A method for locating broadband oscillation disturbance sources based on compressed sensing and graph convolutional neural networks
By combining compressed sensing and graph convolutional neural networks, the problem of accurate localization of broadband oscillation disturbance sources in power systems has been solved. This has enabled precise localization and efficient reconstruction of broadband oscillation sources, adapting to various operating conditions and improving localization accuracy.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SICHUAN UNIV
- Filing Date
- 2022-11-25
- Publication Date
- 2026-05-26
Smart Images
Figure CN115912349B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of electrical technology, and in particular to a method for locating broadband oscillation disturbance sources based on compressed sensing and graph convolutional neural networks. Background Technology
[0002] The rapid development of large-scale new energy power generation, high-voltage direct current (HVDC) transmission, and high-power DC loads is driving the power system towards a "dual-high" trend of high-proportion new energy power generation and high-proportion power electronic equipment. However, broadband oscillations caused by the interaction between power electronic equipment and the power grid have become a significant issue affecting the safe and stable operation of the power grid. Therefore, locating the disturbance source of broadband oscillations in the power system, ranging from several hertz to hundreds of hertz, is a major challenge in this field. Currently, wide-area measurement systems (WAMS) based on synchronous phasor measurement units (PMUs) are widely used in the real-time monitoring of low-frequency oscillations. Existing methods utilize synchronous phasor data to establish calculation formulas for the energy flow of low-frequency oscillations in the network, achieving oscillation source location; further methods use measured data from WAMS to analyze the phase relationship of generator electromagnetic power fluctuations to achieve rapid and accurate location of low-frequency oscillation sources. Regarding the location of subsynchronous / supersynchronous broadband oscillations, current research utilizes the relationship between transient energy flow and subsynchronous / supersynchronous power, and establishes its connection with damping, to conduct preliminary research on locating subsynchronous forced oscillations using transient energy flow. The above methods are all based on physical models to locate the oscillation source. However, since broadband oscillations in power systems are complex system problems caused by the interaction of multiple types of equipment and multiple time scales, their precise parameters are difficult to obtain, electromagnetic transient equivalent models are difficult to construct, and they have significant randomness and strong nonlinearity. Therefore, existing methods are difficult to comprehensively analyze broadband oscillation problems in actual systems.
[0003] Artificial intelligence (AI) offers new solutions to the broadband oscillation problem in power systems due to its superior performance, including low dependence on system models, powerful learning ability for complex nonlinear relationships between large amounts of data, and rapid adaptability to stochastic and time-varying environments. Currently, AI employs a combination of autoencoder signal compression and Long Short-Term Memory (LSTM) networks to locate broadband oscillation sources. Encoding and compressing power system measurement signals using autoencoders, and then inputting the compressed data into an LSTM network to locate subsynchronous oscillation sources, requires improvements to existing PMU devices. Furthermore, the electrical signals compressed by the autoencoder lack interpretability. Broadband oscillations exhibit significant spatiotemporal distribution characteristics, with interconnected nodes in the system. While LSTM neural networks analyze the relationships between multiple time-series data, the exchange of oscillation energy between different devices cannot be instantaneous but requires a time lag, exhibiting spatial characteristics. Therefore, this method neglects the power grid topology, which significantly influences oscillation propagation and dynamic characteristics. Summary of the Invention
[0004] To address the aforementioned shortcomings of existing broadband oscillation disturbance source localization methods, this invention provides a broadband oscillation disturbance source localization method based on compressed sensing and graph convolutional neural networks.
[0005] The broadband oscillation disturbance source localization method based on compressed sensing and graph convolutional neural network provided by this invention mainly includes two stages: offline training and online localization.
[0006] The offline training process includes the following steps:
[0007] (1) Using the measurement data of the actual system or based on the simulation of the example, the electrical quantities in the subsynchronous / supersynchronous broadband oscillation mode are obtained. The electrical quantities include line current, node voltage, active power, etc., forming a graph data sample. The sample is labeled according to the unit number in which the oscillation occurs, and the broadband oscillation offline sample library is constructed.
[0008] (2) Compressed sensing technology is used to encode and compress various electrical quantities in the offline sample library to obtain the feature vectors of each node of each image, forming a feature matrix.
[0009] (3) Input the feature matrix and adjacency matrix of each image and the corresponding label of each image into the constructed graph convolutional neural network (GCN) localization model for training and learning, dynamically adjust the network structure and hyperparameters until the test set reaches the target localization accuracy, and obtain and save the broadband oscillation localization model.
[0010] The online positioning process includes the following steps:
[0011] (1) When the power system experiences broadband oscillation, the substation collects electrical quantity data and uses compressed sensing technology to compress and encode the collected electrical quantities.
[0012] (2) Upload the data of each substation to the main station through the data communication network; input the feature matrix and system adjacency matrix into the trained GCN localization model at the main station, and output the oscillation source location.
[0013] The compressed sensing technology includes the selection of sampling matrix, sparse transformation basis, and reconstruction algorithm.
[0014] The sampling matrix is a Gaussian matrix with dimensions M×N for the matrix Φ. Each element in the matrix follows a mean of 0 and a variance of . It follows a Gaussian normal distribution.
[0015] The sparse transform basis is the discrete cosine transform. For an N-dimensional signal x, its discrete cosine transform is expressed as:
[0016]
[0017] In the formula, k = 1, 2, ..., N-1.
[0018] The reconstruction algorithm employs an orthogonal matching pursuit algorithm, which uses a greedy approach to select a local optimum in each iteration to gradually approximate the original signal. The compressed sensing reconstruction effect is measured using the L2 norm of the difference phasor, and its expression is:
[0019]
[0020] In the formula, It is an N×1 dimensional reconstructed signal.
[0021] The structure of the Graph Convolutional Neural Network (GCN) includes a Graph Conv layer. The network input is graph structured data (X, A), where X is the information matrix composed of the features of each node, and A is the adjacency matrix of the graph. The output feature extraction rule for each Graph Conv layer is expressed as follows:
[0022]
[0023]
[0024] In the formula, D is the degree matrix of the graph, and the matrix... W is obtained by adding the adjacency matrix A to the identity matrix I; (l) Let H( be the parameter matrix) l ) represents the characteristics of each node in the adjacency matrix A; i and j represent the index numbers of the degree matrix, and n is the number of nodes.
[0025] Compared with the prior art, the advantages of the present invention are:
[0026] (1) This invention utilizes compressed sensing theory to compress and sample broadband oscillation data at the substation. The compressed electrical quantities have actual physical meaning and reduce data redundancy. The broadband oscillation signal is compressed and sampled by compressed sensing, which breaks through the limitation of the sampling theorem and can meet the data transmission under the existing bandwidth. At the same time, the master station can also accurately reconstruct the signal using the OMP algorithm based on the compressed signal.
[0027] (2) The main station can directly integrate the spatiotemporal information of oscillations based on the uploaded compressed data and system topology, and use graph convolutional neural networks to locate broadband oscillation disturbance sources. This eliminates the need to rely on system mathematical models and make assumptions and simplifications about the system, and has better adaptability to broadband oscillations under various operating conditions. GCN utilizes the topology and integrates the spatiotemporal characteristics of power system oscillations, and can deeply explore the mapping relationship between the oscillation source location and electrical quantities, thereby achieving more accurate oscillation source location.
[0028] (3) Considering the noise in the raw data collected by the PMU, the positioning accuracy of the substation PMU when data is lost or incorrect during data upload to the main station, this method still has good reconstruction effect and high positioning accuracy.
[0029] Other advantages, objectives and features of the present invention will become apparent in part from the following description, and in part from those skilled in the art through study and practice of the invention. Attached Figure Description
[0030] Figure 1 Flowchart of the algorithm for oscillation source localization based on compressed sensing and graph convolutional neural network.
[0031] Figure 2 A framework diagram of a broadband oscillation localization method based on compressed sensing and graph convolutional neural networks.
[0032] Figure 3 A schematic diagram of the GCN model.
[0033] Figure 4 Comparison chart of compressed sensing reconstruction effects.
[0034] Figure 5 Comparison chart of localization performance of different algorithms.
[0035] Figure 6 Data missing location performance graph.
[0036] Figure 7 Performance chart for locating data errors. Detailed Implementation
[0037] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.
[0038] like Figure 1 and 2 As shown, the broadband oscillation disturbance source localization method based on compressed sensing and graph convolutional neural network provided by the present invention includes two stages: offline training and online localization.
[0039] The offline training process includes the following steps:
[0040] (1) Using the measurement data of the actual system or based on the simulation of the example, the electrical quantities in the broadband oscillation mode such as subsynchronous / supersynchronous are obtained. The electrical quantities include line current, node voltage, active power, etc., forming a graph data sample. The sample is labeled according to the unit number in which the oscillation occurs, and the broadband oscillation offline sample library is constructed.
[0041] (2) Compressed sensing technology is used to encode and compress various electrical quantities in the offline sample library to obtain the feature vectors of each node of each image, forming a feature matrix, and finally obtaining the training set and test set.
[0042] (3) Input the feature matrix and adjacency matrix of each image in the training set and the corresponding label of each image into the constructed graph convolutional neural network (GCN) localization model for training and learning, dynamically adjust the network structure and hyperparameters until the test set reaches the target localization accuracy, and obtain and save the broadband oscillation localization model.
[0043] The online positioning process includes the following steps:
[0044] (1) When the power system experiences broadband oscillation, the substation collects electrical quantity data and uses compressed sensing technology to compress and encode the collected electrical quantities.
[0045] (2) Upload the data of each substation to the main station through the data communication network; input the feature matrix and system adjacency matrix into the trained GCN localization model at the main station, and output the oscillation source location.
[0046] The principle of compressed sensing technology used in the above method is as follows:
[0047] Compressed sensing theory shows that if a signal is sparse in a certain domain, it can be accurately reconstructed from a small amount of measurement data through a nonlinear recovery process using far fewer sampling points than required by the Shannon sampling theorem. For an N×1 signal x, the acquisition of the measurement value y can be expressed as:
[0048] y=Φx (1)
[0049] In the formula, Φ is called the sampling matrix, with dimensions M×N; y has dimensions N×1. The basic requirement for accurately reconstructing the original signal x from the measured value y is that x is sparse. However, since x itself does not possess sparsity, if it is sparse in a certain transform domain:
[0050] x=ΨS (2)
[0051] In the formula, Ψ is called the sparse basis matrix with dimension N×N, and S represents the projection of the signal x onto the sparse domain, called the sparse domain coefficients, with dimension N×1. If S has only K (K << N) non-zero elements, then S is K-sparse. In this case, the observation model of CS can be expressed as:
[0052] y=ΦΨS=ΘS (3)
[0053] Since y, Φ, and Ψ are all known, the problem is transformed into solving for S, and then x can be solved by equation (2), thus realizing the reconstruction of the signal.
[0054] Since M << N in general, equation (3) is underdetermined and has no definite solution, making it difficult to solve. However, since S is sparse, the problem can be transformed into the following sparse recovery problem:
[0055] min||s||0, sty=ΦΨx (4)
[0056] If Φ in the above equation satisfies the Finite Isometry Property (RIP), then the K coefficients can yield an optimal solution from the M measurements. The RIP condition can be stated as: if there exists one δ k ∈(0,1) such that for all vectors x, ||x||0<K, the following condition is met:
[0057]
[0058] Compressed sensing of broadband oscillating signals mainly involves the selection of sampling matrix, sparse transform basis, and reconstruction algorithm.
[0059] This invention selects the Discrete Cosine Transform (DCT) as the sparse transform basis for compressed sensing. The DCT is a discrete leaf transform that limits the input signal. While a broadband oscillating signal may result in a complex number after the Discrete Fourier Transform (DFT), the DCT only returns the real part, thus better removing data redundancy and achieving better reconstruction results. For an N-dimensional signal x, its DCT is expressed as:
[0060]
[0061] In the formula, k = 1, 2, ..., N-1.
[0062] The sampling matrix is typically designed as a random matrix, such as a Gaussian matrix or a Bernoulli matrix. Such a sampling matrix has a very high probability of satisfying the finite isometry property. This invention selects a Gaussian matrix as the sampling matrix, with the matrix Φ having dimensions of M×N. Within the matrix, each element follows a mean of 0 and a variance of... It follows a Gaussian normal distribution.
[0063] This invention selects the Orthogonal Matching Pursuit (OMP) algorithm from the greedy algorithm family to reconstruct the original signal. Its principle is to use a greedy approach, selecting a locally optimal solution in each iteration to gradually approximate the original signal. The compressed sensing reconstruction effect is measured using the L2 norm of the difference phasor, and its expression is:
[0064]
[0065] in It is an N×1 dimensional reconstructed signal.
[0066] The principle of the graph convolutional neural network used in this invention is as follows:
[0067] Graph Convolutional Neural Networks (GCNs) are an extension of convolutional neural networks in non-Euclidean space, processing graph data. Graph data G can be represented by an ordered set of pairs (V, E). Here, V is called the vertex set, representing each node, and E is called the edge set, describing the connections between the nodes.
[0068] Figure 3 The general structure of a graph convolutional neural network is described. Graph Conv is the graph convolutional layer, and the network input is graph structured data (X, A), where X is the information matrix composed of the features of each node, and A is the adjacency matrix of the graph, and its expression is as follows:
[0069]
[0070] The output of each GraphConv layer can be represented as:
[0071] H (l+1) =f(H (l) (A), i = 0, 1, ..., L
[0072] In the formula, f is a nonlinear function, and L is the number of hidden layers. When l equals 0, H equals the input X; when l equals L, H equals the output Y.
[0073] The input to each GraphConv layer is the adjacency matrix A and the features H of each node. (l) Multiply the adjacency matrix and node features, and then use the trainable parameter matrix W. (l) By performing a linear transformation and finally applying an activation function σ, we obtain the expression for the nonlinear function f of each layer:
[0074] f(H (l) ,A)=σ(AH (l) W (l) )
[0075] Since nodes in a topological graph do not have self-connections, the adjacency matrix A has values of 0 on its diagonal. When multiplied by the feature matrix H, only the weighted sum of the features of all the nodes' neighbors is calculated, ignoring the node's own features. To solve this problem, the adjacency matrix A can be added to the identity matrix I, resulting in a matrix... This is equivalent to adding a self-join to each node. It is expressed as follows:
[0076]
[0077] Furthermore, the adjacency matrix A was not normalized, which may be detrimental to network representation after passing through multiple layers. Therefore, the following expression is used for normalization:
[0078]
[0079] In the formula, D is the degree matrix of the graph, which is a diagonal matrix. Numerically, it is equal to the sum of the corresponding rows or columns of the node in the adjacency matrix A, and its expression is as follows:
[0080]
[0081] Therefore, the feature extraction rule for a GCN network layer can be expressed as:
[0082]
[0083] The effectiveness analysis and comparison of this method are as follows:
[0084] (1) Construct an auto-encoder (AE) model consisting of a fully connected network and compare it with compressed sensing in terms of reconstruction error and reconstruction time. Figure 4 The original oscillation waveforms and reconstructed waveforms at various frequency bands are shown. It can be seen that the CS reconstructed waveform fits the original curve better than the AE waveform, indicating that the oscillation signal features extracted by compressed sensing are more representative of the original signal.
[0085] (2) To demonstrate the accuracy of the GCN-based oscillation source localization method, its localization performance was compared with that of convolutional neural networks (CNN), temporal convolutional networks (TCN), and feedforward neural networks (FNN). Multiple experiments were conducted using a trial-and-error method. Figure 5 As can be seen from Table 1, GCN outperforms other methods in both the localization accuracy of each oscillation source and the overall localization accuracy, and the accuracy gradually decreases from GCN to FNN; TCN takes the longest network training time, while FNN takes the shortest.
[0086] Table 1. Training time for different methods
[0087]
[0088] (3) Considering the noise in the raw data collected by the PMU, and the positioning accuracy of the substation PMU in cases of data loss or error during data transmission to the main station, such as... Figure 6 and Figure 7As shown, the calculation results prove that the method of the present invention still has good reconstruction effect and high positioning accuracy.
[0089] In summary, the broadband oscillation disturbance source localization method of the present invention utilizes compressed sensing theory to compress and sample broadband oscillation data at the substation. The compressed electrical quantities have actual physical meaning, while reducing data redundancy. The master station can directly integrate the spatiotemporal information of the oscillation based on the uploaded compressed data and system topology, and use graph convolutional neural networks to locate the broadband oscillation disturbance source. This method overcomes the shortcomings of relying on system mathematical models and requiring assumptions and simplifications about the system, and has good adaptability to broadband oscillations under various operating conditions.
[0090] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.
Claims
1. A method for locating broadband oscillation disturbance sources based on compressed sensing and graph convolutional neural networks, characterized in that, It includes two stages: offline training and online localization; The offline training process includes the following steps: (1) Using the measurement data of the actual system or based on the simulation of the example, the electrical quantities in the sub / supersynchronous broadband oscillation mode are obtained, and the graph data samples are formed. The samples are labeled according to the unit number in which the oscillation occurs, and the construction of the broadband oscillation offline sample library is completed. (2) Compressed sensing technology is used to encode and compress various electrical quantities in the offline sample library to obtain the feature vectors of each node of each image, forming a feature matrix, and thus obtaining the training set and the test set. (3) Input the feature matrix and adjacency matrix of each image in the training set and the corresponding label of each image into the constructed graph convolutional neural network (GCN) localization model for training and learning, dynamically adjust the network structure and hyperparameters until the test set reaches the target localization accuracy, and obtain and save the broadband oscillation localization model. The online positioning process includes the following steps: (1) When the power system experiences broadband oscillation, the substation collects electrical quantity data and uses compressed sensing technology to compress and encode the collected electrical quantities; (2) Upload the data of each substation to the main station through the data communication network; input the feature matrix and system adjacency matrix into the trained GCN localization model at the main station, and output the oscillation source location.
2. The broadband oscillation disturbance source localization method based on compressed sensing and graph convolutional neural networks as described in claim 1, characterized in that, The electrical quantities include line current, node voltage, and active power.
3. The broadband oscillation disturbance source localization method based on compressed sensing and graph convolutional neural networks as described in claim 1, characterized in that, The compressed sensing technology includes the selection of sampling matrix, sparse transformation basis, and reconstruction algorithm.
4. The broadband oscillation disturbance source localization method based on compressed sensing and graph convolutional neural networks as described in claim 3, characterized in that, The sampling matrix is a Gaussian matrix with dimensions M×N for the matrix Φ. Each element in the matrix follows a mean of 0 and a variance of . It follows a Gaussian normal distribution.
5. The broadband oscillation disturbance source localization method based on compressed sensing and graph convolutional neural networks as described in claim 3, characterized in that, The sparse transform basis is the discrete cosine transform. For an N-dimensional signal x, its discrete cosine transform is expressed as: In the formula, k = 1, 2, ..., N-1.
6. The broadband oscillation disturbance source localization method based on compressed sensing and graph convolutional neural networks as described in claim 3, characterized in that, The reconstruction algorithm employs an orthogonal matching pursuit algorithm, which uses a greedy approach to select a local optimum in each iteration to gradually approximate the original signal. The compressed sensing reconstruction effect is measured using the L2 norm of the difference phasor, and its expression is: In the formula, It is an N×1 dimensional reconstructed signal.
7. The broadband oscillation disturbance source localization method based on compressed sensing and graph convolutional neural networks as described in claim 1, characterized in that, The structure of the Graph Convolutional Neural Network (GCN) includes a Graph Conv layer. The network input is graph structured data (X, A), where X is the information matrix composed of the features of each node, and A is the adjacency matrix of the graph. The output feature extraction rule for each Graph Conv layer is expressed as follows: In the formula, D is the degree matrix of the graph, and the matrix... W is obtained by adding the adjacency matrix A to the identity matrix I; (l) H is a parameter matrix. (l) These are the characteristics of each node in the adjacency matrix A; i and j represent the index numbers of the degree matrix, and n is the number of nodes.