Multi-direct-current system full-spectrum response characteristic analysis method and system based on node participation factor matrix

Abstract

The invention relates to a multi-direct-current system full-spectrum response characteristic analysis method and system based on a node participation factor matrix, and the method comprises the steps: building an S-domain port model for an electrical element in a multi-direct-current system, and constructing an S-domain node admittance matrix of the whole system; by solving a determinant equation of a node admittance matrix, determining a resonance mode of the system in a full frequency spectrum range, and identifying an unstable or weak damping resonance mode; for a target resonance mode, calculating a left feature vector and a right feature vector of a zero feature root corresponding to the node admittance matrix, and constructing a node participation factor matrix by using the product of the two; and according to element numerical values of the node participation factor matrix, an oscillation source or a key influence node causing the resonance mode is accurately positioned, so that an accurate direction is provided for subsequent parameter optimization and oscillation suppression.

Description

Technical Field

[0001] This invention belongs to the field of power system optimization technology, specifically relating to a method and system for analyzing the full spectrum response characteristics of a multi-DC system based on the node participation factor matrix. Background Technology

[0002] With the advancement of the "dual carbon" goals and the transformation of the energy structure, the power system is showing significant characteristics of a high proportion of renewable energy and a high proportion of power electronic equipment. Especially in cross-regional power transmission scenarios such as the West-to-East Power Transmission Project, the receiving-end grid often integrates multiple high-voltage direct current transmission systems, forming a complex multi-DC feed-in grid structure.

[0003] However, the widespread application of power electronic equipment, especially fully controlled power electronic devices such as flexible DC-DC converters (VSC-HVDC), has introduced complex dynamic characteristics, leading to new types of mid-to-high frequency broadband oscillations in power systems. These oscillations are characterized by a wide frequency range, sudden occurrence, and are often closely related to the controller parameters of the power electronic equipment and the characteristics of the transmission network, posing a serious threat to the safe and stable operation of the power system. Several oscillation accidents caused by power electronic equipment have occurred in practice, such as subsynchronous oscillations in wind farms and resonance between flexible DC systems and the AC grid. Currently, the main methods for analyzing oscillation problems in power-electronic power systems are time-domain analysis methods, such as the state-space method, and frequency-domain analysis methods, such as frequency scanning, modal analysis, and impedance analysis.

[0004] For complex power systems containing multiple DC systems, these existing methods have certain limitations in analyzing their wide-band, full-spectrum resonance characteristics, accurately identifying resonance sources, and evaluating the overall stability of the system. There is a lack of a comprehensive method that can fully consider the transient characteristics of complex transmission networks, accurately describe the dynamic characteristics of multiple power electronic devices, and intuitively locate resonance sources.

[0005] Therefore, there is an urgent need to propose an effective method for analyzing the full spectrum response characteristics of multiple DC systems in order to prevent and suppress potential oscillation problems. Summary of the Invention

[0006] One of the objectives of this invention is to at least solve one or more of the aforementioned problems in the prior art. In other words, one of the objectives of this invention is to provide a method and system for analyzing the full spectrum response characteristics of a multi-DC system based on a node participation factor matrix that meets one or more of the aforementioned requirements.

[0007] To achieve the above-mentioned objectives, the present invention adopts the following technical solution: In a first aspect, the present invention provides a method for analyzing the full-spectrum response characteristics of a multi-DC system based on a node participation factor matrix, applicable to multi-DC systems including at least two DC circuits, characterized in that it includes: An S-domain port model is established for electrical components in a multi-DC system, and the node admittance matrix of the multi-DC system in the S-domain is constructed. Solve the nodal admittance matrix to determine the unstable or weakly damped resonant modes in the resonant modes of a multi-DC system; For unstable or weakly damped resonant modes, calculate the left and right eigenvectors of the node admittance matrix corresponding to the zero eigenvalue in that mode; Calculate the node participation factor matrix corresponding to the unstable or weakly damped resonance mode. The node participation factor matrix is ​​obtained by multiplying the left eigenvector and the right eigenvector. Based on the element values ​​of the node participation factor matrix, identify the oscillation source or key influencing node of unstable or weakly damped resonance mode.

[0008] As a preferred implementation, the oscillation source or key influencing node of the unstable or weakly damped resonance mode is determined based on the element values ​​of the node participation factor matrix, including: Determine the elements in the node participation factor matrix, where each element represents the degree of influence of the injected current of one node on the node voltage of another node under unstable or weakly damped resonant modes. The nodes corresponding to the elements in the node participation factor matrix whose amplitudes are greater than a preset threshold are identified as oscillation sources or key influencing nodes that lead to unstable or weakly damped resonance modes.

[0009] As a preferred embodiment, the method further includes: Determine the resonance type of unstable or weakly damped resonance modes.

[0010] As a further preferred implementation, determining the resonance type of the unstable or weakly damped resonance mode specifically includes: The right eigenvector is used as the nodal voltage mode shape vector; Compare the phase angles of the corresponding elements at different nodes in the nodal voltage mode vector; If there are two groups of nodes with opposite phases, the resonance mode is determined to be a cross-sectional oscillation mode. If the phase angle difference of all nodes is within the preset in-phase range, the resonance mode is determined to be the terminal oscillation mode.

[0011] As a preferred embodiment, determining the unstable or weakly damped resonant modes in the resonant modes of a multi-DC system includes: The solution to the nodal admittance matrix is ​​a number of complex roots, each representing a resonant mode. Extract the real part of the complex root. If the real part is less than 0, the corresponding resonance mode is an unstable resonance mode. If the real part is less than the preset damping threshold, the corresponding resonance mode is a weakly damped resonance mode.

[0012] As a preferred embodiment, the method further includes: The node corresponding to the element with the largest value in the node participation factor matrix is ​​selected as the best node for system observation.

[0013] As a preferred implementation, for flexible DC converters in multi-DC systems, the S-domain port impedance model is established by considering the dynamic characteristics of its internal controller parameters and topology.

[0014] On the other hand, the present invention provides a multi-DC system full-spectrum response characteristic analysis system based on the node participation factor matrix, characterized in that it includes: The S-domain modeling and matrix construction module is used to establish S-domain port models for electrical components in multi-DC systems and construct the node admittance matrix of the multi-DC system in the S-domain. The resonant mode identification module is used to solve the nodal admittance matrix and determine the unstable or weakly damped resonant modes in the resonant modes of a multi-DC system. The eigenvector calculation module is used to calculate the left and right eigenvectors of the node admittance matrix corresponding to the zero eigenvalue in an unstable or weakly damped resonant mode. The participation factor matrix generation module is used to calculate the node participation factor matrix corresponding to unstable or weakly damped resonant modes. The node participation factor matrix is ​​obtained by multiplying the left eigenvector and the right eigenvector. The oscillation source localization module is used to determine the oscillation source or key influencing node of unstable or weakly damped resonance mode based on the element values ​​of the node participation factor matrix.

[0015] As a preferred implementation, the oscillation source localization module is specifically configured as follows: Determine the elements in the node participation factor matrix, where each element represents the degree of influence of the injected current of one node on the node voltage of another node under unstable or weakly damped resonant modes. The nodes corresponding to the elements in the node participation factor matrix whose amplitudes are greater than a preset threshold are identified as oscillation sources or key influencing nodes that lead to unstable or weakly damped resonance modes.

[0016] As a preferred embodiment, the system further includes: The resonance type determination module is used to determine the resonance type of unstable or weakly damped resonance modes. The specific configuration of the resonance type determination module is as follows: the right eigenvector is used as the node voltage mode vector; Compare the phase angles of the corresponding elements at different nodes in the nodal voltage mode vector; If there are two groups of nodes with opposite phases, the resonance mode is determined to be a cross-sectional oscillation mode. If the phase angle difference of all nodes is within the preset in-phase range, the resonance mode is determined to be the terminal oscillation mode.

[0017] Compared with existing technologies, the method and system for analyzing the full-spectrum response characteristics of multi-DC systems based on the node participation factor matrix provided by this invention have the following advantages: This invention constructs the S-domain node admittance matrix and solves its determinant equation, directly scanning and determining all resonance modes of the system in the full S-domain plane. It can cover the potential oscillation risks of subsynchronous oscillation, supersynchronous oscillation and other generalized resonances, and achieve a comprehensive understanding of the wide-frequency dynamic characteristics of multi-DC systems.

[0018] Based on this, this invention calculates the left and right eigenvectors of the zero eigenvalue of the S-domain node admittance matrix under a specific resonance mode, and constructs a node participation factor matrix using their product. The elements in this matrix have clear physical meanings, intuitively quantifying the influence of the injected current of any node on the voltage of another node in the network. By extracting elements from this matrix that satisfy a specific value range, the oscillation source or key influencing node causing oscillations at a specific frequency can be quickly identified, providing precise guidance for subsequent parameter optimization and oscillation suppression.

[0019] Furthermore, this invention utilizes the right eigenvector as the node voltage mode vector. By analyzing the relative relationship of the voltage phases at each node, it can effectively distinguish whether the oscillation belongs to the grid section oscillation mode or the terminal oscillation mode, which helps in the subsequent analysis of the spatial distribution law of the reference oscillation in the power grid. Attached Figure Description

[0020] Figure 1 This is a flowchart of the full-spectrum response characteristic analysis method for multi-DC systems based on the node participation factor matrix according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the system architecture for an example multi-DC system scenario; Figure 3 This is a nodal voltage mode shape diagram of a verification example of the present invention; Figure 4 This is a schematic diagram of the structure of the multi-DC system full-spectrum response characteristic analysis system based on the node participation factor matrix according to an embodiment of the present invention. Detailed Implementation

[0021] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0022] The following description provides examples and does not limit the scope, applicability, or examples set forth in the claims. Changes may be made to the function and arrangement of the described elements without departing from the scope of the invention. Various processes or components may be appropriately omitted, substituted, or added to the various examples. For example, the described methods may be performed in a different order than described, and various steps may be added, omitted, or combined. Furthermore, features described with respect to some examples may be combined into other examples.

[0023] Reference Figure 1 The flowchart below shows a method for analyzing the full-spectrum response characteristics of a multi-DC system based on a node participation factor matrix, which is provided in an embodiment of the present invention. This method can be applied to multi-DC systems including at least two DC systems and includes the following steps S100-S500.

[0024] S100 establishes an S-domain port model for electrical components in a multi-DC system and constructs the node admittance matrix of the multi-DC system in the S-domain.

[0025] In an embodiment of the present invention, firstly, the topology of the multi-DC system to be analyzed is constructed, so as to... Figure 2 The example shown is a typical multi-DC system scenario. The system includes two flexible DC systems, each connected to the same receiving-end AC grid via a modular multilevel converter. The topology also includes conventional components such as AC transmission lines, transformers, and possibly traditional synchronous generators.

[0026] For all electrical components in this multi-DC system, establish their respective port impedance models and admittance models in the S-domain.

[0027] For modular multilevel converters in the system, their dynamic characteristics are significantly affected by their complex controllers and body structures. In the embodiments of the present invention, the fundamental frequency and disturbance components of the converter can be modeled with small signals and combined with S-domain transformation to establish its S-domain port impedance model. This model can accurately reflect the dynamic response characteristics of the converter to the power grid in a wide frequency band, including the negative resistance effect that it may generate.

[0028] For conventional AC components such as transmission lines and transformers, their dynamic characteristics can be expressed as series impedance and parallel admittance in the S-domain.

[0029] In addition, as needed, an equivalent impedance model of the synchronous generator in the S-domain can be established to fully consider its impact on broadband resonance.

[0030] After obtaining the S-domain models of all components, by equivalencing and integrating these models, the node admittance matrix of the entire system can be constructed based on the network topology of the multi-DC system. .

[0031] The diagonal elements of this matrix represent nodal self-admittance, and the off-diagonal elements represent nodal mutual admittance, comprehensively reflecting the dynamic characteristics of the power system network structure and all components.

[0032] S200, solve the nodal admittance matrix to determine the unstable or weakly damped resonant modes in the resonant modes of a multi-DC system.

[0033] According to circuit theory, when a network undergoes free oscillations, the nodal admittance matrix exhibits singularity. Therefore, the determinant equation can be solved numerically or iteratively. A series of complex roots can be obtained. Each complex root represents a resonant mode of the system.

[0034] In some embodiments, step S200 also provides a method for determining the resonant mode: The real part of a complex root As the attenuation factor, if Then the resonant mode is stable, and The larger the value, the greater the damping of the mode and the better the stability. If If the corresponding resonance mode is determined to be an unstable resonance mode, the system will exhibit continuous oscillation under this mode. If the value is greater than 0 but less than the preset damping threshold, the corresponding resonance mode is determined to be a weakly damped resonance mode.

[0035] The absolute value of the complex root reflects the degree of unstable resonance. The resonant angular frequency is divided by... The resonant frequency can then be obtained. .

[0036] The above method can identify all possible resonance modes and quantify their frequencies and stability by scanning and solving the determinant equation across the entire spectrum, thereby enabling subsequent methods to achieve a comprehensive evaluation of the full-spectrum response characteristics of multiple DC systems.

[0037] S300 calculates the left and right eigenvectors of the node admittance matrix corresponding to the zero eigenvalue in the unstable or weakly damped resonant mode.

[0038] For the selected target resonance mode Due to the S-domain nodal admittance matrix There exists a corresponding zero eigenvalue. Using singular value decomposition or eigenvalue decomposition methods, calculate the eigenvalue that satisfies... right eigenvector .

[0039] This is the node voltage mode shape vector of the resonance mode. The amplitude and phase of each element in this vector reflect the relative amplitude and phase of the voltage oscillation at the corresponding node when resonance occurs.

[0040] The left eigenvector can be calculated using the same method. .

[0041] Some embodiments of the present invention also provide a method for analyzing right eigenvectors. This can help determine the resonance type of unstable or weakly damped resonance modes: Specifically, methods for determining the resonance type of unstable or weakly damped resonance modes include: Compare right eigenvectors That is, the phase angle of the corresponding elements of different nodes in the nodal voltage mode vector; If there are two groups of nodes with opposite phases, it indicates that the resonance occurs between two regions of the power grid and has the characteristics of cross-sectional oscillation. The resonance mode is determined to be a cross-sectional oscillation mode. If the phase angles of all nodes are basically the same and the differences are all within the preset in-phase range, it indicates that the resonance is mainly concentrated in a certain end region of the power grid and has the characteristics of local oscillation. The resonance mode is determined to be the end oscillation mode.

[0042] S400. Calculate the node participation factor matrix corresponding to the unstable or weakly damped resonance mode. The node participation factor matrix is ​​obtained by multiplying the left eigenvector and the right eigenvector.

[0043] To more accurately identify the main influencing regions and key factors of resonance, the resonance mode is calculated. Corresponding node participation factor matrix .

[0044] This matrix is ​​derived from the S-domain node admittance matrix. It is formed by the product of the left and right unit eigenvectors of the corresponding zero eigenvalue.

[0045] Specifically, the node participation factor matrix .

[0046] in The left unit eigenvector, This is the right unit eigenvector.

[0047] Elements of node participation factor matrix Reflects in the resonant mode The extent to which the injected current at node i affects the node voltage at node j.

[0048] S500: Based on the element values ​​of the node participation factor matrix, determine the oscillation source or key influencing node of unstable or weakly damped resonance mode.

[0049] Specifically, step S500 analyzes the elements with larger amplitude values ​​in the matrix to locate the main influencing areas and determine the node group or geographical area that contributes the most to the resonance mode; it can identify key influencing factors, and combined with the specific components of these nodes, it can determine the key power electronic equipment, control parameters or network structure that leads to resonance, select the best observation / test node, and find the node that best reflects the resonance mode in simulation or actual measurement.

[0050] In some specific implementations, analysts or automated programs can traverse the node-based factor matrix and, if certain elements are found in the matrix... If the amplitude of an element is significantly greater than a preset threshold, or if the value is the largest among all elements, then the node corresponding to that element is determined to be the oscillation source or key node of an unstable or weakly damped oscillation mode, and the main influence area, key influencing factors and oscillation type of the unstable or weakly damped resonance mode are further determined.

[0051] In some implementations, by selecting the node corresponding to the element with the largest value in the node participation factor matrix, the power electronic equipment, transmission line, or AC power grid area that causes resonance can be accurately identified. Such nodes can be used as the best nodes for system observation, enabling precise monitoring of the power system.

[0052] In some embodiments of the present invention, the method further includes S600, determining the resonance type of an unstable or weakly damped resonance mode.

[0053] Using the method proposed in this invention, by... A wide-band S-domain sweep solution is performed. The sweep covers a defined frequency range to include subsynchronous oscillations (SSO), supersynchronous oscillations (SFO), and other generalized resonances that may be induced by power electronic devices. Numerical methods are used to find... Zero point.

[0054] In one verification example of the present invention, the resonant modes of the system in the frequency range of 1 Hz-1500 Hz were analyzed using the s-domain nodal admittance matrix method. The analysis results are shown in Table 1.

[0055] Table 1 System Resonant Mode Scan Results

[0056] As can be seen from Table 1, the system has a total of 23 resonant modes in the frequency range of 1 Hz-1500 Hz, and there is an unstable resonant mode (29.3 Hz) in the subsynchronous frequency range, which poses a risk of resonant instability.

[0057] Furthermore, the research team analyzed the nodal voltage mode shape and participation factor matrix of the unstable resonant mode (29.3 Hz), and the results are as follows: Table 2. Node participation factor matrix in the 29.3 Hz resonant mode

[0058] from Figure 3 As shown in the node voltage mode diagram, there are two node groups with completely opposite node voltage mode phases in the 29.3 Hz resonant mode, indicating that this resonant mode is a grid section resonant mode. From the participation factor matrix shown in Table 2, node Bus 16 is the main participating node in this resonant mode. Therefore, the main influence area of ​​the resonant mode is the area near node Bus 16, that is, near the MMC2 grid connection node. This indicates that the resonant mode is mainly caused by MMC2. Due to the negative resistance effect of MMC2, the resonant mode becomes resonantly unstable.

[0059] Through the analysis of this IEEE 39-node example, the method of this invention successfully identified the weakly damped and unstable resonance modes in the system, determined their oscillation types using the node voltage mode shape vectors, and then precisely located the dynamic interaction of MMC2 and its connected AC network as the main contributors to the 29.3 Hz unstable oscillation using the node participation factor matrix. These detailed analysis results provide clear guidance for taking targeted suppression measures. The above example verifies the comprehensiveness, accuracy, and practicality of the method of this invention in the full-spectrum response characteristic analysis of multi-DC systems.

[0060] This invention also provides a system for analyzing the full-spectrum response characteristics of multiple DC systems based on the node participation factor matrix. Please refer to... Figure 4 The system includes: The S-domain modeling and matrix construction module 100 is used to establish S-domain port models for electrical components in a multi-DC system and to construct the node admittance matrix of the multi-DC system in the S-domain.

[0061] The resonance mode identification module 101 is used to solve the nodal admittance matrix and determine the unstable or weakly damped resonance modes of the system through wideband scanning.

[0062] The feature vector calculation module 102 is used to calculate the corresponding left and right feature vectors for the target pattern.

[0063] The participation factor matrix generation module 103 is used to generate a node participation factor matrix based on the product of eigenvectors.

[0064] The oscillation source location module 104 is used to automatically output the key node number that causes the oscillation based on the magnitude of the participating factor.

[0065] Specifically, in some embodiments, the resonance mode identification module 101 is configured to determine the unstable or weakly damped resonance mode of the system using the following method.

[0066] Solving determinant equations through numerical scanning or iterative methods A series of complex roots can be obtained. Each complex root represents a resonant mode of the system.

[0067] In some embodiments, step S100 also provides a method for determining the resonant mode: The real part of a complex root As the attenuation factor, if Then the resonant mode is stable, and The larger the value, the greater the damping of the mode and the better the stability. If If the corresponding resonance mode is determined to be an unstable resonance mode, the system will exhibit continuous oscillation under this mode. If the value is greater than 0 but less than the preset damping threshold, the corresponding resonance mode is determined to be a weakly damped resonance mode.

[0068] The absolute value of the complex root reflects the degree of unstable resonance. The resonant angular frequency is divided by... The resonant frequency can then be obtained. .

[0069] In some embodiments, the system further includes a resonance type determination module 105, which is used to output the oscillation type based on the phase distribution of the voltage mode vector.

[0070] The resonance type determination module 105 is specifically configured to determine the oscillation mode using the following method: Compare right eigenvectors That is, the phase angle of the corresponding elements of different nodes in the nodal voltage mode vector; If there are two groups of nodes with opposite phases, it indicates that the resonance occurs between two regions of the power grid and has the characteristics of cross-sectional oscillation. The resonance mode is determined to be a cross-sectional oscillation mode. If the phase angles of all nodes are basically the same and the differences are all within the preset in-phase range, it indicates that the resonance is mainly concentrated in a certain end region of the power grid and has the characteristics of local oscillation. The resonance mode is determined to be the end oscillation mode.

[0071] Those skilled in the art will recognize that the modules and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0072] The foregoing description is merely an exemplary embodiment of this disclosure and should not be construed as limiting the scope of this disclosure. Any equivalent changes and modifications made in accordance with the teachings of this disclosure shall still fall within the scope of this disclosure. Those skilled in the art will readily conceive of other embodiments of this disclosure upon considering the specification and practicing the disclosure herein. This invention is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not described herein. The specification and embodiments are to be considered exemplary only, and the scope and spirit of this disclosure are defined by the claims.

Claims

1. A method for analyzing the full-spectrum response characteristics of a multi-DC system based on a node participation factor matrix, applicable to multi-DC systems including at least two DC circuits, characterized in that, include: An S-domain port model is established for the electrical components in the multi-DC system, and the node admittance matrix of the multi-DC system in the S-domain is constructed. Solve the node admittance matrix to determine the unstable or weakly damped resonant modes in the resonant modes of the multi-DC system; For the unstable or weakly damped resonance mode, calculate the left and right eigenvectors of the node admittance matrix corresponding to the zero eigenvalue in that mode; Calculate the node participation factor matrix corresponding to the unstable or weakly damped resonance mode, wherein the node participation factor matrix is ​​obtained by multiplying the left eigenvector and the right eigenvector; Based on the element values ​​of the node participation factor matrix, the oscillation source or key influencing node of the unstable or weakly damped resonance mode is determined.

2. The method for analyzing the full-spectrum response characteristics of a multi-DC system based on the node participation factor matrix as described in claim 1, characterized in that, Based on the element values ​​of the node participation factor matrix, the oscillation source or key influencing node of the unstable or weakly damped resonance mode is determined to include: Determine the elements in the node participation factor matrix, wherein the elements characterize the degree of influence of the injected current of one node on the node voltage of another node under the unstable or weakly damped resonance mode. The nodes corresponding to the elements in the node participation factor matrix whose amplitudes are greater than a preset threshold are identified as oscillation sources or key influencing nodes that cause the unstable or weakly damped resonance mode.

3. The method for analyzing the full-spectrum response characteristics of a multi-DC system based on the node participation factor matrix as described in claim 1, characterized in that, The method further includes: Determine the resonance type of the unstable or weakly damped resonance mode.

4. The method for analyzing the full-spectrum response characteristics of a multi-DC system based on the node participation factor matrix as described in claim 3, characterized in that, Determining the resonance type of the unstable or weakly damped resonance mode specifically includes: The right eigenvector is used as the nodal voltage mode shape vector; Compare the phase angles of the corresponding elements at different nodes in the nodal voltage mode shape vector; If there are two groups of nodes with opposite phases, the resonance mode is determined to be a cross-sectional oscillation mode. If the phase angle difference of all nodes is within the preset in-phase range, the resonance mode is determined to be the end oscillation mode.

5. The method for analyzing the full-spectrum response characteristics of a multi-DC system based on the node participation factor matrix as described in claim 1, characterized in that, Determining the unstable or weakly damped resonant modes in the resonant modes of the multi-DC system includes: Calculate the solution of the nodal admittance matrix, wherein the solution is a plurality of complex roots, each representing a resonant mode; Extract the real part of the complex root. If the real part is less than 0, the corresponding resonance mode is an unstable resonance mode. If the real part is less than a preset damping threshold, the corresponding resonance mode is a weakly damped resonance mode.

6. The method for analyzing the full-spectrum response characteristics of a multi-DC system based on the node participation factor matrix as described in claim 1, characterized in that, The method further includes: The node corresponding to the element with the largest value in the node participation factor matrix is ​​selected as the best node for system observation.

7. The method for analyzing the full-spectrum response characteristics of a multi-DC system based on the node participation factor matrix as described in claim 1, characterized in that, For the flexible DC converter in the multi-DC system, the S-domain port impedance model is established by considering the dynamic characteristics of its internal controller parameters and topology.

8. A system for analyzing the full-spectrum response characteristics of a multi-DC system based on a node participation factor matrix, characterized in that, include: The S-domain modeling and matrix construction module is used to establish S-domain port models for electrical components in the multi-DC system and construct the node admittance matrix of the multi-DC system in the S-domain. The resonance mode identification module is used to solve the node admittance matrix and determine the unstable or weakly damped resonance modes in the resonance modes of the multi-DC system. The eigenvector calculation module is used to calculate the left and right eigenvectors of the node admittance matrix corresponding to the zero eigenvalue in the unstable or weakly damped resonance mode. The participation factor matrix generation module is used to calculate the node participation factor matrix corresponding to the unstable or weakly damped resonance mode. The node participation factor matrix is ​​obtained by multiplying the left eigenvector and the right eigenvector. The oscillation source localization module is used to determine the oscillation source or key influencing node of the unstable or weakly damped resonance mode based on the element values ​​of the node participation factor matrix.

9. The system for analyzing the full-spectrum response characteristics of a multi-DC system based on a node participation factor matrix as described in claim 8, characterized in that, The oscillation source localization module is specifically configured as follows: Determine the elements in the node participation factor matrix, wherein the elements characterize the degree of influence of the injected current of one node on the node voltage of another node under the unstable or weakly damped resonance mode. The nodes corresponding to the elements in the node participation factor matrix whose amplitudes are greater than a preset threshold are identified as oscillation sources or key influencing nodes that cause the unstable or weakly damped resonance mode.

10. The system for analyzing the full-spectrum response characteristics of a multi-DC system based on a node participation factor matrix according to claim 8, characterized in that, The system also includes: The resonance type determination module is used to determine the resonance type of the unstable or weakly damped resonance mode. The resonance type determination module is specifically configured to use the right eigenvector as the node voltage mode vector. Compare the phase angles of the corresponding elements at different nodes in the nodal voltage mode shape vector; If there are two groups of nodes with opposite phases, the resonance mode is determined to be a cross-sectional oscillation mode. If the phase angle difference of all nodes is within the preset in-phase range, the resonance mode is determined to be the end oscillation mode.

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