Power system harmonic impedance partitioning method based on Leiden community division algorithm

Abstract

The invention relates to the technical field of power systems, and discloses a power system harmonic impedance partitioning method based on a Leiden community partitioning algorithm, which comprises the following steps: obtaining harmonic impedance data; performing feature extraction on the harmonic impedance data to generate a multi-dimensional feature matrix; outputting harmonic impedance characteristics after dimension reduction; calculating the Euclidean distance between the buses based on the harmonic impedance characteristics after dimension reduction, and constructing a harmonic impedance difference edge weight matrix; combining the power grid topology adjacency matrix and the harmonic impedance difference edge weight matrix, and utilizing a Leiden community division algorithm to carry out clustering partition; and outputting the partition label of each bus to form a power grid harmonic impedance partition result. According to the power system harmonic impedance partitioning method based on the Leiden community partitioning algorithm, a power grid is divided into a plurality of regions with similar dynamic characteristics according to impedance similarity, basic data support is provided for grid-side impedance regulation and oscillation risk management, and cross-band dynamic stability analysis and regional collaborative management are achieved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power systems, and particularly relates to a power system harmonic impedance partitioning method based on a Leiden community partitioning algorithm. BACKGROUND

[0002] With the continuous advancement of the "double carbon" strategy, the penetration rate of new energy in the power system continues to rise. Compared with the traditional power system dominated by synchronous generators, modern power systems are gradually evolving towards high proportions of power electronics. The access of large-scale power electronic equipment, while improving system flexibility and renewable energy consumption capacity, also poses new challenges to the stability of the power system. In particular, the wide frequency oscillation problem caused by the interaction between new energy equipment and the power grid has become an important factor restricting the safe and stable operation of the power system.

[0003] Harmonic impedance can reflect the response characteristics of the system at different frequencies and is one of the important tools for stability analysis of new energy power systems. By analyzing the harmonic impedance frequency spectrum characteristics of the bus, potential resonance risks in the wide frequency band of the system can be effectively identified, and quantitative references for system dynamic stability can be provided. In this context, power grid partitioning technology based on harmonic impedance has gradually gained attention. By analyzing the similarity of harmonic impedance, the power grid can be divided into several regions with similar dynamic characteristics, thereby achieving targeted governance of local oscillation risks. In addition, this type of partitioning technology can also provide technical support for the rational access and location of distributed new energy, reducing the potential risks of power electronic system operation.

[0004] However, traditional power grid partitioning methods are mostly based on network topology, fundamental frequency flow or low frequency impedance, with voltage stability, power angle stability or power transmission safety as the optimization target. This type of method has good applicability in power grids dominated by synchronous machines, but in power electronic systems with high proportions of new energy access, traditional methods are difficult to effectively reveal the wide frequency oscillation characteristics produced by the interaction between power electronic equipment and grid impedance. In particular, for the impedance characteristics of new energy access points and their mutual coupling with grid-side impedance, existing partitioning schemes often fail to achieve fine-grained regional identification and coordinated control. In existing patents and research work, power grid partitioning methods based on harmonic impedance are still limited, mostly focusing on power transmission or filter design fields.

[0005] A power grid partitioning method is disclosed in a Chinese patent (publication date: November 8, 2022, publication number: CN115310242A). The method involves obtaining a topology graph of the actual power grid structure, randomly partitioning the topology graph of the actual power grid structure according to a set total partition number, obtaining a particle swarm, calculating the load loss risk value generated by the particle swarm under extreme conditions when subjected to external attacks, and then using an improved particle swarm algorithm to reduce and stabilize the load loss risk value generated by the particle swarm under extreme conditions when subjected to external attacks. The actual power grid structure is partitioned when the load loss risk value generated by the particle swarm under extreme conditions when subjected to external attacks is reduced and stabilized. This scheme partitions the power grid to improve the limit survival capability of the power grid, reduces the power outage range and load loss when the power grid is subjected to external attacks, and ensures continuous power supply for important users. However, this method focuses on power transmission safety.

[0006] A power grid partitioning method under high proportion of new energy access is disclosed in a Chinese patent (publication date: March 28, 2025, publication number: CN119726693A). The method includes the following steps: step S1: giving an electrical distance index from the perspectives of line flow and line impedance, and constructing an electrical distance matrix; step S2: defining a correction coefficient based on a typical scenario set of new energy output, and correcting the electrical distance matrix to obtain a full-dimensional electrical distance matrix; step S3: based on the electrical distance matrix, using a clustering algorithm to partition the power grid. This method is important for improving the ability of the power grid to cope with new energy output uncertainty and the level of new energy consumption. However, it still focuses on the impact of new energy output uncertainty on the transmission network.

[0007] A Chinese patent (publication date: March 28, 2025, publication number: CN110188386A) discloses an alternating current system harmonic impedance partitioning method, device, equipment and storage medium. The method comprises: determining the maintenance mode of the to-be-maintained equipment according to the basic operation mode of the substation site, the to-be-maintained equipment including lines and transformers arranged between substation sites; scanning the harmonic impedance of the maintenance mode in a set frequency band according to a set step, obtaining the resistance value and reactance value of the harmonic impedance of the power system at each scanning frequency point under each maintenance mode; extracting the harmonic impedance resistance value and reactance value of each maintenance mode at each scanning frequency point under k times harmonic, and combining a preset margin to establish a scatter plot of impedance and reactance; using a preset angle threshold to partition and count the points in the scatter plot of impedance and reactance, and establishing a fan-shaped plot of impedance and reactance. The method can effectively reduce the coverage of harmonic impedance partitioning, provide effective data basis for filter design, and reduce the design difficulty of the filter. However, the method is still limited to fixed frequency band analysis, and lacks deep description of the dynamic characteristics of complex power electronic systems in the full frequency band. SUMMARY

[0008] The purpose of the present application is to overcome the above technical deficiencies, and to provide a power system harmonic impedance partitioning method based on the Leiden community partitioning algorithm. By feature extraction, dimensionality reduction analysis and community partitioning, the power grid is divided into multiple regions with similar dynamic characteristics according to impedance similarity, providing basic data support for grid-side impedance regulation and oscillation risk management, and realizing cross-frequency dynamic stability analysis and regional collaborative management.

[0009] To achieve the above purpose, the power system harmonic impedance partitioning method based on the Leiden community partitioning algorithm comprises the following steps: S1) Obtain harmonic impedance data of each bus in the power grid; S2) Perform feature extraction on the harmonic impedance data to generate a multi-dimensional feature matrix; S3) Perform dimensionality reduction on the multi-dimensional feature matrix using a uniform manifold approximation and projection method, and output the dimensionally reduced harmonic impedance features; S4) Calculate the Euclidean distance between the buses based on the dimensionally reduced harmonic impedance features, and construct a harmonic impedance difference edge weight matrix; S5) Combine the power grid topology adjacency matrix and the harmonic impedance difference edge weight matrix, and use the Leiden community partitioning algorithm for clustering partitioning; S6) Output the partitioning labels of each bus to form the power grid harmonic impedance partitioning result.

[0010] Preferably, in the step S1), the harmonic impedance data of each bus is represented in the form of frequency domain, covering a wide frequency domain of 0-3000 Hz, the obtained harmonic impedance data is represented by amplitude and phase angle, and is subjected to resampling, interpolation, normalization, filtering and outlier rejection processing, and the harmonic impedance data is stored in the form of complex impedance, including real part and imaginary part, the resolution is unified through resampling and interpolation, the consistency of data is enhanced through normalization, filtering and outlier rejection, and the harmonic impedance data is stored in a matrix form for subsequent analysis.

[0011] Preferably, in the step S2), when the feature extraction is performed on the harmonic impedance data, the global feature, the spectral feature, the frequency band feature and the frequency variation feature are obtained after the feature extraction of the harmonic impedance data of each bus, a multi-dimensional feature matrix is formed, the distinguishing feature indexes are extracted from different angles, the multi-scale description of global and local is established, and batch processing, automatic normalization and missing data filling are adopted.

[0012] Preferably, the global feature includes one or more of average impedance modulus, curve smoothness, overall phase angle trend, phase angle standard deviation, energy center frequency, high-frequency phase angle mutation, modulus mutation, phase angle offset, high-frequency trend and system inductance; The spectral feature includes one or more of low-frequency energy ratio, spectral entropy, ultra-low-frequency phase stability, phase inversion energy ratio, modulus-phase angle spectral correlation and joint spectral energy extracted by performing fast Fourier transform on the amplitude and phase angle of the bus harmonic impedance data; The frequency band feature includes one or more of average resistance value, average Q factor and energy integral extracted in each frequency band after the frequency is divided into several frequency bands; The frequency variation feature includes one or more of amplitude and phase angle correlation, resonance peak strength, resonance frequency positioning and phase consistency index obtained by analyzing the dynamic change characteristics of the bus in each frequency band after the frequency is divided into several frequency bands; The multi-dimensional feature matrix is a feature matrix with dimensions , n is the number of buses, d is the number of features of each bus.

[0013] Preferably, the average impedance modulus is wherein, Z( f ) is the complex impedance of the bus at the frequency point f , f min and f max are the lower limit and the upper limit of the scanning frequency range, respectively; Spectrum entropy: wherein, N is the number of frequency points, p i is the normalized power spectrum weight of the i frequency point, z f i is the complex impedance at the frequency point f i z f j is the complex impedance at the frequency point f j , which is used to measure the dispersion degree of the harmonic impedance capability distribution.

[0014] Preferably, the step S3) specifically comprises: S31) feature normalization: receiving a multi-dimensional feature matrix, performing feature normalization, and normalizing the multi-dimensional feature matrix to prevent dimensional difference from affecting similarity; S32) high-dimensional space fuzzy K-neighbor graph construction: using cosine distance to measure the impedance difference between buses, and establishing a K-neighbor graph for each bus point in the high-dimensional space; S33) fuzzy adjacency probability graph construction: using a Gaussian kernel function to convert the adjacency relationship into an adjacency probability form, and generating a symmetric high-dimensional adjacency probability matrix P; S34) low-dimensional space embedding initialization: initializing the low-dimensional embedding coordinates Y of the adjacency probability matrix P by the PCA method; S35) topology preservation optimization: using a cross-entropy loss function to optimize the low-dimensional embedding coordinates Y, generating a low-dimensional adjacency probability matrix Q, and minimizing the difference between the high-dimensional adjacency probability matrix and the low-dimensional adjacency probability matrix Q, so that the low-dimensional embedding maximally reflects the high-dimensional structure; S36) embedding coordinate output: outputting a two-dimensional embedding coordinate matrix.

[0015] Preferably, the two-dimensional embedding coordinate matrix X reduced as follows: wherein n represents the number of buses, and each row represents the embedding position of each bus in the low-dimensional space.

[0016] ​​​Preferably, in the step S5), each element in the harmonic impedance difference edge weight matrix corresponds to the impedance difference degree of two buses in the dimension reduction space, and is mapped by a distance-similarity function to generate a weighted adjacency matrix suitable for graph clustering, and an impedance difference edge weight graph is generated in combination with the power grid topology adjacency matrix, and the Leiden community division algorithm is executed on the basis of the impedance difference edge weight graph to perform clustering partitioning, the Leiden community division algorithm is based on modularity optimization, and can guarantee the local similarity of buses while realizing the optimal division of full partitioning.

[0017] Preferably, the power grid topology adjacency matrix A is a power grid physical topology representation constructed by collecting and analyzing the connection relationship between buses in the power grid. A completely characterizes the node-edge relationship of the power grid, and the power grid topology adjacency matrix A is a symmetric matrix, wherein represents a bus i has a direct connection with a bus j if there is no connection .

[0018] Preferably, in the step S6), when outputting the partition labels of each bus, each bus node after clustering is assigned to a unique area label, and a bus partition label matrix is outputted as the final partition result.

[0019] Compared with the prior art, the present application has the following advantages: 1. By feature extraction, dimension reduction analysis and community division, the power grid is divided into multiple regions with similar dynamic characteristics according to impedance similarity, which provides basic data support for grid-side impedance regulation and oscillation risk management, and realizes dynamic stability analysis and regional collaborative management across frequency bands; 2. By clustering partitioning in the harmonic impedance feature space, basic support is provided for grid-side harmonic impedance regulation and regional collaborative control, the risk of wideband oscillation caused by new energy access is reduced, and a feasible path is provided for subsequent grid-side harmonic impedance optimization scheme, the combination of UMAP (Uniform Manifold Approximation and Projection) + Leiden can realize fast clustering while maintaining nonlinear characteristics, and is suitable for large power grids with thousands of nodes; 3. Only relying on grid-side bus impedance data, without obtaining internal parameters of new energy equipment, it can be directly used for dispatching analysis and regional management strategy making, so that the power grid has more stability and adaptability under high penetration of new energy; 4. The impedance method based on the characteristics of the full frequency band of 0-3000 Hz of the power grid bus harmonic impedance is used to realize the analysis of partition and collaborative management, and the impedance method plays an important role in the stability analysis of the new energy power system, especially under the background of the increasingly prominent wide frequency oscillation problem, by analyzing the impedance characteristics of the grid side, the potential stability risk of the new energy power system coupled with the power grid can be revealed, the full frequency band Bode chart data of the bus impedance is used in the application, which is converted into a multi-dimensional feature matrix, and the bus area is divided through the method of dimension reduction and clustering, thereby providing basic data support for the partition control and collaborative optimization of the power grid; 5. In the feature extraction link, the dynamic behavior and nonlinear characteristics of the power grid impedance are fully described through multi-dimensional parameters such as global features, frequency band features, spectral features and frequency variable features, so that the buses in the feature space can clearly distinguish the electrical similarity, then the UMAP nonlinear dimension reduction method is introduced to map the high-dimensional feature space into a low-dimensional manifold embedding space, which not only retains the local similarity of the impedance curve, but also avoids the calculation complexity problem caused by the dimension disaster, and the low-dimensional feature space lays a foundation for the subsequent clustering division based on the electrical distance; 6. In the partition stage, based on the harmonic impedance difference matrix between the buses and the power grid topology information, the Leiden community division algorithm is used to cluster and partition the buses, compared with the traditional clustering method, the Leiden algorithm can quickly converge on a large-scale power grid graph, and the stability and global optimality of the partition structure are guaranteed, through this method, the buses with similar harmonic impedance characteristics can be effectively divided into the same area, and the possibility of collaborative analysis and management of the impedance method in the grid side power grid is realized. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 It is a flowchart of the power system harmonic impedance partition method based on the Leiden community division algorithm of the application; Figure 2 It is a flowchart of the feature extraction of the harmonic impedance data in the application; Figure 3 It is a flowchart of the dimension reduction of the multi-dimensional feature matrix in the application; Figure 4 It is a flowchart of the clustering partition using the Leiden community division algorithm in the application; Figure 5 It is a partition effect diagram of the harmonic impedance power grid in the embodiment of the application; Figures 6~12 It is a harmonic impedance comparison diagram of two buses in each area in the embodiment of the application. DETAILED DESCRIPTION

[0021] The technical solutions of the present application will be clearly and completely described below in combination with the drawings and examples. Obviously, the described examples are part of the examples of the present application, rather than all the examples. Based on the examples in the present application, all other examples obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0022] As shown in Figure 1 A power system harmonic impedance partitioning method based on Leiden community division algorithm, comprising the following steps: S1) obtaining harmonic impedance data of each bus in the power grid; S2) extracting features from the harmonic impedance data to generate a multi-dimensional feature matrix; S3) using uniform manifold approximation and projection method to reduce the dimension of the multi-dimensional feature matrix, and outputting the reduced harmonic impedance features; S4) calculating the Euclidean distance between the buses based on the reduced harmonic impedance features, and constructing a harmonic impedance difference edge weight matrix; S5) combining the power grid topology adjacency matrix and the harmonic impedance difference edge weight matrix, and using the Leiden community division algorithm for clustering partitioning; S6) outputting the partitioning labels of each bus to form the power grid harmonic impedance partitioning result.

[0023] Specifically, in step S1), the harmonic impedance data of each bus is represented in the frequency domain, covering a wide frequency domain of 0-3000 Hz. The obtained harmonic impedance data is represented as amplitude and phase angle, and is subjected to resampling, interpolation, normalization, filtering and outlier rejection processing. The harmonic impedance data is stored in the form of complex impedance, including real and imaginary parts.

[0024] In step S2), in combination with Figure 2 As shown, when extracting features from the harmonic impedance data, the harmonic impedance data of each bus obtains global features, spectral features, frequency band features and frequency variation features after feature extraction, forming a multi-dimensional feature matrix.

[0025] The global features include one or more of average impedance modulus, curve smoothness, overall phase angle trend, phase angle standard deviation, energy center frequency, high-frequency phase angle mutation, modulus mutation, phase angle offset, high-frequency trend and system inductance; The spectral features include one or more of low-frequency energy ratio, spectral entropy, ultra-low-frequency phase stability, phase inversion energy ratio, modulus-phase angle spectral correlation and joint spectral energy extracted by performing fast Fourier transform on the amplitude and phase angle of the bus harmonic impedance data; The frequency band features include one or more of average resistance value, average Q factor and energy integral extracted in each frequency band after dividing the frequency into several frequency bands; Frequency variation characteristics include one or more of the following: amplitude and phase angle correlation, resonance peak intensity, resonance frequency location, and phase consistency index, obtained by analyzing the dynamic change characteristics of the bus in each frequency band after dividing the frequency into several frequency bands. The multidimensional feature matrix has a dimension of eigenmatrix n Number of busbars d The number of features for each busbar.

[0026] Among them, the average impedance magnitude is: Among them, Z( f () represents the bus at the frequency point f The complex impedance below, f min and f max These are the lower and upper limits of the scanning frequency range, respectively. Spectral entropy: in, N The number of frequency points, p i For the first i Normalized power spectral weights at frequency points z ( f i ) is at the frequency point f i Complex impedance at that point, z ( f j ) is at the frequency point f j The complex impedance at a certain point is used to measure the degree of dispersion of the harmonic impedance capability distribution. Other characteristics can be calculated using conventional mathematical methods such as polynomial fitting, fast Fourier transform, or peak analysis. The specific calculation methods will not be elaborated here.

[0027] Combination Figure 3 As shown, step S3) specifically includes: S31) Feature normalization: Receive a multidimensional feature matrix and perform feature normalization; S32) Construction of high-dimensional fuzzy K-nearest neighbor graph: Cosine distance is used to measure the impedance difference between buses, and a K-nearest neighbor graph is built for each bus point in high-dimensional space; S33) Construction of fuzzy adjacency probability graph: Use the Gaussian kernel function to convert the adjacency relationship into the adjacency probability form, and generate a symmetric high-dimensional adjacency probability matrix P; S34) Low-dimensional space embedding initialization: Initialize the low-dimensional embedding coordinates Y of the adjacency probability matrix P using the PCA method; S35) Topology preserving optimization: The low-dimensional embedding coordinates Y are optimized using the cross-entropy loss function to generate a low-dimensional adjacency probability matrix Q, minimizing the difference between the high-dimensional adjacency probability matrix and the low-dimensional adjacency probability matrix Q, and maximizing the low-dimensional embedding to reflect the high-dimensional structure; S36) Embedding coordinate output: Output the two-dimensional embedding coordinate matrix, and the two-dimensional embedding coordinate matrix X reduced As follows: Wherein n represents the number of buses, and each row represents the embedding position of each bus in the low-dimensional space.

[0028] In step S5, each element in the harmonic impedance difference edge weight matrix corresponds to the impedance difference degree of two buses in the reduced dimension space, and the edge weight mapping is performed through the distance-similarity function, thereby generating a weighted adjacency matrix suitable for graph clustering, as shown in Figure 4 The impedance difference edge weight graph is generated in combination with the power grid topology adjacency matrix, and the Leiden community division algorithm is executed on the basis of the impedance difference edge weight graph for clustering partitioning to obtain the partitioning label of each bus.

[0029] Wherein, the power grid topology adjacency matrix A is a physical topology representation of the power grid constructed by collecting and analyzing the connection relationship between buses in the power grid, and the power grid topology adjacency matrix A completely characterizes the node-edge relationship of the power grid, and the power grid topology adjacency matrix A is a symmetric matrix, wherein represents the bus i and the bus j have a direct connection, and if there is no connection .

[0030] In step S6, when outputting the partitioning label of each bus, each clustered bus node is assigned to a unique area label, and a bus partitioning label matrix is output as the final partitioning result.

[0031] In this embodiment, the IEEE 39-node system is taken as the research object, the harmonic impedance features of each bus are extracted and clustered and partitioned, and the result is as shown in Figure 5As shown, the system is divided into 7 regions, region 1: bus 1, 4, 5, 6, 7, 8, 9, 31, 39; region 2: bus 2, 3, 18, 25, 30, 37; region 3: bus 15, 16, 17, 21, 24, 27; region 4: bus 10, 11, 12, 13, 14, 32; region 5: bus 26, 28, 38, 39; region 6: bus 19, 20, 33, 34; region 7: bus 22, 23, 35, 36. To verify the rationality of the partition, the amplitude and phase angle of the harmonic impedance of two buses in the same region are compared and shown, such as Figures 6~12 As shown, the results show that the harmonic impedance curves of the buses in the partition are not completely the same, but the overall trend and characteristics show high consistency.

[0032] The application is based on a power system harmonic impedance partition method of Leiden community division algorithm, which divides the power grid into multiple regions with similar dynamic characteristics by feature extraction, dimensionality reduction analysis and community division according to impedance similarity, provides basic data support for network side impedance regulation and oscillation risk management, realizes cross-frequency dynamic stability analysis and regional collaborative management; through the clustering partition of the harmonic impedance characteristic space, it provides basic support for network side harmonic impedance regulation and regional collaborative control, reduces the wideband oscillation risk of new energy access, and provides a feasible path for subsequent network side harmonic impedance optimization scheme, the combination of UMAP (Uniform Manifold Approximation and Projection) + Leiden can realize fast clustering while maintaining nonlinear characteristics, which is suitable for large power grids with thousands of nodes; only relying on network side bus impedance data, without obtaining internal parameters of new energy equipment, it can be directly used for dispatching analysis and regional management strategy making, making the power grid more stable and adaptable under high penetration of new energy; using the harmonic impedance characteristics of the power grid bus in the full frequency band of 0~3000 Hz, the partition and collaborative management analysis based on impedance method are realized, the impedance method plays an important role in the stability analysis of new energy power system, especially under the background of increasing wideband oscillation problems, by analyzing the network side impedance characteristics, the potential stability risk of new energy power system coupled with the power grid can be revealed, the application utilizes the full frequency band Bode chart data of the power grid bus impedance, converts it into a multi-dimensional feature matrix, and divides the bus area through dimensionality reduction and clustering method, thereby providing basic data support for the partition control and collaborative optimization of the power grid; in the feature extraction link, through multi-dimensional parameters such as global features, frequency band features, spectral features and frequency variable features, the dynamic behavior and nonlinear characteristics of the power grid impedance are fully described, so that each bus can clearly distinguish the electrical similarity in the feature space, then the UMAP nonlinear dimensionality reduction method is introduced, which maps the high-dimensional feature space into a low-dimensional manifold embedding space, which not only preserves the local similarity of the impedance curve, but also avoids the computational complexity problem caused by the curse of dimensionality, the low-dimensional feature space lays a foundation for subsequent clustering partition based on electrical distance; in the partition stage, based on the harmonic impedance difference matrix between buses and the power grid topology information, the Leiden community division algorithm is used for clustering and partitioning the buses, compared with traditional clustering methods, the Leiden algorithm can quickly converge on large-scale power grid maps, ensuring the stability and global optimality of the partition structure, through this method, buses with similar harmonic impedance characteristics can be effectively divided into the same region, realizing the possibility of collaborative analysis and management of impedance method in the network side power grid.

[0033] It should be noted that the above technical solutions are exemplary, and the present specification can be embodied in different forms, and should not be interpreted as being limited to the technical solutions set forth herein. Rather, providing these descriptions will make the present disclosure thorough and complete, and will fully convey the scope disclosed by the present specification to those skilled in the art. In addition, the technical solutions of the present application are limited only by the scope of the claims.

[0034] The aspects disclosed for describing the present specification and claims are merely examples, and thus the present specification and claims are not limited to the shown details. In the above description, when detailed descriptions of related known functions or configurations are determined to unnecessarily obscure the points of the present specification and claims, detailed descriptions will be omitted.

[0035] Finally, it should be noted that the above is a further detailed description of the application in conjunction with the specific embodiments, and should not be considered as limiting the specific embodiments of the application. For those skilled in the art, any simple replacement without departing from the concept of the present application should be considered as falling within the scope of protection of the present application. The above examples are only representative examples of the present application. Obviously, the present application is not limited to the above examples, and there can be many variations. Any simple modification, equivalent change and modification made in accordance with the technical essence of the present application to the above examples shall be considered as falling within the scope of protection of the present application.

Claims

1. A power system harmonic impedance partitioning method based on Leiden community division algorithm, characterized in that: The method comprises the following steps: S1) obtaining harmonic impedance data of each bus in the power grid; S2) extracting features from the harmonic impedance data to generate a multi-dimensional feature matrix; S3) reducing the dimension of the multi-dimensional feature matrix using a uniform manifold approximation and projection method, and outputting the reduced harmonic impedance features; S4) calculating the Euclidean distance between the buses based on the reduced harmonic impedance features, and constructing a harmonic impedance difference edge weight matrix; S5) combining the power grid topology adjacency matrix and the harmonic impedance difference edge weight matrix, and using the Leiden community division algorithm for clustering and partitioning; S6) outputting the partition labels of each bus to form the harmonic impedance partition result of the power grid.

2. The method of claim 1, wherein the Leiden community-based algorithm is used to partition the power system harmonic impedance. In the step S1), the harmonic impedance data of each bus is represented in the frequency domain, covering a wide frequency domain of 0-3000Hz. The obtained harmonic impedance data is represented by amplitude and phase angle. It is processed by resampling, interpolation, normalization, filtering and outlier rejection. The harmonic impedance data is stored in the form of complex impedance, including real and imaginary parts.

3. The method of claim 1, wherein the Leiden community-based algorithm is used to partition the power system harmonic impedance. In the step S2), when extracting features from the harmonic impedance data, the global features, spectral features, frequency band features and frequency variation features of each bus harmonic impedance data are obtained after feature extraction, forming a multi-dimensional feature matrix.

4. The power system harmonic impedance partitioning method based on the Leiden community partitioning algorithm as described in claim 3, characterized in that: The global features include one or more of average impedance modulus, curve smoothness, overall phase angle trend, phase angle standard deviation, energy center frequency, high-frequency phase angle mutation, modulus mutation, phase angle offset, high-frequency trend and system inductance; The spectral features include one or more of low-frequency energy ratio, spectral entropy, ultra-low frequency phase stability, phase inversion energy ratio, modulus-phase spectrum correlation and joint spectral energy extracted by fast Fourier transform of the amplitude and phase angle of the bus harmonic impedance data; The frequency band features include one or more of average resistance value, average Q factor and energy integral extracted in each frequency band after dividing the frequency into several frequency bands; The frequency variation features include one or more of amplitude and phase angle correlation, resonance peak strength, resonance frequency positioning and phase consistency index obtained by analyzing the dynamic change characteristics of the bus in each frequency band after dividing the frequency into several frequency bands; The multi-dimensional feature matrix is a feature matrix with dimensions , n is the number of buses, d is the number of features of each bus.

5. The power system harmonic impedance partitioning method based on the Leiden community partitioning algorithm as described in claim 4, characterized in that: Average impedance modulus: wherein Z f is the complex impedance of the bus at the frequency point f f min and f max are the lower and upper limits of the scan frequency range, respectively.​ Spectrum entropy: wherein N is the number of frequency points, p i is the first i is the normalized power spectral weight of the frequency point, z f i is the complex impedance at the frequency point f i z f j is the complex impedance at the frequency point f j , which feature is used to measure the degree of dispersion of the harmonic impedance capability distribution.​​​ 6. The power system harmonic impedance partitioning method based on the Leiden community partitioning algorithm as described in claim 1, characterized in that: The step S3) specifically includes: S31) Feature normalization: receiving the multi-dimensional feature matrix and performing feature normalization; S32) High-dimensional space fuzzy K-neighbor graph construction: using cosine distance to measure the impedance difference between buses, and establishing a K-neighbor graph for each bus point in the high-dimensional space; S33) Fuzzy adjacency probability graph construction: using a Gaussian kernel function to convert the adjacency relationship into an adjacency probability form, generating a symmetric high-dimensional adjacency probability matrix P; S34) Low-dimensional space embedding initialization: initializing the low-dimensional embedding coordinates Y of the adjacency probability matrix P through the PCA method; S35) Topology preservation optimization: using a cross-entropy loss function to optimize the low-dimensional embedding coordinates Y, generating a low-dimensional adjacency probability matrix Q, and minimizing the difference between the high-dimensional adjacency probability matrix and the low-dimensional adjacency probability matrix Q, so that the low-dimensional embedding maximizes the reflection of the high-dimensional structure; S36) Embedding coordinate output: outputting the two-dimensional embedding coordinate matrix.

7. The method of claim 6, wherein the Leiden community-based algorithm is used to partition the power system harmonic impedance. Two-dimensional embedding coordinate matrix X reduced As follows: wherein n represents the number of buses, and each row represents the embedding position of each bus in the low-dimensional space.

8. The method of claim 1, wherein the Leiden community-based algorithm is used to partition the power system impedance based on the harmonic. In the step S5), each element in the harmonic impedance difference edge weight matrix corresponds to the impedance difference degree of two buses in the dimension reduction space, and is mapped by the distance-similarity function to generate a weighted adjacency matrix suitable for graph clustering. The impedance difference edge weight graph is generated in combination with the power grid topology adjacency matrix. The Leiden community division algorithm is executed on the basis of the impedance difference edge weight graph to perform clustering partition.

9. The power system harmonic impedance partitioning method based on the Leiden community partitioning algorithm as described in claim 81, characterized in that: Power grid topology adjacency matrix A A power grid topology adjacency matrix is constructed for a power grid physical topology representation by collecting and analyzing the connection relationships between buses in the power grid A A power grid topology adjacency matrix fully characterizes the node-edge relationship of the power grid A A power grid topology adjacency matrix is constructed for a power grid physical topology representation by collecting and analyzing the connection relationships between buses in the power grid A power grid topology adjacency matrix is constructed for a power grid physical topology representation by collecting and analyzing the connection relationships between buses in the power grid A power grid topology adjacency matrix is constructed for a power grid physical topology representation by collecting and analyzing the connection relationships between buses in the power grid i A power grid topology adjacency matrix is constructed for a power grid physical topology representation by collecting and analyzing the connection relationships between buses in the power grid j A power grid topology adjacency matrix is constructed for a power grid physical topology representation by collecting and analyzing the connection relationships between buses in the power grid A power grid topology adjacency matrix is constructed for a power grid physical topology representation by collecting and analyzing the connection relationships between buses in the power grid 10. The power system harmonic impedance partitioning method based on the Leiden community partitioning algorithm as described in claim 1, characterized in that: In the step S6), when outputting the partition labels of each bus, each bus node after clustering is assigned to a unique area label, and a bus partition label matrix is output as the final partition result.

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