A power system critical line identification method based on hypergraph model

Abstract

The application discloses a power system key line identification method based on a hypergraph model, which comprises the following steps: 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; step 2, performing K-Shell decomposition on the hypergraph model to calculate the structural importance of each power transmission line; step 3, calculating the power flow size borne by the hyperedge and using an entropy weight method to fuse the branch structural importance and the power flow size borne by the hyperedge to calculate the weight size of the hyperedge; step 4, sorting the hyperedge weight in descending order to output a key line sequence; step 5, constructing a node transition probability matrix based on the hyperedge weight; step 6, screening unconnected high transition probability node pairs to generate a candidate branch set; and step 7, taking the maximum load balance entropy LBE as an evaluation index and adding branches until the LBE reaches a peak value to complete structural optimization. The application can improve the identification accuracy of key lines and realize balanced distribution of power flow.

Description

Technical Field

[0001] This invention belongs to the field of power system security analysis and optimization technology, and in particular relates to a method for identifying critical power system lines based on a hypergraph model. Background Technology

[0002] Although the causes of large-scale power outages vary, they all share a common characteristic: a cascading failure triggered by a critical line fault, leading to system collapse. Therefore, accurately identifying the critical line has become the foundation for ensuring power grid safety and operational reliability.

[0003] Currently, to address this challenge, scholars both domestically and internationally have conducted a series of studies. Conventional graph theory methods only describe binary connectivity relationships and cannot characterize transmission paths involving multiple lines working together. While various methods for identifying critical transmission lines have been proposed, comprehensively considering multiple structural and electrical indicators, thus improving the accuracy of critical line identification, none of these methods consider the impact of dynamic power flow distribution on line importance, leading to biases in critical line identification. Furthermore, existing structural optimization models typically aim at minimizing losses, lacking a quantitative assessment of load balancing and struggling to couple system structure with real-time power flow conditions. Summary of the Invention

[0004] To address the aforementioned issues, this invention proposes a method for identifying critical power system lines based on a hypergraph model. By fusing structural hierarchy (K-Shell) and power flow weights, the method can improve the accuracy of identifying critical lines. Furthermore, by generating candidate branches based on random walks and using the maximization of load balance entropy as the evaluation metric to guide topology reconfiguration, a balanced power flow distribution can be achieved.

[0005] To achieve the above objectives, the technical solution adopted by this invention is: a method for identifying critical power system lines based on a hypergraph model, comprising the following steps:

[0006] Step 1: Using power flow tracing, define each transmission path as a superedge and each line as a node to construct a hypergraph model of the power system;

[0007] Step 2: Perform K-Shell decomposition on the hypergraph model and calculate the structural importance K of each transmission line. sum (e);

[0008] Step 3: Calculate the superedge load-bearing power flow magnitude P min (e) and using the entropy weight method to integrate the importance K of the branch structure. sum (e) and the magnitude of the superedge-borne power flow P min (e) is used to calculate the size of the hyperedge weight w(e);

[0009] Step 4: Sort the critical path sequence in descending order according to the superedge weight w(e);

[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 a candidate branch set;

[0012] Step 7: With the goal of maximizing the load balancing entropy (LBE) as the evaluation metric, structural optimization is completed by adding branches cumulatively until the LBE reaches its peak.

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

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

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

[0016] Iteratively remove nodes with a degree of 1 and their associated hyperedges from the hypergraph, assigning the same K value to each node 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 importance K of the branch structure. sum (e) and the magnitude of the superedge-borne power flow P min (e) is used to calculate the size of the hyperedge weight w(e);

[0018] The formula for the hyperedge weight is:

[0019] w(e) = α·K sum (e)+β·P min (e);

[0020] In the formula, 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) represents the importance of the branch structure, β is the weight corresponding to the magnitude of the superedge carrying power flow, and P min (e) is the magnitude of the superedge carrying current.

[0021] Furthermore, following step 4, a verification step is included to compare the load loss rate of the critical path sequence under deliberate attack. Based on the load loss rate verification, it was found that the new method's load loss rate is lower than the other three traditional methods, with a minimum value of 0.42, indicating that this method has higher accuracy and reliability in identifying critical paths in power systems.

[0022] Furthermore, in step 5, the node transition probability matrix P(u,v) is decomposed into the joint probability of the two stages;

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

[0024]

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

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

[0027]

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

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

[0030]

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

[0032] Furthermore, in step 6, when filtering unconnected high-transfer-probability node pairs to generate a candidate branch set, it is necessary to exclude existing connections in the system and direct connections between generators and load nodes.

[0033] Furthermore, in 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] Furthermore, in step 7, the strategy for cumulatively adding branches is to add candidate branches in descending order of transition probability P(u,v), and recalculate LBE after each branch is added, until LBE no longer increases significantly.

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

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

[0039] This invention significantly improves the accuracy of identifying critical power system lines. It innovatively integrates power grid topology and dynamic power flow characteristics, using a hypergraph model to define transmission paths as hyperedges and transmission lines as nodes, overcoming the limitation of traditional graph models that can only describe binary relationships. Furthermore, it introduces a hyperedge weight w(e) to comprehensively consider the importance K of branch structures. sum (e) and the magnitude of the superedge-borne power flow P min (e) This method significantly improves the accuracy of identifying critical paths. In the verification of the IEEE 39-node system, the load loss rate of this method under the deliberate attack scenario was reduced to as low as 0.42, which is about 20% to 35% lower than the traditional method, proving that this method can more accurately locate the core paths that truly affect the stability of the system.

[0040] The system optimization effect of this invention is outstanding: This invention comprehensively considers the collaborative modeling of electrical topology and dynamic power flow characteristics. In the new branch strategy, a node transition probability matrix is ​​constructed based on a random walk model. With the goal of maximizing the evaluation index Load Balance Entropy (LBE), the results show that after adding a high transition probability branch in the IEEE 39-node system, the load balance entropy increases from 3.3319 to 3.4484, an increase of 8.6%, indicating a significant improvement in the uniformity of power flow distribution. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of a method for identifying critical power system lines based on a hypergraph model according to the present invention.

[0042] Figure 2 This is a topology diagram of the IEEE 39-node system in an embodiment of the present invention.

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

[0044] Figure 4 This is a diagram illustrating the K-Shell decomposition process in an embodiment of the present invention;

[0045] Figure 5 This is a diagram showing the distribution of hyperedge weights in an embodiment of the present invention.

[0046] Figure 6 This is a comparison chart of load loss rates for different identification methods in embodiments of the present invention.

[0047] Figure 7 This is a three-dimensional histogram of the node transition probability matrix in an embodiment of the present invention;

[0048] Figure 8 This is a candidate branch screening constraint diagram in an embodiment of the present invention;

[0049] Figure 9 This is an optimized topology diagram of the IEEE 39-node system in an embodiment of the present invention. Detailed Implementation

[0050] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described below with reference to the accompanying drawings.

[0051] In this embodiment, the target system is an IEEE 39-node power grid (including 39 nodes and 46 branches), demonstrating the complete process of critical line identification and structural optimization. A hypergraph model of the power system is established using power flow tracing, and the structural importance of each line is initially quantified using the K-shell index. Simultaneously, considering power flow dynamics, the magnitude P of the power flow carried by the hyperedge is calculated. min (e) and using the entropy weight method to integrate the importance K of the branch structure. sum (e) and the magnitude of the superedge-borne power flow P min (e) is used to calculate the magnitude of the hyperedge weight w(e), thus identifying the key circuits of the system. Based on the hyperedge weight, a node transition probability matrix is ​​constructed, and unconnected high transition probability node pairs are selected to generate a candidate branch set. With the goal of maximizing the load balancing entropy (LBE) evaluation index, branches are added cumulatively until the LBE reaches its peak, thus completing the structural optimization.

[0052] See Figure 1 As shown, this invention proposes a method for identifying critical lines in power systems based on a hypergraph model, mainly consisting of two parts: critical line identification and structural optimization. First, a hypergraph model of the power system is established, and the K-shell index is used to quantify the structural importance of lines, calculating the power flow magnitude P carried by the hyperedge. min (e) and using the entropy weight method to integrate the importance K of the branch structure. sum (e) and the magnitude of the superedge-borne power flow P min (e) is used to calculate the size of the hyperedge weight w(e) to identify the key circuits of the system; then, a node transition probability matrix is ​​constructed based on the hyperedge weight w(e), and unconnected high transition probability node pairs are selected to generate a candidate branch set. With the goal of maximizing the evaluation index load balance entropy (LBE), branches are added cumulatively until LBE reaches its peak value to complete the structural optimization.

[0053] Including the following steps:

[0054] Step 1: Using power flow tracing, define each transmission path as a superedge 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 superedge load-bearing power flow magnitude P min (e) and using the entropy weight method to integrate the importance K of the branch structure. sum (e) and the magnitude of the superedge-borne power flow P min (e) is used to calculate the size of the hyperedge weight w(e);

[0057] Step 4: Sort the critical path sequence in descending order according to the superedge weight w(e);

[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 a candidate branch set;

[0060] Step 7: Maximize the Load Balancing Entropy (LBE) evaluation metric as the optimization objective. Add branches cumulatively until the LBE reaches its peak value to complete the structural optimization.

[0061] like Figure 3 The diagram illustrates in detail the hypergraph modeling process for power systems according to this invention. Taking the IEEE 39-bus system as an example, 68 paths were found by tracing the power flow under steady-state conditions. Based on the definition of a hypergraph, the power flow transmission paths are designated as hyperedges, and the lines contained within them are designated as hyperedge nodes, thus constructing a hypergraph model.

[0062] This invention performs K-Shell decomposition on the hypergraph model and uses K-shell metrics to quantify the structural importance of the circuits. For example... Figure 4 As shown, in K-Shell analysis, nodes with degree 1 and their connected hyperedges are first removed from the network. After the removal, new nodes with degree 1 appear in the network, and these new nodes with degree 1 and their connected hyperedges are then removed. This operation is repeated, assigning the same K value to the nodes that are removed each time.

[0063] Traditional K-Shell analysis only considers the power grid topology and lacks consideration of the impact of power flow calculations on lines. Therefore, we propose an improved method to calculate the magnitude P of the superedge-borne power flow. min (e) and using the entropy weight method to integrate the importance K of the branch structure. sum(e) and the magnitude of the superedge-borne power flow P min (e) is used to calculate the magnitude of the hyperedge weight w(e), which quantifies the weight of each transmission path. For example... Figure 5 As shown, the superedge weight w(e) is calculated, and the identified critical paths are 46, 14, 20, 37, 33, 35, 39, 41, 10, and 34.

[0064] The formula for the hyperedge weight is:

[0065] w(e) = α·K sum (e)+β·P min (e);

[0066] In the formula, 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) represents the importance of the branch structure, β is the weight corresponding to the magnitude of the superedge carrying power flow, and P min (e) is the magnitude of the superedge carrying current.

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

[0068] The node transition probability matrix describes the relative probability of power flow shifting from one node to another in a system. Higher transition probability values ​​typically indicate that the node pair plays a crucial role in power flow transmission. Therefore, the transition probability matrix can be viewed as a mapping of the importance of potential power flow paths in the system. Based on this, the transition probability matrix serves as the basis for structural optimization: on the one hand, it identifies currently disconnected node pairs with significant transition probabilities as candidate connections for potential efficient paths; on the other hand, it identifies lines with extremely low transition probabilities among existing connections as adjustable or downgraded redundant edges in structural optimization. For example... Figure 7 The diagram shows the calculation results of the node transition probability matrix. Red represents the high-probability core region, yellow represents the medium-probability hub region, and blue represents the low-probability edge region.

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

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

[0071]

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

[0073] In the hypergraph model of a power system, 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 being selected by the power flow, thus avoiding the distortion of the judgment of the importance of key channels due to the redundancy of the hyperedge structure.

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

[0075]

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

[0077] Node selection conditional probability is a 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). Through the inverse structure degree weighted power flow capability, it can ensure that the power flow tends to flow to areas with strong loads but more peripheral structures, thus promoting the overall load balance of the system.

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

[0079]

[0080] In the formula, C(u) is the power flow demand of 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 probabilities in the node transition probability matrix are prioritized as candidate connection lines. However, the selection of connection lines must adhere to two constraints: existing connection lines in the system must be excluded to avoid duplicate connections or disturbances to the original topology; direct connections between generators and load nodes must be excluded because, although such direct connections may have extremely high transition probabilities, they could bypass the transmission network for power supply in actual power grid operation, disrupting the power flow scheduling hierarchy, and therefore are not adopted. Figure 8 As shown, 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] Entropy, as an important indicator of the orderliness of a system, reaches its maximum when the power system is in equilibrium, exhibiting a highly uniform energy distribution. Based on this theory, this paper aims to maximize the load balance entropy (LBE) as an evaluation metric to quantify the balance of load distribution and uses it as a key evaluation criterion for structural optimization models.

[0083] The evaluation indicators are:

[0084]

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

[0086] A lower LBE value indicates that the power flow is concentrated on a few critical paths, resulting in poor system load balancing. Conversely, a higher LBE value indicates a more even distribution of power transfer probability, better line load balancing, and stronger system resilience to disturbances. Using the maximization of load balancing entropy (LBE) as the optimization objective, an objective function was established. Candidate branches were added sequentially from high to low transfer probability. The LBE was recalculated after each branch was added until it no longer increased significantly, at which point the LBE reached its peak, completing the structural optimization. Before optimization, the overall system load balancing entropy was 3.3319. Based on the branch selection criteria, after adding line L47 (connecting nodes 28-38), the load balancing entropy increased to 3.4484. This result demonstrates that the optimized network structure achieves a more balanced load distribution, significantly enhances system robustness, and aligns with the entropy maximization theory's expectation of system stability.

[0087] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for identifying critical power system lines based on a hypergraph model, characterized in that, Including the following steps: Step 1: Using power flow tracing, define each transmission path as a superedge 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 superedge load-bearing power flow magnitude P min (e) and using the entropy weight method to integrate the importance K of the branch structure. sum (e) and the magnitude of the superedge-borne power flow P min (e) is used to calculate the size of the hyperedge weight w(e); Step 4: Sort the critical path sequence in descending order according to the superedge weight w(e); 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 a candidate branch set; Step 7: With the goal of maximizing the load balancing entropy (LBE) as the evaluation metric, structural optimization is completed by adding branches cumulatively until the LBE reaches its peak.

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

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

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

5. The method for identifying critical power system lines based on a hypergraph model according to claim 1, characterized in that, Following step 4, a verification step is also included, which compares the load loss rate of the critical path sequence under deliberate attack.

6. The method for identifying critical power system lines 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 the two stages; The formula for calculating the node transition probability matrix P(u,v) is as follows: ； In the formula, P(u,v) is the transition probability from node u to node v, and π action (e) is the choice probability of hyperedge e, π action (v|e) is the conditional probability of selecting node v in hyperedge e.

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

8. The method for identifying critical power system lines based on a hypergraph model according to claim 1, characterized in that, In step 6, a candidate branch set is generated by filtering unconnected high-transfer-probability node pairs, excluding existing connections in the system and direct connections between generators and load nodes.

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

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

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