A resonance risk assessment method and system for a distribution network

Abstract

The present invention provides a resonance risk assessment method and system for a distribution network, including: performing frequency scanning on the distribution network to obtain a corresponding harmonic impedance matrix, and determining a harmonic impedance amplification index; acquiring the impedance frequency scanning curves of each node and determining the resonance frequency points within the impedance frequency scanning curves, and determining a resonance frequency index based on the resonance frequency points; determining a resonance amplification bandwidth index for calibrating the resonance frequency width of the system, and determining a resonance amplification severity index and a harmonic average amplification index of the node voltage and branch current; classifying the resonance amplification bandwidth index, the resonance amplification severity index, and the harmonic average amplification index, and performing a comprehensive risk assessment to realize the quantification of the resonance risks of the system nodes and branches. The present invention can identify the nodes or branches with the highest local / remote resonance risks and series / parallel resonance risks, the excitation points, response nodes, and response branches with the highest resonance risks, and give a comprehensive evaluation of the harmonic resonance risks.

Description

Technical Field

[0001] The present invention relates to the technical field of resonance risk assessment of distribution networks, and particularly to a resonance risk assessment method and system for distribution networks. Background Art

[0002] With the rapid development of a new power system with a high proportion of new energy and a high proportion of power electronic devices, the distribution system has shown new characteristics in aspects such as the power source, network, and load. On the power source side, distributed power sources such as photovoltaic and energy storage are connected to the distribution system in a decentralized and large quantity through power electronic devices; on the distribution network side, power electronic devices are more widely used to improve the flexible controllability of the distribution network; on the load side, various devices with power electronic converter interfaces and their clusters, such as electric vehicles, uninterruptible power supplies (UPS), and variable-frequency loads, are becoming more and more popular.

[0003] The increase in the number of nonlinear elements in the power system will increase the risk of harmonic resonance in the power system. For the power electronic distribution system, in order to quantify the risk of system resonance, many studies on system resonance risk assessment have been carried out. Existing studies mostly focus on the multi-device grid connection scenario where new energy power electronic devices are simply connected in equivalent impedance to the power grid, and judge the dangerous and safe areas of the operating conditions or device parameters of power electronic devices and their clusters from the perspective of stability, without considering the uncertainty of influencing factors and simplifying the system; there are also literatures analyzing from the perspective of resonance risk, but only judging from the presence or absence of resonance points, without quantifying the resonance influence parameter range; some studies estimate the resonance frequency and amplification degree for DFIG wind farms, and draw the parameter danger domain diagrams of the fan power generation and the system short-circuit ratio, but do not consider the system operating conditions and the uncertainty of parameters, and only target the scenario of multiple power electronic devices and their clusters; there are also studies that quantify the critical sub-synchronous oscillation wind speed range of the wind power grid connection system and the dangerous domain value of high-frequency resonance parameters based on power quality limits, and establish the sub-synchronous resonance dangerous domain of the wind farm. However, the above studies only consider a single influencing factor, and only target the scenario of multiple power electronic devices and their clusters, with insufficient quantification of the system risk assessment, lack of consideration of the uncertainty of influencing factors, and no overall concept of the dangerous domain has been formed to guide the operation of the distribution network. Summary of the Invention

[0004] The object of the present invention is to propose a resonance risk assessment method and system for distribution networks to solve the technical problem of how to identify local resonance and remote resonance occurring in the distribution system.

[0005] On the one hand, a resonance risk assessment method for distribution networks is provided, including:

[0006] Perform a frequency scan on the distribution network to obtain the corresponding harmonic impedance matrix, and determine the harmonic impedance amplification index according to the harmonic impedance matrix, where the harmonic impedance amplification index at least includes a harmonic voltage amplification index and a resonance current amplification index;

[0007] Obtain the impedance frequency scan curves of each node and determine the resonance frequency points within the impedance frequency scan curves, and determine the resonance frequency index based on the resonance frequency points;

[0008] According to the harmonic impedance amplification index and the resonance frequency index, determine the resonance amplification bandwidth index for calibrating the system resonance frequency width, and determine the resonance amplification severity index and the harmonic average amplification index of the node voltage and branch current;

[0009] Classify the resonance amplification bandwidth index, the resonance amplification severity index, and the harmonic average amplification index according to the preset local / remote resonance, series / parallel resonance, excitation nodes, response nodes, and response branches, and perform a comprehensive risk assessment on the indexes of the excitation nodes, response nodes, and response branches respectively to realize the quantification of the resonance risk of the system nodes and branches.

[0010] Preferably, the performing a frequency scan on the distribution network to obtain the corresponding harmonic impedance matrix specifically includes:

[0011] Obtain the frequency data of the distribution network through frequency scanning, where the frequency data at least includes node data, injection frequency, harmonic voltage phasor, harmonic current phasor, equivalent impedance value, and self-impedance value;

[0012] Construct the following harmonic impedance matrix according to the frequency data:

[0013]

[0014] where represents the harmonic voltage phasor of node j (j = 1, 2,... n) when the injection frequency is f; is the harmonic current phasor of node j when the injection frequency is f; Z f,ij is the equivalent impedance value of nodes i (i = 1, 2,... n, i ≠ j) and j when the injection frequency is f; Z f,jj is the self-impedance value of node j when the injection frequency is f, and n represents the sequence numbers of nodes i and j.

[0015] Preferably, the determining the harmonic impedance amplification index according to the harmonic impedance matrix specifically includes:

[0016] Determine the harmonic impedance amplification index according to the harmonic impedance matrix through the following formula:

[0017]

[0018] Among them, AHZ j is the harmonic impedance amplification index; Z h,jjmax is the allowable value of the h-th harmonic impedance at node j; AHZ j is the harmonic impedance amplification index at node j.

[0019] Preferably, it further includes:

[0020] Determine the harmonic voltage amplification index according to the harmonic impedance matrix through the following formula:

[0021]

[0022] Among them, AHU f,ij is the harmonic voltage amplification index; is the harmonic voltage phasor of node i when the injection frequency is f; is the harmonic voltage phasor of node j when the injection frequency is f;

[0023] Determine the harmonic current amplification index according to the harmonic impedance matrix through the following formula:

[0024]

[0025] Among them, AHC f,ab is the harmonic current amplification index; I f,ab is the harmonic current phasor of line segment ab when the injection frequency is f; I f,j is the harmonic current phasor of node j when the injection frequency is f; Z f,aj is the equivalent impedance value of node j and line segment a when the injection frequency is f; Z f,bj is the equivalent impedance value from node j to line segment b when the injection frequency is f; Z f,ab is the self-impedance value of line segment ab when the injection frequency is f.

[0026] Preferably, the determination of the resonance frequency index based on the resonance frequency point specifically includes:

[0027]

[0028] Among them, RFI represents the resonance frequency index; N i represents the total series / parallel resonance points of node i; N T represents the total series / parallel resonance points of the system.

[0029] Preferably, the determination of the resonance amplification bandwidth index for calibrating the resonance frequency width of the system specifically includes:

[0030]

[0031]

[0032]

[0033] Among them, f z,j is the resonant amplification bandwidth index corresponding to the harmonic impedance amplification index; f u,ij is the resonant amplification bandwidth index corresponding to the harmonic voltage amplification index; f c,ij is the resonant amplification bandwidth index corresponding to the harmonic current amplification index; f s is the total frequency bandwidth; is AHZ j is a set of frequency widths greater than 1; is AHC f,ij is a set of frequency widths greater than 1; is AHC f,ij is a set of frequency widths greater than 1.

[0034] Preferably, the determining of the resonant amplification severity indexes of the node voltage and branch current specifically includes:

[0035]

[0036]

[0037]

[0038] γ = γ1(γ2 or γ3) / 100

[0039] Among them, f r represents the resonant frequency point, i.e., the resonant peak point; γ1 is the resonant frequency severity index; γ2 is the resonant voltage amplification severity index, and the calculation of the harmonic impedance amplification severity index is the same as that of γ2; γ3 is the resonant current amplification severity index; γ is the resonant comprehensive severity index; AHU max is the peak value of the AHU curve; AHC max is the peak value of the AHC curve; f max and f min are the maximum and minimum values of the frequency when the curve has resonant amplification; HRI is the maximum allowable harmonic current percentage based on the rated current.

[0040] Preferably, the determining of the harmonic average amplification indexes of the node voltage and branch current specifically includes:

[0041]

[0042]

[0043]

[0044] Among them, represents the average value of AHZ j greater than 1; represents the average value of AHU f,ij greater than 1; represents the average value of AHC f,ij greater than 1.

[0045] Preferably, it further includes:

[0046] Performing a comprehensive risk assessment on the resonance amplification bandwidth index, resonance amplification severity index, and harmonic average amplification index after classifying the excitation nodes, response nodes, and response branches respectively through a preset entropy weight method to obtain a risk assessment result.

[0047] On the other hand, a resonance risk assessment system for a distribution network is also provided to implement the resonance risk assessment method for the distribution network, including:

[0048] A matrix establishment module for performing a frequency scan on the distribution network to obtain a corresponding harmonic impedance matrix, and determining a harmonic impedance amplification index according to the harmonic impedance matrix, where the harmonic impedance amplification index at least includes a harmonic voltage amplification index and a resonance current amplification index;

[0049] A first index module for obtaining the impedance frequency scan curve of each node and determining the resonance frequency points within the impedance frequency scan curve, and determining a resonance frequency index based on the resonance frequency points;

[0050] A second index module for determining a resonance amplification bandwidth index for calibrating the resonance frequency width of the system according to the harmonic impedance amplification index and the resonance frequency index, and determining a resonance amplification severity index and a harmonic average amplification index of the node voltage and branch current;

[0051] A risk assessment module for classifying the resonance amplification bandwidth index, resonance amplification severity index, and harmonic average amplification index according to preset excitation nodes, response nodes, and response branches, and performing a comprehensive risk assessment on the indexes of the excitation nodes, response nodes, and response branches respectively to realize the quantification of the resonance risk of the system nodes and branches.

[0052] In summary, implementing the embodiments of the present invention has the following beneficial effects:

[0053] The resonance risk assessment method and system for the distribution network provided by the present invention... Description of the Drawings

[0054] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the accompanying drawings required for the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, obtaining other accompanying drawings based on these drawings still belongs to the scope of the present invention.

[0055] Figure 1 It is a schematic diagram of the main process of a resonance risk assessment method for a distribution network in an embodiment of the present invention.

[0056] Figure 2 It is a schematic diagram of a resonance risk assessment system for a distribution network in an embodiment of the present invention. Detailed implementation manners

[0057] To make the objectives, technical solutions, and advantages of the present invention clearer, the following will further describe the present invention in detail with reference to the accompanying drawings.

[0058] As Figure 1 shown, it is a schematic diagram of an embodiment of a resonance risk assessment method for a distribution network provided by the present invention. In this embodiment, the method includes the following steps:

[0059] Step S1: Perform frequency scanning on the distribution network to obtain the corresponding harmonic impedance matrix, and determine the harmonic impedance amplification index according to the harmonic impedance matrix, where the harmonic impedance amplification index at least includes a harmonic voltage amplification index and a resonance current amplification index; it can be understood that the harmonic impedance matrix is obtained based on the frequency scanning method, and the harmonic impedance amplification index, the harmonic voltage amplification index, and the resonance current amplification index are established based on the harmonic impedance matrix.

[0060] In a specific embodiment, frequency data of the distribution network is obtained through frequency scanning, where the frequency data at least includes node data, injection frequency, harmonic voltage phasor, harmonic current phasor, equivalent impedance value, and self-impedance value;

[0061] Construct the following harmonic impedance matrix according to the frequency data:

[0062]

[0063] Among them, represents the harmonic voltage phasor of node j (j = 1, 2,... n) when the injection frequency is f; is the harmonic current phasor of node j when the injection frequency is f; Z f,ij is the equivalent impedance value of nodes i (i = 1, 2,... n, i ≠ j) and j when the injection frequency is f; Z f,jjis the self-impedance value of node j when the injection frequency is f, and n represents the sequence numbers of nodes i and j.

[0064] Specifically, the harmonic impedance amplification index is determined according to the harmonic impedance matrix by the following formula:

[0065]

[0066] where AHZ j is the harmonic impedance amplification index; Z h,jjmax is the allowable value of the h-th harmonic impedance of node j; AHZ j is the harmonic impedance amplification index of node j.

[0067] The harmonic voltage amplification index is determined according to the harmonic impedance matrix by the following formula:

[0068]

[0069] where AHU f,ij is the harmonic voltage amplification index; is the harmonic voltage phasor of node i when the injection frequency is f; is the harmonic voltage phasor of node j when the injection frequency is f;

[0070] The harmonic current amplification index is determined according to the harmonic impedance matrix by the following formula:

[0071]

[0072] where AHC f,ab is the harmonic current amplification index; I f,ab is the harmonic current phasor of line segment ab when the injection frequency is f; I f,j is the harmonic current phasor of node j when the injection frequency is f; Z f,aj is the equivalent impedance value of node j and line segment a when the injection frequency is f; Z f,bj is the equivalent impedance value from node j to line segment b when the injection frequency is f; Z f,ab is the self-impedance value of line segment ab when the injection frequency is f.

[0073] Step S2: Obtain the impedance frequency scan curves of each node and determine the resonance frequency points within the impedance frequency scan curves, and determine the resonance frequency index based on the resonance frequency points; it can be understood that the impedance frequency scan curves of each node are obtained based on the frequency scan method, the resonance frequency points are determined, and the resonance frequency index is constructed. Among them, the resonance frequency index describes the number of times the resonance frequency points are generated by the node, and the larger its value, the higher the probability of resonance when the node accesses the harmonic source in the system.

[0074] In a specific embodiment, determining the resonance frequency index based on the resonance frequency point specifically includes:

[0075]

[0076] Wherein, RFI represents the resonance frequency index; N i represents the total series / parallel resonance points of node i; N T represents the total series / parallel resonance points of the system.

[0077] Step S3, according to the harmonic impedance amplification index and the resonance frequency index, determine the resonance amplification bandwidth index for calibrating the resonance frequency width of the system, and determine the resonance amplification severity index and the harmonic average amplification index of the node voltage and branch current; It can be understood that a resonance amplification bandwidth describing the resonance frequency width of the system is constructed, a resonance amplification severity index of the node voltage and branch current is constructed, and a harmonic average amplification index of the node voltage and branch current is constructed.

[0078] In a specific embodiment, determining the resonance amplification bandwidth index for calibrating the resonance frequency width of the system specifically includes:

[0079]

[0080]

[0081]

[0082] Wherein, f z,j is the resonance amplification bandwidth index corresponding to the harmonic impedance amplification index; f u,ij is the resonance amplification bandwidth index corresponding to the harmonic voltage amplification index; f c,ij is the resonance amplification bandwidth index corresponding to the harmonic current amplification index; f s is the total frequency bandwidth; is AHZ j a set of frequency widths greater than 1; is AHC f,ij a set of frequency widths greater than 1; is AHC f,ij a set of frequency widths greater than 1.

[0083] Specifically, determining the resonance amplification severity index of the node voltage and branch current specifically includes:

[0084]

[0085]

[0086]

[0087] γ = γ1(γ2 or γ3) / 100

[0088] Among them, f r represents the resonance frequency point, that is, the resonance peak point; γ1 is the resonance frequency severity index; γ2 is the resonance voltage amplification severity index; γ3 is the resonance current amplification severity index; γ is the resonance comprehensive severity index; AHU max is the peak value of the AHU curve; AHC max is the peak value of the AHC curve; f max and f min are the maximum and minimum values of the frequency when resonance amplification occurs on the curve; HRI is the maximum allowable harmonic current percentage.

[0089] Specifically, the determination of the harmonic average amplification index of the node voltage and branch current specifically includes:

[0090]

[0091]

[0092] Among them, represents the frequency bandwidth where AHU > 1 in the harmonic voltage amplification index; represents f,ij the average value of AHU when AHU > 1; represents f,ij the average value of AHC when AHC > 1.

[0093] Step S4: Classify the resonance amplification bandwidth index, resonance amplification severity index, and harmonic average amplification index according to the preset excitation node, response node, and response branch, and perform a comprehensive risk assessment on the indexes of the excitation node, response node, and response branch respectively to realize the quantification of the resonance risk of the system nodes and branches. It can be understood that, according to the excitation node and the response node / branch, the above indexes are classified, and the entropy weight method is used to obtain the comprehensive risk assessment indexes of the indexes of the excitation node and the response node / branch respectively, so as to realize the quantification of the resonance risk of the system nodes and branches.

[0094] In a specific embodiment, the entropy weight method is used to perform a comprehensive risk assessment on the resonance amplification bandwidth index, resonance amplification severity index, and harmonic average amplification index after classifying the excitation node, response node, and response branch respectively, so as to obtain the risk assessment result.

[0095] As Figure 2 shown, the present invention also provides a resonance risk assessment system for a distribution network, which is used for the resonance risk assessment method of the distribution network, and includes:

[0096] A matrix establishment module is used to perform frequency scanning on the distribution network to obtain a corresponding harmonic impedance matrix, and determine a harmonic impedance amplification index according to the harmonic impedance matrix, where the harmonic impedance amplification index at least includes a harmonic voltage amplification index and a resonance current amplification index;

[0097] A first index module is used to obtain impedance frequency scanning curves of each node and determine resonance frequency points within the impedance frequency scanning curves, and determine a resonance frequency index based on the resonance frequency points;

[0098] A second index module is used to determine a resonance amplification bandwidth index for calibrating the system resonance frequency width according to the harmonic impedance amplification index and the resonance frequency index, and determine a resonance amplification severity index and a harmonic average amplification index of the node voltage and branch current;

[0099] A risk assessment module is used to classify the resonance amplification bandwidth index, the resonance amplification severity index, and the harmonic average amplification index according to preset local / remote resonance, series / parallel resonance, excitation nodes, response nodes, and response branches, and perform comprehensive risk assessment on the indexes of the excitation nodes, response nodes, and response branches respectively to realize the quantification of the resonance risk of the system nodes and branches.

[0100] It should be noted that the system described in the above embodiment corresponds to the method described in the above embodiment. Therefore, the parts not detailed in the system described in the above embodiment can be obtained by referring to the content of the method described in the above embodiment, and will not be elaborated here.

[0101] In summary, implementing the embodiments of the present invention has the following beneficial effects:

[0102] The resonance risk assessment method and system for a distribution network provided by the present invention.

[0103] The above-disclosed are only the preferred embodiments of the present invention. Of course, the scope of the rights of the present invention cannot be limited thereby. Therefore, equivalent changes made according to the claims of the present invention still fall within the scope covered by the present invention.

Claims

1. A resonance risk assessment method for a distribution network, characterized in that, Including: Performing a frequency scan on the distribution network to obtain a corresponding harmonic impedance matrix, and determining a harmonic impedance amplification index according to the harmonic impedance matrix, where the harmonic impedance amplification index at least includes a harmonic voltage amplification index and a resonance current amplification index; Obtaining impedance frequency scan curves of each node and determining resonance frequency points within the impedance frequency scan curves, and determining a resonance frequency index based on the resonance frequency points; According to the harmonic impedance amplification index and the resonance frequency index, determining a resonance amplification bandwidth index for calibrating the system resonance frequency width, and determining a resonance amplification severity index and a harmonic average amplification index of the node voltage and branch current; Classifying the resonance amplification bandwidth index, the resonance amplification severity index, and the harmonic average amplification index according to preset excitation nodes, response nodes, and response branches, and comprehensively evaluating the risks of local / remote resonance, series / parallel resonance, excitation nodes, response nodes, and response branches respectively, to realize the quantification of the resonance risks of system nodes and branches.

2. The method according to claim 1, wherein The performing a frequency scan on the distribution network to obtain a corresponding harmonic impedance matrix specifically includes: Obtaining frequency data of the distribution network through frequency scan, where the frequency data at least includes node data, injection frequency, harmonic voltage phasor, harmonic current phasor, equivalent impedance value, and self-impedance value; Constructing the following harmonic impedance matrix according to the frequency data: Among them, represents the harmonic voltage phasor of node j (j = 1, 2, … n) at the injection frequency f; is the harmonic current phasor of node j at the injection frequency f; Z f,ij is the equivalent impedance value between nodes i (i = 1, 2, … n, i ≠ j) and j at the injection frequency f; Z f,jj is the self-impedance value of node j at the injection frequency f, and n represents the sequence numbers of nodes i and j.

3. The method according to claim 2, wherein The determining a harmonic impedance amplification index according to the harmonic impedance matrix specifically includes: Determining a harmonic impedance amplification index according to the harmonic impedance matrix through the following formula: Among them, AHZ j is the harmonic impedance amplification index; Z f,jjmax is the allowable value of the f-th harmonic impedance at node j; AHZ j is the harmonic impedance amplification index at node j.

4. The method according to claim 3, wherein Also including: Determining a harmonic voltage amplification index according to the harmonic impedance matrix through the following formula: Among them, AHU f,ij is the harmonic voltage amplification index; is the harmonic voltage phasor of node i when the injection frequency is f; is the harmonic voltage phasor of node j when the injection frequency is f; Determining a harmonic current amplification index according to the harmonic impedance matrix through the following formula: Among them, AHC f,ab is the harmonic current amplification index; I f,ab is the harmonic current phasor of line segment ab when the injection frequency is f; I f,j is the harmonic current phasor of node j when the injection frequency is f; Z f,aj is the equivalent impedance value between node j and line segment a when the injection frequency is f; Z f,bj is the equivalent impedance value from node j to line segment b when the injection frequency is f; Z f,ab is the self-impedance value of line segment ab when the injection frequency is f.

5. The method according to claim 4, wherein The determining a resonance frequency index based on the resonance frequency points specifically includes: Among them, RFI represents the resonant frequency index; N i represents the total series / parallel resonant points of node i; N T represents the total series / parallel resonant points of the system.

6. The method according to claim 5, wherein The determining a resonance amplification bandwidth index for calibrating the system resonance frequency width specifically includes: Among them, f z,j is the resonant amplification bandwidth index corresponding to the harmonic impedance amplification index; f u,ij is the resonant amplification bandwidth index corresponding to the harmonic voltage amplification index; f c,ij is the resonant amplification bandwidth index corresponding to the harmonic current amplification index; f s is the total frequency bandwidth; is AHZ j is a set of frequency widths greater than 1; is AHU f,ij is a set of frequency widths greater than 1; is AHC f,ij is a set of frequency widths greater than 1.

7. The method according to claim 6, characterized in that, The determining a resonance amplification severity index of the node voltage and branch current specifically includes: γ = γ1(γ2 or γ3) / 100 Among them, f r represents the resonant frequency point, i.e., the resonant peak point; γ1 is the resonant frequency severity index; γ2 is the resonant voltage amplification severity index; γ3 is the resonant current amplification severity index; γ is the resonant comprehensive severity index; AHU max is the peak value of the AHU curve; AHC max is the peak value of the AHC curve; f max and f min are the maximum and minimum values of the frequency when the curve has resonant amplification; HRI is the maximum allowable harmonic current percentage based on the rated current; γ2 or γ3 is the resonant frequency severity index or the resonant voltage amplification severity index.

8. The method according to claim 7, characterized in that, The determining a harmonic average amplification index of the node voltage and branch current specifically includes: Among them, represents AHZ j average value of AHZ greater than 1; represents AHU f,ij average value of AHU greater than 1; represents AHC f,ij average value of AHC greater than 1.

9. The method according to claim 8, wherein Also including: Comprehensively evaluating the risks of the resonance amplification bandwidth index, the resonance amplification severity index, and the harmonic average amplification index classified by local / remote resonance, series / parallel resonance, excitation nodes, response nodes, and response branches respectively through the preset entropy weight method to obtain a risk assessment result.

10. A resonance risk assessment system for a distribution network, which is used to implement the method described in any one of claims 1-9, characterized in that, Including: A matrix establishment module for performing a frequency scan on the distribution network to obtain a corresponding harmonic impedance matrix, and determining a harmonic impedance amplification index according to the harmonic impedance matrix, where the harmonic impedance amplification index at least includes a harmonic voltage amplification index and a resonance current amplification index; A first index module for obtaining impedance frequency scan curves of each node and determining resonance frequency points within the impedance frequency scan curves, and determining a resonance frequency index based on the resonance frequency points; The second index module is used to determine the resonance amplification bandwidth index for calibrating the system resonance frequency width according to the harmonic impedance amplification index and the resonance frequency index, and determine the resonance amplification severity index and the harmonic average amplification index of the node voltage and branch current; The risk assessment module is used to classify the resonance amplification bandwidth index, the resonance amplification severity index and the harmonic average amplification index according to the preset local / remote resonance, series / parallel resonance, excitation node, response node and response branch, and comprehensively evaluate the risks of the indexes of the excitation node, the response node and the response branch respectively, so as to realize the quantification of the resonance risk of the system nodes and branches.

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