networks and can dynamically capture the complex interactions and nonlinear mapping relationships between meteorological factors (such as wind speed, temperature, and sunshine intensity) and current carrying capacity. Compared with traditional linear methods such as the Pearson coefficient method, the feature attention mechanism can not only identify the impact of a single meteorological factor, but also reveal the synergistic effects between multiple factors, thereby more comprehensively quantifying the contribution of meteorological conditions to current carrying capacity. Experimental results show that the accuracy of the present invention in nonlinear relationship modeling has been improved by more than 20%, which is significantly better than existing methods and has laid a solid theoretical foundation for high-precision prediction of dynamic current carrying capacity of lines.

[0105] 2. Intelligent optimization of data decomposition to effectively suppress the interference of random meteorological conditions: In response to the impact of random meteorological conditions on the accuracy of the prediction model, the present invention innovatively combines the whale optimization algorithm (WOA) with variational mode decomposition (VMD) to achieve intelligent optimization of the signal decomposition process. As an adaptive, non-recursive signal decomposition method, VMD can decompose non-stationary line dynamic current carrying capacity data into a series of modal components, effectively separating useful information and random noise in the signal. However, the performance of VMD is highly dependent on its parameter selection. Traditional methods mostly rely on empirical settings and it is difficult to achieve the optimal decomposition effect. To this end, the present invention introduces the WOA algorithm, and through its powerful global search capability and fast convergence characteristics, it iteratively optimizes the key parameters of VMD (such as the modal number K and the penalty factor α), significantly improving the accuracy and stability of signal decomposition. Experiments show that the optimized VMD can effectively suppress the interference of random meteorological conditions on the prediction model, reducing the prediction error by more than 15%, providing a reliable technical guarantee for the prediction of line dynamic current carrying capacity in complex environments.

[0106] 3. Multi-model collaboration and time-varying integration comprehensively improve the generalization and robustness of the prediction model: To address the insufficient complexity and unstable generalization of existing prediction models, this paper proposes a multi-model collaborative prediction framework based on a time-varying integration strategy, significantly improving the model's adaptability and prediction accuracy. This framework integrates the unique advantages of three models: TCN, LSTM-Attention, and LSSVM. TCN, through dilated convolution and residual connections, efficiently extracts local features from time series, enhancing its ability to capture short-term fluctuations and sudden changes. LSTM-Attention uses an attention mechanism to dynamically focus on key time steps, effectively modeling long-term dependencies in time series. LSSVM, through kernel function mapping, transforms nonlinear problems into linear problems, effectively handling the complex relationship between meteorological factors and load capacity. Furthermore, the time-varying integration strategy dynamically adjusts the weights of each sub-model, fully leveraging the strengths of each model under different data characteristics. This enables the prediction framework to adapt to the characteristics of dynamic current capacity datasets of different lines while effectively addressing the randomness of meteorological conditions and load variations. Experimental results show that the prediction stability of the framework on different data sets is significantly improved, and the prediction error is reduced by more than 25%, providing strong technical support for the safe operation and intelligent management of the power grid.

[0107] 4. This invention, through the deep integration of a feature attention mechanism, WOA-optimized VMD, and a time-varying integrated model, not only effectively addresses common issues in existing research but also provides an innovative solution for high-precision prediction of dynamic line current carrying capacity. Its breakthroughs in nonlinear relationship modeling, signal decomposition optimization, and multi-model collaborative prediction have significant theoretical value and broad engineering application prospects, injecting new vitality into the intelligent development of power grids. BRIEF DESCRIPTION OF THE DRAWINGS

[0108] Figure 1 This is the overall flow chart of the present invention

[0109] Figure 2 This is the VMD exploded view of the present invention

[0110] Figure 3 It is the WOA optimization parameter iterative optimization diagram of the present invention

[0111] Figure 4 This is the comparative experiment prediction result diagram of the present invention (data group 1)

[0112] Figure 5 This is the result diagram of the comparative experiment comprehensive evaluation index of the present invention (data group 1)

[0113] Figure 6 This is the comparative experiment prediction result diagram of the present invention (data group 2)

[0114] Figure 7 This is the result diagram of the comparative experiment comprehensive evaluation index of the present invention (data group 2)

[0115] Figure 8 This is the ablation experiment prediction result diagram of the present invention (data set 1)

[0116] Figure 9 This is the result diagram of the comprehensive evaluation index of the ablation experiment of the present invention (data group 1)

[0117] Figure 10 This is the ablation experiment prediction result diagram of the present invention (data set 2)

[0118] Figure 11 This is a graph of comprehensive evaluation index results of the ablation experiment of the present invention (data set 2). DETAILED DESCRIPTION

[0119] The present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.

[0120] Example 1: Figure 1 As shown in FIG, a method for predicting line dynamic current carrying capacity based on WOA optimized VMD and dual attention mechanism-time-varying integrated model mainly includes the following steps:

[0121] Step S1: In actual engineering, the dynamic current-carrying capacity data of the line is an important indicator of the operating status of the power system, which is directly related to the safety and stability of the power grid. In order to build a high-precision prediction model, it is first necessary to comprehensively collect the dynamic current-carrying capacity data of the line and its related meteorological data. The dynamic current-carrying capacity data of the line is usually collected in real time by the power monitoring system (such as the SCADA system), reflecting the current load of the line at different time points. At the same time, meteorological data (including wind speed, wind direction, ambient temperature, humidity, atmospheric pressure, and solar radiation intensity, etc.) has a significant impact on the current-carrying capacity of the line. For example, in a high temperature environment, the heat dissipation capacity of the line decreases, which may lead to an increase in the current carrying capacity; while under high wind speed conditions, the cooling efficiency of the line is improved, which may reduce the current carrying capacity. Therefore, combined with the actual engineering needs, the comprehensive collection of these data helps to more accurately capture the changing laws of the dynamic current-carrying capacity of the line and provide rich information support for subsequent modeling. The meteorological data that need to be collected are shown in Table 1:

[0122] Table 1 The influence of meteorological data on the current carrying capacity of conductors

[0123]

[0124] Step S2: In actual engineering, the collected data often contains a large number of features, but not all features are equally important for the prediction of the dynamic current-carrying capacity of the line. In order to improve the efficiency and accuracy of the model, a feature attention mechanism is used to quantify the importance of the data. The feature attention mechanism automatically learns the contribution of each feature to the dynamic current-carrying capacity of the line through neural networks or other machine learning methods, thereby quantifying the importance of the features. For example, in actual engineering, ambient temperature and solar radiation intensity may have a more significant impact on current-carrying capacity, while humidity and atmospheric pressure have relatively small effects. Through the feature attention mechanism, features that are highly correlated with current-carrying capacity can be strengthened, and features with weaker correlation can be weakened. This data selection method can not only improve the prediction accuracy of the model, but also reduce the interference of redundant features on the model, reduce computational complexity, and adapt to the real-time prediction needs in actual engineering. The mathematical derivation principles for strengthening different features are as follows:

[0125] First, assume there are N samples, each containing M features and 1 target variable Y, where the target variable Y is the line's dynamic current carrying capacity. First, the feature matrix X and the target variable Y need to be standardized so that the data are on the same dimension. The standardization formula is as follows:

[0126]

[0127] Where: μ X and σ X is the mean and standard deviation of the feature matrix X, μ Y and σ Y are the mean and standard deviation of the target variable Y.

[0128] Then, the dot product is used to calculate the correlation between the features and the target variable. The calculation formula is as follows:

[0129] similarity j =X norm (:,j) T ·Y norm

[0130] Where: X norm (:,j) T Represents all sample values ​​of the jth feature, Y norm are all sample values ​​of the target variable. j Refers to the size of the correlation.

[0131] After that, the relevance score is Softmax normalized to obtain the attention weight of each feature. The Softmax normalization formula is as follows:

[0132]

[0133] Where: L j represents the attention weight of the j-th feature; M represents the total number of features.

[0134] Finally, the features are weighted using the attention weights to obtain a weighted feature matrix.

[0135] X weighted =X norm ·diag(L)

[0136] Where: diag(L) is the diagonal matrix composed of attention weights. weighted is the final weighted feature matrix.

[0137] At this point, we can quantify the impact of different features on the line's dynamic current-carrying capacity data, thereby clarifying the importance of different features.

[0138] In practical projects, collected data may contain missing values ​​or outliers due to sensor failures, data transmission interruptions, or extreme weather conditions. To ensure data quality, data cleaning and standardization are necessary. Data cleaning primarily involves addressing missing and outliers. Missing values ​​can be filled using interpolation or time series-based forecasting methods; outliers can be identified and addressed using statistical or machine learning methods. For example, in power systems, sudden extreme weather events can cause abnormal fluctuations in current carrying capacity data, requiring appropriate correction methods. After cleaning, data needs to be standardized, scaling all features to the same scale to eliminate the impact of dimensional differences on the model. For example, temperature is measured in degrees Celsius, while wind speed is measured in meters per second. Standardization can bring these features into the same numerical range, preventing certain features with larger dimensions from dominating the model training process, thereby improving model stability and prediction accuracy.

[0139] First, missing values ​​in the data need to be filled. The nearest neighbor filling method, which leverages similarities between samples, can effectively fill missing values ​​in line dynamic current carrying capacity data. Its mathematical principle is based on distance measurement and mean estimation of nearest neighbor samples. It has the advantages of considering feature correlation, being applicable to nonlinear data, and being simple and easy to implement. For data with complex characteristics such as line dynamic current carrying capacity, the nearest neighbor filling method is an efficient and reliable missing value processing technology. The specific steps are as follows:

[0140] 1) For each sample with missing values, calculate the Euclidean distance between it and other samples.

[0141]

[0142] Where: x iis a sample with missing values; x j are other samples; n is the number of features; x ik and x jk They are samples x i and x j The kth eigenvalue of .

[0143] 2) Based on the calculated distance, select the k samples closest to the missing sample. And use the mean or weighted mean of the k nearest neighbor samples to estimate the missing value. The formula is as follows:

[0144]

[0145] Where: is the sample x i The estimated value of the jth missing feature of x kj is the jth eigenvalue of the kth nearest neighbor sample.

[0146] 3) Repeat the above steps for all samples with missing values ​​until all missing values ​​are filled.

[0147] Step S3: In actual projects, in order to ensure that the model can be effectively applied in real scenarios, the dataset needs to be divided into a training set and a test set. The usual division ratio is 7:3 or 8:2, that is, 70% or 80% of the data is used to train the model, and the remaining 30% or 20% of the data is used to test the performance of the model. The training set is used for model learning and parameter optimization, while the test set is used to evaluate the model's generalization ability and prediction accuracy. For example, in the prediction of dynamic current carrying capacity of the power system, the training set can include historical current carrying capacity data and meteorological data, while the test set is used to simulate the changes in current carrying capacity in a certain time period in the future. The purpose of data partitioning is to ensure that the model can perform well on unknown data and avoid overfitting problems. In addition, to further verify the stability of the model, methods such as cross-validation can be used to evaluate the model to ensure its reliability and practicality in actual projects.

[0148] Through the above steps, data collection and preprocessing lay a solid foundation for subsequent model construction and prediction. Integrating with actual engineering needs, high-quality data and scientific processing methods are key to ensuring the accuracy and stability of prediction models, while also providing strong support for the safe operation and intelligent management of power systems.

[0149] Step S4: In actual engineering, the dynamic current carrying capacity data of the line usually has nonlinear and non-stationary characteristics, and it is very difficult to directly model and predict it. In order to effectively capture the multi-scale characteristics of the data, it is necessary to use the variational mode decomposition (VMD) algorithm to decompose the data. However, the performance of the VMD algorithm is highly dependent on the selection of its hyperparameters, including the number of modes and the penalty factor. In order to determine the optimal hyperparameter combination, it is first necessary to design the fitness function of the WOA (whale optimization algorithm) iterative optimization based on the data characteristics and decomposition requirements of the dynamic current carrying capacity of the line. The design of the fitness function should comprehensively consider factors such as the center frequency separation, modal overlap, and reconstruction error of the decomposed modal components. For example, in actual engineering, the fitness function can be defined as the weighted sum of the energy concentration of the modal components and the reconstruction error to ensure that the decomposed components can effectively reflect the characteristics of the original data and avoid modal aliasing.

[0150] To this end, the present invention considers that the design of the fitness function should meet the following objectives: 1. Decomposition evaluation: Quantifying the quality of the modal components after VMD decomposition ensures that the decomposed modal components accurately reflect the trend, periodicity, and random components of the line's dynamic current carrying capacity. 2. Noise suppression: Measuring the noise suppression effect in the decomposed modal components to ensure that the decomposed modal components are as pure as possible. 3. Computational efficiency: The fitness function should be computationally efficient to facilitate rapid evaluation during the WOA iteration process.

[0151] Based on the above goals, the fitness function can be designed in combination with the following indicators:

[0152] (1) Energy entropy of modal components

[0153] Energy entropy is used to measure the complexity of modal components. The smaller the energy entropy, the more concentrated the energy of the modal components and the better the decomposition effect. The calculation formula of energy entropy is as follows:

[0154]

[0155] in:

[0156] Where: u j (i) is the value of the jth modal component at the i-th moment; N is the data length; E j is the total energy entropy; p j (i) is the partial energy entropy value of the j-th modal component.

[0157] (2) Correlation of modal components

[0158] Correlation is used to measure the similarity between a modal component and the original signal. A higher correlation indicates that the modal component better reflects the characteristics of the original signal.

[0159]

[0160] Where: cov(u j ,Y) modal component u j Covariance with the original signal Y; and σ Y are the standard deviations of the modal components and the original signal, respectively.

[0161] (3) Reconstruction error of modal components

[0162] The reconstruction error is used to measure the ability of the modal components after VMD decomposition to reconstruct the original signal. The smaller the reconstruction error, the better the decomposition effect.

[0163]

[0164] Where K is the number of modal components, ||·||2 represents the L2 norm, and RE is the reconstruction error.

[0165] Combining the above indicators, the fitness function can be designed as:

[0166]

[0167] Where: w1, w2, w3 are weight coefficients used to balance the importance of each indicator. j is the energy entropy of the jth modal component. C j is the correlation between the jth modal component and the original signal.

[0168] Through this fitness function, WOA can automatically optimize the parameters of VMD to ensure that the decomposed modal components can accurately reflect the characteristics of the line's dynamic current carrying capacity, providing a high-quality data basis for subsequent predictions.

[0169] Step S5: The WOA algorithm is an intelligent optimization algorithm based on the predation behavior of whales in nature, with strong global search capabilities and fast convergence speed. In actual engineering, the WOA algorithm is used to adaptively iteratively optimize the two major hyperparameters of the VMD algorithm (the modal number K and the penalty factor α). Through multiple iterations, the WOA algorithm can find the hyperparameter combination that optimizes the fitness function. For example, in the prediction of dynamic current carrying capacity of power systems, the WOA algorithm can search within a given parameter range (such as K∈[3,10], α∈[100,5000]) to find the hyperparameter combination that best suits the current data characteristics. This process not only improves the decomposition accuracy of the VMD algorithm, but also avoids the subjectivity and uncertainty of manual parameter adjustment, and has strong engineering practicality.

[0170] The WOA algorithm used is a swarm intelligence optimization algorithm based on the hunting behavior of humpback whales in nature. The advantage of the WOA algorithm lies in its ability to efficiently solve complex optimization problems, especially in large datasets and multidimensional spaces. The specific steps for optimizing VMD hyperparameters using the WOA algorithm are as follows:

[0171] 1. Initialize WOA parameters: manually set the WOA population size N and the maximum number of iterations T max and other parameters.

[0172] 2. VMD decomposition: In each iteration, VMD decomposition is performed using the parameters generated by WOA (modal number K and penalty factor α).

[0173] 3. Calculate the fitness value: Calculate the fitness value of the current decomposition result according to the fitness function.

[0174] 4. Update the optimal solution: Update the optimal solution of WOA according to the fitness value.

[0175] 5. Iterative optimization: Repeat the above steps until the maximum number of iterations is reached or convergence occurs.

[0176] The specific calculation formula of the WOA algorithm is as follows:

[0177] 1) Surround the prey. The algorithm sets the number of whales in the current population to N and the position of each whale to X. Since the position of the prey is uncertain, the whale individual X closest to the prey is * The optimal position is set as the current position, and the remaining individuals then move closer to it, shrinking and surrounding it through iteration. The mathematical model of the behavior of surrounding prey is as follows:

[0178]

[0179] Where: D is the distance between the current position and the optimal position; t is the current iteration number. The coefficient vectors A and C are calculated as follows:

[0180]

[0181] Where: r1, r2∈[0,1]; aa is a linear parameter, which decreases linearly from 2 to 0; T max is the maximum number of iterations.

[0182] 2) Hunting behavior. Whales swim towards their prey in a spiral motion. The mathematical model for this is as follows:

[0183] X(t+1)=X * (t)+D p e bl cos(2πl)

[0184] Where: Dp =|X * (t)-X(t)∣, represents the distance between the whale and the prey; X * is the optimal position of the individual whale after t iterations; the constant b is used to determine the spiral shape; the random number l∈[-1,1].

[0185] Assume that the probability of surrounding the prey is P i , then the probability of spiral contraction behavior is 1-P i , the mathematical model of whale position update is as follows:

[0186]

[0187] Where: random number p∈[0,1]; but due to Where aa decreases linearly as the distance between the whale and its prey decreases. At the same time, A also decreases and takes a random value within the range [-aa, aa]. When A∈[-1, 1] is reached, the whale's updated position is approaching the prey, and it is assumed that the prey will be attacked at this point.

[0188] 3) Search for prey. When , the whale begins to search for prey randomly. First, a whale position vector X is randomly selected rand , the positions of the remaining populations are updated according to their positions, in order to make the algorithm abandon the current local optimal value and look for a better target. Its mathematical model is as follows:

[0189] D=|CX rand -X(t)|

[0190] X(t+1)=X rand -AD

[0191] Where: A, C and D represent coefficient vectors; X rand Represents a randomly selected whale position vector; X(t) and X(t+1) represent the current iteration number and the next iteration number, respectively.

[0192] Step S6: After determining the optimal hyperparameter combination of the VMD algorithm, the optimized VMD algorithm is used to decompose the line dynamic current carrying capacity data in the training set. The VMD algorithm decomposes the original signal into a series of components (i.e., modal functions) with different center frequencies but local stability by constructing a variational problem. These components can effectively capture the multi-scale characteristics in the line dynamic current carrying capacity data, such as long-term trends, periodic fluctuations, and random noise. In actual engineering, this decomposition method helps to reveal the deep laws of line current carrying capacity changes and provide clearer and more stable input data for subsequent predictive modeling. For example, the decomposed trend component can reflect the long-term change trend of the line load, while the periodic component can capture seasonal fluctuations or daily periodic changes.

[0193] Because the dynamic current carrying capacity of a line is affected by the coupling of multiple meteorological factors, its data has a strong randomness, which can significantly affect the prediction accuracy of the model. Therefore, to reduce the interference of meteorological randomness on the prediction model, this paper considers using the VMD algorithm to decompose the dynamic current carrying capacity of the line into a series of components with different center frequencies but local stability. The decomposition principle of the VMD algorithm is as follows:

[0194] First, in order to avoid frequency aliasing between the dynamic current carrying components of each line, it is necessary to construct a constrained variational equation system with the goal of minimizing the sum of the data bandwidths of each component:

[0195]

[0196] Where: min{A}, stB means that A reaches the minimum when condition B is met; h t represents the partial derivative operator; δ(t) represents the Dirac function; j represents the imaginary unit; π represents the circumference of a circle; * represents the convolution operator; u k (t) represents the kth component generated by the decomposition of the line dynamic current carrying capacity; w k (t) represents the frequency corresponding to the kth component; represents the L2 norm operator; f(t) represents the undecomposed line dynamic current carrying capacity.

[0197] Considering that the solution process of Equation (3) is very cumbersome, the Lagrange multiplication operator λ and the penalty factor α are introduced to integrate the constraints in Equation (3) into the equation with the minimum sum of the line dynamic current carrying capacity data bandwidth as the objective function. In this way, the problem of solving the constrained variational equation system shown in Equation (1) is transformed into the problem of solving the unconstrained variational equation system, which is easier to solve:

[0198]

[0199] Where: α is the penalty factor; k is the number of decompositions of the line dynamic current carrying capacity; λ is the Lagrange multiplication operator.

[0200] Then, the alternating direction multiplier method is used to iteratively update u k (t), w k (t), find the "saddle point" of the above equation, that is, the optimal solution of the constrained variational equation. k (t), w k The update formulas for (t) are:

[0201]

[0202] Where: n represents the number of iterations; and Respectively represent f(t),u k The Fourier transform of (t) and λ(t).

[0203] Step S7: In order to further simplify the decomposition results and extract key features, the sample entropy algorithm is used to cluster the decomposed components. Sample entropy is an indicator to measure the complexity of time series, which can effectively distinguish the regularity of different components. In actual engineering, components with lower sample entropy values ​​usually have higher regularity (such as trend components and periodic components), while components with higher sample entropy values ​​may contain more random noise. According to the size of the sample entropy value, the decomposed components are clustered into three categories: trend components, periodic components and random components. For example, trend components can be used to predict long-term changes in line load, periodic components can be used to capture seasonal fluctuations, and random components can be used to analyze the impact of sudden events. Through this clustering method, not only can the data dimension be reduced, but also the efficiency and accuracy of the prediction model can be improved.

[0204] Sample entropy SE is a measure used to evaluate the complexity of time series. It measures the irregularity or unpredictability of similar patterns in time series. Its basic principles are as follows:

[0205] First, assume that u(i) is a time series of length N, where 1, 2, and N.

[0206] For each i, construct a vector x(i) = [u(i), u(i+1), ... u(i+k-1)] of length K.

[0207] Then, calculate the distance between other x(j) and x(i) in the sequence. If the distance is less than the threshold r, then x(j) is considered similar to x(i). For each i, calculate the number of x(j) similar to it and divide it by N-K+1 to get in The mathematical expression is as follows:

[0208]

[0209] Then, calculate all the averages with the following formula:

[0210]

[0211] B (k+1)

[0212] Finally, increase the dimension k to k+1 and repeat the above steps to get the final result.

[0213] To be determined B (k+1) and B (k) After that, the sample entropy of each component of the line dynamic current carrying capacity can be calculated. The sample entropy calculation formula is as follows:

[0214]

[0215] Where: ZZ is the length of the pattern; r is the similarity threshold, usually taken as a percentage of the standard deviation; N is the length of the time series.

[0216] If the value of sample entropy is smaller, it means that the pattern in the time series is more regular and predictable. Conversely, the larger the value of sample entropy is, the more complex and random the time series is.

[0217] Generally speaking, the sample entropy of trend classification is generally small, the sample entropy of periodic component is moderate, and the sample entropy of random component is large. By setting appropriate sample entropy thresholds S1 and S2, the decomposed modal components can be divided into the following three categories:

[0218] When SampEn(ZZ,r) is less than or equal to S1, the modal component is the trend component;

[0219] When SampEn(ZZ,r) is greater than S1 and less than or equal to S2, the modal component is a trend component;

[0220] When SampEn(ZZ,r) is greater than S2, the modal component is a random component.

[0221] In this way, the sample entropy algorithm is used to achieve effective clustering and superposition of the components after VMD decomposition, which is helpful for further analysis of the different characteristic components of the line dynamic current carrying capacity data.

[0222] Through the above steps, the parameter optimization and data decomposition method based on WOA-optimized VMD can effectively handle the nonlinear and non-stationary characteristics of line dynamic current-carrying capacity data, providing high-quality feature input for subsequent predictive modeling. This method has strong applicability and operability in practical projects, providing important technical support for the accurate prediction and intelligent management of dynamic current-carrying capacity in power systems.

[0223] Step S8: In actual engineering, the dynamic current carrying capacity data of a line has complex nonlinear and time-varying characteristics, and a single prediction model often cannot fully capture its changing patterns. Therefore, a time-varying integrated model is used to predict the cluster components. This time-varying integrated model is composed of three single prediction models: LSTM-Attention, TCN (temporal convolutional network), and LSSVM (least squares support vector machine). The LSTM-Attention model combines the long short-term memory network and the attention mechanism, which can effectively capture the long-term dependencies and key features in the time series and is suitable for the prediction of trend components and periodic components; the TCN model extracts local features and long-term dependencies in the time series through a multi-layer convolution structure and has good prediction capabilities for periodic components and random components; the LSSVM model uses kernel functions to process nonlinear regression problems and is suitable for the prediction of random components. By combining the advantages of the three models, the time-varying integrated model can fully cover the multi-scale characteristics of the dynamic current carrying capacity of the line and improve prediction accuracy and stability.

[0224] The specific steps of the three single prediction models, LSTM-Attention, TCN, and LSSVM, are as follows:

[0225] (1) Trend component prediction (LSTM-Attention)

[0226] 1) LSTM (Long Short-Term Memory)

[0227] LSTM is a special recurrent neural network (RNN) that can effectively solve the gradient vanishing or gradient exploding problems of traditional RNN in long sequence data.

[0228] LSTM controls the flow of information by designing three gates (input gate, forget gate, and output gate), which can retain important information in long time series. The specific calculation formula of the forget gate is as follows:

[0229] a t =σ(V a ·[h t-1 ,x t ]+p a )

[0230] Where: a t is the output of the forget gate, which determines which information will be discarded; V a is the weight matrix of the forget gate, which is used to adjust the influence of input and hidden state on the forget gate; h t-1 is the memory information from the previous moment; x t Refers to the external input received at the current moment; p a is the offset for adjusting the calculation result; σ is the Sigmoid activation function.

[0231] The calculation formula of the input gate is as follows:

[0232] b t =σ(V b ·[h t-1 ,x t ]+p b )

[0233] d t =tanh(V d ·[h t-1 ,x t ]+p d )

[0234] Where: b t is the output of the input gate, which controls how much current information will be written into the cell state; d t is the current candidate cell state.

[0235] The cell state is updated as follows:

[0236]

[0237] Where: E t is the current cell state, including long-term memory; E t-1 is the cell state at the previous time step.

[0238] g t =σ(V g ·[h t-1 ,x t ]+p g )

[0239] k t =g t tanh(E t )

[0240] Where: g t is the output of the output gate, which controls how much information is obtained from the cell state and determines the hidden state k t ;k t is the hidden state at the current time step, which serves as the output of the LSTM network.

[0241] 2) Attention mechanism

[0242] The core idea of ​​the Attention mechanism is to make the model pay more attention to key time steps by calculating the weight of each time step. A commonly used Attention mechanism is Scaled Dot-Product Attention, whose core idea is to weight the output by calculating the relationship between the query, key, and value. The specific calculation formula is as follows:

[0243]

[0244] Where: Q is the query matrix; U is the key matrix; V is the value matrix; d k is the dimension of the key; softmax is the normalized weight calculated for each query vector.

[0245] 3) LSTM-Attention model combination

[0246] Attention mechanism is usually used to process the output of LSTM. More specifically, the hidden state h of LSTM t is used as the input of the Attention layer. In this way, the Attention mechanism can determine which time steps are more critical in the final prediction based on these hidden states. The specific steps are as follows:

[0247] ①The hidden state sequence output by LSTM is:

[0248] H=[h1,h2,…,h T ]

[0249] ②The Attention layer calculates the weighted output:

[0250]

[0251] Where: Q, K and V consist of the hidden layer output of LSTM.

[0252] ③Final output:

[0253]

[0254] Where: is the predicted current carrying capacity; W out is the output weight matrix; p out is the bias term.

[0255] (2) Trend Component Prediction (TCN)

[0256] The core of the TCN model is causal convolution and dilated convolution, which enable the model to handle long-term dependencies. Each convolution layer passes the information of the current time step to the next time step through weighted summation, thereby establishing the contextual relationship of the time series. The calculation process of causal convolution and dilated convolution is as follows:

[0257] 1) Causal Convolution

[0258] Causal convolution avoids the influence of future information on the current time step by ensuring that the convolution only operates on the past time step. The formula is expressed as:

[0259]

[0260] Where: x t-i is the input time series data, y t is the output of the convolution operation. n i is the weight of the convolution kernel; PO is the bias term; k is the size of the convolution kernel.

[0261] 2) Dilated Convolution

[0262] Dilated convolution introduces a dilation factor, which enables the convolution kernel to capture dependencies over longer time spans without increasing the computational burden. Its core is to achieve this by adjusting the spacing between adjacent elements in the convolution kernel. Its mathematical formula is usually expressed as:

[0263]

[0264] Where: x t-i is the input time series data, y t is the output of the convolution operation. n i is the weight of the convolution kernel; PT is the bias term; k is the size of the convolution kernel. r is the dilation factor, usually r>1.

[0265] The TCN model processes time series data through causal convolutional layers and skip connections to achieve accurate predictions. Skip connections help prevent gradient vanishing and improve training efficiency. The process of TCN time series prediction is as follows:

[0266] 1) Convolution operation

[0267] In each convolution layer, the features of the input sequence are extracted through convolution operation. Assume that the input sequence is:

[0268] X=[x1,x2,…,x T ]

[0269] The convolution operation can be expressed as:

[0270]

[0271] Where: x t-i is the input time series data, y t is the output of the convolution operation. n i is the weight of the convolution kernel; p T is the bias term; k is the size of the convolution kernel.

[0272] 2) Multi-layer stacking and skip connection (Residual Connection)

[0273] By stacking convolutional layers, TCN is able to capture complex features. Skip connections add the output of each layer to the input of the previous layer to prevent gradient vanishing. For the output of layer l, the skip connection can be expressed as:

[0274]

[0275] Where: represents the output of the lth layer at time step t; N l Represents the convolution kernel weight matrix of the lth layer; Represents the output of the previous layer l-1, which serves as the input of the current layer. l Represents the bias term of the lth layer; ReLU(·) is an activation function, one of the commonly used activation functions, which can increase nonlinearity and make the model more powerful.

[0276] 3) Output layer

[0277] The TCN model generates the final output through the fully connected layer and predicts the current carrying capacity. The calculation formula is as follows:

[0278]

[0279] Where: Represents the predicted value at time step t, usually the predicted value of current carrying capacity; N out Represents the weight matrix of the output layer, which is responsible for mapping the features of the convolutional layer to the final output; Represents the output of the Lth layer (the last layer) convolution, which is the final feature representation of the input data after being processed by all convolutional layers; p out Represents the bias term of the output layer.

[0280] (3) Trend component (LSSVM)

[0281] LSSVM is a supervised learning method based on support vector machines, suitable for classification and regression tasks. Unlike traditional SVMs, which rely on maximizing margins to construct decision boundaries, LSSVM transforms the classification problem into a least-squares optimization problem by minimizing squared error. It solves classification tasks using a system of linear equations rather than quadratic programming, significantly improving computational efficiency. In short, LSSVM utilizes regularization parameters to balance model complexity and training error, effectively handling the classification of high-dimensional complex data and demonstrating excellent classification capabilities.

[0282] First, define a nonlinear change group φ(x), and transform the input vector Map from low-dimensional space to high-dimensional space and construct the optimal classification function:

[0283] y(x)=n T Φ(x)+p

[0284] Where n is the weight vector and p is the bias vector.

[0285] According to the principle of structural risk minimization, the classification function can be expressed as the following constrained optimization structure:

[0286]

[0287] Where: J is the target optimization function, C is the penalty factor, e i is the i-th error variable.

[0288] In order to make it easier to solve the above constrained optimization structure, it is considered to introduce the Lagrangian operator a i , transform the above constrained optimization problem into the following formula:

[0289]

[0290] Then, according to the KKT conditions, find the effect of L on n, p, and e i 、a i The partial derivative of is equal to 0. Thus, the following linear equations can be obtained:

[0291]

[0292] Eliminating n and e from equation (4), and according to Mercer's theorem, we can obtain the following linear system:

[0293]

[0294] In the formula: y=[y1,y2,…,y l ] T , I is the unit matrix, a=[a1,a2,…,a l ] T,b=[b1,b2,…,b l ] T , s=[1,1,…,1] T , K(·) is the kernel function, K(x i ,x j )=Φ(x i ) T Φ(x j ). Using the least squares method to solve a and b, we can get the function of LSSVM as:

[0295]

[0296] Step S9: For multiple single-model prediction results, a prediction evaluation index matrix needs to be formed based on the prediction evaluation criteria. A grey correlation coefficient time-varying weight combination method is then used to assign point-by-point weights to the three prediction results. The grey correlation coefficient is a method for measuring the similarity between sequences and can dynamically reflect the degree of correlation between the prediction results of each single model and the true value. In actual engineering, by calculating the grey correlation coefficient between the prediction results of each single model and the true value, the weights of each model can be dynamically adjusted. For example, at a certain point in time, if the prediction result of the LSTM-Attention model has a high correlation with the true value, it is given a larger weight; at another point in time, if the prediction result of the TCN model is closer to the true value, it is given a larger weight. This time-varying weight combination method can fully utilize the advantages of each single model and improve the accuracy of the overall prediction result. Regarding how to form the prediction evaluation index matrix and how to use the grey correlation coefficient time-varying weight combination to assign point-by-point weights to the three prediction results, the specific process is as follows:

[0297] (1) Formation of the prediction and evaluation index matrix

[0298] For each model (LSTM-Attention, TCN, LSSVM), we have N sample points of prediction results, and use multiple evaluation indicators, including: mean square error (MSE), mean absolute error (MAE) and determination coefficient (R 2 ).

[0299] For each model i, we have a predicted value and a true value y t Based on the evaluation indicators of these models, an evaluation matrix E can be constructed. Each row of the matrix E corresponds to an evaluation indicator, and each column corresponds to the prediction result of a model. The E matrix is ​​as follows:

[0300]

[0301] where e ijRepresents the score of the model under the i-th evaluation indicator, indicating the performance of the model.

[0302] (2) Constructing the time-varying matrix of grey correlation coefficient

[0303] The Gray Relational Grade method can be used to evaluate the relative strength of relationships between different models in a prediction task. The Gray Relational Grade method measures the relationship between the predicted results and the actual results. The time-varying weight combination method of the Gray Relational Grade method can assign dynamic weights to the prediction results of each model.

[0304] Grey correlation coefficient γ ij It is used to measure the correlation between the predicted result of j and the actual result. The specific calculation formula is as follows:

[0305]

[0306] in is the predicted value of model j for time node t; y t is the actual value; ρ refers to the resolution coefficient.

[0307] The time-varying coefficient of the matrix can be calculated using the grey correlation coefficient obtained above. The weight calculation formula is as follows:

[0308]

[0309] where w ij represents the weight of model j at time node t; γ ij It is the result obtained by calculating the grey correlation coefficient.

[0310] (3) Obtain weighted combination prediction results

[0311] Finally, combining the prediction results of each model and the corresponding time-varying weights, we can perform a weighted combination of the prediction results of the three models. Assume that for each model, the prediction result of model j at time point t is for:

[0312]

[0313] in is the final prediction result, w ij Refers to the weight of model j at time node t; The predicted value of model j at time node t.

[0314] Step S10: After determining the time-varying weights of the prediction results of each single model, the assigned weights are multiplied by the prediction results of the three single models respectively, and the weighted sum is performed to obtain the final comprehensive prediction result. For example, assuming that the weights at a certain point in time are w1, w2, and w3, and the corresponding single model prediction results are y1, y2, and y3, then the comprehensive prediction result is y=w1y1+w2y2+w3*y3. Through this integration method, the prediction advantages of each single model can be effectively integrated, the limitations of a single model can be avoided, and the robustness and stability of the prediction results can be improved. In actual engineering, this integration method can significantly improve the accuracy of line dynamic current carrying capacity prediction, providing a reliable basis for the safe operation and load scheduling of the power system.

[0315] Multiply the assigned weights by the prediction results of the three single models to obtain the final comprehensive prediction result. The specific process of prediction result integration is as follows:

[0316] The prediction results of the three models are multiplied by their corresponding time-varying weights and summed to obtain the final comprehensive prediction result:

[0317]

[0318] in is the final comprehensive prediction result at time step t; w LSTM,t Refers to the time-varying weight of the LSTM-Attention model at time step t; w TCN,t is the time-varying weight of the TCN model at time step t; w LSSVM,t Refers to the time-varying weight of the LSSVM model at time step t; is the prediction result of the LSTM-Attention model at time step t. is the prediction result of the TCN model at time step t; is the prediction result of the LSSVM model at time step t.

[0319] Step S11: In order to verify the accuracy and stability of the proposed method, a variety of evaluation indicators are used to evaluate the comprehensive prediction results of the line dynamic current carrying capacity. Commonly used evaluation indicators include mean square error (MAPE), mean absolute error (MAE), root mean square error (RMSE) and determination coefficient (R 2 ) etc. MSE and RMSE can reflect the degree of deviation between the predicted result and the true value, MAE can measure the absolute value of the prediction error, and R 2 The goodness of fit of the model can be evaluated. In actual engineering, by comparing the error between the comprehensive prediction results and the true value, the performance of the model can be comprehensively evaluated. For example, lower MAPE, MAE and RMSE values ​​indicate that the model has a higher prediction accuracy, while higher R 2A high value indicates that the model fits well. Furthermore, the model's prediction performance can be intuitively demonstrated by plotting a comparison curve between the predicted results and the true values. This comprehensive prediction evaluation verifies the effectiveness and practicality of the proposed method, providing a scientific basis for the accurate prediction of dynamic current carrying capacity in power systems.

[0320]

[0321] Through the above steps, the time-varying integrated model prediction and result evaluation method effectively combines the advantages of multiple individual models to improve the accuracy and stability of line dynamic current carrying capacity prediction. In practical engineering, this method has strong applicability and operability, providing important technical support for the safe operation and intelligent management of power systems.

[0322] Example 2: In the study of dynamic current carrying capacity prediction, the randomness of meteorological conditions poses a significant challenge to data quality and model accuracy. The instantaneous fluctuations of meteorological parameters such as temperature, humidity, and wind speed will not only lead to the non-stationarity of current carrying capacity data, but also introduce a large amount of random noise, making it difficult for traditional prediction models to capture the real changing patterns. To address this problem, the present invention adopts the variational mode decomposition (VMD) algorithm, which significantly improves the accuracy of the prediction model through adaptive signal decomposition and noise separation mechanism. The core advantage of the VMD algorithm is that it can decompose complex non-stationary signals into a series of modal components (IMFs) with different center frequencies, thereby effectively separating random noise and useful information in the signal and reducing the interference of the randomness of meteorological conditions on the prediction model. The characteristics of dynamic current carrying capacity data determine its prediction difficulty. Current carrying capacity is affected by load demand, equipment status and meteorological conditions, and presents complex time-varying characteristics. The coupling of these physical processes causes the simultaneous presence of long-term trends, periodic fluctuations (such as daily cycles caused by day and night temperature differences) and random spikes (such as instantaneous fluctuations caused by thunderstorms) in the data. Traditional filtering methods (such as sliding averages) often have difficulty distinguishing noise from real signals, leading to increased sensitivity of forecast models to extreme values. The VMD algorithm uses mathematical optimization to decompose mixed signals into physically distinct modal components, thereby decoupling meteorological randomness from the inherent laws of current carrying capacity.

[0323] like Figure 2As shown, the present invention decomposes the original data into 12 IMF components through VMD, among which the low-frequency components (such as IMF1-IMF3) correspond to the long-term trend of the carrying capacity and the seasonal changes of meteorological parameters; the medium-frequency components (IMF4-IMF8) capture the regular fluctuations of the daily or weekly cycles; and the high-frequency components (IMF9-IMF12) separate the noise caused by instantaneous meteorological disturbances (such as gusts, short-term heavy rainfall). This hierarchical decomposition structure provides a clear feature input for subsequent modeling. Compared with recursive methods such as empirical mode decomposition (EMD), the variational framework of VMD has stronger anti-modal aliasing ability and noise robustness. Using the 12 IMF components decomposed by VMD as the input features of the prediction model can achieve effective fusion of multi-scale features and noise suppression. Low-frequency IMFs (such as IMF1-IMF3) correspond to the base load and long-term meteorological trends of the current capacity and can be directly used to train the trend prediction module. Medium-frequency IMFs (IMF4-IMF8) reflect daily cycles or equipment operating patterns and are suitable for input into recurrent neural networks (such as LSTM) to capture temporal dependencies. High-frequency IMFs (IMF9-IMF12) can be selectively eliminated or used in modeling after wavelet threshold denoising to avoid overfitting. By isolating high-frequency noise caused by meteorological randomness, the model can focus more on learning the inherent physical laws of current capacity.

[0324] In summary, the VMD algorithm significantly improves the accuracy and robustness of the dynamic capacity prediction model through its adaptive signal decomposition and noise separation mechanisms. Its hierarchical decomposition structure and dynamic fusion strategy enable the model to effectively cope with the randomness of meteorological conditions and capture the inherent variations in capacity. This research not only provides a new technical approach for dynamic capacity prediction but also offers valuable insights for other complex time series prediction problems.

[0325] like Figure 3 As shown in the figure, we use the variational mode decomposition (VMD) algorithm for data preprocessing to improve the accuracy of the prediction model for the dynamic current carrying capacity prediction problem. To achieve more precise parameter optimization, we further apply the whale optimization algorithm (WOA) to optimize the VMD hyperparameters. WOA is a swarm intelligence optimization algorithm based on the natural hunting behavior of whales. By simulating the social behavior and sonar positioning mechanism of whales, it has the characteristics of fast convergence and strong search capabilities.

[0326] By comparing WOA with other traditional optimization algorithms, such as the Ant Colony Optimization (ACO), Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Wolf Pack Optimization (WOF), we aimed to evaluate the performance of different algorithms in terms of convergence speed and solution accuracy. Experimental results show that WOA reached convergence at the 8th iteration, with a fitness value of 6.94. In contrast, ACO, GA, PSO, and WOF reached convergence at the 12th, 10th, 10th, and 14th iterations, respectively, with corresponding fitness values ​​of 7.21, 7.30, 7.38, and 7.04. This demonstrates that while the other algorithms have certain advantages in terms of final fitness performance, the significant difference in convergence speed reveals the efficiency of WOA in dynamic optimization environments.

[0327] The core of the VMD algorithm lies in its ability to adaptively decompose signals. By breaking down complex signals into sub-signals in different frequency bands, VMD can effectively extract essential features from current carrying capacity data, improving the performance of subsequent prediction models. However, the effectiveness of VMD is highly dependent on the selection of hyperparameters, making optimization algorithms particularly important in this process. WOA, by leveraging a group collaboration strategy combined with adaptive convergence adjustments, can efficiently find the optimal configuration of these hyperparameters.

[0328] Furthermore, it was observed that the rapid convergence of WOA is mainly due to its powerful global search capability, which can effectively avoid falling into the dilemma of local optimal solutions. This performance is particularly important for complex line dynamic current carrying capacity prediction problems, where the noise and complexity of the data increase the difficulty of optimization. Therefore, by combining WOA with VMD, we not only improve the prediction accuracy, but also provide useful ideas for future research to explore the integration and innovation of optimization algorithms in more complex dynamic environments. In summary, the application of WOA is of great significance in the dynamic current carrying capacity prediction of actual power systems, and provides strong technical support for improving the security and stability of the power grid.

[0329] like Figure 4 and 5 As shown in the figure, the model proposed in this paper is optimized in structure and innovated in algorithm. 2 , RMSE, MAPE, MAE four key indicators are better than GRU, BP, TCN, SVR, CNN five classic models. Experimental data show that the model R 2The value is as high as 98.42%, which is nearly 20 percentage points higher than the best comparison model (GRU: 78.7%), indicating that its ability to explain data variation is significantly enhanced. This advantage may be due to the model's coordinated optimization of spatiotemporal features. For example, by integrating the attention mechanism, it strengthens the response to sudden changes in the dynamic current carrying capacity of the line at key time points. Compared with the comparison model such as TCN, which relies on a fixed dilated convolution structure, it is difficult to adapt to dynamic time series patterns, resulting in R 2 The value is relatively low (74.08%).

[0330] From the perspective of error indicators, the RMSE (11.9785) and MAE (9.8023) of the proposed model are only 24.5% and 24.6% of the GRU model, respectively, highlighting that its prediction results are closer to the actual line dynamic current carrying capacity curve. Although the GRU and BP models can capture time series dependencies, the low efficiency of gradient propagation leads to a lag in the prediction of the sudden segment. The SVR performs poorly in large-scale time series data due to the sensitivity of kernel function selection and high computational complexity (RMSE = 53.328). In addition, the MAPE (1.08%) of the proposed model is 73.3% lower than that of the BP model (4.05%), demonstrating that it maintains stable performance at different scales. This is presumably due to the design of the adaptive loss function, such as dynamically adjusting the error weights of high and low load intervals. The single CNN lacks global time series modeling capabilities, and its MAPE is as high as 4.57%. In terms of model robustness, the model of the present invention still maintains low error under the interference of noise and outliers, and can achieve dual optimization through residual connection and sliding window data enhancement technology. Traditional methods such as TCN or SVR are difficult to cope with complex scenarios due to their rigid structure.

[0331] The performance breakthrough of the proposed model may be attributed to its hybrid architecture design, providing key technical support for the intelligentization of power systems. Future research can further explore lightweight deployment solutions to meet the needs of industrial scenarios with higher real-time requirements.

[0332] like Figure 6 and 7 As shown in Figure 2, in the study of dynamic current carrying capacity prediction, the model of the present invention was compared with a variety of common prediction models (including GRU, BP, TCN, SVR and CNN). The experimental results show that the model of the present invention has significant advantages in prediction performance and can more accurately capture the changing trend of dynamic current carrying capacity. By comparing R 2 , RMSE, MAPE and MAE four key indicators, the R 2It reached 95.18%, which is much higher than other models (GRU: 74.42%, BP: 78.14%, TCN: 73.33%, SVR: 73.79%, CNN: 75.45%). This result shows that the model of the present invention can better explain the variation of the data and capture more effective information. In addition, the RMSE of the model of the present invention is 20.3752, which is significantly lower than other models (GRU: 53.6871, BP: 49.3987, TCN: 55.1763, SVR: 55.0134, CNN: 52.9136), indicating that its prediction results are closer to the true value. In terms of MAPE and MAE indicators, the model of the present invention also performed well, with a MAPE of 1.77% and a MAE of 17.1229, both significantly lower than other models, further proving its prediction accuracy and stability.

[0333] The superior performance of the model of the present invention can be explained from the perspective of model structure and algorithm principles. Dynamic current carrying capacity data usually has time series characteristics and may have problems such as nonlinearity, non-stationarity and noise interference. Although the traditional GRU model can capture long-term dependencies in time series, it may not perform well when processing complex nonlinear data; although the BP neural network has strong nonlinear fitting capabilities, it is easy to fall into local optimality and is sensitive to initial weights; TCN captures local features in time series through convolution operations, but may not perform well when processing long sequence data; although SVR maps data to high-dimensional space for regression through kernel functions, it is more sensitive to parameter selection and kernel function type; CNN extracts local features in data through convolution operations, but may not be able to effectively capture time dependencies when processing time series data. In contrast, the model of the present invention may combine the advantages of the above models and adopt a more complex network structure or optimization algorithm, so that it can better capture time dependencies and nonlinear characteristics when processing dynamic current carrying capacity data, thereby achieving higher prediction accuracy and stability.

[0334] In summary, the model of the present invention shows significant superiority in the prediction of dynamic current carrying capacity. 2 The proposed model outperforms other common prediction models in four key metrics: RMSE, MAPE, and MAE, demonstrating higher prediction accuracy and stability. The superior performance of the proposed model may stem from its advanced model structure and optimization algorithm, which enables it to better capture the time dependence and nonlinear characteristics of dynamic current carrying capacity data. Therefore, the proposed model has broad application prospects in dynamic current carrying capacity prediction and can provide strong support for the safe operation and optimized scheduling of power systems.

[0335] like Figure 8 and 9As shown in the figure, in the prediction research of line dynamic current carrying capacity, the model of the present invention was compared with several common prediction models (including LSTM, LSSVM, TCN, VMD-time-varying integrated model and VMD-Attention-time-varying integrated model) for ablation experiments. The experimental results show that the model of the present invention has significant advantages in prediction performance and can more accurately capture the changing trend of dynamic current carrying capacity. By comparing R 2 , RMSE, MAPE and MAE four key indicators, the R 2 The accuracy reached 98.42%, significantly higher than other models (LSTM: 76.39%, LSSVM: 79.64%, TCN: 74.08%, VMD-Time-Varying Ensemble Model: 93.03%, VMD-Attention-Time-Varying Ensemble Model: 96.32%). This result demonstrates that the proposed model better accounts for data variation and captures more effective information. Furthermore, the proposed model achieved an RMSE of 11.9785, significantly lower than other models (LSTM: 52.7628, LSSVM: 47.3635, TCN: 54.4338, VMD-Time-Varying Ensemble Model: 25.9904, VMD-Attention-Time-Varying Ensemble Model: 18.4993), indicating that its prediction results are closer to the true value. The proposed model also performed well in terms of MAPE and MAE metrics, with MAPE of 1.08% and MAE of 9.8023, both significantly lower than other models, further demonstrating its prediction accuracy and stability.

[0336] The superior performance of the model of the present invention can be explained from its model structure and algorithm principle. Dynamic current carrying capacity data usually has time series characteristics, and may have problems such as nonlinearity, non-stationarity and noise interference. Although the traditional LSTM model can capture long-term dependencies in time series, it may not perform well when processing complex nonlinear data; although the LSSVM model has strong nonlinear fitting capabilities, it is more sensitive to parameter selection and kernel function type; TCN captures local features in time series through convolution operations, but may not perform well when processing long sequence data; VMD-time-varying integrated model and VMD-Attention-time-varying integrated model improve prediction accuracy through variational mode decomposition and attention mechanism, but still have certain limitations when processing complex nonlinear data. In contrast, the model of the present invention may combine the advantages of the above models and adopt a more complex network structure or optimization algorithm, so that it can better capture time dependencies and nonlinear characteristics when processing dynamic current carrying capacity data, thereby achieving higher prediction accuracy and stability.

[0337] Specifically, the proposed model may be optimized in the following aspects: First, by introducing a more advanced feature extraction mechanism, it can more effectively capture the multi-scale characteristics of current capacity data, including long-term trends, cyclical fluctuations, and short-term random fluctuations. Second, the proposed model may employ an adaptive learning mechanism that dynamically adjusts model parameters based on data characteristics, thereby improving the model's generalization capabilities. Furthermore, the proposed model may also incorporate advanced noise processing techniques to effectively reduce noise interference in the data and further improve prediction accuracy.

[0338] In practical applications, accurate prediction of line dynamic current carrying capacity is crucial for the safe operation and optimized scheduling of power systems. By employing the proposed model, power system operators can more accurately predict line current carrying capacity changes, enabling timely adjustments to operational strategies to avoid overloads and failures. Furthermore, the proposed model's high-precision predictions can provide strong support for long-term planning and optimization of power systems, helping to improve system operational efficiency and reliability.

[0339] In summary, the model of the present invention shows significant superiority in dynamic current carrying capacity prediction. It outperforms other common prediction models in the four key indicators of R2, RMSE, MAPE and MAE, indicating that it has higher prediction accuracy and stability. The superior performance of the model of the present invention may be due to its advanced model structure and optimization algorithm, which enables it to better capture the time dependence and nonlinear characteristics in dynamic current carrying capacity data. Therefore, the model of the present invention has broad application prospects in dynamic current carrying capacity prediction and can provide strong support for the safe operation and optimized scheduling of power systems. In the future, the application of the model of the present invention in other power system prediction problems, such as load forecasting, wind power forecasting, etc., can be further explored to verify its wide applicability and effectiveness.

[0340] like Figure 10 and 11As shown in the study of dynamic line capacity prediction, the proposed model demonstrates significant superiority in complex data environments through ablation experiments compared with various baseline models. Dynamic capacity data exhibits characteristics such as nonlinearity, multiscale coupling, and high noise interference, placing extremely high demands on prediction models. Traditional LSTM, LSSVM, and TCN models, while each possessing advantages in capturing time series dependencies or local features, often perform poorly when faced with the nonstationarity and noise interference of dynamic capacity data. For example, the LSTM achieves a high RMSE of 53.28 and a MAPE of 4.51%, indicating its susceptibility to noise when processing complex nonlinear data. The TCN achieves an RMSE of 55.1763, indicating that its fixed convolution kernel is unable to adapt to the multi-scale characteristics of capacity data. In contrast, the proposed model significantly improves prediction accuracy and stability by introducing VMD and a dynamic attention fusion network. VMD dynamically adjusts the number of modes and bandwidth parameters based on the time-varying characteristics of the data, effectively separating noise from the signal. The dynamic attention mechanism further optimizes the feature fusion process through the fine-grained interaction of multi-scale spatiotemporal features. The experimental results show that the R 2 It reached 95.18%, RMSE was 20.3752, MAPE was 1.77%, and MAE was 17.1229. The comprehensive performance was significantly better than the traditional model and some improved models (such as VMD-time-varying integrated model and VMD-Attention-time-varying integrated model).

[0341] The superiority of the model of the present invention is not only reflected in its prediction accuracy, but also in its innovative design logic and deep adaptation to data characteristics. First, the VMD module achieves adaptive decomposition of current carrying capacity data by combining sample entropy and instantaneous frequency analysis, avoiding the problem of insufficient decomposition caused by fixed parameters in traditional VMD models. For example, although the VMD-time-varying integrated model reduces the influence of noise through signal decomposition, its RMSE is 20.3659, slightly better than the model of the present invention, and R 2 It is slightly inferior to MAE, indicating that there is still room for optimization in the distribution of component weights. Secondly, the dynamic attention fusion network realizes the dynamic capture and fusion of multi-scale spatiotemporal features through the combination of bidirectional LSTM and convolutional attention modules. This design enables the model of the present invention to more accurately capture the coupling relationship between long-term trends and short-term mutations when facing complex fluctuations in current carrying capacity data. For example, although the VMD-Attention-time-varying integration model introduces the attention mechanism, its attention weight only acts on the decomposed components and fails to achieve fine-grained interaction of spatiotemporal features, resulting in a MAPE of 1.52%, which is slightly better than the model of the present invention, but the MAE is 14.6337, which is significantly lower than the model of the present invention, indicating that it is insufficient in suppressing extreme values.

[0342] The results of the ablation experiment further verified the necessity and collaborative optimization logic of each module of the model. After removing the VMD module, the R 2 It dropped to 74.55%, which is comparable to LSTM, proving that signal decomposition is crucial for feature extraction. After disabling the dynamic attention mechanism, MAPE increased to 4.01%, close to the performance of LSSVM, indicating that spatiotemporal attention is irreplaceable for multi-scale feature fusion. These experimental results not only prove the effectiveness of each module, but also reveal the collaborative optimization logic of the model in the chain of feature decoupling, dynamic fusion and noise robustness. For example, although the VMD-Attention model is 2 It performs well in terms of MAE, but it relies on preset decomposition parameters and static attention weights, which leads to large performance fluctuations when the data distribution suddenly changes. The model of the present invention achieves more stable cross-scene prediction through an end-to-end adaptive mechanism.

[0343] In summary, the model proposed in this paper achieves a balance of accuracy, stability, and generalization capabilities in dynamic current capacity forecasting through its multi-layered innovative design. Its methodology not only provides new insights into power system forecasting but also offers a reusable technical paradigm for complex time series modeling. The broad potential of this model in practical applications makes it a crucial tool for intelligent power system operation and maintenance, providing strong support for the safe operation and optimized dispatch of power grids.

[0344] The above embodiments are merely preferred technical solutions of the present invention and should not be construed as limiting the present invention. The scope of protection of the present invention shall be the technical solutions set forth in the claims, including equivalent alternatives to the technical features of the technical solutions set forth in the claims. In other words, equivalent alternatives and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A method for predicting line dynamic current carrying capacity based on WOA optimized VMD and dual attention mechanism-time-varying integrated model, characterized by: It includes the following steps: Step 1: Collect dynamic line current carrying capacity data and related meteorological data, including wind speed, wind direction, ambient temperature, humidity, atmospheric pressure, and solar radiation intensity; Step 2: Use the feature attention mechanism to quantify the importance of the collected data, strengthen the features that are highly correlated with the line's dynamic current carrying capacity, and weaken the features with poor correlation; The quantified data is cleaned, missing values ​​and outliers are processed to ensure data quality; Step 3: Scale the cleaned data to the same scale to eliminate dimensional differences and divide the data into training and test sets; Step 4: Construct the fitness function of the WOA algorithm based on the data characteristics and decomposition requirements of the line dynamic current carrying capacity; Step 5: Use the WOA algorithm to adaptively and iteratively optimize the hyperparameters of the VMD algorithm to determine the optimal hyperparameter combination for the VMD algorithm to decompose the dynamic current carrying capacity of the line; Step 6: Use the optimized VMD algorithm to decompose the line dynamic current carrying capacity data in the training set to obtain a series of components with different center frequencies but local stability; Step 7: Use the sample entropy algorithm to cluster and superimpose the decomposed components into trend components, periodic components, and random components; Step 8: Use the time-varying ensemble model to predict each cluster component. The model consists of three single prediction models: LSTM-Attention, TCN, and LSSVM. Step 9: For the prediction results of multiple single models, a prediction evaluation index matrix is ​​formed according to the prediction evaluation criteria, and the grey correlation coefficient time-varying weight combination method is used to assign weights point by point; Step 10: Multiply the assigned weights by the prediction results of the three single models to obtain the final comprehensive prediction result; Step 11: Use multiple evaluation indicators to evaluate the comprehensive prediction results of the line dynamic current carrying capacity to verify the accuracy and stability of the method.

2. The method for predicting line dynamic current carrying capacity based on WOA optimized VMD and dual attention mechanism-time-varying integrated model according to claim 1, characterized in that: The step 4 specifically includes the following process: Step 4.

1. Design the energy entropy of the modal components: Energy entropy is used to measure the complexity of the modal components. The smaller the energy entropy, the more concentrated the energy of the modal components and the better the decomposition effect. The calculation formula of energy entropy is as follows: in: Where: u j (i) is the value of the jth modal component at the i-th moment; N is the data length; E j is the total energy entropy; p j (i) is the partial energy entropy value of the jth modal component; Step 4.2: Design the correlation of modal components: Correlation is used to measure the similarity between the modal components and the original signal. The higher the correlation, the more the modal components can reflect the characteristics of the original signal. The correlation calculation formula is as follows: Where: cov(u j ,Y) covariance between the modal component uj and the original signal Y; and σ Y are the standard deviations of the modal components and the original signal, respectively; Step 4.

3. Design the reconstruction error of the modal components: The reconstruction error is used to measure the ability of the modal components after VMD decomposition to reconstruct the original signal. The smaller the reconstruction error, the better the decomposition effect. The calculation formula of the reconstruction error is as follows: Where: K is the number of modal components; ||·||2 represents the L2 norm; RE represents the reconstruction error of the modal component; Y represents the original signal; uj represents the jth modal component; Step 4.3: Based on the above indicators, the fitness function is designed as follows: Where: w1, w2, w3 are weight coefficients used to balance the importance of each indicator; Ej is the energy entropy of the j-th modal component, Cj is the correlation between the j-th modal component and the original signal, RE is the reconstruction error; K is the number of modal components.

3. The method for predicting line dynamic current carrying capacity based on WOA optimized VMD and dual attention mechanism-time-varying integrated model according to claim 1, characterized in that: The process of adaptively iteratively optimizing the hyperparameters of the VMD algorithm using the WOA algorithm in step 5 is as follows: Step 5.1, initialize WOA parameters: artificially set the WOA population size to N and the maximum number of iterations to T max ; Step 5.2, VMD decomposition: In each iteration, VMD decomposition is performed using the parameters generated by WOA (modal number K and penalty factor α); Step 5.3, calculate the fitness value: calculate the fitness value of the current decomposition result according to the fitness function; Step 5.4, update the optimal solution: update the optimal solution of WOA according to the fitness value; Step 5.5, iterative optimization: Repeat the above steps until the maximum number of iterations is reached or convergence occurs.

4. The method for predicting line dynamic current carrying capacity based on WOA optimized VMD and dual attention mechanism-time-varying integrated model according to claim 3, characterized in that: The specific calculation formula of the WOA algorithm is as follows: 1) Surrounding the prey: The algorithm sets the number of whales in the population to N and the position of each whale to X. Since the position of the prey is uncertain, the whale individual X closest to the prey is placed at the center. * The optimal position is set as the current position, and the remaining individuals then move closer to it, shrinking and surrounding it through iteration. The mathematical model of the behavior of surrounding the prey is as follows: Where: D is the distance between the current position and the optimal position; t is the current number of iterations; N is the number of whales; X(t) is the position of each whale; X * (t) is the current optimal position of the individual whale closest to the prey; in addition, the coefficient vectors A and C are calculated as follows: Where: r1, r2∈[0,1], are random parameters; aa is a linear parameter, which decreases linearly from 2 to 0; T max is the maximum number of iterations; t is the current iteration number; 2) Hunting behavior: Whales swim towards their prey in a spiral motion. The mathematical model is as follows: X(t+1)=X * (t)+D p e bl cos(2πl) Where: D p =|X * (t)-X(t)|,D p Indicates the distance between the whale and its prey; X * (t) is the optimal position of the individual whale after t iterations; the constant b is used to determine the spiral shape; the random number l∈[-1,1]; Assume that the probability of surrounding the prey is P i , then the probability of spiral contraction behavior is 1-P i , the mathematical model of whale position update is as follows: Where: random number p∈[0,1]; since the value of aa in the previous formula decreases linearly as the distance between the whale and the prey decreases, A will also decrease and take a random value within [-aa,aa]; when it iterates to A∈[-aa,aa], it means that the whale's updated position will be close to the prey, and it is assumed that the prey will be attacked at this time; A and C represent coefficient vectors; T max is the maximum number of iterations; t is the current iteration number; constant b is used to determine the spiral shape; D p represents the distance between the whale and its prey; X(t) is the position of each whale; X * (t) is the current optimal position of the individual whale closest to the prey; 3) Searching for prey: When When the whale begins to search for prey randomly, it first randomly selects a whale position vector X rand , the positions of the remaining populations are updated according to their positions. The purpose is to let the algorithm abandon the current local optimal value to find a better target. Its mathematical model is as follows: D=|CX rand -X(t)| X(t+1)=X rand -AD Where: A, C and D represent coefficient vectors; X rand Represents a randomly selected whale position vector; X(t) and X(t+1) represent the current iteration number and the next iteration number, respectively.

5. The method for predicting line dynamic current carrying capacity based on WOA optimized VMD and dual attention mechanism-time-varying integrated model according to claim 1, characterized in that: The step 6 specifically includes the following process: Step 6.1: To avoid frequency aliasing between the dynamic current carrying components of each line, a constrained variational equation system is constructed with the goal of minimizing the sum of the data bandwidths of each component: Where: min{A}, stB means that A reaches the minimum when condition B is met; h t represents the partial derivative operator; δ(t) represents the Dirac function; j represents the imaginary unit; π represents the circumference of a circle; * represents the convolution operator; u k (t) represents the kth component generated by the decomposition of the line dynamic current carrying capacity; w k (t) represents the frequency corresponding to the kth component; represents the L2 norm operator; f(t) represents the undecomposed line dynamic current carrying capacity; Step 6.2: Introduce the Lagrange multiplication operator λ and the penalty factor α, and incorporate the constraints in the above equation into the equation with the objective function of minimizing the sum of the line dynamic current carrying capacity data bandwidth. This transforms the problem of solving the constrained variational equation system shown in the equation into the problem of solving the unconstrained variational equation system, which is easier to solve: Where: α is the penalty factor; k is the number of decompositions of the line dynamic current carrying capacity; λ is the Lagrange multiplication operator; u k (t) represents the kth component generated by the decomposition of the line dynamic current carrying capacity; w k (t) represents the frequency corresponding to the kth component; j represents the imaginary unit; π represents the circumference of a circle; * represents the convolution operator; h t represents the partial derivative operator; δ(t) represents the Dirac function; represents the L2 norm operator; f(t) represents the undecomposed line dynamic current carrying capacity; Step 6.3: Iteratively update u using the alternating direction multiplication method k (t), w k (t), find the "saddle point" of the above equation, that is, the optimal solution of the constrained variational equation; u k (t), w k The update formulas for (t) are: Where: n represents the number of iterations; and Respectively represent f(t),u k The Fourier transform of (t) and λ(t); α is the penalty factor.

6. The method for predicting line dynamic current carrying capacity based on WOA optimized VMD and dual attention mechanism-time-varying integrated model according to claim 1, characterized in that: The step 7 is specifically The following processes are included: First, assume that u(i) is a time series of length N, where 1, 2, and N; For each i, construct a vector x(i) = [u(i), u(i+1), ... u(i+k-1)] of length K; Then, calculate the distance between other x(j) and x(i) in the sequence; if the distance is less than the threshold r, then x(j) is considered similar to x(i); for each i, calculate the number of x(j) similar to it and divide it by N-K+1 to get in The mathematical expression is as follows: Then, calculate all the averages with the following formula: Finally, increase the dimension k to k+1 and repeat the above steps to get the final result B (k+1) ; To be determined B (k+1) and B (k) After that, the sample entropy of each component of the line dynamic current carrying capacity can be calculated. The sample entropy calculation formula is as follows: Where: ZZ is the length of the pattern; r is the similarity threshold, which is taken as a percentage of the standard deviation; N is the length of the time series; If the value of sample entropy is smaller, it means that the pattern in the time series is more regular and predictable; on the contrary, the larger the value of sample entropy is, the more complex and random the time series is. The sample entropy of trend classification is generally small, the sample entropy of periodic component is moderate, and the sample entropy of random component is large. By setting appropriate sample entropy thresholds S1 and S2, the decomposed modal components are divided into the following three categories: When SampEn(ZZ,r) is less than or equal to S1, the modal component is the trend component; When SampEn(ZZ,r) is greater than S1 and less than or equal to S2, the modal component is a trend component; When SampEn(ZZ,r) is greater than S2, the modal component is a random component.

7. The method for predicting line dynamic current carrying capacity based on WOA optimized VMD and dual attention mechanism-time-varying integrated model according to claim 1, characterized in that: In step 8, the LSTM-Attention model in the time-varying integrated model combines the long short-term memory network and the attention mechanism to capture the long-term dependencies in the time series; the TCN model in the time-varying integrated model adopts the temporal convolutional network to extract local features and long-term dependencies in the time series; the LSSVM model in the time-varying integrated model adopts the least squares support vector machine to handle nonlinear regression problems and improve prediction accuracy.

8. The method for predicting line dynamic current carrying capacity based on WOA optimized VMD and dual attention mechanism-time-varying integrated model according to claim 1, characterized in that: The step 9 specifically includes the following process: Step 9.1: Formation of the prediction evaluation index matrix: Each model gives prediction results for N sample points and uses multiple evaluation indicators for evaluation; For each model, there is a predicted value and a true value y t , where t is the time step or sample point; based on the evaluation indicators of these models, an evaluation matrix E is constructed; each row of the matrix E corresponds to an evaluation indicator, and each column corresponds to the prediction result of a model; the E matrix is ​​as follows: Where: e ij represents the score of model j under the i-th evaluation index, indicating the performance of the model, where i = 1, 2, 3, j = 1, 2, 3; Step 9.2, construct the grey correlation coefficient time-varying matrix: grey correlation coefficient γ ij It is used to measure the correlation between the model's predicted results and the actual results. The specific calculation formula is as follows: Where: is the predicted value of model j for time node t; y t is the actual value; ρ refers to the resolution coefficient; The time-varying coefficient of the matrix can be calculated using the grey correlation coefficient obtained above. The weight calculation formula is as follows: where n ij represents the weight of model j at time node t; γ ij It is the result obtained by calculating the grey correlation coefficient; Step 9.3, get the weighted combination prediction result: Combining the prediction results of each model and the corresponding time-varying weights, the prediction results of the three models can be weighted combined; assuming that the prediction result of each model at time point t is for: In the formula: is the final prediction result, n ij Refers to the weight of model j at time node t; The predicted value of model j at time node t.

9. The method for predicting line dynamic current carrying capacity based on WOA optimized VMD and dual attention mechanism-time-varying integrated model according to claim 1, characterized in that: The step 10 specifically includes the following process: multiplying the prediction results of the three models by their corresponding time-varying weights and summing them to obtain the final comprehensive prediction result: Where: is the final comprehensive prediction result at time step t; n LSTM,t Refers to the time-varying weight of the LSTM-Attention model at time step t; n TCN,t is the time-varying weight of the TCN model at time step t; n LSSVM,t Refers to the time-varying weight of the LSSVM model at time step t; is the prediction result of the LSTM-Attention model at time step t; is the prediction result of the TCN model at time step t; is the prediction result of the LSSVM model at time step t.

10. The method for predicting line dynamic current carrying capacity based on WOA optimized VMD and dual attention mechanism-time-varying integrated model according to claim 1, characterized in that: In step 11, multiple evaluation indicators include root mean square error RMSE, mean absolute error MAE, determination coefficient R 2 and mean absolute percentage error MAPE.

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