A power network vulnerable node fusion identification method and system considering structure and function indexes

Abstract

The application discloses a kind of considering structure and function index's electric power network fragile node fusion identification method and system, method includes the following steps: constructing electric power network model, and calculating the four-dimensional index of node in electric power network model;TOPSIS-CRITIC fusion evaluation model is constructed;Based on TOPSIS-CRITIC fusion evaluation model, the closeness of each node in four-dimensional index is calculated, and node is ranked based on closeness, and then based on ranking, fragile node is identified.The application compared with traditional method, establishes TOPSIS-CRITIC mixed evaluation model, comprehensively considers degree centrality, betweenness centrality and other structure indexes, and electrical coupling connection degree, electrical betweenness and other function indexes, realizes the overall representation of node vulnerability.

Description

Technical Field

[0001] This invention belongs to the field of power system network technology, and specifically relates to a method and system for fusion identification of vulnerable nodes in power networks that considers structural and functional indicators. Background Technology

[0002] Currently, climate change is intensifying and natural disasters are occurring more frequently, highlighting the importance of power system network operation and maintenance security. Scientifically assessing the vulnerabilities of power networks and identifying key nodes that pose potential threats to system stability in advance is crucial for optimizing power system structure and enhancing network robustness.

[0003] Research on power network vulnerability mainly falls into two categories. The first is structural vulnerability analysis based on complex network theory. This method abstracts the power network into a graph model and uses topological indices such as degree centrality and betweenness centrality to quantify the importance of nodes within the network's geometry. Its advantages are simplicity and efficiency, quickly revealing the network's topological core; its disadvantage is that it ignores the network's electrical and physical properties, failing to accurately reflect the actual operating characteristics of the power system. The second category is functional vulnerability analysis based on power system theory. This method focuses on electrical parameters and power flow distribution, using functional indices such as electrical coupling connectivity and electrical betweenness to measure the actual role of nodes in power network transmission. Its advantage is that it better reflects the system's electrical characteristics; its disadvantage is that it ignores the impact of the power network's topology on system robustness. Summary of the Invention

[0004] This invention aims to address the shortcomings of existing technologies and provides the following solutions: A fusion identification method for vulnerable nodes in power networks considering structural and functional indicators includes the following steps: Construct a power network model and calculate the four-dimensional indices of the nodes in the power network model; Construct a TOPSIS-CRITIC fusion evaluation model; The proximity of each node in the four-dimensional indicators is calculated based on the TOPSIS-CRITIC fusion evaluation model, and the nodes are ranked based on the proximity. Vulnerable nodes are then identified based on the ranking.

[0005] Preferably, the method for constructing the power network model includes: The power system is abstracted as an undirected weighted graph, with each component described as a node and the transmission lines connecting the components described as edges. For each line of the power system l Its impedance weight is: In the formula, Rl Indicates the resistance of the circuit. XlIndicates the reactance of the line. Zl This indicates the impedance magnitude of the line.

[0006] Preferably, the four-dimensional indicators include: degree centrality, betweenness centrality, electrical coupling connectivity, and electrical betweenness; The degree centrality is: in, DC ( u ) represents degree centrality. N ( u ) represents a node u The neighborhood group, huv Represents a node u With nodes v The connection relationship; The betweenness centrality is: in, BC ( u ) denotes betweenness centrality, Indicates from node s To the node t The total number of shortest paths, Indicates passing through nodes i The number of shortest paths; The electrical coupling degree is: in, ECC ( u ) indicates the degree of electrical coupling. n Indicates the total number of system nodes. Duv Represents a node u To the node v Electrical distance; The electrical intermediate number is: in, EBk Indicates electrical betweenness, sx Indicates the generator node. tx Indicates the load node. l Represents nodes u The lines of the connected power system, Fl ( sx , tx ) indicates generator node xs To load nodes tx When transmitting unit power, through the line l The power flow.

[0007] Preferably, the TOPSIS-CRITIC fusion evaluation model includes: a CRITIC objective weighting module and a TOPSIS module.

[0008] Preferably, the workflow of the CRITIC objective weighting module includes: The four-dimensional indicators are standardized to obtain four standardized indicators. Calculate the standard deviation of each standardized indicator and the correlation coefficient between each standardized indicator; Based on the standard deviation and the correlation coefficient, the information content and weight of each standardized indicator are calculated.

[0009] Preferably, the workflow of the TPOPSIS module includes: For the power network model, a standardized evaluation matrix is ​​constructed; The weights of the four-dimensional indicators are determined using the CRITIC objective weighting method, and the standardized evaluation matrix is ​​weighted to construct a weighted evaluation matrix. The Euclidean distance between each node and the ideal solution is calculated based on the weighted evaluation matrix, and the proximity is calculated based on the Euclidean distance.

[0010] The present invention also provides a power network vulnerable node fusion identification system that considers structural and functional indicators. The system applies the above-mentioned method and includes: an indicator calculation module, a model construction module, and a vulnerable node identification module. The index calculation module is used to construct a power network model and calculate the four-dimensional indexes of the nodes in the power network model. The model building module is used to build the TOPSIS-CRITIC fusion evaluation model; The vulnerable node identification module calculates the proximity of each node in the four-dimensional indicators based on the TOPSIS-CRITIC fusion evaluation model, ranks the nodes based on the proximity, and then identifies vulnerable nodes based on the ranking.

[0011] Compared with the prior art, the beneficial effects of the present invention are as follows: Compared to traditional methods, this invention establishes a TOPSIS-CRITIC hybrid evaluation model, comprehensively considering structural indicators such as degree centrality and betweenness centrality, as well as functional indicators such as electrical coupling connectivity and electrical betweenness, achieving a comprehensive characterization of node vulnerability. Experimental results in classic cases show that, compared with other evaluation methods, the proposed method identifies four typical types of vulnerable nodes: "super hub" type, "choke point" type, "functional core" type, and "comprehensive balance" type, providing important reference for targeted protection of power systems. Attached Figure Description

[0012] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the network topology of the IEEE 118-node system according to an embodiment of the present invention; Figure 3 This diagram illustrates the network efficiency variations of six different removal methods according to embodiments of the present invention. Detailed Implementation

[0014] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0015] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0016] Example 1 In this embodiment, as Figure 1 As shown, a fusion identification method for vulnerable nodes in power networks considering structural and functional indicators includes the following steps: S1. Construct a power network model and calculate the four-dimensional indices of the nodes in the power network model.

[0017] In this embodiment, the method for constructing a power network model includes: The power system is abstracted as an undirected weighted graph. Each component is described as a node, and the power lines connecting the components are described as edges; where, Represents a set of nodes. Represents the set of edges; This represents the set of edge weights, expressed as the impedance of the line. For each line in the power system... l Its impedance weight is: In the formula, Rl Indicates the resistance of the circuit. Xl Indicates the reactance of the line. ZlIt represents the impedance magnitude of the line, reflecting its total ability to impede current.

[0018] The four-dimensional metrics include: degree centrality, betweenness centrality, electrical coupling connectivity, and electrical betweenness.

[0019] Degree centrality primarily measures the number of directly connected neighbors a node has, reflecting its local influence. For nodes... u Its calculation expression is: in, DC ( u ) represents degree centrality. N ( u ) represents a node u The neighborhood group, huv Represents a node u With nodes v The connection relationship; Betweenness centrality primarily measures a node's ability to act as a "bridge" for shortest paths, characterizing its global hub role. For nodes... u Its calculation expression is: in, BC ( u ) denotes betweenness centrality, Indicates from node s To the node t The total number of shortest paths, Indicates passing through nodes i The number of shortest paths; Electrical coupling connectivity takes into account the electrical characteristics of the power system and is used to measure the degree of electrical connection between a node and its neighboring nodes. For a node... u Its calculation expression is: in, ECC ( u ) indicates the degree of electrical coupling. n Indicates the total number of system nodes. Duv Represents a node u To the node v Electrical distance; Electrical betweenness, based on power flow distribution patterns, measures the mediating role of a node in the power transmission path. For any node in a power system network... u Its electrical betweenness is defined as the electrical betweenness of all branches connected to it. l Half of the sum of electrical betweennesses is calculated using the following expression: in, EBkIndicates electrical betweenness, sx Indicates the generator node. tx Indicates the load node. l Represents nodes u Connected power system lines l , Fl ( sx , tx ) indicates generator node xs To load nodes tx When transmitting unit power, through the line l The power flow.

[0020] S2. Construct the TOPSIS-CRITIC fusion evaluation model.

[0021] The TOPSIS-CRITIC integrated evaluation model includes the CRITIC objective weighting module and the TOPSIS module.

[0022] In this embodiment, the workflow of the CRITIC objective weighting module includes: The four-dimensional indicators are standardized to obtain four standardized indicators; the standardization formula is as follows: in, xij Indicates the first i The node at the th j The original values ​​of each indicator Min( represents the standardized value.) xj ) indicates that all nodes are at the . j The minimum value of each indicator, max( xj ) indicates that all nodes are at the . j The maximum value on each indicator.

[0023] Calculate the standard deviation of each standardized indicator to reflect the degree of dispersion of the indicator: in, σj Indicates the first j The standard deviation of each indicator Indicates the standardized first j The average of the indicators, n This indicates the total number of system nodes.

[0024] Calculate the correlation coefficients among the standardized indicators to measure the degree of information overlap between them: in, rjk Indicators j With indicators k The Pearson correlation coefficient.

[0025] Based on the standard deviation and correlation coefficient, calculate the information content and weight of each standardized indicator: in, Cj Indicates the amount of information. m Indicates the number of evaluation indicators. qj Indicates the weight.

[0026] In this embodiment, the workflow of the TPOPSIS module includes: For the power network model, a standardized evaluation matrix is ​​constructed. For the complex network G, there is... n There are nodes, m The initial evaluation matrix for network nodes is as follows: Since comparisons between different indicator data are involved, data standardization is necessary to eliminate the influence of differences in range and units on the results. The data standardization expression is shown below: in, yij Represents a node i The j The standardized values ​​of each evaluation indicator are shown below. The processed standardized matrix is ​​as follows: in, Y This represents the standardized matrix.

[0027] The weights of the four-dimensional indicators are determined using the CRITIC objective weighting method, and the standardized evaluation matrix is ​​weighted to construct a weighted evaluation matrix: Where Z represents the weighted evaluation matrix.

[0028] The Euclidean distance between each node and the ideal solution is calculated based on the weighted evaluation matrix, and the proximity is calculated based on the Euclidean distance.

[0029] Specifically, calculate the Euclidean distance between the ideal solution and the Euclidean solution. Select the maximum and minimum values ​​of each index to form positive / negative ideal optimal solution vectors. A + and A —: in, Table Indicators j The positive ideal optimal solution Indicators jThe negative ideal optimal solution. This represents the maximum value of all nodes on the j-th index. This represents the minimum value of all nodes on the j-th index. j =1,2,…, m Calculate the Euclidean distance between each node and the ideal optimal solution vector: in, Represents a node i In the j Standardized weighted values ​​for each indicator Represents a node i The distance to the positive ideal solution. Represents a node i Distance to the negative ideal solution. Proximity is calculated based on Euclidean distance: in, Si Indicates proximity. The higher the proximity value, the more important the node.

[0030] S3. Calculate the proximity of each node in the four-dimensional indicators based on the TOPSIS-CRITIC fusion evaluation model, rank the nodes based on the proximity, and then identify vulnerable nodes based on the ranking.

[0031] Example 2 To verify the effectiveness of the proposed method, the IEEE 118-bus system provided by the MATPOWER 8.0 toolbox was selected as an experimental case. This system comprises 118 bus nodes and 186 transmission lines, and is a standard test case widely used in power system research. Its network topology is as follows: Figure 2 As shown.

[0032] The CRITIC method was used to objectively assign weights to the four evaluation indicators, and the calculation results are shown in Table 1.

[0033] Table 1 .

[0034] As can be seen from Table 1, the weights of the four indicators are relatively balanced. Among them, the electrical coupling connectivity has the highest weight (0.344), followed by the betweenness centrality (0.240). This indicates that the structural and functional indicators have irreplaceable importance in the assessment of node vulnerability, and verifies the rationality of the structural-functional comprehensive evaluation index system constructed in this paper.

[0035] The TOPSIS-CRITIC method was used to calculate the ranking of vulnerable nodes in the IEEE 118-node system, as well as their rankings in degree centrality (DC), betweenness centrality (BC), electrical coupling connectivity (ECC), and electrical betweenness (EB). The ranking of the top 15 vulnerable nodes is shown in Table 2.

[0036] Table 2 .

[0037] The top-ranked nodes (such as nodes 49, 80, and 77) showed high importance in multiple individual indicators, but few nodes ranked first in all indicators. This indicates that the vulnerability of the power grid is a comprehensive reflection of multidimensional characteristics.

[0038] If ranked solely by degree centrality, node 65 would only rank 34th, but it ranks 1st in both functional metrics, ultimately achieving a combined ranking of 5th. This demonstrates that evaluations based on a single metric are biased and may overlook important nodes across other dimensions.

[0039] Node 69 ranks 1st in betweenness centrality, 12th in degree centrality, and ultimately 4th overall. This demonstrates the complementary nature of structure-function indices.

[0040] To verify the effectiveness of the proposed method, a node deletion attack was employed on the network. Six attack strategies were used: DC ranking attack, BC ranking attack, ECC ranking attack, EB ranking attack, TOPSIS-CRITIC ranking attack, and random attack, deleting nodes from the network in descending order of ranking. The performance degradation of the network under different attack strategies was evaluated using network efficiency as the metric, expressed as: in, E ( q ) indicates the first q Network efficiency after the attack dij Represents a node u To the node v The shortest impedance path, N Indicates the initial number of nodes.

[0041] The network efficiency of the IEEE 118-node system varies under different attack strategies as follows: Figure 3 And as shown in Table 3. From Figure 3 It can be seen that the attack curve based on TOPSIS-CRITIC sorting is basically at the bottom of all curves, indicating that when removing the same number of nodes, the node sorting result of the TOPSIS-CRITIC method has the most significant destructive effect on network performance.

[0042] Table 3 .

[0043] Further comparison of the data in Table 3 shows that when the first 10 nodes are removed, the TOPSIS strategy and the betweenness centrality strategy perform the best, with a network efficiency of 0.999 after the attack. The electrical betweenness strategy, degree centrality strategy, and electrical coupling connectivity strategy are the next best, while the random attack strategy performs the worst.

[0044] When removing the first 20 nodes, the TOPSIS strategy performed best, with a post-attack network efficiency of 0.566. This was followed by betweenness centrality, degree centrality, electrical betweenness, and electrical coupling connectivity. The random attack strategy performed the worst.

[0045] When removing the first 30 nodes, the TOPSIS strategy performed best, with a post-attack network efficiency of 0.277. This was followed by electrical betweenness, degree centrality, betweenness centrality, and electrical coupling connectivity. The random attack strategy performed the worst.

[0046] The results show that the TOPSIS-CRITIC method can integrate multi-dimensional information from both structural and functional levels, and has significant advantages in identifying node vulnerabilities.

[0047] By analyzing the calculation results of the TOPSIS-CRITIC method (see Table 2), the following types of critical vulnerable nodes in the IEEE 118 network can be identified.

[0048] Node 49 is a "super hub" node. It ranks first in degree centrality, connects the most neighboring nodes in the system, and is the absolute core of the network topology. If this node fails, it will cause a large number of connection interruptions, severely impacting network connectivity.

[0049] Node 69 is a "choke point" node, ranking first in betweenness centrality and undertaking a large number of shortest path relay tasks in the network. The failure of this type of node will significantly increase the transmission distance between other nodes in the network and reduce the network's transmission efficiency.

[0050] Node 65 is a "functional core" node, ranking first in both functional metrics (ECC and EB), and is a critical node for power transmission. Failure of this type of node will directly affect the power system's transmission capacity and operational efficiency.

[0051] Nodes 80 and 77 are "comprehensively balanced" nodes, maintaining high rankings across various indicators, demonstrating a good balance between structural and functional importance. These types of nodes are often the most dangerous vulnerabilities because they possess multiple types of importance simultaneously.

[0052] Example 3 In this embodiment, a power network vulnerable node fusion identification system considering structural and functional indicators includes: an indicator calculation module, a model building module, and a vulnerable node identification module. The index calculation module is used to construct a power network model and calculate the four-dimensional indexes of the nodes in the power network model; the model construction module is used to construct the TOPSIS-CRITIC fusion evaluation model; the vulnerable node identification module calculates the proximity of each node in the four-dimensional indexes based on the TOPSIS-CRITIC fusion evaluation model, ranks the nodes based on the proximity, and then identifies vulnerable nodes based on the ranking.

[0053] The above embodiments are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for fusing identification of vulnerable nodes in power networks considering structural and functional indicators, characterized in that, Includes the following steps: Construct a power network model and calculate the four-dimensional indices of the nodes in the power network model; Construct a TOPSIS-CRITIC fusion evaluation model; The proximity of each node in the four-dimensional indicators is calculated based on the TOPSIS-CRITIC fusion evaluation model, and the nodes are ranked based on the proximity. Vulnerable nodes are then identified based on the ranking.

2. The power network vulnerable node fusion identification method considering structural and functional indicators according to claim 1, characterized in that, The method for constructing the power network model includes: The power system is abstracted as an undirected weighted graph, with each component described as a node and the transmission lines connecting the components described as edges. For each line of the power system l Its impedance weight is: In the formula, Rl Indicates the resistance of the circuit. Xl Indicates the reactance of the line. Zl This indicates the impedance magnitude of the line.

3. The power network vulnerable node fusion identification method considering structural and functional indicators according to claim 1, characterized in that, The four-dimensional metrics include: degree centrality, betweenness centrality, electrical coupling connectivity, and electrical betweenness; The degree centrality is: in, DC ( u ) represents degree centrality. N ( u ) represents a node u The neighborhood group, huv Represents a node u With nodes v The connection relationship; The betweenness centrality is: in, BC ( u ) denotes betweenness centrality, Indicates from node s To the node t The total number of shortest paths, Indicates passing through nodes i The number of shortest paths; The electrical coupling degree is: in, ECC ( u ) indicates the degree of electrical coupling. n Indicates the total number of system nodes. Duv Represents a node u To the node v Electrical distance; The electrical intermediate number is: in, EBk Indicates electrical betweenness, sx Indicates the generator node. tx Indicates the load node. l Represents nodes u The lines of the connected power system, Fl ( sx , tx ) indicates generator node xs To load nodes tx When transmitting unit power, through the line l The power flow.

4. The power network vulnerable node fusion identification method considering structural and functional indicators according to claim 1, characterized in that, The TOPSIS-CRITIC fusion evaluation model includes: the CRITIC objective weighting module and the TOPSIS module.

5. The power network vulnerable node fusion identification method considering structural and functional indicators according to claim 4, characterized in that, The workflow of the CRITIC objective weighting module includes: The four-dimensional indicators are standardized to obtain four standardized indicators. Calculate the standard deviation of each standardized indicator and the correlation coefficient between each standardized indicator; Based on the standard deviation and the correlation coefficient, the information content and weight of each standardized indicator are calculated.

6. The power network vulnerable node fusion identification method considering structural and functional indicators according to claim 4, characterized in that, The workflow of the TPOPSIS module includes: For the power network model, a standardized evaluation matrix is ​​constructed; The weights of the four-dimensional indicators are determined using the CRITIC objective weighting method, and the standardized evaluation matrix is ​​weighted to construct a weighted evaluation matrix. The Euclidean distance between each node and the ideal solution is calculated based on the weighted evaluation matrix, and the proximity is calculated based on the Euclidean distance.

7. A fusion identification system for vulnerable nodes in a power network considering structural and functional indicators, wherein the system applies the method described in any one of claims 1-6, characterized in that, include: The module includes an indicator calculation module, a model building module, and a vulnerable node identification module. The index calculation module is used to construct a power network model and calculate the four-dimensional indexes of the nodes in the power network model. The model building module is used to build the TOPSIS-CRITIC fusion evaluation model; The vulnerable node identification module calculates the proximity of each node in the four-dimensional indicators based on the TOPSIS-CRITIC fusion evaluation model, ranks the nodes based on the proximity, and then identifies vulnerable nodes based on the ranking.

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