A method and system for harmonic resonance analysis considering harmonic source location

Abstract

This invention belongs to the field of harmonic analysis technology, and provides a method and system for harmonic resonance analysis considering the location of harmonic sources. It obtains the network topology and component parameters of a power system, constructs the node admittance matrix of the system at a specific frequency, and performs eigenvalue decomposition on the node admittance matrix. Based on modal analysis theory, each element of the node impedance matrix is ​​represented as a superposition of all modal impedances, establishing a mapping relationship between each node impedance and modal impedance, left eigenvector, and right eigenvector. According to the modal superposition expression, an improved modal participation factor considering the location of harmonic sources is constructed and screened to quantify the resonance degree and modal composition of each node in the system, identifying the key resonant nodes and dominant modes of the system. This invention solves the problem of large evaluation deviations of traditional participation factors under complex operating conditions with complex network structures and multiple resonant points, improving the accuracy and applicability of harmonic resonance analysis.

Description

Technical Field

[0001] This invention belongs to the field of power system harmonic analysis technology, specifically relating to a harmonic resonance analysis method and system that considers the location of harmonic sources. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] With the large-scale integration of power electronic equipment and renewable energy, the harmonic levels and impedance characteristics of power systems have changed significantly, making harmonic resonance problems increasingly prominent. When the frequency of a harmonic source matches the equivalent impedance characteristics of the system, series or parallel resonances will form at certain frequency points, leading to branch overcurrents or bus overvoltages, which seriously affect the safe operation of electrical equipment insulation and protection devices.

[0004] Currently, modal analysis is a common method for studying harmonic resonance in power systems. This method is based on the system's node admittance matrix and transforms the original network into modal space through eigenvalue decomposition, decomposing the coupled multi-node resonance problem into several independent resonant modes. By analyzing the modal impedance curves, the resonant frequencies of each mode are obtained; combined with node participation factors and component sensitivity indices, key nodes and component information for resonance are identified, providing a basis for the evaluation and suppression of harmonic resonance.

[0005] However, existing methods for characterizing participation factors in harmonic resonant mode analysis still have certain limitations: First, existing methods define the mode with the highest impedance at a certain frequency as the critical mode, and often assume that the impedance of the critical mode near the resonant frequency is much greater than that of other modes. However, in real-world complex power networks with numerous nodes and components, multiple resonant points often exist within the same frequency band. When a certain mode resonates, other modes may still maintain large modal impedances near that frequency. Existing methods only consider a single critical mode and ignore the superposition contribution of other modes to the node impedance, resulting in a large error in the calculated participation factor, making it difficult to accurately reflect the true degree of node resonance. Second, existing techniques ignore the influence of the harmonic source injection location. In reality, when harmonic currents are injected from different nodes, the impedance response of the system nodes changes, and the distribution of harmonic voltages excited by each node also changes accordingly. Existing techniques cannot simultaneously reflect the influence of modal characteristics and excitation location on the node response.

[0006] With the increasing complexity of power grid structures and the growing number of resonant points, existing analysis methods are prone to significant deviations under complex operating conditions with multiple resonant points, failing to provide a reliable basis for the accurate assessment and suppression of harmonic resonances. Summary of the Invention

[0007] To address the aforementioned problems, this invention proposes a harmonic resonance analysis method and system that considers the location of harmonic sources. This invention establishes a unified characterization of node voltage response, modal characteristics, and harmonic source location, solving the problem of large evaluation deviations of traditional participation factors under complex operating conditions with complex network structures and multiple resonant points, thereby improving the accuracy and applicability of harmonic resonance analysis.

[0008] According to some embodiments, the present invention adopts the following technical solution: A harmonic resonance analysis method considering the location of harmonic sources includes the following steps: Obtain the network topology and component parameters of the power system, construct the node admittance matrix of the power system at a specific frequency, and perform eigenvalue decomposition on the node admittance matrix to obtain the eigenvalue diagonal matrix, the left eigenvector matrix, and the right eigenvector matrix; Based on modal analysis theory, each element of the node impedance matrix is ​​represented as a superposition of all modal impedances, and a mapping relationship is established between each node impedance and modal impedance, left eigenvector and right eigenvector. Based on the expression for modal superposition, an improved modal participation factor considering the location of harmonic sources is constructed to quantify the resonance severity of each node and each mode under different harmonic injection locations. By utilizing the improved modal participation factor, the participation factors of each node and mode in the system at specific harmonic source injection locations are calculated and screened to identify the key resonant nodes and dominant modes of the power system.

[0009] As an alternative implementation method, the process of obtaining the network topology and component parameters of the power system and constructing the node admittance matrix of the power system at a specific frequency includes: establishing the system's admittance matrix at a specific frequency based on the network parameters of the power system to be analyzed. f The nodal admittance matrix below Y f Satisfying the nodal equations: ,in, V f For node voltage vectors, I f This is the injected current vector.

[0010] As an alternative implementation, the process of performing eigenvalue decomposition on the node admittance matrix includes: decomposing the node admittance matrix... Y f The eigenvalue decomposition is performed using the following formula: ,in, Λ It is an eigenvalue diagonal matrix. L, T These are the left and right eigenvector matrices, respectively, and they have... L = T -1 ; Define modal voltage and modal current as follows: U f = TV f , J f = TI f ,but: ; In the formula, n Define the reciprocal of the characteristic value as the total number of system nodes. For "modal impedance", when the first k Each mode at frequency f eigenvalues ​​under When it approaches zero, the corresponding modal impedance The presence of a peak value indicates that the mode is resonating.

[0011] As an alternative implementation, based on modal analysis theory, the process of representing each element of the nodal impedance matrix as a superposition of all modal impedances includes: converting the system nodal impedance matrix... Z Each element is represented as a superposition of the modal impedances: ; In the formula, For the first k Modal impedance of each mode, L ik , i =1, 2, 3, ... n , corresponding to the left eigenvector matrix of the th i line, number k Column elements, T kj , j =1, 2, 3, ... n , corresponding to the right eigenvector matrix of the th k line, number j The elements of the column.

[0012] As an alternative implementation, the process of constructing an improved modal participation factor considering the location of harmonic sources, based on the modal superposition expression, includes: based on the nodal impedance matrix... Z When from node Injected harmonic current I j At that time, any node in the system voltage response V i Represented as: ; In the formula, Z ij The first node impedance matrix in the system is the...i line, number j Column elements; Define the improved modal participation factor: ,in, k Modal numbering, j Inject node numbers into the harmonic sources. i The improved modal participation factor is used to characterize the nodes by assigning them numbers. j When harmonic current is injected, the node i In the k The degree of resonance under the modal, among which L ik Characterizing the first k Each modality at the node i Response characteristics at that location T kj Representation Nodes j For the first k Excitation characteristics of each mode.

[0013] As an alternative implementation method, the process of calculating and screening the participation factors of each node and each mode of the system at a specific harmonic source injection location using the improved modal participation factor includes: calculating the participation factors of each node and each mode of the system at a specific harmonic source injection location, and arranging them in descending order according to their amplitude.

[0014] Introduce preset engineering error tolerance T Find the maximum number of participating factors that need to be retained. m : ; In the formula, the denominator The sum of the improvement participation factors of all nodes and modes in the system characterizes the intensity of the global resonant response; molecule For sorting before m The sum of the magnitudes of the largest participating factors; T The error tolerance threshold is set according to the actual engineering requirements; Find the smallest positive integer. m Screening out the key factors that have a crucial impact on system resonance m One participating factor, by tracing this m By assigning node and mode numbers to each participating factor, the key resonant nodes and dominant modes can be identified.

[0015] A harmonic resonance analysis system that considers the location of harmonic sources includes: The data acquisition and mode decomposition module is configured to acquire the network topology and component parameters of the power system, construct the node admittance matrix of the power system at a specific frequency, and perform eigenvalue decomposition on the node admittance matrix to obtain the eigenvalue diagonal matrix, the left eigenvector matrix, and the right eigenvector matrix. The nodal impedance modal superposition modeling module is configured to represent each element of the nodal impedance matrix as a superposition of all modal impedances based on modal analysis theory, and to establish the mapping relationship between each nodal impedance and modal impedance, left eigenvector and right eigenvector. The improved participation factor calculation module is configured to construct an improved mode participation factor that takes into account the location of harmonic sources based on the expression of mode superposition, and to quantify the resonance severity of each node and each mode under different harmonic injection locations. The harmonic resonance assessment module is configured to use an improved mode participation factor to calculate and screen the participation factors of each node and mode in the system at a specific harmonic source injection location, thereby identifying the key resonant nodes and dominant modes of the power system.

[0016] An electronic device includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the steps in the method described above.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) This invention proposes an improved mode participation factor analysis method for harmonic resonance considering the location of harmonic sources. It overcomes the shortcomings of traditional methods that only consider a single key mode and ignore the contributions of other modes. Under complex working conditions with complex network structures and multiple resonance points, it can significantly improve the accuracy of resonance risk identification and avoid governance blind spots. (2) The improved participation factor constructed in this invention introduces harmonic source location information, which can accurately reflect the changes in system voltage response under different harmonic source node excitations, solves the problem that traditional participation factors cannot characterize the influence of excitation location, and provides a more detailed quantitative basis for the accurate evaluation of resonance degree. (3) By screening the improved modal participation factors, this invention extracts the participation factors that play a key role in the global resonant response, realizes the efficient identification of the key resonant nodes and the dominant modes, and provides a more accurate and efficient theoretical basis for the formulation of resonant suppression strategies for complex power systems.

[0018] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0019] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0020] Figure 1 A flowchart of an improved mode participation factor analysis method for harmonic resonance considering the location of harmonic sources is provided as one embodiment. Figure 2 Voltage spectrum diagram of each node after injecting harmonic current into node 22 according to one embodiment; Figure 3 The distribution diagram of the improved participation factors of each node and each mode at a resonant frequency of 450Hz is provided as an embodiment. Figure 4 An improved participation factor distribution diagram of each node at a 450Hz resonant frequency is provided as an embodiment. Figure 5 A distribution diagram of the conventional participation factor at a resonant frequency of 450Hz is provided for one embodiment. Figure 6 The actual simulated voltage response at a resonant frequency of 450Hz is provided as an embodiment. Detailed Implementation

[0021] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0022] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0023] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, 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.

[0024] Where there is no conflict, the embodiments and features described in this application may be combined with each other.

[0025] Example 1 like Figure 1 As shown in this embodiment, a method for improving the mode participation factor analysis of harmonic resonance considering the location of harmonic sources includes: S101: Obtain the network topology and component parameters of the power system, construct the node admittance matrix of the system at a specific frequency, and perform eigenvalue decomposition on the node admittance matrix to obtain the eigenvalue diagonal matrix, the left eigenvector matrix, and the right eigenvector matrix.

[0026] Based on the network parameters of the power system to be analyzed, establish the system at a specific frequency. f The nodal admittance matrix below Y f Satisfying the nodal equations: ; In the formula, V f For node voltage vectors, I f This is the injected current vector.

[0027] With respect to the nodal admittance matrix Y f The eigenvalue decomposition is performed using the following formula: ; In the formula, Λ It is an eigenvalue diagonal matrix. L, T These are the left and right eigenvector matrices, respectively, and they have... L = T -1 .

[0028] Define modal voltage and modal current as follows: U f = TV f , J f = TI f ,but: ; In the formula, n Define the reciprocal of the characteristic value as the total number of system nodes. For "modal impedance", when the first k Each mode at frequency f eigenvalues ​​under When it approaches zero, the corresponding modal impedance It exhibits a peak value, at which point the modal current is very small. J k It will also cause a large modal voltage. U k This indicates that the mode is in resonance.

[0029] S102: Based on modal analysis theory, each element of the node impedance matrix is ​​represented as a superposition of all modal impedances, and the mapping relationship between each node impedance and modal impedance, left eigenvector and right eigenvector is established.

[0030] To simplify the formula, subscripts are omitted. f The system node impedance matrix Z Each element is represented as a superposition of the modal impedances: ; In the formula, For the first k Modal impedance of each mode, L ik ( i =1, 2, 3, ... n ) corresponds to the left eigenvector matrix of the first i line, number k Column elements, T kj ( j =1, 2, 3, ... n ) corresponds to the right eigenvector matrix of the first k line, number j The elements of the column.

[0031] As shown in the above equation, the elements in the nodal impedance matrix are determined by all modes of the system, and the contribution of each mode to the nodal impedance is characterized by the modal impedance and its corresponding left and right eigenvectors. Among these, L ik Characterizing the first k Each modality at the node i Response characteristics at that location T kj Representation Nodes j For the first k The excitation characteristics of each mode. When the impedance of one or more modes increases significantly at a certain frequency, the contribution of the corresponding mode to the node impedance also increases accordingly, thus causing the node resonant response to exhibit multimode superposition characteristics.

[0032] S103: Based on the modal superposition expression, construct an improved modal participation factor that considers the location of the harmonic source to quantify the resonance severity of each node and each mode under different harmonic injection locations.

[0033] Based on the node impedance matrix Z When from node Injected harmonic current I j At that time, any node in the system voltage response V i It can be represented as: ; In the formula, Z ij The first node impedance matrix in the system is the... i line, number j The elements of the column. Based on this, the improved modal participation factor is defined: ; In the formula, k Modal numbering, j Inject node numbers into the harmonic sources. i Number the observed nodes. This participation factor is used to characterize the activity at the nodes. j When harmonic current is injected, the node i In the k The degree of resonance under different modes. This participation factor can be used to accurately quantify the degree of resonance of each node in the system at different harmonic source locations, revealing the actual contribution of each mode to the node resonance.

[0034] S104: Using the improved modal participation factor, calculate and screen the participation factors of each node and mode of the system at a specific harmonic source injection location, and identify the key resonant nodes and dominant modes of the system.

[0035] Based on the improved modal participation factor calculation method obtained in step S103, the harmonic source nodes of the system are determined, thereby calculating the participation factors of each node and mode at a specific harmonic source injection location. Given that in actual power system networks, typically only a few nodes and modes contribute decisively to the global resonant response, to improve evaluation efficiency and engineering practicality, all calculated participation factors are sorted in descending order of their amplitude. Let the descending sorted... p Each participating factor is denoted as .

[0036] To extract the participating factors that play a dominant role in resonance, a preset engineering error tolerance is introduced. T The maximum number of participating factors to be retained can be calculated using the following formula. m : ; In the formula, the denominator The sum of the improvement participation factors of all nodes and modes in the system characterizes the intensity of the global resonant response; molecule For sorting before m The sum of the magnitudes of the largest participating factors; T The error tolerance threshold is set according to the actual engineering requirements.

[0037] The smallest positive integer can be found using the above inequality. m This allows us to screen out the key factors that have a crucial impact on system resonance.m One participating factor. By tracing this m By identifying the node and mode numbers corresponding to each participating factor, the key resonant nodes and dominant modes can be identified, effectively filtering out redundant information and providing a more accurate and efficient theoretical basis for the resonance suppression strategy of the power system.

[0038] To verify the effectiveness of the method in this embodiment, a simulation analysis is performed using the IEEE-30 node system as an example. Harmonic current is injected from node 22, and the voltage spectrum of the system is as follows: Figure 2 As shown, the system resonates at 450Hz. The improved participation factor analysis method proposed in this embodiment is used to analyze the resonant point at 450Hz, and the results are as follows. Figure 3 As shown. From Figure 3 As can be seen, by improving the participation factor, the contribution of each node and mode to the resonance can be clearly observed. Only a small number of nodes and modes contribute significantly to the global resonant response, and this method can effectively screen out these dominant nodes and modes. It can also be seen that, under this condition, in addition to the single critical mode, other modes also contribute significantly to the resonance. This means that if resonance is suppressed by adjusting the component parameters, the sensitivity under these modes needs to be considered when solving for the modal sensitivity of the component. If traditional modal analysis is used, the influence of these non-critical modes will be ignored.

[0039] The results of the improvement participation factor calculation for each node are as follows: Figure 4 As shown, the traditional participation factor calculation results for each node are as follows: Figure 5 As shown, the actual simulation results of the voltage response at each node are as follows: Figure 6 As shown in the figure, the comparison reveals that the improved participation factor calculation results are highly consistent with the voltage response magnitudes of each node in the simulation, proving the correctness and accuracy of this method when considering the location of harmonic sources and multimodal superposition. In contrast, the participation factor obtained by the traditional method differs significantly from the actual node voltage response in the simulation, and cannot accurately predict the voltage response distribution of each node.

[0040] Example 2 A harmonic resonance improved mode participation factor analysis system considering the location of harmonic sources includes: The data acquisition and mode decomposition module is used to acquire the network topology and component parameters of the power system, construct the node admittance matrix of the system at a specific frequency, and perform eigenvalue decomposition on the node admittance matrix to obtain the eigenvalue diagonal matrix, the left eigenvector matrix, and the right eigenvector matrix. The nodal impedance modal superposition modeling module is used to represent each element of the nodal impedance matrix as a superposition of all modal impedances based on modal analysis theory, and to establish the mapping relationship between each nodal impedance and modal impedance, left eigenvector and right eigenvector. An improved participation factor calculation module is used to construct an improved mode participation factor that takes into account the location of harmonic sources based on the mode superposition expression, so as to quantify the resonance severity of each node and each mode under different harmonic injection locations. The harmonic resonance evaluation module is used to calculate and screen the participation factors of each node and mode of the system at a specific harmonic source injection location by using the improved mode participation factor, and to identify the key resonant nodes and dominant modes of the system.

[0041] Example 3 A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps described above in the method for analyzing the improved mode participation factor of harmonic resonance considering the location of harmonic sources: namely, obtaining power system parameters to construct a node admittance matrix; constructing a mode superposition expression for node impedance based on mode analysis; deriving the improved mode participation factor considering the location of harmonic sources; and using the factor to identify the key resonant nodes and dominant modes of the system.

[0042] Example 4 A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the steps in the harmonic resonance improved mode participation factor analysis method considering the location of harmonic sources as described above.

[0043] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of one or more computer-usable storage media (including, but not limited to, disk storage, etc.) containing computer-usable program code. CD - ROM It takes the form of a computer program product implemented on (such as optical memory, etc.).

[0044] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0045] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0046] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0047] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made by those skilled in the art without creative effort within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for harmonic resonance analysis considering the location of harmonic sources, characterized in that, Includes the following steps: Obtain the network topology and component parameters of the power system, construct the node admittance matrix of the power system at a specific frequency, and perform eigenvalue decomposition on the node admittance matrix to obtain the eigenvalue diagonal matrix, the left eigenvector matrix, and the right eigenvector matrix; Based on modal analysis theory, each element of the node impedance matrix is ​​represented as a superposition of all modal impedances, and a mapping relationship is established between each node impedance and modal impedance, left eigenvector and right eigenvector. Based on the expression for modal superposition, an improved modal participation factor considering the location of harmonic sources is constructed to quantify the resonance severity of each node and each mode under different harmonic injection locations. By utilizing the improved modal participation factor, the participation factors of each node and mode in the system at specific harmonic source injection locations are calculated and screened to identify the key resonant nodes and dominant modes of the power system.

2. The harmonic resonance analysis method considering the location of harmonic sources as described in claim 1, characterized in that, The process of obtaining the network topology and component parameters of a power system and constructing the node admittance matrix of the power system at a specific frequency includes: establishing the system's admittance matrix at a specific frequency based on the network parameters of the power system to be analyzed. f The nodal admittance matrix below Y f Satisfying the nodal equations: ,in, V f For node voltage vectors, I f This is the injected current vector.

3. The harmonic resonance analysis method considering the location of harmonic sources as described in claim 1, characterized in that, The process of performing eigenvalue decomposition on the node admittance matrix includes: decomposing the node admittance matrix... Y f The eigenvalue decomposition is performed using the following formula: ,in, Λ It is an eigenvalue diagonal matrix. L, T These are the left and right eigenvector matrices, respectively, and they have... L = T -1 ; Define modal voltage and modal current as follows: U f = TV f , J f = TI f ,but: ； In the formula, n Define the reciprocal of the characteristic value as the total number of system nodes. For modal impedance, when the first k Each mode at frequency f eigenvalues ​​under When it approaches zero, the corresponding modal impedance The presence of a peak value indicates that the mode is resonating.

4. The harmonic resonance analysis method considering the location of harmonic sources as described in claim 1, characterized in that, Based on modal analysis theory, the process of representing each element of the nodal impedance matrix as a superposition of all modal impedances includes: converting the system nodal impedance matrix... Z Each element is represented as a superposition of the modal impedances: ； In the formula, For the first k Modal impedance of each mode, L ik , i =1, 2, 3, ... n , corresponding to the left eigenvector matrix of the th i line, number k Column elements, T kj , j =1, 2, 3, ... n , corresponding to the right eigenvector matrix of the th k line, number j The elements of the column.

5. The harmonic resonance analysis method considering the location of harmonic sources as described in claim 1, characterized in that, Based on the superposition expression of modes, the process of constructing an improved mode participation factor considering the location of harmonic sources includes: based on the nodal impedance matrix... Z When from node Injecting harmonic current I j At that time, any node in the system voltage response V i Represented as: ； In the formula, Z ij The first node impedance matrix in the system is the... i line, number j Column elements; Define the improved modal participation factor: ,in, k Modal numbering, j Inject node numbers into the harmonic sources. i The improved modal participation factor is used to characterize the nodes by assigning them numbers. j When harmonic current is injected, the node i In the k The degree of resonance under the modal, among which L ik Characterizing the first k Each modality at the node i Response characteristics at that location T kj Representation Nodes j For the first k Excitation characteristics of each mode.

6. The harmonic resonance analysis method considering the location of harmonic sources as described in claim 1, characterized in that, The process of calculating and screening the participation factors of each node and each mode of the system at a specific harmonic source injection location using the improved modal participation factor includes: calculating the participation factors of each node and each mode of the system at a specific harmonic source injection location, and sorting them in descending order according to their amplitude. Introduce preset engineering error tolerance T Find the maximum number of participating factors that need to be retained. m : ； In the formula, the denominator The sum of the improvement participation factors of all nodes and modes in the system characterizes the intensity of the global resonant response; molecule For sorting before m The sum of the magnitudes of the largest participating factors; T The error tolerance threshold is set according to the actual engineering requirements; Based on finding the smallest positive integer m Screening out the key factors that have a crucial impact on system resonance m One participating factor, by tracing this m By assigning node and mode numbers to each participating factor, the key resonant nodes and dominant modes can be identified.

7. A harmonic resonance analysis system considering the location of harmonic sources, characterized in that, include: The data acquisition and mode decomposition module is configured to acquire the network topology and component parameters of the power system, construct the node admittance matrix of the power system at a specific frequency, and perform eigenvalue decomposition on the node admittance matrix to obtain the eigenvalue diagonal matrix, the left eigenvector matrix, and the right eigenvector matrix. The nodal impedance modal superposition modeling module is configured to represent each element of the nodal impedance matrix as a superposition of all modal impedances based on modal analysis theory, and to establish the mapping relationship between each nodal impedance and modal impedance, left eigenvector and right eigenvector. The improved participation factor calculation module is configured to construct an improved mode participation factor that takes into account the location of harmonic sources based on the expression of mode superposition, and to quantify the resonance severity of each node and each mode under different harmonic injection locations. The harmonic resonance assessment module is configured to use an improved mode participation factor to calculate and screen the participation factors of each node and mode in the system at a specific harmonic source injection location, thereby identifying the key resonant nodes and dominant modes of the power system.

8. An electronic device, characterized in that, It includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, which, when executed by the processor, perform the steps of the method according to any one of claims 1-6.

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