Power grid key node identification method based on neighbor nodes

Abstract

The invention discloses a power grid key node identification method based on neighbor nodes, and relates to the technical field of power networks. Comprising the steps that all nodes vi in a power grid model G are acquired, the degree d (vi) of each node and the Ks value Ks (vi) of each node are calculated, and then the influence SI (vi) of each node is calculated; calculating actual influence PNI (vj) provided for the node vi by all neighbor nodes vj of the node vi; and adding the influence SI (vi) of the node vi and the actual influence PNI (vj) provided by all neighbor nodes vj to obtain the overall influence K (vi) of the node, and determining the key degree of the node in the power grid according to the value of the overall influence K (vi) of the node. The method not only considers the influence of all the nodes in the power grid model, but also considers the influence provided by the neighbor nodes for the nodes, so that the key nodes are identified more comprehensively and more comprehensively and accurately.

Description

Technical Field

[0001] The present invention relates to the technical field of power networks, and particularly to a method for identifying key nodes of a power grid based on neighbor nodes. Background Art

[0002] Nodes or links that occupy a core position in a power network generally occupy a central position in the power topology structure or bear a relatively high power transmission volume. Therefore, it is crucial to effectively identify important nodes and links in the power network to avoid a failure in one place from spreading to the rest. By introducing the method for identifying key nodes of a complex network into the power system, that is, by abstracting the power network into a complex network model and using the method for identifying key nodes in the complex network to determine the influence and key degree of each node in the power network.

[0003] Existing methods for identifying key nodes generally calculate the vulnerability index of key lines through the shortest transmission distance between a power source node and a load node and each power supply path from the power source node to the load node, and determine whether a load node is an important node or link according to the vulnerability index of the key line.

[0004] The defect of the above existing technology is that by determining important nodes through the shortest transmission distance between a power source node and a load node, only the load nodes directly connected to the power source node are considered, and other load nodes not directly connected to the power source node are not considered, lacking comprehensiveness and integrity, and being inaccurate. Summary of the Invention

[0005] Based on this, it is necessary to provide a method for identifying key nodes of a power grid based on neighbor nodes for the above technical problems.

[0006] An embodiment of the present invention provides a method for identifying key nodes of a power grid based on neighbor nodes, including:

[0007] Obtain all nodes vi in the power grid model G, calculate the degree d(vi) and Ks value Ks(vi) of each node respectively, and add the degree d(vi) and Ks value Ks(vi) of each node to obtain the influence SI(vi) of each node itself;

[0008] Calculate the actual influence PNI(vj) provided by all neighbor nodes vj of node vi for node vi;

[0009] Add the influence SI(vi) of node vi itself and the actual influence PNI(vj) provided by all neighbor nodes vj to obtain the overall influence K(vi) of the node, and determine the key degree of the node in the power grid according to the value of the overall influence K(vi) of the node to identify key nodes of the power grid;

[0010] Among them, the actual influence PNI(vj) provided by all neighbor nodes vj of the computing node vi includes:

[0011] Calculate the influence Γ(vj) of the neighbor node vj itself and find the exclusive neighborhood of the neighbor node vj, and calculate the influence I(vj) provided by the nodes in the exclusive neighborhood; add the influence Γ(vj) of the neighbor node vj itself to the influence I(vj) provided by the nodes in the exclusive neighborhood to obtain the initial influence NI(vj) provided by the neighbor node vj;

[0012] Calculate the correlation H(vi, vj) between the computing node vi and the neighbor node vj; multiply the initial influence NI(vj) provided by the neighbor node vj by the correlation H(vi, vj) to obtain the actual influence PNI(vj) provided by the neighbor node vj.

[0013] In addition, the power grid model G is: G = (V, E), where V is the set of all nodes in the power grid system, and E is the connection edge between the power grid nodes.

[0014] In addition, the Ks value of the node is obtained by the K-shell method.

[0015] In addition, the calculation of the influence Γ(vj) of each neighbor node vj itself includes:

[0016]

[0017] where k max is the maximum value of the degrees of all nodes in the power network.

[0018] In addition, the influence I(vj) provided by the exclusive neighborhood of the neighbor node includes:

[0019]

[0020] where k max is the maximum value of the degrees of all nodes in the power network, and vr is the node in the exclusive neighborhood of the node vj relative to the node vi.

[0021] In addition, the calculation of the correlation H(vi, vj) between the computing node vi and the neighbor node vj includes:

[0022]

[0023] where N(vi) is the set of neighbor nodes of the node vi, N(vj) is the set of neighbor nodes of the node vj, and nums is the total number of nodes in the power network.

[0024] In addition, the overall influence K(vi) of each node includes:

[0025]

[0026] Among them, SI(vi) is the influence of each node itself, and PNI(vj) is the actual influence provided by the neighbor node vj.

[0027] The above method for identifying key nodes in a power grid based on neighbor nodes provided by the embodiments of the present invention has the following beneficial effects compared with the prior art:

[0028] By adding the influence SI(vi) of the node vi itself and the actual influence PNI(vj) provided by all neighbor nodes vj, the overall influence K(vi) of the node is obtained, and the key degree of the node in the power grid is determined according to the value of the overall influence K(vi) of the node; not only the influence of all nodes themselves in the power grid model is considered, but also the influence provided by neighbor nodes for the node is considered, making the identification of key nodes more comprehensive, more comprehensive and accurate. Description of the Drawings

[0029] Figure 1 It is a power network model diagram of a method for identifying key nodes in a power grid based on neighbor nodes provided in an embodiment;

[0030] Figure 2 It is a schematic diagram taking the node v4 as an example of a method for identifying key nodes in a power grid based on neighbor nodes provided in an embodiment;

[0031] Figure 3 It is a line graph of Kendallτ values of a method for identifying key nodes in a power grid based on neighbor nodes provided in an embodiment;

[0032] Figure 4 It is a sequence diagram of the propagation ability of each node in the SIR model of a method for identifying key nodes in a power grid based on neighbor nodes provided in an embodiment;

[0033] Figure 5 It is an infection ability graph of the first 10 nodes in the SIR model of a method for identifying key nodes in a power grid based on neighbor nodes provided in an embodiment. Detailed Embodiments

[0034] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0035] In one embodiment, a method MNEN for identifying key nodes in a power grid based on neighbor nodes is provided. The method includes: In the MNEN method, it is considered that the influence of a node in the power grid depends not only on itself but also on the influence that its neighbor nodes can provide for it, that is, the contribution of neighbor nodes to it. When a node has strong self-influence and its neighbor nodes can provide more influence for it, then the node is more important in the power network. In addition, the position of a node in the power network is also one of the important factors of the node's importance. When a node is in a more core position in the power network, the influence of the node is greater. When a node is in an edge position, the influence of the node is smaller. Therefore, in the MNEN method, when calculating the self-influence of a node, the number of directly connected neighbor nodes of the node and the position of the node are considered, that is, the degree of the node and the Ks value of the node; when calculating the contribution of neighbor nodes, first calculate the initial contribution of neighbor nodes to this node. Here, the number of one-hop neighbor nodes of neighbor nodes (that is, the degree of neighbor nodes), the Ks value, and the exclusive domain of neighbor nodes relative to this node are introduced; then calculate the probability that neighbor nodes provide contributions for this node, and multiply the initial influence of neighbor nodes by the probability to obtain the influence contribution that neighbor nodes can finally provide.

[0036] To more clearly elaborate on the basic idea of the MNEN method, an illustration is given here according to the power network model. A power network model is as Figure 1 shown. In Figure 1 , taking the node v4 as an example to elaborate on the basic idea: The influence of v4 is jointly determined by v4 itself and its neighbor nodes. v5 is one of the neighbor nodes of v4. Taking v5 as an example for calculation to illustrate the contribution it provides to v4, which is specifically described in Figure 2 .

[0037] Figure 2 (a) shows the nodes v4, v5 and the neighbor nodes of two nodes. Figure 2 (b) shows v4 and its neighbor node set {v1, v2, v3, v5, v11, v12}, Figure 2 (c) shows v5 and its neighbor node set {v2, v4, v14}. Among them, v2 and v14 are the common neighbor nodes of v4 and v5. Since v2 is already a neighbor node of v4 and has been included when calculating the influence of its neighbor nodes, when calculating the influence of node v5 on v4's contribution, it is removed to avoid double counting the influence of the common neighbor node v2, otherwise it will lead to an increase in the proportion of v2 in the overall influence of v4 and cause deviation in the results. When calculating the influence provided by v5 for v4, only the node v14 is included. This node is the two-hop neighbor node of node v4 passing through node v5 under certain conditions, that is, the exclusive neighborhood node. In Figure 2In the example, to avoid the number of nodes in the exclusive neighborhood being 0 in special cases, v4 is included in the calculation. For v5 relative to v4, its exclusive neighborhood is {v14, v4}.

[0038] Regarding how to measure the influence of a node, it needs to be achieved through calculation. In this method, the influence of a node consists of the influence of the node itself and the influence provided by all its neighbor nodes. Assume that G=(V, E) is a power network model.

[0039] Definition 1 (Influence of a node itself): The influence of node vi itself is determined by the Ks value Ks(vi) of the node and the degree d(vi) of the node. The calculation formula is as follows:

[0040] SI(vi)=Ks(vi)+d(vi) (1)

[0041] Among them, the Ks value of the node is obtained by the K-shell method.

[0042] Definition 2 (Exclusive neighborhood of a node): Taking node vi as an example, node vj is a neighbor node of node vi, N(vi) is the set of neighbor nodes of vi, N(vj) is the set of neighbor nodes of vj, CN(vi, vj) is the set of common neighbor nodes of node vi and vj, and EN(vi, vj) is the set of exclusive neighbor nodes of node vj relative to node vi, that is, the exclusive neighborhood. The calculation formula is as follows:

[0043] CN(vi, vj)=N(vi)∩N(vj) (2)

[0044] EN(vi, vj)=N(vj)-CN(vi, vj) (3)

[0045] Definition 3 (Initial influence of a neighbor node): For node vi, the initial influence provided by its neighbor node vj is NI(vj). NI(vj) consists of two parts: the influence Γ(vj) provided by node vj itself for vi, and the influence I(vj) provided by the exclusive neighborhood of node vj. The calculation formulas for Γ(vj) and I(vj) are as follows:

[0046]

[0047]

[0048] The calculation formula for NI(vj) is as follows:

[0049] NI(vj)=Γ(vj)+Ι(vj) (6)

[0050] Among them, k maxLet \(\Delta\) be the maximum degree of all nodes in the power grid, and \(v_r\) be the nodes in the exclusive neighborhood of node \(v_j\) relative to node \(v_i\).

[0051] Definition 4 (Relevance degree between nodes): The final influence provided by the neighbor node \(v_j\) of node \(v_i\) is related to the relevance degree \(H(v_i, v_j)\) between the two nodes. Since it is possible that the value is 0 because there may be no common neighbor nodes between the two nodes, it is necessary to improve it. The calculation formula is as follows:

[0052]

[0053] where \(N(v_i)\) is the set of neighbor nodes of node \(v_i\), \(N(v_j)\) is the set of neighbor nodes of node \(v_j\), and \(nums\) is the total number of nodes in the power grid.

[0054] Definition 5 (Actual influence provided by neighbor nodes): When calculating the actual influence that the neighbor node \(v_j\) of \(v_i\) can provide, if the initial influence value of node \(v_j\) on \(v_i\) is directly provided to \(v_i\), it will cause the influence provided by the neighbor node to be too large and reduce the importance of the node itself. In actual situations, when calculating the influence of nodes in a power grid, the node itself occupies an important position. Therefore, it is necessary to reduce the influence provided by neighbor nodes to a certain extent. In the MNEN method, the relevance degree between two nodes is introduced, and it is considered that the greater the relevance between a node and its neighbor node, the more important the neighbor node is. Therefore, the initial influence value of node \(v_j\) is multiplied by the relevance degree between the two nodes. The calculation formula is as follows:

[0055]

[0056] Definition 6 (Overall influence of a node): The overall influence of node \(v_i\) in the power grid is composed of its own influence and the influence that all its neighbor nodes can provide for it. The calculation formula is as follows:

[0057]

[0058] where \(N(v_i)\) is the set of neighbor nodes of node \(v_i\).

[0059] Calculating the influence value of a node in the power grid mainly consists of three steps:

[0060] (1) Calculate the influence of the node itself according to the degree of the node and the \(K_s\) value of the node;

[0061] (2) Calculate the influence that all neighbor nodes can provide for it. In this step, first calculate the influence of a certain neighbor node itself, and then find the exclusive neighborhood of the neighbor node (the nodes in the exclusive neighborhood belong to the two-hop neighbor nodes under certain conditions), and calculate the influence that the exclusive neighborhood can provide. Since the calculated result of this value is relatively large, the correlation between nodes is introduced to process it to reduce its proportion in the calculation of the final influence of the node; adding up the influence contributions of all neighbor nodes gives the final influence value that the neighbor nodes can provide for it.

[0062] (3) Add the values calculated in the first and second steps to obtain the overall influence of the node and sort it.

[0063] The specific working process is as follows:

[0064]

[0065] In this paper, Python is used to write a program to obtain the sorting results of the top 15 nodes of the BC, CC, EC, K-shell, PR, Gravity, PL, ELKSS, GIN, GSM, ECRM, and MNEN methods in the power network model; the SIR model is used to calculate the influence of each node, and the infection probability α = 0.01 and the number of iterative runs t = 1000 are set. The sorting results of each method and SIR are shown in Table 1.

[0066] Table 1 Sorting results of each method, and the last column is the SIR sorting

[0067]

[0068] In Table 1, among the top 10 nodes of the MNEN method and SIR, 9 nodes are the same, and the first 6 nodes are exactly the same and in the same sequence. Therefore, the MNEN method has a good effect on identifying node influence.

[0069] Experimental verification

[0070] In this section, the MNEN method, 11 key node identification methods, and the SIR model are simulated in the power grid network, and the obtained simulation results are compared and verified, and different situations are analyzed. The 11 key node identification methods are: BC, CC, EC, K-shell, PR, Gravity, PL, ELKSS, GIN, GSM, and ECRM. All method experiments are run on a desktop computer with the operating system Win10, CPU i3-10100, and memory 16GB.

[0071] 1. Datasets used in the experiment

[0072] In the experiment on the key node recognition performance of the MNEN method, it was verified in the Powergrid network, which has 4941 nodes, 6594 edges, an average degree of 2.669, an average clustering coefficient of 0.107, and the maximum node degree in the network is 19.

[0073] 2. Evaluation Metrics

[0074] In this paper, the SIR propagation model is used to evaluate the node ranking sequences obtained by various methods running on different networks. The SIR model is a relatively classic evaluation criterion for key node recognition effects. Although there are currently multiple evaluation methods for key node recognition effects, the SIR model is still widely used.

[0075] 3. Experimental Performance Analysis

[0076] The MNEN, 11 comparison methods, and the SIR model were implemented using a Python program, and then applied to the Powergrid network to calculate the influence of nodes and sort them. In the SIR model, the infection effect of nodes is measured according to the number of infected nodes and recovered nodes. Due to the randomness of this model, in order to obtain relatively stable and reliable data, it is run multiple times iteratively in SIR and the average value is taken. When setting the number of iterative runs, the set value is 1000.

[0077] (1) The first 15 node sequences of 12 methods and SIR in the Powergrid network

[0078] Table 2 The first 15 node sequences of different methods in the Powergrid network

[0079]

[0080] As can be seen from Table 2, in the Powergrid network, the first 3 nodes of MNEN are the same as those of the SIR model, and 12 of the first 15 nodes are the same as those of the SIR model, and the sequences are relatively consistent. Therefore, the node recognition effect of this method is good.

[0081] (2) Kendall values under different infection probabilities

[0082] Suppose the node sequence obtained by a certain method in the Powergrid network is R, and the node sequence obtained by using the SIR model is S. Set the infection probability of the SIR model to range from 0.01 to 0.1, incrementing by 0.01 each time, and a total of 10 values are taken. At each probability, a sequence can be obtained. All sequences can be represented by R = {R1, R2,... Rm} (m = 10). Calculate the sequence S and Ri (1 ≤ i ≤ 10) using formula (10) to obtain the Kendall τ values under different infection probabilities.

[0083]

[0084] Show the Kendall τ values of 12 methods in the Powergrid network in the form of a line graph, specifically as Figure 3 shown.

[0085] In the Powergrid network, compared with the other 11 methods, the MNEN method has higher Kendall τ values from 0.01 to 0.1 than the other methods. The larger the Kendall τ value, the more consistent the node sequence obtained by the method in the network is with the node sequence obtained by the SIR model, and the better the key node identification effect of the method. Therefore, in the Powergrid network, the overall performance of the MNEN method is better.

[0086] (3) Comparison of the propagation ability values of 12 methods on the SIR model

[0087] Use 12 methods to calculate the influence values of different nodes in the Powergrid network with the SIR. Compare the sequences obtained by different methods with the sequence obtained by the SIR respectively, so as to obtain the propagation ability sequence of each node in the SIR model for each method. Show the experimental results in the form of a stacked graph, specifically as Figure 4 shown.

[0088] In the Powergrid network, due to the large number of nodes, the infection ability data of each node is displayed in the form of lg10. When the curve shows a smooth downward trend from left to right, the effect of the method is better. The importance of a node is proportional to its infection ability. The higher the consistency between the node importance sequence obtained by each method and the sequence obtained by the SIR model, the fewer the areas where the curve fluctuates. Therefore, Figure 4 it can be seen that in the Powergrid network, the MNEN method has the best effect.

[0089] (4) Infectivity of the top 10 nodes as seed nodes

[0090] In the SIR model, analyze the influence of the top 10 nodes identified by different methods. In this experiment, take the top 10 nodes of different methods as seed nodes, set the time step t from 1 to 30, calculate the number of nodes infected by the 10 nodes and the number of nodes that recover after being infected at time t, and analyze the infectivity of the top 10 nodes according to this numerical value. Set the infection probability to 0.1 and the recovery probability to 1.

[0091] Select the top 10 nodes of 12 methods in the Powergrid network, and calculate their infectivity as seed nodes in the SIR model, specifically as Figure 5 shown.

[0092] Figure 5 Show the infectivity of the top 10 nodes selected by all methods calculated using the SIR model over time in the Powergrid network. As the time step t changes, the infectivity F(t) gradually stabilizes. In different networks, the value of t at which F(t) stabilizes is different, but it basically reaches a stable state before t = 10. According to Figure 5 it can be seen that in the Powergrid network, the infectivity of the top 10 nodes of the MNEN method is higher than that of other methods, and the overall effect is better.

[0093] The above-described embodiments merely represent several implementation manners of the present application. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the invention patent. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several deformations and improvements can still be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the appended claims.

Claims

1. A method for identifying key nodes of a power grid based on neighbor nodes, characterized in that, Including: Obtain all nodes \(v_i\) in the power grid model \(G\), calculate the degree \(d(v_i)\) and \(Ks\) value \(Ks(v_i)\) of each node respectively, and add the degree \(d(v_i)\) and \(Ks\) value \(Ks(v_i)\) of each node to obtain the influence SI\((v_i)\) of each node itself; Calculate the actual influence PNI\((v_j)\) provided by all neighbor nodes \(v_j\) of node \(v_i\) for node \(v_i\); Add the influence SI\((v_i)\) of node \(v_i\) itself and the actual influence PNI\((v_j)\) provided by all neighbor nodes \(v_j\) to obtain the overall influence \(K(v_i)\) of the node, and determine the criticality of the node in the power grid according to the value of the overall influence \(K(v_i)\) of the node to identify the critical nodes in the power grid; Among them, the calculation of the actual influence PNI\((v_j)\) provided by all neighbor nodes \(v_j\) of node \(v_i\) includes: Calculate the influence \(\Gamma(v_j)\) of neighbor node \(v_j\) itself and find the exclusive neighborhood of neighbor node \(v_j\), and calculate the influence \(I(v_j)\) provided by the nodes in the exclusive neighborhood; Add the influence \(\Gamma(v_j)\) of neighbor node \(v_j\) itself and the influence \(I(v_j)\) provided by the nodes in the exclusive neighborhood to obtain the initial influence NI\((v_j)\) provided by neighbor node \(v_j\); Calculate the correlation degree \(H(v_i, v_j)\) between node \(v_i\) and neighbor node \(v_j\); Multiply the initial influence NI\((v_j)\) provided by neighbor node \(v_j\) by the correlation degree \(H(v_i, v_j)\) to obtain the actual influence PNI\((v_j)\) provided by neighbor node \(v_j\).

2. The method for identifying key nodes of a power grid based on neighbor nodes according to claim 1, characterized in that, The power grid model \(G\) is: \(G=(V, E)\), where \(V\) is the set of all nodes in the power grid system, and \(E\) is the connection edge between power grid nodes.

3. The method for identifying key nodes of a power grid based on neighbor nodes according to claim 1, wherein The \(Ks\) value of the node is obtained by the K-shell method.

4. The method for identifying key nodes of a power grid based on neighbor nodes according to claim 1, characterized in that, The calculation of the influence \(\Gamma(v_j)\) of each neighbor node \(v_j\) itself includes: where k max is the maximum value of the degrees of all nodes in the power grid.

5. The method for identifying key nodes of a power grid based on neighbor nodes according to claim 1, wherein The influence \(I(v_j)\) provided by the exclusive neighborhood of the neighbor node includes: where k max is the maximum value of the degrees of all nodes in the power network, and vr is the node in the exclusive neighborhood of node vj relative to node vi.

6. The method for identifying key nodes of a power grid based on neighbor nodes according to claim 1, wherein, The calculation of the correlation degree \(H(v_i, v_j)\) between node \(v_i\) and neighbor node \(v_j\) includes: Among them, \(N(v_i)\) is the set of neighbor nodes of node \(v_i\), \(N(v_j)\) is the set of neighbor nodes of node \(v_j\), and nums is the total number of nodes in the power network.

7. The method for identifying key nodes of a power grid based on neighbor nodes according to claim 1, wherein The overall influence \(K(v_i)\) of each node includes: Among them, SI\((v_i)\) is the influence of each node itself, and PNI\((v_j)\) is the actual influence provided by neighbor node \(v_j\).

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