A Harmonic Source Location Method Based on Improved Extreme Learning Machine

Abstract

The present invention provides a harmonic source localization method based on an improved extreme learning machine, comprising the following steps: (1) Using the reconstructed feature set as the input, based on the improved extreme learning machine, a multi-label classification model is established to achieve harmonic source localization. (2) The sufficient statistic of the monitoring data is used to mine the harmonic information during the measurement period, and at the same time, the label-specific feature learning algorithm is used to reconstruct the feature set; (3) Based on the adjacency matrix and sensitivity analysis, the optimal configuration of the measurement points is realized, and the reconstructed feature set is used as the input of the multi-label classification model to achieve harmonic source localization.

Description

Technical Field

[0001] The invention relates to the technical field of harmonic source positioning, in particular to a harmonic source positioning method based on an improved extreme learning machine. Background Art

[0002] With the large-scale grid connection of power electronic equipment, the harmonic pollution problem in the power system has become more and more serious. Harmonic source location can identify the source of harmonic pollution and divide the harmonic responsibility, which helps to improve the power supply reliability and operation economy of the power system.

[0003] Synchronous phasor monitoring devices are expensive and cannot be deployed in large numbers in power grids. Power quality monitoring devices (PQMDs) are low-cost and are therefore widely used in existing harmonic monitoring systems. Power quality monitoring devices generally count the average, maximum, minimum and 95% probability maximum values of monitoring data every 3 or 5 minutes. The statistical monitoring data recorded is in a unified format and has high measurement accuracy. Although this type of harmonic monitoring data can provide strong data support for harmonic source location, it cannot meet the synchronization requirements. In addition, the deployment of power quality monitoring devices is also difficult to meet observability requirements. To address this problem, this paper uses the sufficient statistics of the state quantity amplitude as a feature, converts the harmonic source location problem into a multi-label classification problem, and proposes a harmonic source location method based on an improved extreme learning machine. This method is based on existing statistical harmonic monitoring data and can achieve accurate positioning of harmonic sources without the need to deploy special monitoring equipment.

[0004] Traditional harmonic source location methods based on harmonic state estimation require the use of special equipment to synchronously measure harmonic voltages and branch harmonic currents. However, the current harmonic monitoring system usually provides harmonic statistics within the monitoring period, so the engineering application of traditional methods is limited. In addition, harmonic state estimation methods require that the measurement points meet the observability requirements of the entire network. When the observability requirements are not met, the underdetermined harmonic state estimation model has multiple solutions. In addition, the above methods are easily affected by factors such as the measurement point location, measurement noise, and asynchronous measurement of the measurement points, resulting in positioning failure. Summary of the invention

[0005] In view of this, the purpose of the present invention is to provide a harmonic source positioning method based on an improved extreme learning machine based on the existing statistical harmonic monitoring data, taking the sufficient statistics of the monitoring quantity as the original input feature of the positioning model, and at the same time using the label specific features to reconstruct the feature set to mine the harmonic information of the measurement period and avoid the influence of data asynchrony on the positioning accuracy, and ensure the strong correlation and discriminability between the features in the reconstructed feature set and the labels, and use the reconstructed feature set as the input feature of the extreme learning machine, and use the extreme learning machine to establish a multi-label classification model to achieve harmonic source positioning.

[0006] To achieve the above object, the present invention adopts the following technical solutions: A harmonic source localization method based on an improved extreme learning machine, comprising the following steps:

[0007] (1) Based on the improved extreme learning machine, establish a multi-label classification model to achieve harmonic source localization;

[0008] (2) Use the sufficient statistic of the monitoring data to mine the harmonic information of the measurement period, and at the same time use the label-specific feature learning algorithm to reconstruct the feature set;

[0009] (3) Based on the adjacency matrix and sensitivity analysis, realize the optimal configuration of the measurement points, use the reconstructed feature set as the input of the multi-label classification model, and achieve harmonic source localization.

[0010] In a preferred embodiment, the multi-label model based on the extreme learning machine is specifically:

[0011] Whether there is a harmonic source at each node is represented as a binary label variable, taking 1 when there is a harmonic source, and 0 otherwise, so as to generate a label vector y = [y1,..., y l , where l is the number of nodes, called the multi-class label vector; multi-label learning trains a multi-label classification model through samples, and then outputs the class labels of the samples to be discriminated; the expression of the multi-label classification model is as follows;

[0012] y = F(x) (1)

[0013] In the formula: y = {y1, y2,..., y l} is a set of l-dimensional class labels, that is, the harmonic source distribution vector; x is the input variable of the model, and its dimension is p; the input of the training set is represented as a matrix The output is represented as a matrix Y = (Y1, Y2,.., Y n ) T ∈{0, 1} n×l , where n is the number of samples; taking the i-th sample (X i , Y i ) as an example, where X i = (x i1 , x i2 ,.., x ip ); Y i = (y i1 , y i2 ,.., y il ) is a binary label vector. If X i belongs to the j-th label, then y ij = 1, otherwise y ij = 0;

[0014] By separately determining the label values of each dimension, the multi-label problem is converted into one or more independent binary classification sub-problems, and each binary classification model is expressed as Equation (2);

[0015] y j = F(x) j = 1,..., l (2)

[0016] Assume that the extreme learning machine model has K hidden layers, and its activation function is g k (x), then the extreme learning machine network model is expressed as:

[0017]

[0018] In the formula: y j represents the j-th label, that is, the network output value; β jk represents the weight vector between the output vector and the k-th hidden layer; a jk is the weight connecting the nodes of the k-th hidden layer and the input nodes; b jk is the bias of the k-th hidden layer; g k (a jk x + b jk ) is the activation function of the k-th hidden layer;

[0019] Equation (3) is expressed in the matrix form as shown in Equation (4);

[0020]

[0021] In the formula: represents the j-th column of matrix Y; H(X) is the output matrix of the hidden layer; the extreme learning machine searches for the optimal weight β j to minimize the error function, which is expressed as the following optimization problem;

[0022]

[0023] Derive and obtain the solution formula using ridge regression;

[0024]

[0025] In the formula: ρ is the ridge coefficient; after obtaining the parameter ; given the test data X test , predict the label Y according to Equation (7) test ;

[0026]

[0027] In a preferred embodiment, the selection of the input features of the multi-label classification model is specifically:

[0028] Select the h - th order node harmonic voltage U h and the h - th order branch harmonic current I h The maximum, minimum and average values are used as data sources, calculate the sufficient statistics of this data source and use them as model input features; assume that each state quantity satisfies a normal distribution, and the sufficient statistics of the state quantity X are shown in Equation (8);

[0029]

[0030] For the node harmonic voltage U h and branch harmonic current I h monitored at the measurement point, calculate the corresponding sufficient statistics T1(U h ), T2(U h ), T1(I h ) and T2(I h ) respectively according to Equation (9), and use them as input features of the ELM model;

[0031] y j = F(T1(U h ), T2(U h ), T1(I h ), T2(I h )) j = 1,..., l (9)

[0032] Use the label - specific feature learning algorithm to reconstruct the sample feature set. This method can extract label - specific features from the original feature set based on the attributes of label - specific features;

[0033] The optimization problem of LLSF is expressed as the formula:

[0034]

[0035] In the formula: is the matrix formed by the element (1 - c ij ); Tr(·) represents the trace operation of the matrix; ||·|| F represents the F - norm operation of the matrix;

[0036] If W ij = 0, it indicates that there is no correlation between the i - th original feature and the j - th class label; each non - zero element in W j corresponds to a feature that is correlated with the j - th label y j ; Therefore, these features are regarded as label - specific features of the label y j , and their number is much less than p;

[0037] Define f(W) and x(W) as follows, that is, F(W)= f(W)+ x(W):

[0038]

[0039] ξ(W) = η||W||1 (12)

[0040] Introduce the accelerated proximal gradient method to minimize the function after the second-order approximation of F(W) at M (t) as expressed in Equation (13);

[0041]

[0042] where: L f is the Lipschitz constant, and the calculation formula of L f is

[0043]

[0044] M (t) has an iterative formula as shown in (15);

[0045]

[0046] where the substitution formula of λ is as follows;

[0047]

[0048] Let then there is Equation (17);

[0049]

[0050] Equation (17) is equivalent to Equation (18);

[0051]

[0052] where: S ε (·) is the soft threshold operator, and its definition is as shown in Equation (19);

[0053]

[0054] The LLSF model needs to preset two initial values of the model parameters; let λ0 = λ1 = 1; use the least squares method to set the initial value of W, and let W (0) = W (1) = (X T X) -1 X T Y;

[0055] After obtaining the calculated value of W, extract the label feature set according to the values of the W elements and use it as the input feature of the harmonic source location model.

[0056] In a preferred embodiment, the harmonic source location based on the extreme learning machine is specifically as follows:

[0057] The specific representation of the adjacency matrix A of the system is as follows:

[0058]

[0059] where the element a in the matrix ij takes the value as shown in Equation (21);

[0060]

[0061] Taking the h - th harmonic and node m as an example, when the h - th harmonic current I d,h is injected at node d, the influence factor δ m,h on the harmonic voltage U md,h of the node is as shown in Equation (22);

[0062]

[0063] In the formula: Z md,h is the h - th harmonic transfer impedance between node d and m;

[0064] Taking the h - th branch harmonic current I mj,h flowing from node m to node j as an example, the influence factor δ d,h of I mj,h on I mj,d,h is as shown in Equation (23);

[0065]

[0066] In the formula: z mj,h is the h - th harmonic impedance of the m - j branch, and Y tg,mj,h is the equivalent parameter of the h - th line admittance in the line Π - type equivalent circuit;

[0067] If the measurement point is located at node m, the branch harmonic current related to node m and the harmonic voltage of node m can be measured. The total sensitivity factor E m of node m is as shown in Equation (24);

[0068]

[0069] Calculate the total sensitivity factor E of each node according to Equation (24), and select the node with the largest E as the primary selected node;

[0070] When one end of the short line is selected as the measurement point, the harmonic current of this branch does not need to be considered when calculating the total sensitivity factor of the other end node; after selecting the primary selected node, update the adjacency matrix A. Let the initial node be m, and let a mj= 0, where j = 1,…,N; on this basis, if the line between nodes m and j is short, let a jm = 0, where j = 1, ..., N; then, the total sensitivity factor E of all nodes except the initially selected node is recalculated according to formula (24), and the node with the largest E is selected as the access position of the next measuring point; the above process is repeated until all measuring devices are configured;

[0071] The proposed harmonic source location method requires sufficient training samples to learn the mathematical relationship between harmonic source distribution and harmonic state quantity; the training data needs to include the location information of the harmonic source and the corresponding monitoring data of the measuring point, but there is no harmonic source access information in the historical data, so it is necessary to generate the required training samples through digital simulation; the purpose of simulation is not to simulate the real historical harmonic data, but to generate virtual data that can correctly reflect the relationship between the harmonic source, circuit topology and harmonic measurement value, and use the virtual data to train the model, so as to explore the mathematical relationship between the harmonic source distribution and the harmonic state quantity;

[0072] In the process of generating the training set, a threshold is introduced to define the distribution label vector of the harmonic source; when the h-order harmonic current injected into the node is greater than the threshold, it is considered that the node has an h-order harmonic source, and the corresponding element of the label vector is taken as 1, thereby excluding the interference of small harmonic sources during the training process; the threshold h h The definition of is as follows;

[0073]

[0074] Where: I h is the national standard h-order harmonic current limit, I set is the reference current, μ is the set proportional coefficient, which is generally selected in the range of 0.2 to 0.8;

[0075] The number and position of harmonic sources and the harmonic currents injected by them are randomly set to traverse the possible distribution of harmonic sources in the system; training samples with different numbers of harmonic sources are generated, and then multiple training models corresponding to different harmonic orders are generated, so that the training model can locate each harmonic source.

[0076] Compared with the prior art, the present invention has the following beneficial effects: The present invention proposes a new harmonic source localization method. Based on the existing statistical harmonic monitoring data, multi-harmonic source localization can be achieved without deploying dedicated monitoring equipment. First, according to the physical relationship between harmonic state variables and harmonic currents, the optimal configuration of measuring devices is realized based on the adjacency matrix and sensitivity analysis; after obtaining the statistical harmonic monitoring data, the sufficient statistic of the monitored quantity is calculated as the input feature of the localization model to mine the harmonic information during the measurement period and avoid the influence of data asynchrony on the localization accuracy; thereafter, the feature set is reconstructed using the label-specific features to ensure the strong correlation and discriminability between the features in the reconstructed feature set and the label. The reconstructed feature set is used as the input feature of the extreme learning machine, and a multi-label classification model is established using the extreme learning machine to achieve harmonic source localization. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 It is a flowchart of the LLSF algorithm for a preferred embodiment of the present invention;

[0078] Figure 2 It is a flowchart of the configuration of measuring devices for a preferred embodiment of the present invention;

[0079] Figure 3 It is a schematic diagram of the harmonic source localization method based on the improved ELM for a preferred embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0080] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0081] It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present application belongs.

[0082] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application; as used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0083] A harmonic source localization method based on an improved extreme learning machine, refer to Figures 1 to 3 , and includes the following steps:

[0084] (1) Based on the improved extreme learning machine, establish a multi-label classification model to achieve harmonic source localization;

[0085] (2) Utilize the sufficient statistic of the monitoring data to mine the harmonic information in the measurement period, and at the same time, use the label-specific feature learning algorithm to reconstruct the feature set;

[0086] (3) Based on the adjacency matrix and sensitivity analysis, realize the optimal configuration of the measurement points. Take the reconstructed feature set as the input of the multi-label classification model to achieve harmonic source localization.

[0087] The multi-label model based on the extreme learning machine is specifically as follows:

[0088] Represent whether there is a harmonic source at each node as a binary label variable, taking 1 when there is a harmonic source and 0 otherwise, so as to generate the label vector y = [y1,..., y l , where l is the number of nodes, which is called the multi-class label vector in statistics. Multi-label learning trains a multi-label classification model through samples, and then outputs the class labels of the samples to be discriminated. The expression of the multi-label classification model is as follows.

[0089] y = F(x) (1)

[0090] In the formula: y = {y1, y2,..., y l} is the set of l-dimensional class labels, which is the harmonic source distribution vector in this article; x is the input variable of the model, and its dimension is p. The input of the training set is represented as a matrix The output is represented as a matrix Y = (Y1, Y2,.., Y n ) T ∈{0, 1} n×l , where n is the number of samples. Take the i-th sample (X i , Y i ) as an example, where X i = (x i1 , x i2 ,.., x ip ); Y i = (y i1 , y i2 ,.., y il ) is a binary label vector. If X i belongs to the j-th label, then y ij = 1, otherwise y ij = 0.

[0091] By separately discriminating the label values of each dimension, the multi-label problem is converted into one or more independent binary classification sub-problems, and each binary classification model can be expressed as formula (2).

[0092] y j = F(x) j = 1,..., l (2)

[0093] Assume that the extreme learning machine (ELM) model has K hidden layers, and its activation function is g k (x). Then the extreme learning machine network model can be expressed as:

[0094]

[0095] In the formula: y j represents the j-th label, that is, the network output value; β jk represents the weight vector between the output vector and the k-th hidden layer; a jk is the weight connecting the nodes of the k-th hidden layer and the input nodes; b jk is the bias of the k-th hidden layer; g k (a jk x + b jk ) is the activation function of the k-th hidden layer.

[0096] Equation (3) can be expressed in the matrix form as shown in Equation (4).

[0097]

[0098] In the formula: represents the j-th column of the matrix Y; H(X) is the output matrix of the hidden layer. The extreme learning machine searches for the optimal weight β j to minimize the error function, which is expressed as the following optimization problem.

[0099]

[0100] Using ridge regression, the solution formula can be derived.

[0101]

[0102] In the formula: ρ is the ridge coefficient. After obtaining the parameters , given the test data X test , the label Y test can be predicted according to Equation (7).

[0103]

[0104] The specific selection of the input features of the multi-label classification model is as follows:

[0105] Select the maximum value, minimum value, and average value of the h-th node harmonic voltage U h and the h-th branch harmonic current I h as the data source, calculate the sufficient statistics of this data source and use it as the model input feature.

[0106] Assume that each state quantity satisfies a normal distribution, and the sufficient statistic of the state quantity X is shown in Equation (8).

[0107]

[0108] For the node harmonic voltage U monitored by the measuring point h and the branch harmonic current I h , according to Equation (8), calculate the corresponding sufficient statistics T1(U h ), T2(U h ), T1(I h ) and T2(I h ) respectively, and use them as the input features of the ELM model.

[0109] y j = F(T1(U h ), T2(U h ), T1(I h ), T2(I h )) j = 1,..., l (9)

[0110] Use the learning label-specific features (LLSF) algorithm to reconstruct the sample feature set. This method can extract label-specific features from the original feature set based on the attributes of label-specific features.

[0111] The optimization problem of LLSF can be expressed as Equation (10).

[0112]

[0113] In the formula: is the matrix formed by the element (1 - c ij ); Tr(·) represents the trace operation of the matrix; ||·|| F represents the F-norm operation of the matrix.

[0114] If W ij = 0, it indicates that there is no correlation between the i-th original feature and the j-th class label; each non-zero element in W j corresponds to a feature that is correlated with the j-th label y j . Therefore, these features can be regarded as label-specific features of the label y j , and their number is much smaller than p.

[0115] Define f(W) and x(W) as follows, that is, F(W) = f(W) + x(W):

[0116]

[0117] ξ(W) = η||W||1 (12)

[0118] The accelerated proximal gradient method is introduced to minimize the function after the second-order approximation of F(W) at M (t) as shown in Equation (13).

[0119]

[0120] In the formula: L f is the Lipschitz constant, and the calculation formula of L f is

[0121]

[0122] M (t) The iteration formula is as shown in (15).

[0123]

[0124] The substitution formula of λ is as follows.

[0125]

[0126] Let then there is Equation (17).

[0127]

[0128] Equation (17) is equivalent to Equation (18).

[0129]

[0130] In the formula: S ε (·) is the soft threshold operator, and its definition is as shown in Equation (19).

[0131]

[0132] The LLSF model needs to preset two initial values of the model parameters. Let λ0 = λ1 = 1; use the least squares method to set the initial value of W, and let W (0) = W (1) = (X T X) -1 X T Y.

[0133] After obtaining the calculated value of W, the label feature set can be extracted according to the values of the W elements and used as the input features of the harmonic source localization model. The LLSF algorithm is as Figure 2 shown.

[0134] The harmonic source localization based on the extreme learning machine is specifically as follows:

[0135] The specific representation of the adjacency matrix A of the system is as follows:

[0136]

[0137] Where the element a in the matrix ij takes the value as shown in Equation (21).

[0138]

[0139] Taking the h - th harmonic and node m as an example, when the h - th harmonic current I d,h is injected into node d, the influence factor δ m,h on the harmonic voltage U md,h of the node is as shown in Equation (22).

[0140]

[0141] In the formula: Z md,h is the h - th harmonic transfer impedance between node d and m.

[0142] Taking the h - th branch harmonic current I mj,h flowing from node m to node j as an example, the influence factor δ d,h of I mj,h on I mj,d,h is as shown in Equation (23).

[0143]

[0144] In the formula: z mj,h is the h - th harmonic impedance of the m - j branch, and Y tg,mj,h is the equivalent parameter of the h - th line admittance in the Π - type equivalent circuit of the line.

[0145] If the measurement point is located at node m, the branch harmonic current related to node m and the harmonic voltage of node m can be measured. The total sensitivity factor E m of node m is as shown in Equation (24).

[0146]

[0147] Calculate the total sensitivity factor E of each node according to Equation (24), and select the node with the largest E as the primary selected node.

[0148] When one end of the short line is selected as the measurement point, the harmonic current of this branch does not need to be considered when calculating the total sensitivity factor of the other end node. After selecting the primary selected node, update the adjacency matrix A. Let the initial node be m, and set a mj = 0, where j = 1,…,N. On this basis, if there is a short line between nodes m and j, then set a jm= 0, where j = 1, …, N. Thereafter, the total sensitivity factor E of all nodes except the initially selected nodes is recalculated according to Equation (24), and the node with the largest E is selected as the access location of the next measurement point. The above process is repeated until all measuring devices are configured. The harmonic measurement point configuration process is as Figure 2 shown.

[0149] The proposed harmonic source localization method requires sufficient training samples to learn the mathematical relationship between the harmonic source distribution and the harmonic state variables. The training data needs to contain the location information of the harmonic sources and the corresponding monitoring data of the measurement points. Since there is no harmonic source access information in the historical data, it is necessary to generate the required training samples through digital simulation. The purpose of the simulation is not to simulate the real historical harmonic data, but to generate virtual data that can correctly reflect the relationship among the harmonic source, the circuit topology, and the harmonic measurement values, and use this virtual data to train the model, so as to explore the mathematical relationship between the harmonic source distribution and the harmonic state variables.

[0150] A threshold is introduced in the generation process of the training set to define the distribution label vector of the harmonic sources. When the h -th harmonic current injected into a node is greater than the threshold, it is considered that there is an h -th harmonic source at this node, and the corresponding element of the label vector is taken as 1, so as to exclude the interference of small harmonic sources during the training process. The threshold h h is defined as shown in the following formula.

[0151]

[0152] In the formula: I h is the national standard limit value of the h -th harmonic current, I set is the reference current, and μ is the set proportionality coefficient, which is generally selected within the range of 0.2 to 0.8.

[0153] The number, location of the harmonic sources and the harmonic currents injected by them are randomly set to traverse the possible distribution of harmonic sources in the system. Training samples under different numbers of harmonic sources are generated, and then multiple training models corresponding to different harmonic orders are generated, so that the training models can realize the localization of harmonic sources of each order.

[0154] To sum up, first, the optimal configuration of the measurement points is realized according to the measurement point configuration algorithm proposed in this paper; thereafter, based on the measurement point configuration results, training samples are generated by simulation, and the sufficient statistics of each state variable are calculated; according to the corresponding harmonic order, the LLSF algorithm is used to extract the label - specific features and reconstruct the feature set, and the reconstructed feature set is used as the input of the ELM model to train the localization model of this harmonic order; thereafter, the actual harmonic data, that is, the test set, is input into the localization model, and the location of the harmonic source is output. The flow chart of the harmonic source localization method based on the improved extreme learning machine is as Figure 3 shown.

Claims

1. A harmonic source localization method based on an improved extreme learning machine, characterized in that It includes the following steps: (1) Establish a multi-label classification model based on the improved extreme learning machine; (2) Use the sufficient statistics of the monitoring data to mine the harmonic information of the measurement period, and at the same time use the label-specific feature learning algorithm to reconstruct the feature set; (3) Based on the adjacency matrix and sensitivity analysis, realize the optimal configuration of the measurement points, use the reconstructed feature set as the input of the multi-label classification model, and realize the harmonic source localization; Select the h-th order node harmonic voltage U h and the maximum, minimum, and average values of the h-th order branch harmonic current I h as the data source, calculate the sufficient statistic of this data source and use it as the input feature of the model; Assume that each state quantity satisfies the normal distribution, and the sufficient statistics of the state quantity X are shown in Equation (8); For the node harmonic voltage U measured at the measurement point h and the branch harmonic current I h , according to Equation (8), calculate the corresponding sufficient statistics T1(U h ), T2(U h ), T1(I h ) and T2(I h ) respectively, and use them as the input features of the ELM model; y j = F(T1(U h ), T2(U h ), T1(I h ), T2(I h )) j = 1, ..., l (9) Among them, y j represents the j-th label. The LLSF algorithm is used to reconstruct the sample feature set by learning label-specific features. This method can extract label-specific features from the original feature set based on the attributes of label-specific features; The optimization problem of LLSF is expressed as Equation (10); In the formula: is the matrix formed by the element (1 - c ij ); Tr(·) represents the trace operation of the matrix; ||·|| F represents the F-norm operation of the matrix; After obtaining the calculated value of W, the label feature set is extracted according to the values of the elements of W and used as the input feature of the harmonic source localization model.

2. The harmonic source location method based on an improved extreme learning machine according to claim 1, wherein The multi-label model based on the extreme learning machine is specifically: Whether there is a harmonic source at each node is represented as a binary label variable, taking 1 when there is a harmonic source and 0 otherwise, thus generating a label vector y = [y1, …, y l , where l is the number of nodes, called a multi-class label vector; multi-label learning trains a multi-label classification model through samples and then outputs the class labels of the samples to be discriminated; the expression of the multi-label classification model is as follows; y = F(x) (1) where; x is the input variable of the model, and its dimension is p; the input of the training set is represented as a matrix The output is represented as a matrix Y = (Y1, Y2,.., Y n ) T ∈ {0, 1} n×l , where n is the number of samples; for the i-th sample (X i , Y i ), where X i = (x i1 , x i2 ,.., x ip ); Y i = (y i1 , y i2 ,.., y il ) is a binary label vector. If X i belongs to the j-th label, then y ij = 1, otherwise y ij = 0; The multi-label problem is converted into one or more independent binary classification sub-problems by respectively discriminating the label values of each dimension, and each binary classification model is expressed as Equation (2); y j = F(x) j = 1, ..., l (2) Assume that the extreme learning machine model has K hidden layers, and its activation function is g k (x), then the extreme learning machine network model is expressed as: where: y j represents the j-th label, i.e., the network output value; β jk represents the weight vector between the output vector and the k-th hidden layer; a jk is the weight connecting the nodes of the k-th hidden layer and the input nodes; b jk is the bias of the k-th hidden layer; g k (a jk x + b jk ) is the activation function of the k-th hidden layer; Equation (3) is expressed in the matrix form shown in Equation (4); Where: Y j c represents the j-th column of matrix Y; H(X) is the output matrix of the hidden layer; the extreme learning machine searches for the optimal weight β j to minimize the error function, which is expressed as the following optimization problem; Derivation using ridge regression to obtain solution formula; Where: ρ is the ridge coefficient; obtain the parameter After that; given the test data X test , predict the label Y according to Equation (7) test ; 3. A harmonic source localization method based on an improved extreme learning machine according to claim 2, characterized in that, If W ij = 0, it indicates that there is no correlation between the i-th original feature and the j-th class label; for each W j , the features corresponding to the non-zero elements are correlated with the j-th label y j ; Therefore, these features are regarded as the label-specific features of label y j and the number of them is much less than p; ξ(W) = η||W||1 (12) Introduce the accelerated proximal gradient method to minimize the function after the second-order approximation of F(W) at M (t) as shown in Equation (13); where: L f is the Lipschitz constant, L f is calculated by the formula M (t) The iterative formula of is shown in (15); Among them, the iterative formula of λ is as follows; Let Then there is formula (17); Equation (17) is equivalent to Equation (18); Where: S ε (·) is a soft threshold operator, and its definition is shown in Equation (19); The LLSF model requires two initial values of the model parameters to be set in advance; let λ0 = λ1 = 1; use the least squares method to set the initial value of W, and let W (0) = W (1) = (X T X) -1 X T Y.

4. The harmonic source location method based on an improved extreme learning machine according to claim 3, wherein The harmonic source localization based on the extreme learning machine is specifically: The specific representation of the adjacency matrix A of the system is as follows: where the element a in the matrix Nm takes values as shown in Equation (21); When node d injects the h -th harmonic current I d,h the influence factor δ m,h on the harmonic voltage U md,h of the node is as shown in Equation (22); Where: Z md,h is the h-th harmonic transfer impedance between nodes d and m; I d,h The influence factor δ of I mj,h is shown in Equation (23) as follows; mj,d,h as shown in Equation (23); where: z mj,h is the h-th harmonic impedance of the m-j branch, and Y tg,mj,h is the equivalent parameter of the h-th line admittance in the Π-type equivalent circuit of the line; If the measurement point is located at node m, measure the branch harmonic current related to node m and the harmonic voltage of node m. The total sensitivity factor E of node m m is shown in Equation (24); Calculate the total sensitivity factor E of each node according to Equation (24), and select the node with the largest E as the primary selected node; After selecting the node at one end of the short line as the measurement point, the harmonic current of this branch does not need to be considered when calculating the total sensitivity factor of the node at the other end; after selecting the initial node, update the adjacency matrix A. Let the initial node be m, and set a mj = 0, where j = 1, …, N; on this basis, if the line between nodes m and j is a short line, then set a jm = 0, where j = 1, …, N; then recalculate the total sensitivity factor E of all nodes except the initial node according to Equation (24), and select the node with the largest E as the access position of the next measurement point; repeat the above process until all measuring devices are configured; The proposed harmonic source localization method requires sufficient training samples to learn the mathematical relationship between the harmonic source distribution and the harmonic state quantity; the training data needs to include the position information of the harmonic source and the corresponding monitoring data of the measurement points; During the generation of the training set, a threshold is introduced to define the distribution label vector of the harmonic sources; when the h -th harmonic current injected by a node is greater than the threshold, it is considered that there is an h -th harmonic source at this node, and the corresponding element of the label vector is taken as 1, so as to exclude the interference of small harmonic sources during the training process; the threshold η h is defined as shown in the following formula; Where: I h is the national standard h - order harmonic current limit value, I set is the reference current, μ is the set proportionality coefficient, and the proportionality coefficient is selected within the range of 0.2 to 0.8; Randomly set the number, position of the harmonic sources and the injected harmonic currents to traverse the possible distribution of harmonic sources in the system; generate training samples under different numbers of harmonic sources, and then generate multiple training models corresponding to different harmonic orders, so that the training models can realize the localization of each order of harmonic sources.

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