Power system key line identification method based on hypergraph model

Abstract

The invention discloses an electric power system key line identification method based on a hypergraph model, and the method comprises the steps: 1, defining each power transmission path as a hyperedge through power flow tracking, defining each line as a node, and constructing a hypergraph model of an electric power system; 2, performing K-Shell decomposition on the hypergraph model, and calculating the structural importance of each power transmission line; 3, calculating the magnitude of the load flow of the hyperedge, and calculating the magnitude of the weight of the hyperedge by fusing the importance of the branch structure and the magnitude of the load flow of the hyperedge through an entropy weight method; 4, descending sorting is carried out according to hyperedge weights, and a key line sequence is output; step 5, constructing a node transition probability matrix based on hyperedge weight; step 6, screening unconnected high transition probability node pairs to generate a candidate branch set; and step 7, with maximization of the evaluation index load balancing entropy LBE as a target, adding branches in an accumulated manner until the LBE reaches a peak value, and completing structure optimization. According to the invention, the recognition precision of the key line can be improved, and balanced power flow distribution can be realized.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of power system safety analysis and optimization technology, and particularly relates to a power system key line identification method based on a hypergraph model. BACKGROUND

[0002] Although the causes of large-scale power failure are various, they all have a common feature that the cascading failure caused by the key line failure leads to system collapse, so accurate identification of the key line has become the basis for ensuring the safety and reliable operation of the power grid.

[0003] At present, in order to cope with this challenge, domestic and foreign scholars have carried out a series of researches, and the conventional graph theory method only describes the binary connection relationship and cannot represent the multi-line coordinated power transmission path. A variety of methods for identifying key power transmission lines have been proposed, which comprehensively consider multiple indexes of structure and electricity, and improve the identification accuracy of key lines. However, these methods do not consider the influence of dynamic distribution of power flow on the importance of lines, which will lead to deviation in identification of key lines. At the same time, the existing structure optimization model usually takes the minimum loss as the target, lacks quantitative evaluation of load balance, and is difficult to couple the system structure and real-time power flow state. SUMMARY

[0004] In order to solve the above problems, the application provides a power system key line identification method based on a hypergraph model, which can improve the identification accuracy of key lines by fusing the structure level (K-Shell) and the power flow weight; and can realize the balanced distribution of power flow by generating candidate branches based on random walk and taking the maximum load balance entropy as the target to guide the topology reconstruction.

[0005] To achieve the above purpose, the technical scheme adopted by the application is: a power system key line identification method based on a hypergraph model, comprising the following steps:

[0006] Step 1: defining each power transmission path as a hyperedge and each line as a node by using power flow tracking to construct a hypergraph model of the power system;

[0007] Step 2: K-Shell decomposition is performed on the hypergraph model to calculate the structural importance K sum (e) of each power transmission line;

[0008] Step 3: calculating the power flow size P min (e) carried by each hyperedge, and using the entropy weight method to fuse the branch structure importance K sum (e) and the power flow size P min (e) carried by each hyperedge to calculate the weight w(e) of each hyperedge;

[0009] Step 4: Sort in descending order according to the hyperedge weight w(e) and output the key path sequence;

[0010] Step 5: Construct the node transition probability matrix P(u,v) based on the hyperedge weight w(e);

[0011] Step 6: Filter unconnected high-transition probability node pairs to generate candidate branch sets;

[0012] Step 7: With the goal of maximizing the evaluation index load balancing entropy LBE, complete the structural optimization by cumulatively adding branches until LBE reaches its peak.

[0013] Furthermore, in step 1, the power flow tracking analysis includes:

[0014] The active power transmission path from generator to load is generated based on graph theory algorithm and the lossless network path is reconstructed according to the proportional distribution principle after ignoring line loss.

[0015] Furthermore, in step 2, the K-Shell decomposition includes:

[0016] Iteratively remove nodes and associated hyperedges with a degree of 1 in the hypergraph, and assign the same K to the nodes removed in each round. sum (e) value until the hypergraph is empty.

[0017] Furthermore, in step 3, the entropy weight method is used to fuse the branch structure importance K sum (e) and the magnitude of the super-edge-carrying power flow P min (e) is used to calculate the hyperedge weight w(e);

[0018] The hyperedge weight formula is:

[0019] w(e)=α·K sum (e)+β·P min (e);

[0020] Where, e is the hyperedge corresponding to the transmission path, α is the weight corresponding to the importance of the branch structure, and K sum (e) is the importance of the branch structure, β is the weight corresponding to the size of the super-edge carrying flow, P min (e) is the magnitude of the super-edge-carrying current.

[0021] Furthermore, after step 4, a verification step is included to compare the load loss rate of critical line sequences under deliberate attacks. The load loss rate verification shows that the new method has a lower load loss rate than the other three traditional methods, with the minimum value reaching 0.42, indicating that this method has higher accuracy and reliability in identifying critical lines in the power system.

[0022] Further, in the step 5, the node transition probability matrix P(u,v) is decomposed into two-stage joint probability;

[0023] The formula for calculating the node transition probability matrix P(u,v) is:

[0024]

[0025] In the formula, P(u,v) is the transition probability from node u to node v, π action (e) is the selection probability of hyperedge e, π node (v|e) is the conditional probability of selecting node v in hyperedge e.

[0026] Further, the formula for calculating the selection probability π action (e) of hyperedge e is:

[0027]

[0028] In the formula, w(e) is the hyperedge weight, and δ(e) is the number of edges contained in the hyperedge;

[0029] The formula for calculating the conditional probability π node (v|e) of selecting node v in hyperedge e is:

[0030]

[0031] In the formula, C(u) is the power demand of node u, D(u) is the degree of node u, j is a node contained in hyperedge e, and C(j) represents the power transmission capacity of node j in hyperedge e.

[0032] Further, in the step 6, unconnected high transition probability node pairs are screened to generate a candidate branch set, and existing connections in the system and direct connections between generator and load nodes need to be excluded.

[0033] Further, in the step 7, the evaluation index is:

[0034]

[0035] In the formula, P(u,v) is the transition probability from node u to node v.

[0036] Further, in the step 7, the strategy for adding branches cumulatively is to add candidate branches in order from high to low according to the transition probability P(u,v), and recalculate LBE after adding each branch, until LBE no longer increases significantly.

[0037] The beneficial effects of adopting the technical solution are:

[0038] This invention provides a method for identifying critical circuits in power systems based on a hypergraph model. This method offers a new perspective and approach for identifying and optimizing critical circuits in power systems, helping to more accurately identify vulnerable links in critical circuits. By constructing a hypergraph model of the power system, calculating hyperedge weights w(e) and outputting critical circuits, and performing structural optimization with the goal of maximizing the evaluation metric load balance entropy (LBE), this method improves the accuracy and adaptability of critical circuit identification, providing a more comprehensive and precise approach for assessing system vulnerability and supporting proactive risk mitigation in power grid operations.

[0039] This invention can significantly improve the accuracy of identifying key lines in the power system: it innovatively integrates the topology of the power grid and the dynamic flow characteristics, and uses the hypergraph model to set the transmission path as a hyperedge and the transmission line as a node, overcoming the limitation of the traditional graph model that can only describe binary relationships. At the same time, the hyperedge weight w(e) is introduced to comprehensively consider the importance of the branch structure K sum (e) and the magnitude of the super-edge-carrying power flow P min (e) significantly improves the accuracy of critical line identification. In a validation study on an IEEE 39-node system, this method reduced the load loss rate to as low as 0.42 under a deliberate attack scenario, a reduction of approximately 20% to 35% compared to traditional methods. This demonstrates that this method can more accurately locate the core lines that truly impact system stability.

[0040] The system optimization effect of the present invention is outstanding: the present invention comprehensively considers the electrical topology structure and dynamic power flow characteristics for collaborative modeling. In the new branch strategy, the node transfer probability matrix is ​​constructed based on the random walk model, with the goal of maximizing the evaluation indicator load balancing entropy (LBE). The results show that after adding a high-transfer probability branch in the IEEE 39-node system, the load balancing entropy increases from 3.3319 to 3.4484, an increase of 8.6%, indicating that the uniformity of power flow distribution is significantly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 A schematic flow chart of a method for identifying critical circuits in a power system based on a hypergraph model according to the present invention;

[0042] Figure 2 IEEE 39 node system topology diagram in the embodiment of the present invention

[0043] Figure 3 A schematic diagram of hypergraph modeling in an embodiment of the present invention;

[0044] Figure 4 A diagram of the K-Shell decomposition process in an embodiment of the present invention;

[0045] Figure 5 This is a hyperedge weight distribution diagram in an embodiment of the present invention;

[0046] Figure 6 Loss rate comparison chart for different identification methods in embodiments of the present application

[0047] Figure 7 Three-dimensional column chart of node transition probability matrix in embodiments of the present application

[0048] Figure 8 Constraint chart for candidate branch screening in embodiments of the present application

[0049] Figure 9 IEEE39 node system optimization topology chart in embodiments of the present application DETAILED DESCRIPTION

[0050] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application will be further described below in combination with the drawings.

[0051] In the present embodiment, the target system is an IEEE39 node power grid (containing 39 nodes and 46 branches), and the complete process of key line identification and structure optimization is shown. A hypergraph model of the power system is established by using power flow tracking, the structural importance of each line is quantified using the K-shell index, the power flow size P(e) carried by the hyperedge is calculated considering the power flow dynamics, and the hyperedge weight w(e) size is calculated by using the entropy weight method to fuse the branch structural importance K(e) and the power flow size P(e) carried by the hyperedge, thereby completing the identification of the key lines of the system. The node transition probability matrix is constructed based on the hyperedge weight, the candidate branch set is generated by screening the unconnected high transition probability node pairs, and the structure optimization is completed by adding the branches cumulatively until the load balance entropy (LBE) reaches the peak value. min sum min min sum min

[0052] Referring to Figure 1 The present application proposes a key line identification method for a power system based on a hypergraph model, which mainly includes two parts: key line identification and structure optimization. First, a hypergraph model of the power system is established, the structural importance of the line is quantified using the K-shell index, the power flow size P(e) carried by the hyperedge is calculated, and the hyperedge weight w(e) size is calculated by using the entropy weight method to fuse the branch structural importance K(e) and the power flow size P(e) carried by the hyperedge, thereby completing the identification of the key lines of the system. Second, the node transition probability matrix is constructed based on the hyperedge weight w(e), the candidate branch set is generated by screening the unconnected high transition probability node pairs, and the structure optimization is completed by adding the branches cumulatively until the load balance entropy (LBE) reaches the peak value. ​​​​​​

[0053] Including steps:

[0054] Step 1: Use power flow tracing to define each transmission path as a hyperedge and each line as a node to construct a hypergraph model of the power system.

[0055] Step 2: Perform K-Shell decomposition on the hypergraph model and calculate the structural importance K of each transmission line sum (e);

[0056] Step 3: Calculate the magnitude of the superedge load flow P min (e) and use the entropy weight method to integrate the importance of branch structure K sum (e) and the magnitude of the super-edge-carrying power flow P min (e) is used to calculate the hyperedge weight w(e);

[0057] Step 4: Sort in descending order according to the hyperedge weight w(e) and output the key path sequence;

[0058] Step 5: Construct the node transition probability matrix P(u,v) based on the hyperedge weight w(e);

[0059] Step 6: Filter unconnected high-transition probability node pairs to generate candidate branch sets;

[0060] Step 7: Set the maximum load balancing entropy (LBE) evaluation index as the optimization target, and complete the structural optimization by cumulatively adding branches until LBE reaches the peak.

[0061] like Figure 3 The figure shows a detailed illustration of the hypergraph modeling process for power systems in this invention. Taking the IEEE 39-node system as an example, 68 paths were found for tracing steady-state power flows. Based on the hypergraph definition, the hypergraph model is constructed, with power flow paths as hyperedges and the contained lines as hyperedge nodes.

[0062] The present invention performs K-Shell decomposition on the hypergraph model and uses K-shell indicators to quantify the structural importance of the circuit. Figure 4 As shown in Figure 2, in K-Shell analysis, nodes with degree 1 and their connected hyperedges are first deleted from the network. After the deletion operation, new nodes with degree 1 appear in the network, and then these new nodes with degree 1 and their connected hyperedges are deleted. This operation is repeated, and the same K value is assigned to the nodes deleted together each time.

[0063] The traditional K-Shell analysis method only considers the topological structure of the power grid and lacks the influence of the power flow calculation in the line. Therefore, we propose an improved method to calculate the super-edge load flow size P min (e) and use the entropy weight method to integrate the importance of branch structure K sum(e) and the magnitude of the super-edge-carrying power flow P min (e) is used to calculate the hyperedge weight w(e) to quantify the weight of each transmission path. Figure 5 As shown, the hyperedge weight w(e) is calculated, and the key paths identified are 46, 14, 20, 37, 33, 35, 39, 41, 10, and 34.

[0064] The hyperedge weight formula is:

[0065] w(e)=α·K sum (e)+β·P min (e);

[0066] Where, e is the hyperedge corresponding to the transmission path, α is the weight corresponding to the importance of the branch structure, and K sum (e) is the importance of the branch structure, β is the weight corresponding to the size of the super-edge carrying flow, P min (e) is the magnitude of the super-edge-carrying current.

[0067] In the process of power system analysis and modeling, load loss probability (or rate) is a key indicator, reflecting the probability that the system cannot meet the load demand under specific conditions. Figure 6 As shown in the figure, a comparative analysis of the implementation effects of the present invention and three other traditional methods shows that the load loss rate is significantly lower than the other three traditional methods, with the minimum value reaching 0.42. The results show that the proposed method has higher accuracy and reliability in identifying critical lines in the power system.

[0068] The node transfer probability matrix describes the relative probability of the power flow in the system transferring from one node to another. A higher transfer probability value usually means that the node pair plays an important role in the power flow transmission. Therefore, the transfer probability matrix can be regarded as an importance map of the potential power flow paths in the system. On this basis, the transfer probability matrix is ​​used as the basis for structural optimization: on the one hand, node pairs that are currently unconnected but have significant transfer probabilities are identified as candidate connections for potential efficient paths; on the other hand, lines with extremely low transfer probabilities in existing connections are identified as redundant edges that can be adjusted or downgraded in structural optimization. Figure 7 The figure shows the calculation results of the node transition probability matrix, where red represents the high-probability core area, yellow represents the medium-probability hub area, and blue represents the low-probability edge area.

[0069] The node transition probability matrix P(u,v) can be decomposed into the joint probability of two stages;

[0070] The node transfer probability matrix P(u,v) formula is:

[0071]

[0072] Where P(u,v) is the transition probability from node u to node v, π action (e) is the probability of selecting hyperedge e, π node (v|e) is the conditional probability of selecting node v in hyperedge e.

[0073] In the power system hypergraph model, the hyperedge selection probability is the core indicator of the random walk process. Its essence is to quantify the relative importance of the transmission path selected by the power flow, avoiding the distortion of the importance judgment of the key channels due to the redundancy of the hyperedge structure.

[0074] The selection probability formula of the hyperedge is:

[0075]

[0076] Where, π action (e) is the selection probability of hyperedge e, w(e) is the hyperedge weight, and δ(e) is the number of edges contained in the hyperedge.

[0077] The conditional probability of node selection is the core component of the hypergraph random walk model. Its essence is to quantify the tendency of power flow to choose a specific line (node) under a given transmission path (hyperedge). By weighting the power flow capacity with inverse structural degree, it can ensure that the power flow tends to flow to areas with relatively marginal structures but strong loads, thereby promoting overall load balancing of the system.

[0078] The conditional probability formula for selecting a node in the hyperedge is:

[0079]

[0080] Where C(u) is the power flow demand at node u, and D(u) is the degree of node u.

[0081] When constructing the branch optimization suggestion set, the node pairs with the highest probability in the node transfer probability matrix are preferentially selected as candidate connection lines. However, the selection of connection lines needs to follow two constraints: it is necessary to exclude existing connection lines in the system to avoid duplicate connections or disturbances in the original topology; and exclude direct connections between generators and load nodes. Although such direct connections may have extremely high transfer probabilities, they may bypass the transmission network to supply power in actual grid operation, thus disrupting the power flow scheduling level, and therefore are not adopted. Figure 8 As shown in the figure, the traditional method identified a total of 7 possible connection paths. In contrast, the improved node transfer algorithm identified 13 connection paths under the same conditions, significantly increasing the number of paths and coverage.

[0082] As an important index to measure the order of system, entropy reaches the maximum when the power system is in a balanced state, and the energy distribution is highly uniform. Based on this theory, the load balance entropy (LBE) is used to quantify the uniformity of load distribution, and the maximum of LBE is taken as the objective of the structural optimization model.

[0083] The evaluation index is:

[0084]

[0085] where P(u,v) is the transition probability from node u to node v.

[0086] The lower the LBE value, the more concentrated the power flow is distributed in a few key paths, and the poorer the load balance of the system; on the contrary, the higher the LBE value, the more uniform the power transfer probability distribution, the better the line load balance, and the stronger the system disturbance resistance. The maximum of load balance entropy (LBE) is taken as the optimization objective, the candidate branches are added in turn according to the transition probability from high to low, and the LBE is recalculated after adding each branch, until the LBE no longer increases significantly, at this time the LBE reaches the peak, and the structural optimization is completed. Before optimization, the overall load balance entropy of the system is 3.3319. According to the branch selection standard, after adding the line L47 (connecting nodes 28-38), the load balance entropy is improved to 3.4484. This result shows that the optimized network structure realizes more balanced load distribution, the system robustness is significantly enhanced, and meets the expectation of the entropy maximization theory on system stability.

[0087] The above shows and describes the basic principles and main features of the present application and the advantages of the present application. Those skilled in the art should understand that the present application is not limited to the above examples, and the above examples and descriptions in the specification are only to illustrate the principles of the present application. Without departing from the spirit and scope of the present application, various changes and improvements can be made to the present application, and these changes and improvements all fall within the scope of the claimed present application. The scope of protection of the present application is defined by the appended claims and their equivalents.

Claims

1. A method for identifying critical circuits in a power system based on a hypergraph model, characterized in that: Including steps: Step 1: Use power flow tracing to define each transmission path as a hyperedge and each line as a node to construct a hypergraph model of the power system. Step 2: Perform K-Shell decomposition on the hypergraph model and calculate the structural importance K of each transmission line sum (e); Step 3: Calculate the magnitude of the superedge load flow P min (e) and use the entropy weight method to integrate the importance of branch structure K sum (e) and the magnitude of the super-edge-carrying power flow P min (e) is used to calculate the hyperedge weight w(e); Step 4: Sort in descending order according to the hyperedge weight w(e) and output the key path sequence; Step 5: Construct the node transition probability matrix P(u,v) based on the hyperedge weight w(e); Step 6: Filter unconnected high-transition probability node pairs to generate candidate branch sets; Step 7: With the goal of maximizing the evaluation index load balancing entropy LBE, complete the structural optimization by cumulatively adding branches until LBE reaches its peak.

2. A method for identifying critical circuits in a power system based on a hypergraph model according to claim 1, characterized in that: In step 1, the power flow tracking analysis includes: The active power transmission path from generator to load is generated based on graph theory algorithm and the lossless network path is reconstructed according to the proportional distribution principle after ignoring line loss.

3. The method for identifying critical circuits in a power system based on a hypergraph model according to claim 3, characterized in that: In step 2, K-Shell decomposition includes: Iteratively remove nodes and associated hyperedges with a degree of 1 in the hypergraph, and assign the same K to the nodes removed in each round. sum (e) value until the hypergraph is empty.

4. The method for identifying critical circuits in a power system based on a hypergraph model according to claim 1, characterized in that: In step 3, the entropy weight method is used to fuse the branch structure importance K sum (e) and the magnitude of the super-edge-carrying power flow P min (e) is used to calculate the hyperedge weight w(e); The hyperedge weight formula is: w(e)=α·K sum (e)+β·P min (e); Where, e is the hyperedge corresponding to the transmission path, α is the weight corresponding to the importance of the branch structure, and K sum (e) is the importance of the branch structure, β is the weight corresponding to the size of the super-edge carrying flow, P min (e) is the magnitude of the super-edge-carrying current.

5. The method for identifying critical circuits in a power system based on a hypergraph model according to claim 1, characterized in that: After step 4, a verification step is also included to compare the load loss rate of the key line sequence under the intentional attack.

6. The method for identifying critical circuits in a power system based on a hypergraph model according to claim 1, characterized in that: In step 5, the node transition probability matrix P(u,v) is decomposed into the joint probability of two stages; The calculation formula of the node transfer probability matrix P(u,v) is: Where P(u,v) is the transition probability from node u to node v, π action (e) is the probability of selecting hyperedge e, π node (v|e) is the conditional probability of selecting node v in hyperedge e.

7. A method for identifying critical circuits in a power system based on a hypergraph model according to claim 6, characterized in that: The selection probability π of the hyperedge e action The calculation formula for (e) is: Where w(e) is the hyperedge weight, δ(e) is the number of edges contained in the hyperedge; The conditional probability π of selecting node v in the hyperedge e node The formula for calculating (v|e) is: Where C(u) is the power demand of node u, D(u) is the degree of node u, j is the node included in the hyperedge e, and C(j) represents the power transmission capacity of node j in the hyperedge e.

8. The method for identifying critical circuits in a power system based on a hypergraph model according to claim 1, characterized in that: In step 6, unconnected high-transition-probability node pairs are screened to generate a candidate branch set, excluding existing connections in the system and direct connections between generators and load nodes.

9. The method for identifying critical circuits in a power system based on a hypergraph model according to claim 1, characterized in that: In step 7, the evaluation index is: Where P(u,v) is the transition probability from node u to node v.

10. The method for identifying critical circuits in a power system based on a hypergraph model according to claim 1, characterized in that: In step 7, the strategy of cumulatively adding branches is to add candidate branches in descending order according to the transition probability P(u,v), and recalculate the LBE after each branch is added until the LBE no longer increases significantly.

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