Method for identifying vulnerable lines of power system based on z-index

Abstract

The application discloses a power system fragile line identification method based on a z index, relates to the technical field of power grid fragile line identification, and comprises the following steps: constructing a correlation network according to power transmission lines of a power system; improving the z index based on the edge weight and node degree of a transmission node in the correlation network to obtain a weighted z index; and sorting the power transmission lines according to the weighted z index to identify fragile lines; the weighted z index comprehensively considers the node degree and edge weight of the transmission node in the correlation network, solves the problem that the influence of the transmission node in the power system cannot be determined when the adjacent transmission nodes pointed to by the transmission node are the same in number, and improves the accuracy of identifying fragile lines by applying the weighted z index to the correlation network.

Description

Technical Field

[0001] This invention relates to the field of vulnerable power grid line identification technology, and specifically to a method for identifying vulnerable power system lines based on the z-index. Background Technology

[0002] In recent years, the large-scale integration of distributed power sources and uncertain loads into the power grid has affected the safety of power grid operation. The impact of distributed power sources and uncertain loads is unpredictable and can easily cause large-scale power outages by impacting vulnerable lines. For the weak power grids along high-altitude railway lines, the integration of distributed power sources and uncertain loads will have a greater impact on the power grid itself. Therefore, identifying vulnerable lines in the power system is an effective means of preventing safety accidents.

[0003] Currently, the z-index is used to distinguish the influence of each node in the network. However, the z-index cannot comprehensively consider the two important network characteristics of the transmission node: the node degree and the edge weight. The z-index cannot distinguish the influence of transmission nodes with the same number of adjacent nodes in the network, resulting in low accuracy in identifying vulnerable lines in the power system. Summary of the Invention

[0004] The technical problem to be solved by this invention is to improve the accuracy of identifying vulnerable lines by comprehensively considering the node degree and edge weight of the transmission node. The purpose is to provide a method for identifying vulnerable lines in power systems based on the z-index, which solves the problem that when the number of adjacent transmission nodes pointed to by the aforementioned transmission node is the same, it is impossible to determine the influence of the transmission node in the power system, resulting in low accuracy in identifying vulnerable lines.

[0005] This invention is achieved through the following technical solution:

[0006] The z-index-based method for identifying vulnerable power system lines includes the following steps:

[0007] Based on the connection relationship between the transmission lines and nodes of the power system, and by performing power flow calculations, a dual network of the power system is established.

[0008] Based on the edge weights and node degrees of the transmission nodes in the dual network described above, the weighted z-index is obtained by improving upon the z-index.

[0009] The transmission lines are sorted according to the weighted z-index to identify vulnerable lines.

[0010] The aforementioned weighted z-index comprehensively considers two important network characteristics in dual networks: the node degree and the edge weight. It solves the problem that when the number of adjacent transmission nodes pointed to by the aforementioned transmission node is the same, it is impossible to determine the influence of the transmission node in the power system. Applying the aforementioned weighted z-index to dual networks improves the accuracy of identifying vulnerable lines.

[0011] Furthermore, based on the connection relationships between transmission lines and nodes in the power system and by performing power flow calculations, a dual network for the power system is established, including the following steps:

[0012] The power transmission lines of the aforementioned power system are collected and stored to obtain an initial power transmission line database;

[0013] Power flow calculations are performed on the initial transmission line database to obtain the initial transmission line power flow matrix;

[0014] Disconnect one transmission line from the initial transmission line database in sequence, perform power flow calculations, and obtain the first-level power flow matrix;

[0015] Based on the initial power flow matrix and the first-order power flow matrix of the transmission line mentioned above, the power flow change matrix of the transmission line is obtained;

[0016] Calculate the baseline power flow of each transmission line in the above power system to obtain the capacity margin matrix of each transmission line;

[0017] Based on the power flow variation matrix and capacity margin matrix of the transmission lines mentioned above, the dual matrix is ​​obtained;

[0018] The dual network described above is obtained based on the dual matrix.

[0019] The network obtained from the dual matrix is ​​the dual network of the aforementioned power system.

[0020] Furthermore, disconnect one of the transmission lines in the initial transmission line database. After the transmission line is disconnected, the power flow of the transmission line itself remains unchanged.

[0021] Furthermore, the power flow change matrix of the transmission line is the difference between the first-level power flow matrix and the initial power flow matrix of the transmission line.

[0022] Furthermore, the transmission lines of the aforementioned power system correspond one-to-one with the transmission nodes of the aforementioned dual network.

[0023] Furthermore, the edge weights of the transmission nodes in the dual network described above are elements in the dual matrix.

[0024] The above-mentioned power system transmission lines are used as transmission nodes in the dual network. The elements in the dual matrix are used as edge weights of the transmission nodes, which are the edge weights of the transmission lines. The network obtained from the dual matrix is ​​the dual network. The dual network is a weighted network. Compared with the unweighted network, the weighted network can not only give the interaction between the transmission nodes, but also the intensity difference of the interaction between the transmission nodes, which increases the accuracy of the constructed dual network and thus improves the accuracy of identifying vulnerable lines.

[0025] Furthermore, the node degree of the transmission nodes in the dual network described above is obtained through the following steps:

[0026] Based on the edge weights of the transmission nodes in the dual network described above, establish the edge weight matrix of each transmission node pointing to all transmission nodes and the sum matrix of the edge weights of all transmission nodes pointing to their adjacent transmission nodes.

[0027] Based on the edge weight matrix and the edge weight sum matrix mentioned above, the node degree of the aforementioned transmission node is calculated using the following formula:

[0028]

[0029] Among them, T i a represents the degree of transmission node i. i SUM represents the edge weight matrix from which transmission node i points to all transmission nodes in the dual network. A This represents the sum of edge weights from all transmission nodes to their adjacent transmission nodes, where α and β represent adjustment factors.

[0030] Furthermore, if the aforementioned transmission node is not adjacent to the transmission node it points to, then the edge weight is 0.

[0031] Furthermore, based on the edge weights and node degrees of the transmission nodes in the dual network described above, the weighted z-exponent is calculated using the following formula:

[0032]

[0033] in, A represents the weighted z-index of transmission node i. i This represents the sum of edge weights from transmission node i to its adjacent transmission nodes. T represents the sum of squares of the edge weights from transmission node i to its neighboring transmission node k. i This represents the node degree of transmission node i.

[0034] The aforementioned weighted z-index takes into account both the edge weight and degree of the transmission node, solving the problem that when the number of adjacent transmission nodes pointed to by the aforementioned transmission node is the same, it is impossible to determine the influence of the transmission node in the power system, and further improving the accuracy of identifying vulnerable lines.

[0035] Furthermore, the above-mentioned sorting of transmission lines based on the weighted z-index to identify vulnerable lines specifically involves: calculating the weighted z-index of each transmission line in the power system, arranging the transmission lines in descending order according to the magnitude of the weighted z-index, and determining the vulnerable lines of the power system.

[0036] The transmission nodes of the dual network described above correspond one-to-one with the transmission lines of the power system. The weighted z-index of the transmission nodes is calculated using the dual matrix described above. The transmission nodes are then sorted in descending order according to the magnitude of the weighted z-index. The higher the ranking of the transmission node, the more critical the power system transmission line corresponding to that transmission node is, thereby identifying the vulnerable lines of the power system.

[0037] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0038] Applying the aforementioned weighted z-index to the dual network, which comprehensively considers the two important network characteristics of the transmission node and the edge weight, solves the problem that when the number of adjacent transmission nodes pointed to by the aforementioned transmission node is the same, it is impossible to determine the influence of the transmission node in the power system, thus improving the accuracy of identifying vulnerable lines. Attached Figure Description

[0039] To more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be considered as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort. In the drawings:

[0040] Figure 1 A flowchart provided for Example 1;

[0041] Figure 2 A diagram showing the correspondence between the power system and related network nodes;

[0042] Figure 3 This is a schematic diagram of transmission nodes A, B, C, D and their adjacent transmission nodes;

[0043] Figure 4 This is the power grid system along the high-altitude railway line provided in Example 4;

[0044] Figure 5 The system remaining load under a line sequence attack based on weighted z-exponent provided in Example 4;

[0045] Figure 6 The percentage of remaining system load after sequentially attacking the first 5 transmission lines, as provided in Example 4. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0047] like Figure 3 As shown, transmission node A has 4 adjacent transmission nodes, transmission node B has 3 adjacent transmission nodes, and transmission nodes C and D have 2 adjacent transmission nodes. The influence of transmission nodes with different numbers of adjacent nodes can be determined by unweighted networks and z-exponents. However, the influence of transmission nodes with the same number of adjacent nodes needs to be determined by the method of this invention.

[0048] Example 1

[0049] This embodiment 1 provides a method for identifying vulnerable power system lines based on the z-index, such as... Figure 1 As shown, it includes the following steps:

[0050] S1. Perform power flow calculations on the connection relationships between the power transmission lines and the nodes of the power system to obtain the transmission capacity of the power system. Based on the connection relationships between the power transmission lines and the nodes and the transmission capacity of the power system, establish the dual network of the power system.

[0051] S2. Based on the edge weights and node degrees of the transmission nodes in the dual network described above, the z-index is improved to obtain the weighted z-index.

[0052] S3. Sort the transmission lines according to the weighted z-index above and identify vulnerable lines.

[0053] The aforementioned weighted z-index comprehensively considers two important network characteristics in dual networks: the node degree and the edge weight. It solves the problem that when the number of adjacent transmission nodes pointed to by the aforementioned transmission node is the same, it is impossible to determine the influence of the transmission node in the power system. Applying the aforementioned weighted z-index to dual networks improves the accuracy of identifying vulnerable lines.

[0054] Example 2

[0055] Power flow calculations are performed on the connections between transmission lines and nodes of the power system to obtain the transmission capacity of the power system. Based on the connections between transmission lines and nodes and the transmission capacity, a dual network of the power system is established, including the following steps:

[0056] S11. Collect and store the power transmission lines of the above power system to obtain an initial power transmission line database, and number the power transmission lines in the initial power transmission line database (1 to N).

[0057] S12. Perform power flow calculations on the initial transmission line database to obtain the initial transmission line power flow matrix P0 = [p 01 p 02 , ..., p 0k , ..., p0N (Where, P0 represents the initial transmission line power flow matrix, p...) 0k (Indicates the initial power flow of transmission line k);

[0058] S13. Perform power flow calculations on the aforementioned second transmission line database to obtain the first-level power flow matrix P. i =[p i1 ,p i2 ,...,p ik ,...,p iN (where P) i p represents the first-order power flow matrix after transmission line i is disconnected. ik (This represents the power flow of transmission line k after transmission line i is disconnected);

[0059] S14. Based on the initial transmission line power flow matrix P0 and the first-order power flow matrix P14, i The power flow variation matrix of the transmission line is obtained.

[0060] S15. Calculate the reference power flow of each transmission line in the above power system to obtain the capacity margin matrix of each transmission line.

[0061] S16. Based on the above power flow change matrix of transmission lines From the capacity margin matrix, we obtain the dual matrix A, calculated as follows:

[0062]

[0063]

[0064] Where A is the dual matrix of the power system, a ik The impact of the disconnection of transmission line i on transmission line k. Let B be the change in power flow of transmission line k after transmission line i is disconnected. k Let N be the capacity margin matrix for transmission line k, and N be the total number of transmission lines in the power system.

[0065] S17. The network obtained from the above dual matrix is ​​the dual network of the above power system.

[0066] In a specific embodiment, one transmission line in the initial transmission line database is disconnected. Disconnecting this transmission line does not cause any change in the power flow of that transmission line itself.

[0067] In a specific implementation, after obtaining the power flow change matrix of the transmission line... Previously, the aforementioned first-order power flow matrix P i Establish the power flow matrix of the transmission line P = [P1, P2, ..., Pi ,…,P N ] T The above power flow variation matrix of transmission lines The difference between the power flow matrix P of the transmission line and the initial power flow matrix P0 of the transmission line;

[0068] The above power flow variation matrix of transmission lines The calculation formula is as follows:

[0069]

[0070] in, Let P represent the power flow change matrix of the transmission line, and P0 represent the initial power flow matrix of the transmission line.

[0071] Example 3

[0072] Specific implementation examples, such as Figure 2 As shown, the transmission lines of the power system and the transmission nodes of the dual network correspond one-to-one.

[0073] In a specific embodiment, the edge weights of the transmission nodes in the dual network described above are elements in the dual matrix.

[0074] The above-mentioned power system transmission lines are used as transmission nodes in the dual network. The elements in the dual matrix are used as edge weights of the transmission nodes, which are the edge weights of the transmission lines. The network obtained from the dual matrix is ​​the dual network. The dual network is a weighted network. Compared with the unweighted network, the weighted network can not only give the interaction between the transmission nodes, but also the intensity difference of the interaction between the transmission nodes, which increases the accuracy of the constructed dual network and thus improves the accuracy of identifying vulnerable lines.

[0075] In a specific embodiment, the node degree of the transmission node in the dual network described above is obtained through the following steps:

[0076] Based on the edge weights of the transmission nodes in the dual network described above, construct an edge weight matrix a from each of the aforementioned transmission nodes to all transmission nodes. i And the sum of edge weights from all the aforementioned transmission nodes to their adjacent transmission nodes, SUM. A ;

[0077] The above edge weight matrix a i =[a i1 a i2 … a ik … a iN ];

[0078] The above edge weight sum matrix in, A i a represents the sum of edge weights from transmission node i to its adjacent transmission node k. ik This represents the edge weight from transmission node i to transmission node k.

[0079] Based on the above edge weight matrix a i SUM, the sum of edge weights A The node degree of the aforementioned transmission nodes is calculated using the following formula:

[0080]

[0081] Among them, T i a represents the degree of transmission node i. i SUM represents the edge weight matrix from which transmission node i points to all transmission nodes in the dual network. A This represents the sum of edge weights from all transmission nodes to their adjacent transmission nodes, where α and β represent adjustment factors.

[0082] In a specific embodiment, if the aforementioned transmission node and the pointed-to transmission node are not adjacent, then the edge weight is 0, i.e., a. ik =0(a ik This indicates that transmission node i points to transmission node. k (boundary weights).

[0083] In a specific implementation, the weighted z-exponent is calculated based on the edge weights and node degrees of the transmission nodes in the dual network described above. The calculation formula is as follows:

[0084]

[0085] in, A represents the weighted z-index of transmission node i. i This represents the sum of edge weights from transmission node i to its adjacent transmission nodes. T represents the sum of squares of the edge weights from transmission node i to its neighboring transmission node k. i This represents the node degree of transmission node i.

[0086] The aforementioned weighted z-index takes into account both the edge weight and degree of the transmission node, solving the problem that when the number of adjacent transmission nodes pointed to by the aforementioned transmission node is the same, it is impossible to determine the influence of the transmission node in the power system, and further improving the accuracy of identifying vulnerable lines.

[0087] In a specific embodiment, the above-mentioned sorting of transmission lines based on the weighted z-index to identify vulnerable lines involves: calculating the weighted z-index of each transmission line in the power system, arranging the transmission lines in descending order according to the magnitude of the weighted z-index, and determining the vulnerable lines of the power system.

[0088] The transmission nodes of the dual network described above correspond one-to-one with the transmission lines of the power system. The weighted z-index of the transmission nodes is calculated using the dual matrix described above. The transmission nodes are then sorted in descending order according to the magnitude of the weighted z-index. The higher the ranking of the transmission node, the more critical the power system transmission line corresponding to that transmission node is, thereby identifying the vulnerable lines of the power system.

[0089] Example 4

[0090] The power grid system along high-altitude railway lines (such as...) Figure 4 As shown in Table 1, the tidal current cross-sectional data for the nine traction stations (39-47) are as follows.

[0091] Table 1

[0092]

[0093] According to the method of the present invention, the weighted z-index of each transmission line in the power grid system is calculated, and the transmission lines are arranged in descending order according to the magnitude of the weighted z-index. The sorting results are shown in Table 2.

[0094] Table 2

[0095] sequence Line number sequence Line number sequence Line number 1 7 17 25 32 41 2 3 18 36 33 22 3 27 19 37 34 24 4 21 20 34 35 11 5 19 21 1 36 14 6 18 22 28 37 15 7 8 23 44 38 42 8 10 24 45 39 9 9 29 25 17 40 32 10 5 26 31 41 26 11 38 27 43 42 33 12 20 28 46 43 40 13 30 29 47 44 39 14 2 30 48 45 23 15 35 31 16 46 4 16 12 32 13 47 6

[0096] like Figure 5 As shown, the higher the ranking of the transmission lines, the more critical they are.

[0097] Specific implementation examples, such as Figure 6 As shown, based on the identification results of the weighted z-index, after attacking the first 5 lines, the system's remaining load was only 46%; however, based on the identification results of the weighted H-index, the system's remaining load was 69%, proving that the weighted z-index is more effective than the weighted H-index. The system load loss ratio (CFS) values ​​of the first 7 transmission lines identified by the weighted z-index after simulating cascading failures and the most vulnerable transmission line among 7 randomly selected transmission lines are compared, as shown in Table 3. The results show that the CFS value of the vulnerable lines obtained based on the weighted z-index is significantly higher than the CFS value of the randomly selected lines, further verifying the effectiveness of the method proposed in this invention.

[0098] Table 3

[0099]

[0100] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made 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 identifying vulnerable power system lines based on the z-exponent, characterized in that, Includes the following steps: Based on the connection relationship between the transmission lines and nodes of the power system, and by performing power flow calculations, a dual network of the power system is established. Based on the edge weights and node degrees of the transmission nodes in the dual network, the weighted z-index is obtained by improving upon the z-index. The weighted z-exponent is calculated based on the edge weights and node degrees of the transmission nodes in the dual network, using the following formula: ； in, A represents the weighted z-index of transmission node i. i This represents the sum of edge weights from transmission node i to its adjacent transmission nodes. T represents the sum of squares of the edge weights from transmission node i to its neighboring transmission node k. i Indicates the degree of transmission node i; Transmission lines are sorted according to the weighted z-index to identify vulnerable lines.

2. The method for identifying vulnerable power system lines based on the z-index according to claim 1, characterized in that, Based on the connection relationships between transmission lines and nodes in the power system, and after performing power flow calculations, the dual network of the power system is established, including the following steps: The power system's transmission lines are collected and stored to obtain an initial transmission line database; Power flow calculations are performed on the initial transmission line database to obtain the initial transmission line power flow matrix; Disconnect one transmission line from the initial transmission line database in sequence, perform power flow calculations, and obtain the first-level power flow matrix; Based on the initial power flow matrix and the first-order power flow matrix of the transmission line mentioned above, the power flow change matrix of the transmission line is obtained; Calculate the reference power flow of each transmission line in the power system to obtain the capacity margin matrix of each transmission line; Based on the power flow variation matrix and capacity margin matrix of the transmission line, the dual matrix is ​​obtained; The dual network is obtained based on the dual matrix.

3. The method for identifying vulnerable power system lines based on the z-index according to claim 2, characterized in that, Disconnect one of the transmission lines in the initial transmission line database. After the transmission line is disconnected, the power flow of the transmission line itself remains unchanged.

4. The method for identifying vulnerable power system lines based on the z-index according to claim 2, characterized in that, The power flow variation matrix of the transmission line is the difference between the first-level power flow matrix and the initial power flow matrix of the transmission line.

5. The method for identifying vulnerable power system lines based on the z-index according to claim 1, characterized in that, The power transmission lines of the power system and the transmission nodes of the dual network correspond one-to-one.

6. The method for identifying vulnerable power system lines based on the z-index according to claim 2, characterized in that, The edge weights of the transmission nodes in the dual network are elements in the dual matrix.

7. The method for identifying vulnerable power system lines based on the z-index according to claim 6, characterized in that, The node degree of the transmission node in the dual network is obtained through the following steps: Based on the edge weights of the transmission nodes in the dual network, establish the edge weight matrix of each transmission node pointing to all transmission nodes and the sum matrix of the edge weights of all transmission nodes pointing to their adjacent transmission nodes. The degree of the transmission node is calculated based on the edge weight matrix and the edge weight sum matrix, using the following formula: ； Among them, T i a represents the degree of transmission node i. i SUM represents the edge weight matrix from which transmission node i points to all transmission nodes in the dual network. A This represents the sum of edge weights from all transmission nodes to their adjacent transmission nodes, where α and β represent adjustment factors.

8. The method for identifying vulnerable power system lines based on the z-index according to claim 7, characterized in that, If the transmission node is not adjacent to the transmission node it points to, then the edge weight is 0.

9. The method for identifying vulnerable power system lines based on the z-index according to claim 1, characterized in that, The step of sorting transmission lines according to the weighted z-index to identify vulnerable lines specifically involves: calculating the weighted z-index of each transmission line in the power system, arranging the transmission lines in descending order according to the magnitude of the weighted z-index, and determining the vulnerable lines of the power system.

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