Error Prediction Method of Electromagnetic Current Transformer Based on Weighted Extreme Learning Machine

Abstract

The present invention relates to an electromagnetic current transformer error prediction method based on a weighted extreme learning machine, belonging to the technical field of current transformers. The method includes steps such as data acquisition, outlier removal, normalization processing, variational mode decomposition, construction of a three-phase current characteristic matrix, training of a current transformer error detection model, prediction, and result comparison. The present invention can predict the angular error and ratio error of current transformers, and can effectively guide the operation and maintenance and overhaul work of relevant staff, and is easy to promote and apply.

Description

Technical Field

[0001] The present invention belongs to the technical field of current transformers, and particularly relates to an error prediction method for electromagnetic current transformers based on a weighted extreme learning machine. Background Art

[0002] Electromagnetic current transformers play a crucial role in the power system and are used to measure and monitor large currents. However, after long-term operation, some electromagnetic current transformers may exceed the error limit, so accurate online monitoring and error assessment are required.

[0003] In China, relatively mature and systematic equipment manufacturing technologies and error compensation methods for current transformers have been developed. At the same time, a relatively complete calibration method has been set based on operation experience to ensure the operation stability of current transformers. Currently, the metering characteristics of current transformers are mainly evaluated through periodic calibration methods. However, actual operation data shows that there is a deviation between the off-line measurement error and the actual operation error of current transformers, and the periodic off-line calibration method cannot fully grasp the metering performance of current transformers under actual operating conditions. Current transformers are installed in substations, and the electromagnetic environment in the substations during operation is complex, and there is a possibility of exceeding the allowable error during long-term operation. In order to accurately and timely detect the metering status of operating electromagnetic current transformers and obtain accurate error conditions, the online monitoring technology for the errors of electromagnetic current transformers has become a hot spot and a difficult point in the current development of electric energy metering device technologies.

[0004] In the exploration and development of current transformer calibration methods, it has experienced the development from "static calibration" to "live calibration" and then to "pre-calibration assessment". Currently, the most commonly used method in the power industry is to carry out off-line "static calibration" on transformers under power outage conditions to grasp the operation errors of in-service transformers. In order to reduce the impact of the "static calibration" method on the power grid operation due to power outage, scholars have proposed a "live calibration" method for transformers. This type of method uses an on-line special standard device to calibrate the errors of in-service transformers in the live state. In order to overcome the deficiencies of the "live calibration" method in terms of portability and safety, in recent years, experts and scholars have tried to evaluate the operation errors of all transformers in the network by establishing physical or mathematical models in the direction of "pre-calibration assessment".

[0005] In the research on the error assessment technology of electromagnetic current transformers, it mainly focuses on off-line analysis under simulated actual operating conditions and analyzing the influence degree of multi-dimensional factors on the errors of electromagnetic current transformers. By simulating actual operating conditions, the error performance of electromagnetic current transformers under different conditions can be more accurately evaluated, and the influence degree of various factors on the errors can be analyzed.

[0006] In addition, in the aspect of on-line error assessment of electromagnetic current transformers, research is mainly carried out on electronic current transformers. This method uses traditional current transformers as reference standard devices to compare the relative changes in the errors of electronic current transformers with the same voltage level, the same phase sequence, and the same transformation ratio. By on-line monitoring the error conditions of electromagnetic current transformers, their performance can be monitored in real time, and potential problems can be detected in a timely manner.

[0007] In summary, the on-line monitoring technology of current transformer errors is of great significance for ensuring the accuracy and reliability of electric energy metering. By simulating the actual operating conditions and on-line evaluating the error conditions of electronic current transformers, the monitoring and evaluation capabilities of the performance of current transformers can be improved, thereby effectively preventing and solving the problems of current transformer errors.

[0008] Disadvantages of the prior art:

[0009] (1) At present, off-line evaluation and on-line evaluation often require error comparison with traditional electromagnetic standard transformers. In large-scale application scenarios of transformers, neither safety nor portability is as convenient as the pre-evaluation method. In the pre-evaluation method, some transformer states need to be obtained in advance, and this part of the "pre-calibrated" transformer states has a great impact on the evaluation results.

[0010] (2) In the existing transformer evaluation models based on data-driven methods, there are few inputs that combine time-frequency domain features in the model input features. Even if there are such types of features, they are often extracted through convolutional neural network or time series network models, losing the original feature interpretability.

[0011] (3) The existing transformer error evaluation models do not consider the serious data imbalance between positive and negative samples during the model training process, that is, the sample data in the normal state of the transformer is relatively large, and the samples with out-of-tolerance are relatively small.

[0012] (4) In the existing evaluation models, most of the machine learning models or deep learning models selected are trained based on the principle of backpropagation, resulting in the problem of slow training speed.

[0013] Therefore, how to overcome the deficiencies of the prior art is an urgent problem to be solved in the current transformer technology field. Summary of the Invention

[0014] The purpose of the present invention is to solve the deficiencies of the prior art, and provide an electromagnetic current transformer error prediction method based on a weighted extreme learning machine, specifically an on-line monitoring error evaluation method for electromagnetic current transformers based on variational mode decomposition and weighted extreme learning machine.

[0015] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0016] The electromagnetic current transformer error prediction method based on weighted extreme learning machine includes the following steps:

[0017] Step (1), collecting the secondary side current signal amplitude data of the three-phase current transformer every a minute under normal operating conditions to obtain a three-phase current amplitude matrix; and collecting the angle difference and ratio difference of the three-phase current transformer at the same time;

[0018] Step (2), for the three-phase current amplitude matrix obtained in step (1), remove abnormal values in the matrix data;

[0019] Step (3), standardizing the amplitude data in the three-phase current matrix processed in step (2) to obtain a standardized three-phase current amplitude matrix;

[0020] Step (4), using the Grey Wolf Optimization Algorithm to optimize the parameters of the variational modal decomposition algorithm, and using the optimized variational modal decomposition algorithm to perform variational modal decomposition on the standardized three-phase current amplitude matrix obtained in step (3);

[0021] Step (5), extracting time domain characteristic parameters and frequency domain characteristic parameters from the modal components decomposed in step (4), and concatenating all extracted parameters to obtain a reduced-dimensional three-phase current characteristic matrix;

[0022] Step (6), using the reduced dimension three-phase current feature matrix obtained in step (5) as input, and using the angle difference and ratio difference as output, to train the extreme learning machine model to obtain a current transformer error detection model;

[0023] Step (7), using the secondary side current signal amplitude data of the three-phase current transformer to be detected to obtain the three-phase current amplitude matrix of the three-phase current transformer to be detected; then through steps (2) to (5), the corresponding three-phase current characteristic matrix is obtained, and then input into the current transformer error detection model obtained in step (6) to obtain the predicted angle difference and ratio difference of the three-phase current transformer to be detected;

[0024] Step (8), compare the prediction result of step (7) with the error threshold. If the predicted angle difference and ratio difference are both smaller than the threshold, it indicates that the current transformer is in a normal operating state at this time; otherwise, it is considered that the current transformer may be in an abnormal operating state at this time.

[0025] Furthermore, in step (1), a=15; 900 data points need to be retained for each signal after being eliminated in step (2).

[0026] Further, the specific method of step (2) is:

[0027] According to the maximum and minimum values of historical normal signal changes, abnormal values that exceed the range are removed, and non-numeric values are also eliminated.

[0028] Further, the specific method of step (3) is: performing standardization processing on the data processed in step (2) by using column normalization method.

[0029] Further, in step (4), the specific method of using the grey wolf optimization algorithm to optimize the parameters of the variational mode decomposition algorithm is:

[0030] Step (4.1), initializing the grey wolf algorithm parameters: initializing the basic parameters of the population size, decrement coefficient, random vector, and iteration times of the grey wolf algorithm;

[0031] Step (4.2), initializing the grey wolf position: randomly initializing the decomposition layer number k and penalty factor alpha of the variational mode decomposition algorithm as the initial position of the grey wolf algorithm;

[0032] Step (4.3), calculating the fitness of the grey wolf individuals: the fitness function takes the mean of permutation entropy, and the optimization goal is to minimize the mean of permutation entropy. Save the three wolves with the best fitness, and define the individuals with the smallest first three fitness values as the alpha wolf, beta wolf, and delta wolf in sequence, and their positions are defined as and The rest are uniformly defined as omega wolves;

[0033] Step (4.4), hunting the prey, realizing the hunting of the prey through the following formula

[0034]

[0035] In the formula, is the position of the updated individual; is the position of the current prey; t is the current iteration number of the algorithm; is the distance between the current individual and the prey; the position of the current individual; is a cooperation coefficient vector; are both another cooperation coefficient vector;

[0036] Step (4.5), iteratively updating the grey wolf individuals, and updating the latest position of the grey wolf according to the following four update formulas:

[0037]

[0038] In the formula, and are the direction and step length of the omega wolf moving towards the alpha wolf, beta wolf, and delta wolf; and are the positions of the alpha wolf, beta wolf, and delta wolf; and is the distance between the current individual and the alpha wolf, beta wolf, and delta wolf; recalculate the fitness, and update the alpha wolf, beta wolf, and delta wolf;

[0039] Step (4.5), when the number of iterations is reached, output the optimal decomposition layer k and penalty factor alpha of the VMD algorithm.

[0040] Furthermore, the optimal decomposition layer k is 2.

[0041] Furthermore, in step (5), the time-domain characteristic parameters include the maximum value, minimum value, first-order moment, second-order origin moment, and kurtosis factor; the frequency-domain characteristics include the center frequency, mean square frequency, frequency variance, and multi-scale permutation entropy;

[0042] Among them,

[0043] The formula for the maximum value is: x max = max(x i ); where x i is the current data of the i-th sampling point;

[0044] The formula for the minimum value is: x min = min(x i );

[0045] The formula for the first-order moment is: where N is the number of samplings;

[0046] The formula for the second-order origin moment is:

[0047] The formula for the kurtosis factor is: Among them, is the sampling mean, and σ is the sampling standard deviation;

[0048] The formula for the center frequency is: P(f) is the spectral value at frequency f;

[0049] The formula for the mean square frequency is:

[0050] The formula for the frequency variance is:

[0051] The formula for the multi-scale permutation entropy is:

[0052] For m different numbers, there will be m! possible order patterns π; for the permutation of number π, f(π) represents its frequency in the time series; then the relative frequency is p(π) = f(π) / (N / τ - m + 1).

[0053] Furthermore, in step (5), the specific method of splicing is:

[0054] The reduced three-phase current feature matrix has A-phase samples, B-phase samples, and C-phase samples from top to bottom;

[0055] The A-phase samples are sequentially spliced by 24-dimensional features of each of the three phases A, B, and C;

[0056] The B-phase samples are sequentially spliced by 24-dimensional features of each of the three phases B, A, and C;

[0057] The C-phase samples are sequentially spliced by 24-dimensional features of each of the three phases C, A, and B;

[0058] Thus, a 72×3-dimensional three-phase feature matrix is constructed, that is, the reduced three-phase current feature matrix.

[0059] Further, in the extreme learning machine model, the cost-sensitive weight matrix is embedded into the extreme learning machine objective function, and each weight factor of the newly added weight matrix in the extreme learning machine objective function is constructed in a cost-sensitive manner.

[0060] Further, in step (8), if both the predicted angular difference and ratio difference exceed the corresponding thresholds, the working state of the current transformer is determined to guide the operation and maintenance and overhaul work of relevant staff.

[0061] Further, the threshold range of the angular difference is ±10 minutes, and the threshold range of the ratio difference is ±0.2%; if the predicted angular difference or ratio difference exceeds the corresponding threshold, it is determined that the current transformer is in an out-of-tolerance state, and the staff needs to be reminded of maintenance and overhaul.

[0062] When training in step (6) of the present invention, the data division is set according to the 5-fold cross-validation method. Each time, 4 portions of data are trained and 1 portion of data is tested, and the final accuracy is the average accuracy of 5 times as the final result.

[0063] In step (4.3) of the present invention, the fitness function takes the mean of the permutation entropy, and the optimization objective is to minimize the mean of the permutation entropy. The smaller the mean, the more ordered and regular the data arrangement is.

[0064] Since the optimal decomposition layer number k obtained by variational mode decomposition is 2, in step (5) of the present invention,

[0065] Each modal component extracts 5 time-domain features: maximum value, minimum value, first moment, second origin moment, and kurtosis factor; plus 7 frequency-domain features, center frequency, mean square frequency, frequency variance, and multi-scale permutation entropy (where m of the multi-scale permutation entropy is taken as 4, and the permutation number features on 4 scales are extracted). That is, each modal component extracts 12 features, and a total of 24 features for two modal components.

[0066] Among them, for m different numbers, there will be m! possible order patterns π, also known as permutations; for the permutation with number π, f(π) represents its frequency in the time series; then the relative frequency is

[0067] p(π) = f(π) / (N / τ - m + 1). In the present invention, m is taken as 4.

[0068] The present invention discloses an electromagnetic current transformer metering error prediction and evaluation method based on variational mode decomposition and extreme learning machine, and solves the following technical problems:

[0069] The present invention adopts the method of variational mode decomposition for signal dimensionality reduction and performs dimensionality reduction on the data set. Variational mode decomposition has good denoising effect, can improve the smoothness of displacement data, extract the detailed features of the data, and has stronger signal decomposition ability compared with other decomposition methods. The core idea of this technology is to decompose the signal and extract features, convert the high-dimensional signal data into a low-dimensional representation form, thereby reducing the redundant information of the data and improving the efficiency and accuracy of signal processing. The present invention avoids the problems that the monitored data of the sampled current transformer belongs to a high-dimensional data set, which will increase the operation difficulty and make the model running time longer when directly input into the reliability evaluation and prediction model.

[0070] The present invention selects the weighted extreme learning machine as the regression model. The extreme learning machine only needs to randomly initialize the weights and biases and does not require backpropagation optimization, which well solves the problem of slow training speed in the previous methods. Aiming at the serious imbalance problem of the transformer monitoring data, the present invention solves it by embedding a cost-sensitive weight matrix in the objective function of the extreme learning machine. Specifically as follows:

[0071] Given the dimension-reduced input training set S = {(x i , y i ), i = 1, 2,..., N, y i ∈{+,-}}, first traverse all samples in the training set to count the number of positive and negative samples; construct the diagonal weight factor ω ii of the weight matrix W according to the sample belonging category, and its value is the reciprocal of the total number of samples contained in the corresponding category of the sample, and the rest of W is 0;

[0072] Substitute the weight matrix into the solution formula of the output weight matrix β:

[0073]

[0074] Among them, H is the output matrix of the hidden layer, C is the regularization coefficient, N is the number of samples, L is the number of hidden layer nodes, and Y is the true output value matrix;

[0075] For an unknown current transformer monitoring data sample x, the specific error of the current transformer output by the weighted extreme learning machine is calculated by substituting it into the function f(x) = Hβ.

[0076] Compared with the prior art, based on the characteristics of the output current data of the secondary monitoring of the current transformer, the present invention proposes to formulate an online evaluation process for the metrological performance of current transformers for metrology, and studies a method for dimensionality reduction of current transformer monitoring data with high computational efficiency. It can accurately detect the gradual change of the error of the current transformer through the model, has strong engineering universality, and has broad market promotion conditions.

[0077] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0078] 1. The present invention proposes a method for dimensionality reduction of the secondary side monitoring data of current transformers based on grey wolf optimization variational mode decomposition. By extracting the time-frequency domain features of each modal signal, the original 900-dimensional detection data is reduced to 72 dimensions, realizing the effective dimensionality reduction of the current transformer monitoring data. The GWO algorithm adopts a flexible parameter adjustment and dynamic update strategy, can quickly converge to a better solution, and has strong global search ability; its algorithm process is clear, and the parameter adjustment is relatively intuitive, which is easy to understand and apply. The construction of the three-phase current feature matrix is to construct the reduced sample data according to the original monitoring data and splice the time-frequency domain features. The establishment of this feature matrix takes into account the differences of different phase currents, provides more comprehensive and accurate inputs for the ELM model for predicting the current angle difference ratio difference, and more comprehensively evaluates the performance of single-phase current transformers.

[0079] 2. The present invention selects the weighted extreme learning machine as the error prediction model of the current transformer based on three-phase current data. The weighted extreme learning machine has the characteristics of fast training speed of the traditional extreme learning machine. Only by randomly assigning biases and input weights, calculating the output weight matrix through least squares, and constructing each weight factor of the new weight matrix in the objective function in a cost-sensitive manner, using the mean absolute error MAE (Mean Absolute Error) and the mean square error MSE (Mean Square Error) as the prediction evaluation indicators to train the extreme learning machine.

[0080] 3. Compare the weighted extreme learning machine with other prediction algorithms in the field of machine learning, including the extreme learning machine (ELM), support vector machine (SVM), random forest (Random Forest), and extreme gradient boosting (XGBoost). The results of the comparative experiment are shown in Table 1. It can be seen that the prediction effect of the model of the present invention is the best, and there is a great improvement compared with the ELM model. The reason may be that the addition of the weight matrix better solves the problem of sample imbalance in the current transformer data set.

[0081] Table 1 Comparison of algorithm performance evaluation indicators

[0082] Description of the Drawings

[0083] Figure 1 The performance evaluation process of the current transformer proposed by the present invention.

[0084] Figure 2 Obtaining the optimal parameters of VMD based on the Grey Wolf Optimization algorithm.

[0085] Figure 3 Matrix construction for combining three-phase current characteristics. Detailed Description of the Invention

[0086] The present invention will be further described in detail below in conjunction with the embodiments.

[0087] Those skilled in the art will understand that the following embodiments are only used to illustrate the present invention and should not be construed as limiting the scope of the present invention. For those not specified in the embodiments, the techniques or conditions described in the literature in the art or according to the product specifications shall be followed. For those materials or equipment without indicating the manufacturer, they are all conventional products that can be obtained by purchase.

[0088] The error prediction method of electromagnetic current transformer based on weighted extreme learning machine includes the following steps:

[0089] Step (1): Collect the amplitude data of the secondary side current signals of the three-phase current transformer every a minutes under the normal operation state to obtain a three-phase current amplitude matrix; at the same time, collect the angular difference and ratio difference of the three-phase current transformer;

[0090] Step (2): For the three-phase current amplitude matrix obtained in step (1), remove the outliers in the matrix data;

[0091] Step (3): Standardize the amplitude data in the three-phase current matrix processed in step (2) to obtain a standardized three-phase current amplitude matrix;

[0092] Step (4): Use the Grey Wolf Optimization algorithm to optimize the parameters of the variational mode decomposition algorithm, and use the optimized variational mode decomposition algorithm to perform variational mode decomposition on the standardized three-phase current amplitude matrix obtained in step (3);

[0093] Step (5): Extract the time-domain characteristic parameters and frequency-domain characteristic parameters from the modal components decomposed in step (4), and splice all the extracted parameters to obtain a three-phase current characteristic matrix with reduced dimensions;

[0094] Step (6): Use the three-phase current characteristic matrix with reduced dimensions obtained in step (5) as the input, and the angular difference and ratio difference as the output to train the extreme learning machine model to obtain a current transformer error detection model;

[0095] Step (7), using the amplitude data of the secondary side current signals of the three-phase current transformers to be detected, obtain the three-phase current amplitude matrix of the three-phase current transformers to be detected; then through steps (2) to (5), obtain the corresponding three-phase current characteristic matrix, and then input it into the current transformer error detection model obtained in step (6) to obtain the predicted angular difference and ratio error of the three-phase current transformers to be detected;

[0096] Step (8), compare the prediction results in step (7) with the error threshold. If both the predicted angular difference and ratio error are less than the threshold, it indicates that the current transformer is in normal operation at this time; otherwise, it is considered that the current transformer may be in abnormal operation at this time.

[0097] In step (1), a = 15;

[0098] The specific method of step (2) is: remove the abnormal values beyond the range according to the maximum and minimum values of the historical normal signal changes, and at the same time remove the non-numerical values;

[0099] After being removed by step (2), each signal needs to retain 900 data points.

[0100] The specific method of step (3) is: perform normalization processing on the data processed by step (2) using the column normalization method.

[0101] In step (4), the specific method of using the grey wolf optimization algorithm to optimize the parameters of the variational mode decomposition algorithm is:

[0102] Step (4.1), initialize the grey wolf algorithm parameters: initialize the basic parameters of the population size, decay coefficient, random vector, and iteration times of the grey wolf algorithm;

[0103] Step (4.2), initialize the grey wolf position: randomly initialize the decomposition layer number k and penalty factor alpha of the variational mode decomposition algorithm as the initial position of the grey wolf algorithm;

[0104] Step (4.3), calculate the fitness of the grey wolf individuals: the fitness function takes the mean of the permutation entropy, and the optimization goal is to minimize the mean of the permutation entropy. Save the three wolves with the best fitness, and define the first three individuals with the smallest fitness values as the alpha wolf, beta wolf, and delta wolf in turn, and their positions are defined as and The rest are uniformly defined as omega wolves;

[0105] Step (4.4), hunt the prey, and realize the prey hunting through the following formula

[0106]

[0107] In the formula, is the position of the updated individual; is the position of the current prey; t is the number of iterations of the current algorithm; is the distance between the current individual and the prey; the position of the current individual; is a cooperation coefficient vector; are both another cooperation coefficient vector;

[0108] Step (4.5), iteratively update the gray wolf individuals, and update the latest positions of the gray wolves according to the following four update formulas:

[0109]

[0110] In the formula, and are the direction and step length of the movement of the ω wolf towards the α wolf, β wolf, and δ wolf; and are the positions of the α wolf, β wolf, and δ wolf; and are the distances between the current individual and the α wolf, β wolf, and δ wolf; recalculate the fitness and update the α wolf, β wolf, and δ wolf;

[0111] Step (4.5), when the number of iterations is reached, output the optimal decomposition layer k and the penalty factor alpha of the VMD algorithm.

[0112] The optimal decomposition layer k is 2.

[0113] In step (5), the time-domain characteristic parameters include the maximum value, minimum value, first moment, second origin moment, and kurtosis factor; the frequency-domain characteristics include the centroid frequency, mean square frequency, frequency variance, and multi-scale permutation entropy;

[0114] Among them,

[0115] The calculation formula for the maximum value is: x max = max(x i ); where x i is the current data of the i-th sampling point;

[0116] The calculation formula for the minimum value is: x min = min(x i );

[0117] The calculation formula for the first moment is: where N is the number of samplings;

[0118] The calculation formula for the second origin moment is:

[0119] The calculation formula for the kurtosis factor is: wherein, is the sampling mean value, and σ is the sampling standard deviation;

[0120] The calculation formula of the center frequency is: P(f) is the spectrum value at the frequency f;

[0121] The calculation formula of the mean square frequency is:

[0122] The calculation formula of the frequency variance is:

[0123] The calculation formula of the multi-scale permutation entropy is:

[0124] For m different numbers, there will be m! possible order patterns π; for the permutation with the number π, f(π) represents its frequency in the time series; then the relative frequency is p(π) = f(π) / (N / τ - m + 1).

[0125] In step (5), the specific splicing method is:

[0126] The dimension-reduced three-phase current feature matrix from top to bottom is the A-phase sample, B-phase sample, and C-phase sample;

[0127] The A-phase sample is sequentially spliced by 24-dimensional features of each of the A, B, and C phases;

[0128] The B-phase sample is sequentially spliced by 24-dimensional features of each of the B, A, and C phases;

[0129] The C-phase sample is sequentially spliced by 24-dimensional features of each of the C, A, and B phases;

[0130] Thus, a 72*3-dimensional three-phase feature matrix is constructed, that is, the dimension-reduced three-phase current feature matrix.

[0131] In the extreme learning machine model, the cost-sensitive weight matrix is embedded in the extreme learning machine objective function, and each weight factor of the newly added weight matrix in the extreme learning machine objective function is constructed in a cost-sensitive manner.

[0132] In step (8), when both the predicted angular difference and ratio difference exceed the corresponding thresholds, determine the working state of the current transformer to guide the operation and maintenance and overhaul work of relevant staff.

[0133] The threshold range of the angular difference is ±10 minutes, and the threshold range of the ratio difference is ±0.2%; when the predicted angular difference or ratio difference exceeds the corresponding threshold, it is determined that the current transformer is in an out-of-tolerance state, and the staff needs to be reminded of maintenance and overhaul.

[0134] Application example

[0135] Error prediction method for electromagnetic current transformer based on weighted extreme learning machine, comprising the following steps:

[0136] (1) The performance evaluation process of the transformer in the present invention is as Figure 1 shown.

[0137] ① Collect the amplitude data of the secondary side current signals of the three-phase current transformer every 15 minutes under normal operating conditions.

[0138] ② Remove abnormal values beyond the range according to the maximum and minimum values of the historical normal signal changes, and at the same time remove non-numerical values;

[0139] After removal, each signal needs to retain 900 data points.

[0140] ③ Standardize the three-phase current amplitude data matrix by using the column normalization method.

[0141] ④ Use the grey wolf optimization algorithm to optimize the parameters of the variational mode decomposition algorithm to obtain the best decomposition effect, and obtain 2 intrinsic mode components;

[0142] Perform variational mode decomposition on the obtained standardized three-phase current amplitude matrix by using the optimized variational mode decomposition algorithm;

[0143] ⑤ Calculate the time-domain characteristic parameters and frequency-domain characteristic parameters extracted from the mode components, obtain a 24-dimensional characteristic vector for each phase of data, and splice all the extracted parameters to obtain a reduced-dimensional three-phase current characteristic matrix;

[0144] ⑥ Use the obtained reduced-dimensional three-phase current characteristic matrix as the input and the angular difference and ratio difference as the output to train the extreme learning machine model to obtain a current transformer error detection model;

[0145] ⑦ Use the amplitude data of the secondary side current signals of the three-phase current transformer to be detected to obtain the three-phase current amplitude matrix of the three-phase current transformer to be detected; then obtain the corresponding three-phase current characteristic matrix through the above steps, and then input it into the obtained current transformer error detection model to obtain the predicted angular difference and ratio difference of the three-phase current transformer to be detected;

[0146] ⑧ Compare the angular difference and ratio difference results predicted by the model with the error threshold. If both the predicted angular difference and ratio difference do not exceed the threshold, it indicates that the current transformer is in normal operation at this time; if it is greater than the threshold, it indicates that the three-phase current transformer is likely to be in abnormal operation at this time.

[0147] If the predicted angular difference or ratio difference is greater than the threshold, determine the working state and fault type of the current transformer to guide the operation and maintenance and repair work of relevant staff.

[0148] For the above process, the specific method of process ④ is as follows: a method for dimensionality reduction of current transformer monitoring data based on VMD (Variational Mode Decomposition).

[0149] In the Grey Wolf Optimization algorithm, the fitness value reflects the quality of each individual in the current solution space. Its value indicates the higher the excellence of the individual solution according to whether the optimization goal is smaller or larger. In the present invention, the selection of the fitness function of the Grey Wolf algorithm is based on the mean of permutation entropy, which is regarded as an objective evaluation criterion for the target problem. When using permutation entropy as the goal of the optimization algorithm, generally, the smaller the better. Permutation entropy is an index used to measure the degree of disorder or randomness of a set of data. A smaller permutation entropy indicates that the arrangement of data is more orderly and regular, while a larger permutation entropy indicates that the arrangement of data is more disorderly and random. Here, the optimization aims to minimize the mean of permutation entropy, that is, to make the data arrangement more orderly and regular.

[0150] The said process ④ includes the following steps

[0151] Step (4.1), initialize the parameters of the Grey Wolf algorithm: initialize the basic parameters of the population size, decay coefficient, random vector, and iteration times of the Grey Wolf algorithm;

[0152] Step (4.2), initialize the position of the Grey Wolf: randomly initialize the decomposition layer number k and penalty factor alpha of the Variational Mode Decomposition algorithm as the initial position of the Grey Wolf algorithm;

[0153] Step (4.3), calculate the fitness of the Grey Wolf individuals: the fitness function takes the mean of permutation entropy, and the optimization goal is to minimize the mean of permutation entropy. Save the three wolves with the best fitness, and define the individuals with the smallest first three fitness values as the α-wolf, β-wolf, and δ-wolf in sequence, and their positions are defined as and The rest are uniformly defined as ω-wolves;

[0154] Step (4.4), hunt the prey, and realize the prey hunting through the following formula

[0155]

[0156] In the formula, is the position of the updated individual; is the position of the current prey; t is the current iteration number of the algorithm; is the distance between the current individual and the prey; the position of the current individual; is a cooperation coefficient vector; are both another cooperation coefficient vector;

[0157] Step (4.5), iteratively update the gray wolf individuals, and update the latest positions of the gray wolves according to the following four update formulas:

[0158]

[0159] In the formula, and are the direction and step length of the movement of the ω wolf towards the α wolf, β wolf, and δ wolf; and are the positions of the α wolf, β wolf, and δ wolf; and are the distances between the current individual and the α wolf, β wolf, and δ wolf; recalculate the fitness and update the α wolf, β wolf, and δ wolf;

[0160] Step (4.5), when the number of iterations is reached, output the optimal decomposition layer k and penalty factor alpha of the VMD algorithm.

[0161] The three-phase current amplitude matrix data of 900 * 3 dimensions every 15 minutes of the current transformer is decomposed into 2-layer sub-modal signals by the variational mode decomposition algorithm of GWO (Grey Wolf Optimization), and the time domain (maximum value x max = max(x i ), minimum value x min = min(x i ), first moment second moment about the origin and kurtosis factor and frequency domain features (centroid frequency mean square frequency frequency variance multiscale permutation entropy) are extracted from each of the 2 modal signals, and 24 feature parameters are obtained. Finally, the 900×3 high-dimensional data set is reduced to a 24×3 low-dimensional data set, completing the data dimensionality reduction.

[0162] Before obtaining the frequency domain features, the time domain waveform of the signal is usually converted into a power spectrum by the Fourier transform of the autocorrelation function, converting the signal from the time domain to the frequency domain to obtain its power spectrum. The formula is as follows: In the formula, x(i) is the sampling value of the current transformer signal. After obtaining the spectrum information, the corresponding statistical features can be calculated according to the statistical index formula.

[0163] In the frequency domain features, the construction method of multiscale permutation entropy includes two steps: First, apply the "coarse-graining" process to the time series. For a given time series {x1, x2,..., x N}, a continuous coarse-grained time series is constructed by averaging continuously increasing data points in non-overlapping windows. Multiple coarse-grained time series Each element of is calculated according to the formula where τ represents the scaling factor, and 1 ≤ j ≤ N / τ. The length of each coarse-grained time series is a component of N / τ.

[0164] Next, calculate the permutation entropy of each coarse-grained time series, and then plot it as a function of the scaling factor τ. To calculate the permutation of the coarse-grained time series y j , first derive a sequence of vectors of length m from the signal samples y j , v m (n) = [y n , y n+1 , …, y (n+m-1 , 1 ≤ n ≤ N / τ - m + 1. Then, v m (n) can be arranged in ascending order: For m different numbers, there will be m! possible order patterns π, also known as permutations. For the permutation with number π, f(π) represents its frequency in the time series. Then the relative frequency is p(π) = f(π) / (N / τ - m + 1). The permutation entropy of the time series is defined as where the maximum value of H(m) is log(m!), which means that the probabilities of all permutations are equal. The minimum value of H(m) is zero, which means that the time series is very regular. In other words, the smaller the value of H(m), the more regular the time series. Here, m for the permutation entropy is selected as 4.

[0165] The accuracy of the ratio error and phase angle error of current transformers is often affected by other phase currents, which stems from the mutual correlation and influence among the phase currents in a three-phase system. The present invention proposes a matrix construction of three-phase current characteristics, constructs the reduced-dimensional sample data according to the original monitoring data. According to the case, the A-phase sample is respectively composed of the time-frequency domain characteristics of 24 dimensions of each of the A, B, and C phases spliced together, the B-phase sample is respectively composed of the time-frequency domain characteristics of 24 dimensions of each of the B, A, and C phases spliced together, and the C-phase sample is respectively composed of the time-frequency domain characteristics of 24 dimensions of each of the C, A, and B phases spliced together. This arrangement constructs a three-phase characteristic matrix of 72 * 3 dimensions. The establishment of this characteristic matrix takes into account the differences in different phase currents, provides more comprehensive and accurate inputs for the ELM model for predicting the current phase angle ratio error, and more comprehensively evaluates the performance of single-phase current transformers.

[0166] For the above process, the specific method of process ⑥ is as follows:

[0167] Given the reduced-dimensional input training set S = {(x i , y i ), i = 1, 2,..., N, y i∈{+,-}}, first traverse all samples in the training set to count the number of positive and negative samples; construct the diagonal weight factor ω of the weight matrix W according to the sample belonging category ii , and its value is the reciprocal of the total number of samples included in the category corresponding to the sample. The rest of the positions in W are 0.

[0168] Substitute the weight matrix into the formula for solving the output weight matrix β.

[0169]

[0170] Among them, H is the output matrix of the hidden layer, C is the regularization coefficient, N is the number of samples, L is the number of hidden layer nodes, and Y is the matrix of true output values;

[0171] For the unknown current transformer monitoring data sample x, the specific error of the current transformer output by the weighted extreme learning machine is calculated by substituting it into the function f(x) = Hβ.

[0172] Compare the weighted extreme learning machine with other prediction algorithms in the field of machine learning, including extreme learning machine (ELM), support vector machine (SVM), random forest (Random Forest), and extreme gradient boosting (XGBoost). The results of the comparison experiment are shown in Table 2. It can be seen that the prediction effect of the model is the best, and there is a great improvement compared with the ELM model. The reason may be that the addition of the weight matrix better solves the problem of sample imbalance in the current transformer data set.

[0173] Table 2 Comparison of algorithm performance evaluation indicators

[0174]

[0175] The present invention proposes to use the variational mode decomposition algorithm based on grey wolf optimization to decompose the monitoring data on the secondary side of the current transformer and extract the corresponding time-frequency domain features, and send the finally extracted time-frequency domain features into the weighted extreme learning machine for ratio error and angle error prediction. The present invention uses grey wolf optimization to select the best VMD decomposition parameters for the monitoring current amplitude data on the secondary side of the current transformer: the decomposition layer number and the penalty factor. Based on these optimized parameters, the original high-dimensional current amplitude data is decomposed and the features of the corresponding sub-signals in the time-frequency domain are extracted, so as to realize the dimensionality reduction of the current transformer monitoring data. The use of the weighted extreme learning machine in the prediction model better solves the problem of data imbalance with fewer abnormal samples in the original sample data, and the extreme learning machine, as a representative of the single-hidden-layer feedforward neural network, has faster training and testing speeds than the backpropagation neural network.

[0176] The foregoing has shown and described the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments, and what is described in the above embodiments and the specification is only to illustrate the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements fall within the scope of the present invention claimed. The scope of the present invention claimed is defined by the appended claims and their equivalents.

Claims

1. An electromagnetic current transformer error prediction method based on a weighted extreme learning machine, characterized in that It includes the following steps: Step (1), collect the amplitude data of the secondary side current signals of the three-phase current transformers every a minutes under the normal operation state to obtain a three-phase current amplitude matrix; at the same time, collect the angular difference and ratio error of the three-phase current transformers; Step (2), for the three-phase current amplitude matrix obtained in Step (1), remove the outliers in the matrix data; Step (3), perform standardization processing on the amplitude data in the three-phase current matrix processed in Step (2) to obtain a standardized three-phase current amplitude matrix; Step (4), use the grey wolf optimization algorithm to optimize the parameters of the variational mode decomposition algorithm, and use the optimized variational mode decomposition algorithm to perform variational mode decomposition on the standardized three-phase current amplitude matrix obtained in Step (3); Step (5), extract the time-domain characteristic parameters and frequency-domain characteristic parameters from the modal components decomposed in Step (4), and splice all the extracted parameters to obtain a reduced-dimensional three-phase current characteristic matrix; Step (6), use the reduced-dimensional three-phase current characteristic matrix obtained in Step (5) as the input, and the angular difference and ratio error as the output to train the extreme learning machine model to obtain a current transformer error detection model; Step (7), use the amplitude data of the secondary side current signals of the three-phase current transformer to be detected to obtain the three-phase current amplitude matrix of the three-phase current transformer to be detected; then through Steps (2) to (5), obtain the corresponding three-phase current characteristic matrix, and then input it into the current transformer error detection model obtained in Step (6) to obtain the predicted angular difference and ratio error of the three-phase current transformer to be detected; Step (8), compare the prediction results in Step (7) with the error threshold. If both the predicted angular difference and ratio error are less than the threshold, it indicates that the current transformer is in the normal operation state at this time; otherwise, it is considered that the current transformer may be in the abnormal operation state at this time; In Step (5), the time-domain characteristic parameters include the maximum value, minimum value, first moment, second origin moment, and kurtosis factor; the frequency-domain characteristics include the center frequency, mean square frequency, frequency variance, and multi-scale permutation entropy; Among them, The calculation formula for the maximum value is: ; where is the current data of the i-th sampling point; The calculation formula for the minimum value is: ; The calculation formula for the first moment is as follows: ; where N is the number of samples; The calculation formula for the second-order origin moment is as follows: ; The calculation formula for the kurtosis factor is as follows: ); where is the sampling mean, is the sampling standard deviation; The calculation formula for the center frequency is as follows: ; is the spectral value at frequency f; The calculation formula for the mean square frequency is as follows: ; The calculation formula for the variance of frequency is as follows: ; The calculation formula of multi-scale permutation entropy is as follows: ; For different numbers, there will be possible order patterns ; for a permutation with a number of , represents its frequency in the time series; then the relative frequency is .

2. The electromagnetic current transformer error prediction method based on a weighted extreme learning machine according to claim 1, wherein in Step (1), a = 15; The specific method of Step (2) is: remove the abnormal values outside the range according to the maximum and minimum values of the historical normal signal changes, and at the same time remove the non-numerical values; Each signal needs to retain 900 data points after being removed in Step (2).

3. The electromagnetic current transformer error prediction method based on a weighted extreme learning machine according to claim 1, characterized in that The specific method of Step (3) is: perform standardization processing on the data processed in Step (2) using the column normalization method.

4. The electromagnetic current transformer error prediction method based on a weighted extreme learning machine according to claim 1, characterized in that In Step (4), the specific method of using the grey wolf optimization algorithm to optimize the parameters of the variational mode decomposition algorithm is: Step (4.1), initialize the grey wolf algorithm parameters: initialize the basic parameters of the population size, decrement coefficient, random vector, and number of iterations of the grey wolf algorithm; Step (4.2), initialize the grey wolf position: randomly initialize the decomposition layer number k and penalty factor alpha of the variational mode decomposition algorithm as the initial position of the grey wolf algorithm; Step (4.3), calculate the fitness of each grey wolf individual: The fitness function is the mean of permutation entropy, and the optimization goal is to minimize the mean of permutation entropy. Keep the three wolves with the best fitness. Define the individuals with the three smallest fitness values as the α-wolf, β-wolf, and δ-wolf in sequence, and their positions are defined as , and , and the rest are uniformly defined as ω-wolves; Step (4.4), hunt the prey, and realize the prey hunting through the following formula In the formula, is the position of the updated individual; is the position of the current prey; t is the iteration number of the current algorithm; is the distance between the current individual and the prey; the position of the current individual; is a collaborative coefficient vector; are both another collaborative coefficient vector; Step (4.5), iteratively update the grey wolf individuals, and update the latest position of the grey wolf according to the following four update formulas: In the formula, , and are the direction and step length of the movement of ω wolf towards α wolf, β wolf and δ wolf; , and are the positions of α wolf, β wolf and δ wolf; , and are the distances between the current individual and α wolf, β wolf and δ wolf; Recalculate the fitness and update α wolf, β wolf and δ wolf; Step (4.5), when the number of iterations is reached, output the optimal decomposition level k and the penalty factor alpha of the VMD algorithm.

5. The electromagnetic current transformer error prediction method based on a weighted extreme learning machine according to claim 4, characterized in that The optimal decomposition level k is 2.

6. The electromagnetic current transformer error prediction method based on the weighted extreme learning machine according to claim 1, characterized in that In step (5), the specific method of splicing is as follows: For the dimension-reduced three-phase current feature matrix, from top to bottom are the A-phase samples, B-phase samples, and C-phase samples; The A-phase samples are sequentially spliced by 24-dimensional features of each of the three phases A, B, and C; The B-phase samples are sequentially spliced by 24-dimensional features of each of the three phases B, A, and C respectively; The C-phase samples are sequentially spliced by 24-dimensional features of each of the three phases C, A, and B respectively; Thus, a 72×3-dimensional three-phase feature matrix is constructed, that is, the dimension-reduced three-phase current feature matrix.

7. The electromagnetic current transformer error prediction method based on the weighted extreme learning machine according to claim 1, characterized in that In the extreme learning machine model, the cost-sensitive weight matrix is embedded into the extreme learning machine objective function, and each weight factor of the newly added weight matrix in the extreme learning machine objective function is constructed in a cost-sensitive manner.

8. The electromagnetic current transformer error prediction method based on a weighted extreme learning machine according to claim 1, characterized in that In step (8), if the predicted angular difference or ratio difference exceeds the corresponding threshold, determine the working state of the current transformer to guide the operation and maintenance and overhaul work of relevant staff.

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