Power grid vulnerable line identification method based on improved PageRank algorithm

Abstract

The application discloses a power grid fragile line identification method based on an improved PageRank algorithm, and first, according to a power system optimization model, the energy transaction amount between a generator node and a load node is solved, a virtual circulation is set, and a Google matrix G in the original PageRank algorithm is corrected; second, the initial value of the fragility of all nodes is set, and the initial value vector of the fragility of the nodes is brought into the improved PageRank algorithm formula; finally, the fragility of the nodes is iteratively calculated, and then according to the node fragility index, the sum of the fragilities of the first and last nodes of a line is calculated to obtain the fragility of the power transmission line, so that the fragile line of the power grid is identified. The application can well improve the deficiency of the original PageRank algorithm when applied to the power grid, can accurately identify the fragile line of the power grid under different operating states, provides a key monitoring guide for power grid monitoring and dispatch personnel, and better guarantees the safe and stable operation of the power grid.

Description

Technical Field

[0001] This invention belongs to the technical field of power system vulnerable line identification methods, and specifically relates to a power grid vulnerable line identification method based on an improved PageRank algorithm. Background Technology

[0002] With the continuous optimization of energy supply structure and the rapid growth of power grid scale, the energy trading and operation status of power systems have become more complex and diverse, facing increasing internal and external risks and threats. Research indicates that vulnerable lines in the power grid are a key factor affecting the reliability and stability of the power system, and the development and spread of many large-scale blackouts are closely related to these vulnerable lines. According to accident analysis reports of numerous large-scale blackouts abroad, vulnerable lines are the few important transmission lines operating on the edge of safety and stability in the power grid. They are components prone to failure and play a crucial role in the initiation and development stages of large-scale faults. Before a fault occurs, power grid monitoring and dispatching personnel fail to accurately identify and effectively monitor vulnerable lines. In the initial stage of a fault, the lack of timely and effective control measures and protection for vulnerable lines related to the tripped lines ultimately leads to the continuous expansion and development of the accident, eventually causing a serious incident. Therefore, efficiently and accurately identifying vulnerable lines in the power grid and formulating corresponding monitoring and protection measures can improve the monitoring efficiency of large-scale interconnected power grids, ensure the safety and stability of the power system and energy transmission channels, and effectively prevent large-scale blackouts.

[0003] The PageRank algorithm is a ranking algorithm for calculating the criticality of web pages. In recent years, some scholars have drawn analogies between power systems and the Internet, combining the algorithm with the physical characteristics of power systems to identify critical nodes. The original PageRank algorithm posits that if web page i is linked by web page j, then web page i will gain some of the importance of web page j, thereby increasing its own importance. This importance is defined as the PR value of web page i, denoted as PR(i). The original PageRank algorithm is very accurate and effective in calculating the criticality of web pages. However, due to the structural differences between power systems and the Internet, directly using the original PageRank algorithm to calculate the vulnerability index of power system nodes will present the following problems:

[0004] (1) The original PageRank PR value is distributed evenly based on the number of webpage links. However, different transmission lines connected to the same node in a power system have different power flow magnitudes and physical characteristics. At the same time, the nodes connected to these lines also vary. Therefore, if the PR value is distributed evenly according to the node link situation, the result will have a large error.

[0005] (2) Many load nodes in the power system are suspended nodes of the network (i.e. nodes with an out-degree of 0). During the iterative calculation process, these nodes will cause a "black hole effect", which will cause the PR values ​​of all nodes to eventually converge to 0.

[0006] (3) Many power supply nodes and load nodes in the power system are located at the edge of the network. According to the original PageRank algorithm definition, their influence is low, but this does not reflect the actual situation of the power system.

[0007] In summary, the original PageRank algorithm still has many shortcomings when applied to the identification of vulnerable lines in power systems. Summary of the Invention

[0008] To address the aforementioned problems, the present invention aims to provide a method for identifying vulnerable power grid lines based on an improved PageRank algorithm. This method combines energy trading data between generator nodes and load nodes calculated using a power system optimization operation model with network constraint coefficients to improve the PageRank algorithm. This enables the algorithm to match the structural characteristics of the power system and accurately and efficiently calculate the vulnerability of nodes, as detailed below.

[0009] A method for identifying vulnerable power grid lines based on an improved PageRank algorithm includes the following steps:

[0010] Step 1: Construct an optimal operation model of the power system and solve for the energy trade volume P between generator nodes and load nodes. g,d,t ;

[0011] Step 2: Based on the energy transaction volume P between the generator node and the load node g,d,t Set up a virtual circulation and correct the Google matrix G in the original PageRank algorithm;

[0012] Step 3: Set the vulnerability PR for all nodes 0 Initial value;

[0013] Step 4: Rank the node's vulnerability (PR) 0 The initial value vector is substituted into the improved PageRank algorithm formula;

[0014] Step 5: Iteratively calculate the node vulnerability until the absolute value of the difference between the (k+1)th result and the kth result is less than ε, then output the node vulnerability PR. k ;

[0015] Step 6: Based on the node vulnerability index, the vulnerability of the transmission line is obtained by calculating the sum of the vulnerability of the first and last nodes of the line, thereby identifying the vulnerable lines of the power grid.

[0016] Furthermore, the power system optimization operation model constructed in step 1 solves for the energy transaction volume P between generator nodes and load nodes. g,d,t Specifically, it includes:

[0017] Based on the fundamental principle of power flow transmission distribution factor, the constructed power system optimal operation model includes the energy trade volume P between generator nodes and load nodes. g,d,t The relevant constraints are solved by equations (1)-(4) to obtain the power flow components of the transmission line;

[0018] The output of generator g is equal to the sum of all transactions between the load and generator node g:

[0019]

[0020] The power of load node d is equal to the sum of the transaction volumes between all generators and load d:

[0021]

[0022] The component of energy exchange between all generator node-load node pairs on line l The sum equals the actual power flow P of the line. l,t :

[0023]

[0024] Based on the energy exchange volume and power transmission distribution factor between generator node g and load node d, calculate the power flow components on line l.

[0025]

[0026] Where g and d represent generator nodes and load nodes, respectively; F, D, and T represent the set of generator nodes, the set of load nodes, and the set of scheduling time periods, respectively; L is the set of lines; P g,d,t P represents the energy exchange volume between generator node g and load node d at time t. g,t P represents the active power at generator node g at time t. d,t P represents the active power of load node d at time t. l,t The actual power flow of transmission line l at time t; x represents the energy exchange between generator node g and load node d at time t on transmission line l. ij X is the impedance value of branch l. ig This represents the element in the i-th row and g-th column of the power grid impedance matrix X. jg X id X jd All of these are elements in the power grid impedance matrix X.

[0027] Furthermore, step 2 is based on the energy transaction volume P between the generator node and the load node. g,d,t The virtual circulation is set up and the Google matrix G in the original PageRank algorithm is corrected, as follows:

[0028] Step 2.1: Add a virtual power flow pointer to g from load node d, with the power flow size being the energy trade volume P between generator node and load node. g,d,t ;

[0029] Step 2.2: Set up virtual current conversion: Assume that the generator sets on a certain generator node transmit active power flow to multiple load nodes through transmission lines; based on the energy transaction data between generator nodes and load nodes calculated by the power system optimization operation model, the active power transmission path between generator nodes and load nodes is redirected from the load nodes to the generator node, and the weight of the virtual circulation is set according to the specific transaction volume. Then, all active power sent out by the generator returns to the generator node in the form of virtual circulation.

[0030] By setting up a virtual circulation, the Google matrix G in the PageRank calculation formula is modified. The modified Google matrix is ​​denoted as G. * The specific formula is as follows:

[0031]

[0032]

[0033] In equation (6), P ij For the active power flow of transmission line ij, P out (j) represents the outflow power of node j when considering virtual circulation.

[0034] Furthermore, in step 3, the vulnerability PR of all nodes is set. 0 The formula for calculating the initial value vector is:

[0035]

[0036] Where n is the number of nodes in the power grid;

[0037] In step 4, the vulnerability PR of all nodes is... 0 Substituting the initial value vector into the improved PageRank algorithm formula, as follows:

[0038]

[0039] Where δ is the drag coefficient; PR kLet be the vulnerability obtained in the k-th iteration; e is the relink vector, the value of which is shown in the following formula:

[0040]

[0041] Wherein, represents the probability weight of reconnection of the corresponding node;

[0042] The condition for stopping the iterative calculation in step 5 is shown in the following formula:

[0043] |PR k+1 -PR k |≤ε (10)

[0044] Where ε is a sufficiently small constant.

[0045] The beneficial effects of this invention are: This invention identifies vulnerable lines in the power grid by improving the PageRank algorithm, enabling accurate identification of vulnerable lines under different operating conditions of the power grid; the improved PageRank algorithm proposed in this invention sets up virtual circulation based on the energy trading volume between generator nodes and load nodes, thereby improving the Google matrix. Specifically:

[0046] (1) Improved the problem of large error in the calculation result due to the average distribution of PR values ​​of nodes in the original PageRank algorithm.

[0047] (2) It avoids the problem that when the original PageRank algorithm is applied to the power system, the PR value of all nodes eventually converges to 0 due to the "black hole effect" caused by the load node.

[0048] (3) Improvement: When the original PageRank algorithm is applied to the power system, many power nodes and load nodes located at the edge of the network have low influence, which does not match the actual situation of the power system. Attached Figure Description

[0049] Figure 1 This is a flowchart of the steps of the power grid vulnerable line identification method based on the improved PageRank algorithm of the present invention.

[0050] Figure 2 This is a schematic diagram of the virtual circulation of the present invention.

[0051] Figure 3 This is a topology diagram of the gas-electric coupling system in the example of this invention. Detailed Implementation

[0052] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0053] The present invention provides a method for identifying vulnerable power grid lines based on an improved PageRank algorithm, which consists of steps such as solving the energy transaction volume between generator nodes and load nodes, setting virtual circulation current, setting initial vulnerability values ​​for nodes, iterative calculation, and identifying vulnerable lines.

[0054] First, based on the power system optimization model, solve for the energy trade quantity P between generator nodes and load nodes. g,d,t Based on the energy trade volume P between generator nodes and load nodes g,d,t Configure virtual circulation and correct the Google matrix G in the original PageRank algorithm; then set the vulnerability PR of all nodes. 0 Initial value, the node's fragility PR 0 The initial value vector is substituted into the improved PageRank algorithm formula; finally, the node vulnerability is iteratively calculated until the absolute value of the difference between the (k+1)th result and the kth result is less than ε, and the node vulnerability PR is output. k Then, based on the node vulnerability index, the vulnerability of the transmission line is obtained by calculating the sum of the vulnerability of the first and last nodes of the line, thereby identifying the vulnerable lines of the power grid.

[0055] The flowchart of the steps is as follows Figure 1 As shown, the specific process is as follows:

[0056] Step 1: Based on the power system optimization operation model, solve for the energy transaction volume P between generator nodes and load nodes. g,d,t .

[0057] The energy transaction quantity P between generator nodes and load nodes is directly solved by constructing an optimized operation model of the power system. g,d,t Based on the fundamental principle of power flow transmission distribution factor, the energy trade volume P between generator nodes and load nodes is included in the constructed power system optimal operation model. g,d,t The relevant constraints can be solved by equations (1)-(4) to obtain the power flow components of the transmission line.

[0058] Equation (1) indicates that the output of generator g is equal to the sum of the transactions between all loads and generator node g; Equation (2) indicates that the power of load node d is equal to the sum of the transactions between all generators and load d; Equation (3) indicates the component of energy transactions between all generator node-load node pairs on line l. The sum equals the actual power flow P of the line. l,t Equation (4) calculates the power flow components on line l based on the energy exchange between generator node g and load node d and the PTDF (Power Transmission Distributed Factors).

[0059]

[0060]

[0061]

[0062]

[0063] Where g and d represent generator nodes and load nodes, respectively; F, D, and T represent the set of generator nodes, the set of load nodes, and the set of scheduling time periods, respectively; P g,d,t P represents the energy exchange volume between generator node g and load node d at time t. g,t P represents the active power at generator node g at time t. d,t P represents the active power of load node d at time t. l,t The actual power flow of transmission line l at time t; x represents the energy exchange between generator node g and load node d at time t on transmission line l. ij X is the impedance value of branch l. ig This represents the element in the i-th row and g-th column of the power grid impedance matrix X. jg X id X jd All of these are elements in the power grid impedance matrix X.

[0064] Step 2: Based on the energy transaction volume P between the generator node and the load node g,d,t We set up a virtual circulation and corrected the Google matrix G in the original PageRank algorithm.

[0065] The specific improvement measures are as follows:

[0066] Step 2.1: Based on the energy transaction P between generator node g and load node d g,d,t Configure a virtual circulation flow. Specifically, add a virtual power flow from load node d to generator node g, with the power flow size being the energy exchange volume P between the generator node and the load node. g,d,t .

[0067] Step 2.2: Setting up the virtual circulation is as follows Figure 2 As shown. Figure 2 In this system, the generator units at node 1 transmit active power flow to nodes 3, 6, 7, 10, and 11 via transmission lines. Based on the energy trading data between generator nodes and load nodes calculated using the power system optimization operation model, the active power transmission path between generator nodes and load nodes can be redirected from the load nodes to the generator nodes, and the weight of the virtual circulating current can be set according to the specific trading volume. For example... Figure 2As shown by the dashed line, all active power delivered by the generator returns to the generator node in the form of a virtual circulation. Without adding virtual nodes, the load node's out-degree is no longer equal to 0, thus avoiding the black hole effect while increasing the influence of both the generator and load nodes.

[0068] By setting up a virtual circulation, the Google matrix G in the PageRank calculation formula is modified. The modified matrix is ​​denoted as G. * The specific formula is as follows:

[0069]

[0070]

[0071] In equation (6), P ij For the active power flow of transmission line ij, P out (j) represents the outflow power of node j when considering virtual circulation.

[0072] This invention corrects the Google matrix G by setting up a virtual circulation, thereby solving the problems (1), (2), and (3) of the original PageRank algorithm mentioned in the background art.

[0073] Step 3: Set the vulnerability PR for all nodes 0 Initial value,

[0074] Set the vulnerability PR for all nodes 0 The formula for calculating the initial value vector is:

[0075]

[0076] Where n is the number of nodes in the power grid.

[0077] Step 4: Rank the node's vulnerability (PR) 0 The initial value vector is substituted into the improved PageRank algorithm formula.

[0078]

[0079] Where δ is the drag coefficient, which is usually taken as δ = 0.85 based on experience; e is the relink vector, the value of which is shown in equation (9):

[0080]

[0081] Wherein, represents the probability weight of reconnecting the corresponding node.

[0082] Step 5: Iteratively calculate the node vulnerability until the absolute value of the difference between the (k+1)th result and the kth result is less than ε, then output the node vulnerability PR. k .

[0083] The condition for stopping the iterative calculation is shown in formula (10):

[0084] |PR k+1 -PR k |≤ε (10)

[0085] Where ε is a sufficiently small constant.

[0086] Step 6: Based on the node vulnerability index, the vulnerability of the transmission line is obtained by calculating the sum of the vulnerability of the first and last nodes of the line, thereby identifying the vulnerable lines of the power grid.

[0087] (1) Example Introduction

[0088] To verify the effectiveness of the proposed method for identifying vulnerable power grid lines based on the improved PageRank algorithm, a gas-electric coupling system consisting of the IEEE 24-node power system and the 20-node Belgian natural gas system is used as a case study. Its topology is as follows: Figure 3 As shown, the following three operating scenarios are set: (1) normal operation (scenario S1); (2) production of natural gas well W1 is reduced by 50% (scenario S2); (3) natural gas system has sufficient gas supply (scenario S3). The effectiveness of the method proposed in this invention is verified by comparing and analyzing the identification results of vulnerable lines in the power grid.

[0089] (2) Analysis of the results of the example

[0090] This invention constructs a virtual circulation based on the energy trading data between generator nodes and load nodes obtained in step 1, thereby improving the Google matrix of the PageRank algorithm, and correcting the restart vector of the PageRank algorithm according to the improved network constraint coefficients. Then, based on the improved PageRank algorithm, the vulnerability PR value of power system nodes is calculated. The vulnerability of the transmission line is obtained by calculating the sum of the PR values ​​of the first and last nodes of the transmission line, thereby identifying vulnerable lines in the power grid. The top 10 nodes in terms of PR value in the three scenarios are shown in Table 1.

[0091] Table 1. Ranking of Node PR Values ​​in IEEE 24-Node Power Systems

[0092]

[0093] As shown in Table 1, the top 5 nodes in scenario S1 (nodes 1, 23, 2, 20, and 18) have high PR values, with nodes 1, 2, and 23 being the three most important power supply nodes in scenario S1. Nodes 20 and 18 are not only important load nodes but also key nodes on the energy transmission path, occupying important positions in the network topology. The PR value differences among the top 5 nodes in Table 1 are significant, while the differences in PR values ​​between subsequent nodes, starting from node 11 (ranked sixth), are smaller.

[0094] This indicates that in scenario S1, only a few nodes are critical to the power system, and the associated transmission lines are likely to be vulnerable, requiring focused identification and attention. In scenario S2, due to the influence of the natural gas system, the operating status of the power system and the composition of line power flow components have changed significantly. Therefore, the top five nodes become nodes 23, 13, 20, 11, and 19. Nodes 1 and 2, which were ranked first and third in scenario S1, are not in the top five. This is because the generator output on nodes 1 and 2 has decreased, and the energy trading between nodes has changed. Most of their load has shifted to the generators on nodes 23 and 13, resulting in a significant decrease in their PR values.

[0095] Furthermore, it is worth noting that, in a horizontal comparison of scenarios S1 and S2, the PageRank (PR) values ​​of the top three nodes in scenario S2 all exceed the maximum PR value in scenario S1. This indicates that the vulnerability of some nodes has significantly increased due to the natural gas outage, and the stability and security of the power system are under more serious threat. The comparative analysis of scenarios S1 and S2 demonstrates that the improved PageRank algorithm of this invention can accurately reflect the vulnerability of power grid nodes under different operating conditions.

[0096] In scenario S3, due to sufficient gas supply from the natural gas generators, the overall PageRank (PR) values ​​of the nodes decreased, improving the safety and stability of the power system. However, the top-ranked nodes changed again. For example, node 16, ranked first in scenario S3, and node 10, ranked fifth, did not make the top 5 in scenarios S1 and S2. This indicates that the vulnerability of the power grid nodes was affected by the natural gas system. Therefore, the improved PageRank algorithm proposed in this invention can accurately reflect the node vulnerability under different operating conditions of the power system, providing a good foundation for identifying vulnerable lines in the power grid.

[0097] According to the vulnerability line identification method proposed in this invention, vulnerability lines of the power system under three different scenarios are identified by combining the node PR values ​​in Table 1. The specific results are shown in Table 2.

[0098] Table 2 Vulnerable Lines in IEEE 24-Bus Power Systems

[0099]

[0100] Table 2 shows that four vulnerable lines were identified in scenario S1. The most vulnerable line is transmission line 1-2, which connects two important power sources: generator node 1 and generator node 2. This line also has a large active power capacity and handles energy transactions between multiple important generator nodes and load nodes. Furthermore, this line occupies a critical position in the topology. Therefore, line 1-2 has the highest vulnerability in scenario S1. The second most vulnerable line is line 20-23. Node 20 is an important node in the energy transmission channel and also an important load node. Node 23 is an important power source center in the power system; therefore, line 20-23 has a relatively high vulnerability.

[0101] In scenario S2, six vulnerable lines were identified, more than in the other two scenarios. The overall vulnerability of these lines also increased, indicating that the power system's line vulnerability increased due to the natural gas system failure in scenario S2. A horizontal comparison of the number of vulnerable lines and the vulnerability index values ​​also shows that the power system's safety and stability margins are lower in scenario S2, placing the power system in a dangerous state.

[0102] Specifically, the vulnerable lines in scenario S2 have changed significantly compared to S1. Lines 13-23 have become the most vulnerable, mainly due to the impact of a natural gas system fault. The active power of the generator units at node 13 increased significantly, causing the transmission line between nodes 23 and 13 to bear a heavier energy transmission load, thus greatly increasing its vulnerability. Transmission lines 20-23 remain the second most vulnerable, but their vulnerability index increased from 0.133 in S1 to 0.174 in S2, indicating a significant increase in vulnerability under the influence of the natural gas fault, making them a weak link in the power grid and requiring close attention. The subsequent lines all revolve around the two power centers, generator nodes 13 and 23. On the one hand, these lines themselves have high active power and bear a heavy energy transmission load. On the other hand, they occupy critical positions in the network topology, connecting many important nodes. Therefore, these lines are all highly vulnerable and require focused protection, with timely and effective measures to prevent the occurrence and spread of accidents.

[0103] In scenario S3, due to the removal of gas supply restrictions from the natural gas system, the number of identified vulnerable lines is the fewest among the three scenarios, with only three. The PageRank values ​​for these three lines are also relatively low. Therefore, it is evident that the vulnerable line identification method proposed in this invention effectively addresses the shortcomings of the original PageRank algorithm applied to power grids, accurately identifying vulnerable lines in different operating scenarios, providing key monitoring guidance for power grid monitoring and dispatching personnel, and better ensuring the safe and stable operation of the power grid.

Claims

1. A method for identifying vulnerable power grid lines based on an improved PageRank algorithm, characterized in that, Includes the following steps: Step 1: Construct an optimized operation model of the power system and solve for the energy trade volume between generator nodes and load nodes. ; Step 2: Based on the energy trading volume between generator nodes and load nodes Set up a virtual circulation and correct the Google matrix G in the original PageRank algorithm; Step 3: Set the vulnerability of all nodes Initial value; Step 4: Set the node's vulnerability The initial value vector is substituted into the improved PageRank algorithm formula; Step 5: Iteratively calculate node fragility until the absolute value of the difference between the (k+1)th result and the kth result is less than 1. Output node fragility ; Step 6: Based on the node vulnerability index, the vulnerability of the transmission line is obtained by calculating the sum of the vulnerability of the first and last nodes of the line, thereby identifying the vulnerable lines of the power grid. Step 2 is based on the energy exchange volume between generator nodes and load nodes. The virtual circulation is set up and the Google matrix G in the original PageRank algorithm is corrected, as follows: Step 2.1: Add a virtual power flow pointer to g from load node d, with the power flow size being the energy exchange volume between generator node and load node. ; Step 2.2: Set up virtual circulation: Assume that the generator sets on a certain generator node transmit active power flow to multiple load nodes through transmission lines; based on the energy transaction data between generator nodes and load nodes calculated by the power system optimization operation model, the active power transmission path between generator nodes and load nodes is redirected from the load nodes to the generator node, and the weight of the virtual circulation is set according to the specific transaction volume. Then, all active power sent out by the generator returns to the generator node in the form of virtual circulation. By setting up a virtual circulation, the Google matrix in the PageRank calculation formula is modified. The revised Google matrix is ​​denoted as follows: The specific formula is as follows: （5）； （6）； In equation (6), For power transmission lines - The meritorious trend, When considering virtual circulation nodes The outflow power.

2. The method for identifying vulnerable power grid lines based on the improved PageRank algorithm according to claim 1, characterized in that, The power system optimization operation model constructed in step 1 is used to solve for the energy transaction volume between generator nodes and load nodes. Specifically, it includes: Based on the fundamental principle of power flow transmission distribution factor, the constructed power system optimization operation model includes energy trading volume between generator nodes and load nodes. The relevant constraints are solved by equations (1)-(4) to obtain the power flow components of the transmission line; The output of generator g is equal to the sum of all transactions between the load and generator node g: （1）； The power of load node d is equal to the sum of the transaction volumes between all generators and load d: （2）； The component of energy exchange between all generator node-load node pairs on line l The sum equals the actual power flow of the line. : （3）； Based on the energy exchange volume and power transmission distribution factor between generator node g and load node d, calculate the power flow components on line l. : （4）； Where g and d represent generator nodes and load nodes, respectively; F, D, and T represent the set of generator nodes, the set of load nodes, and the set of scheduling time periods, respectively; and L is the set of lines. Let be the energy exchange volume between generator node g and load node d at time t; Let be the active power of generator node g at time t; Let be the active power of load node d at time t; The actual power flow of transmission line l at time t; Let be the component of the energy exchange between generator node g and load node d at time t on transmission line l; Let L be the impedance value of branch l. This represents the element in the i-th row and g-th column of the power grid impedance matrix X. All of these are elements in the power grid impedance matrix X.

3. The method for identifying vulnerable power grid lines based on the improved PageRank algorithm according to claim 1, characterized in that, In step 3, the vulnerability of all nodes is set. The formula for calculating the initial value vector is: （7）； Where n is the number of nodes in the power grid; In step 4, the vulnerability of all nodes is... Substituting the initial value vector into the improved PageRank algorithm formula, as follows: （8）； in, This is the drag coefficient; Let be the vulnerability obtained in the k-th iteration; e is the relink vector, the value of which is shown in the following formula: （9）； in, This represents the probability weight of reconnecting the corresponding node; The condition for stopping the iterative calculation in step 5 is shown in the following formula: （10）； in, It is a constant.

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