A power system key hub identification method based on degree centrality and density

Abstract

This invention discloses a method for identifying critical hubs in power systems based on degree centrality and density, comprising: S1: defining and calculating a degree centrality index based on the number of directly connected branches of a node; S2: performing static structural checks on nodes based on the degree centrality index, and selecting nodes whose degree centrality index meets a preset reliability standard; S3: setting weighting parameters based on node voltage levels and weighting the degree centrality index; S4: using the PageRank algorithm to evaluate the degree of reference of a node by other nodes; S5: fusing the weighted degree centrality index and PageRank value to generate a comprehensive criticality index, ranking all candidate critical nodes, and outputting the critical hub identification result. This invention significantly improves the comprehensiveness and accuracy of critical hub node identification, providing a comprehensive and accurate decision-making basis for differentiated power grid prevention and control and planning.

Description

Technical Field

[0001] This invention belongs to the field of power system security and stability analysis technology, specifically relating to a method for identifying key hubs in a power system based on degree centrality and density. Background Technology

[0002] Identifying key nodes in a power system is crucial for the safe and stable operation of the power grid, fault prevention, and dispatch control. With the continuous expansion of the power grid and the large-scale integration of new energy sources, the system's operation is becoming increasingly complex. Accurately identifying key nodes that have a decisive impact on the overall stability of the system has become an important research topic in the field of power system operation analysis and planning.

[0003] Currently, the methods for identifying critical nodes in power systems are mainly divided into two categories:

[0004] One type of analysis method is based on complex network topology. These methods typically simplify the power grid as an unweighted, undirected graph and use metrics such as degree centrality, betweenness centrality, and eigenvector centrality to assess node importance. However, these methods have significant drawbacks: first, they ignore the physical nature of the power system, namely Kirchhoff's laws and the constraints of power flow distribution, failing to reflect the actual electrical coupling strength and power transmission direction between nodes; second, they fail to effectively distinguish between a node's "contribution" and "dependency" in power transmission, leading to identification results that are often out of sync with the actual operating conditions of the power grid and making it difficult to accurately reflect the criticality of nodes in real fault scenarios.

[0005] Another category is identification methods based on electrical characteristic analysis. For example, indicators such as electrical betweenness, power flow transfer entropy, and sensitivity analysis are used for node evaluation. Although such methods introduce electrical quantity information, they generally have the following shortcomings: First, most methods only focus on the static characteristics under a single operating section, making it difficult to comprehensively reflect the combined influence of nodes under the combined effects of system topology and power distribution; second, existing methods often neglect the mutual influence between nodes and the "hub effect" when evaluating node importance, that is, they fail to effectively measure the aggregation and distribution role of nodes in the multi-stage power transfer process; third, some high-precision algorithms have high computational complexity, making them difficult to apply to the online or quasi-online evaluation needs of large-scale actual power grids.

[0006] In summary, existing technologies for identifying critical hubs in power systems generally suffer from insufficient physical representation, inadequate integration of topology and electrical characteristics, and weak correlation between identification results and actual operational risks. Therefore, there is an urgent need to propose a hub node identification method that can comprehensively consider the power grid topology, power transmission characteristics, and inter-node coupling relationships to improve the accuracy, comprehensiveness, and engineering applicability of the identification results. Summary of the Invention

[0007] This invention aims to provide a method for identifying critical hubs in power systems based on degree centrality and density. This method overcomes the limitations of traditional methods that rely solely on static topology or simple electrical distance for identification, significantly improving the comprehensiveness and accuracy of critical hub node identification. It provides a comprehensive and accurate decision-making basis for differentiated prevention and control and planning of the power grid.

[0008] To achieve the above objectives, the present invention is implemented using the following technical solution:

[0009] In a first aspect, the present invention provides a method for identifying critical hubs in a power system based on degree centrality and density, comprising the following steps:

[0010] Step S1: Construct a power grid weighted bidirectional graph model of the power system to be evaluated, and calculate the degree centrality index of the nodes based on the power grid weighted bidirectional graph model;

[0011] Step S2: Based on the degree centrality index, select nodes whose degree centrality index meets the preset reliability standard as candidate key nodes;

[0012] Step S3: For the candidate key nodes, set weighting parameters based on the node voltage level, and perform weighting processing on the degree centrality index to obtain the weighted degree centrality index;

[0013] Step S4: Use the PageRank algorithm to evaluate the degree to which each node is referenced by other nodes, and obtain the PageRank value of the candidate key nodes;

[0014] Step S5: Combine the weighted degree centrality index with the PageRank value to generate a comprehensive criticality index, and sort all candidate critical nodes according to the comprehensive criticality index to obtain the critical hub identification results.

[0015] The above setup achieves the following effects: This invention incorporates the physical characteristics of the actual power grid into topology analysis by constructing a weighted bidirectional graph model of the power grid. Based on this, firstly, the degree centrality index is used to screen candidate critical nodes that meet basic reliability standards, eliminating a large number of secondary nodes and improving analysis efficiency. Subsequently, this invention innovatively integrates two complementary evaluation dimensions: on the one hand, degree centrality is weighted based on node voltage levels, quantifying the importance of nodes in the local connectivity structure; on the other hand, the PageRank algorithm is introduced to accurately assess the hub status and citation degree of nodes in the global network by simulating the random walk process of power flow in the power grid. Finally, by generating and ranking a comprehensive criticality index, the quantitative identification of critical hubs is achieved.

[0016] Compared with existing technologies, this invention systematically outputs a list of key hubs reflecting global power flow bottlenecks from the same model, overcoming the limitations of traditional methods that can only provide scattered, single-type key components. It can also reveal "hidden" key points that are easily overlooked in traditional single-index analysis, providing a more comprehensive and accurate decision-making basis for power grid security defense.

[0017] Furthermore, in step S1, the method for constructing a power grid weighted bidirectional graph model of the power system to be evaluated includes:

[0018] A weighted bidirectional graph model of the power system to be evaluated is constructed, where nodes correspond to buses in the power system, edges correspond to transmission lines and transformer branches, and edge weights are defined based on electrical characteristics.

[0019] The above settings achieve the following effect: by abstracting the busbars as nodes, transmission lines and transformer branches as edges, and defining edge weights based on electrical characteristics, the constructed graph model not only retains the topological connections of the power grid, but also incorporates key electrical and physical characteristics, thus laying a model foundation that is closer to the actual operating characteristics of the power system for subsequent topology analysis and vulnerability assessment.

[0020] Furthermore, in step S1, the degree centrality index is calculated as follows: for node i, the degree centrality index is the number of edges connected to that node.

[0021] The above settings achieve the following effect: by directly counting the number of edges connected to a node, a method for quantifying local importance with low computational complexity, clear physical meaning, and strong interpretability is provided, which is convenient for engineering applications.

[0022] Furthermore, in step S2, nodes with a degree centrality index greater than or equal to 3 are selected as candidate key nodes that meet the preset reliability criteria.

[0023] The above settings achieve the following effects: by using the degree centrality index to screen out candidate critical nodes that meet the basic reliability criteria, a large number of secondary nodes are eliminated, reducing computational costs and improving analysis efficiency. This can effectively reduce the computational load of subsequent core analyses and improve overall evaluation efficiency, and is especially suitable for complex and large-scale actual power grid systems.

[0024] Furthermore, the method also includes:

[0025] Static structure checks are performed on the nodes and edges in the weighted bidirectional graph model of the power grid, and nodes and edges that fail the static structure check are removed.

[0026] The static structure test is to check whether it meets the N-1 criterion.

[0027] The above settings achieve the following effects: By introducing the N-1 criterion for static structural verification, it ensures that the selected candidate key nodes have a certain degree of power supply reliability in terms of structure, so that the subsequent evaluation focuses more on the "key" nodes that are truly of engineering significance in the power grid, thereby improving the practical guiding value of the analysis results. This step can effectively reduce the amount of calculation in the subsequent core analysis and improve the overall evaluation efficiency, especially suitable for actual power grid systems with complex structures and large scale.

[0028] Furthermore, in step S3, weighting parameters are set based on node voltage levels, and the degree centrality index is weighted to obtain a weighted degree centrality index, including:

[0029] The weighted parameters of the nodes are set based on the node voltage level;

[0030] Weighted degree centrality index WDC i The calculation formula is:

[0031] ;

[0032] Among them, w i k represents the weighted parameter of node i. i This represents the number of edges connected to node i.

[0033] The effect achieved by the above settings is that by setting weighted parameters according to the voltage classification standards in the power system design code, the key electrical characteristic of voltage level is integrated into the degree centrality index.

[0034] Furthermore, weighted parameters for nodes are set based on node voltage levels, including:

[0035] For nodes with a voltage level of 345kV and above, the weighting parameter is 1.0; for nodes with a voltage level of 161kV, the weighting parameter is 0.7; for nodes with a voltage level of 69kV, the weighting parameter is 0.4; and for nodes with a voltage level of 22kV or 11kV, the weighting parameter is 0.1.

[0036] The above settings achieve the following effect: high-voltage level nodes receive higher weights due to undertaking a wider range of power transmission tasks, making the weighted degree centrality index more accurately reflect the actual importance and differentiated status of equipment in the power grid.

[0037] Furthermore, in step S4, the PageRank algorithm is used to evaluate the degree to which each node is referenced by other nodes to obtain the PageRank value of the candidate key node, including:

[0038] Construct a probability transition matrix M, whose elements M ij This represents the probability of moving from node j to node i.

[0039] ;

[0040] in: This represents the transition weight of the edge from node j to node i; It is the sum of the transition weights of all outgoing edges from node j;

[0041] Assign an initial PageRank value to each node. All nodes have the same initial value, which is 1 / N, where N is the total number of nodes.

[0042] The initial PageRank values ​​of all nodes constitute the initial PageRank value vector R(0), which is solved using the following exponential iteration formula:

[0043] ;

[0044] Where: R(t) is the PageRank value vector after the t-th iteration, M T This is the transpose of the transition matrix M, where α is the damping factor, typically taken as 0.85;

[0045] The power iteration formula indicates that there is a probability α of power transfer along the path in the system, and a probability of (1-α) of random jump to any node in the network, where e is a column vector with all elements equal to 1, and N is the total number of nodes in the network. The vector is a uniformly distributed vector for random jumps;

[0046] Iterative calculation until , Given a preset tolerance, the final R is obtained. i This is the PageRank value of node i.

[0047] The above setup achieves the following effects: Employing the PageRank algorithm to evaluate node importance overcomes the unidirectional limitation of traditional centrality metrics. Through iterative calculation, it accurately measures the degree to which a node is "referenced" or depended upon by other nodes in the global network, effectively identifying the "core" hubs of global power transmission. Furthermore, by flexibly defining edge weights, the model can dynamically adjust according to different evaluation focuses (such as electrical distance, transmission capacity, and real-time operating status), demonstrating strong engineering practicality and scalability.

[0048] Furthermore, in step S5, a comprehensive criticality index is generated, and all candidate critical nodes are ranked according to the comprehensive criticality index to obtain the critical hub identification result, including:

[0049] For a node i, its comprehensive criticality index CI i The calculation is as follows:

[0050]

[0051] in: and These are the weighted degree centrality and PageRank value of node i after min-max normalization, respectively, and θ is the fusion weight coefficient, with a value range of [0,1].

[0052] The minimum-maximum normalization formula is: , where X i This represents the i-th element of set X. Representing element X i The normalized result is given by min(X), which represents the minimum value of set X, and max(X), which represents the maximum value of set X.

[0053] Based on the above formula, calculate the comprehensive criticality index (CI) of all nodes in the network. i All nodes are sorted by CI i The values ​​are sorted from largest to smallest, and a recognition threshold is set to identify the key hubs.

[0054] The above settings achieve the following effect: By introducing adjustable fusion weight coefficients, this invention can flexibly balance the local direct influence of nodes (reflected by weighted degree centrality) and the global network embedding degree (reflected by PageRank value). This allows the identification results to be customized according to different engineering needs, achieving comprehensive and accurate ranking of key hubs, and providing a clear and quantitative basis for subsequently formulating differentiated prevention and control strategies.

[0055] Furthermore, the method also includes:

[0056] Based on the aforementioned power grid weighted bidirectional graph model, the proportion of each node that passes through all shortest paths is calculated.

[0057] Nodes that pass through the shortest path with a proportion higher than a preset value are added as candidate key nodes and merged with the original candidate key nodes to remove duplicates.

[0058] The above settings achieve the following effects: by representing the proportion of all shortest paths passing through the node, the information control capability can be characterized; by statistically analyzing the number of times the shortest path is traversed, the pivotal role of a node or edge in the global power flow transmission of the network can be effectively depicted; a theoretical basis can be provided for identifying lines and nodes that undertake important power transmission tasks; supplementary identification of candidate key nodes can be achieved; key nodes with few connected edges but special locations can be prevented from appearing; and hidden key nodes can be accurately identified through subsequent comprehensive criticality index.

[0059] In a second aspect, the present invention provides a power system critical hub identification system based on degree centrality and density, comprising a processor and a memory, wherein the memory stores a computer program, and the processor executes the computer program to implement the method described in the first aspect.

[0060] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0061] 1. This invention, based on the PageRank algorithm, comprehensively considers the topology, electrical coupling strength, power flow distribution, and effectiveness of power transmission between nodes in a power system, constructing a weighted directed graph model adapted to the characteristics of the power grid. This method not only focuses on the degree centrality of nodes at the topological level but also effectively quantifies the contribution and dependence of nodes in the power transmission path. It overcomes the limitations of traditional methods that rely solely on static topology or simple electrical distance for identification, significantly improving the comprehensiveness and accuracy of identifying key hub nodes.

[0062] 2. By accurately identifying key nodes in the power grid that play a crucial role in power transmission and system stability support, this invention provides a more reliable quantitative basis for assessing the safety and stability of power systems. In anticipated fault analysis, cascading fault simulation, and the location of weak points in the power grid, it can identify potential critical nodes that may lead to system disconnection or large-scale load losses in advance. This provides scientific support for dispatching and operation personnel to formulate differentiated operating strategies and optimize protection and control measures, effectively reducing system operation risks.

[0063] 3. The key hub nodes identified in this invention reflect the backbone structure of power aggregation and distribution in the power grid, providing clear guidance for transmission network expansion planning, key equipment selection, reactive power compensation configuration, and the site selection of new energy grid connection points. By prioritizing the monitoring and reinforcement of high-weight hub nodes, the overall system reliability can be maximized with limited investment, significantly improving the resource utilization efficiency of power grid planning and operation and maintenance.

[0064] 4. Based on the improved PageRank algorithm, this method retains the convergence guarantee of the original algorithm while constructing an iterative solution mechanism suitable for large-scale power systems by introducing actual physical constraints and operational boundary conditions of the power system. This mechanism can fully utilize power grid data resources and achieve efficient computation while ensuring identification accuracy. It is suitable for real-time or near-real-time evaluation scenarios of provincial and above-scale power grids and has good engineering application prospects.

[0065] 5. Strong engineering applicability: This method can be directly implemented based on data in the power grid energy management system (EMS) or common model data (CIM / G) format. It has high computational efficiency, is easy to integrate into existing power grid analysis platforms, forms a closed loop from data to decision-making, and has strong practical applicability. Attached Figure Description

[0066] Figure 1 This is a flowchart of the method of the present invention.

[0067] Figure 2 This is a diagram of the IEEE 39-node system. Detailed Implementation

[0068] The present invention will now be further described. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0069] Example 1:

[0070] This embodiment provides a method for identifying critical hubs in a power system based on degree centrality and density, such as... Figure 1 As shown, it includes the following steps:

[0071] Step S1: Construct a power grid weighted bidirectional graph model of the power system to be evaluated, and calculate the degree centrality index of the nodes based on the power grid weighted bidirectional graph model;

[0072] Step S2: Based on the degree centrality index, select nodes whose degree centrality index meets the preset reliability standard as candidate key nodes;

[0073] Step S3: For the candidate key nodes, set weighting parameters based on the node voltage level, and perform weighting processing on the degree centrality index to obtain the weighted degree centrality index;

[0074] Step S4: Use the PageRank algorithm to evaluate the degree to which each node is referenced by other nodes, and obtain the PageRank value of the candidate key nodes;

[0075] Step S5: Combine the weighted degree centrality index with the PageRank value to generate a comprehensive criticality index, and sort all candidate critical nodes according to the comprehensive criticality index to obtain the critical hub identification results.

[0076] Specifically, step S1: Construct a weighted bidirectional graph model of the power system to be evaluated, and calculate the degree centrality index of the nodes based on the weighted bidirectional graph model, including:

[0077] The purpose of this step is to abstract the actual physical power grid into a mathematical model that can be used for analysis using complex network theory. This model should not only reflect the topological connections of the power grid, but also reflect its electrical and physical characteristics by introducing weights, thereby overcoming the shortcomings of traditional unweighted graph models that are too simplistic and detached from physical reality, and laying the foundation for subsequent accurate analysis.

[0078] S1-1: Definition of graph elements:

[0079] (1) Definition and mapping of nodes (Vertex / Node):

[0080] Mapping rule: The busbars in the power system or the high-voltage side busbars of substations are abstracted as nodes in a complex network. These are the physical points where power flow converges and is distributed.

[0081] Node type handling: For buses connecting generators (PV nodes) and buses connecting loads (PQ nodes), no distinction is made at the topology model level; they are all treated as nodes. The power attributes of generators and loads will be used as node weights or for subsequent power flow calculations, rather than for distinguishing node types.

[0082] Example: A substation that includes generators, transformers and loads is typically represented by a node on its high-voltage side busbar.

[0083] (2) Definition and mapping of edges (Edge / Link):

[0084] Mapping rule: The AC transmission lines, transformer branches, and series reactor branches in the power system are abstracted as edges in a complex network. These components are channels connecting two buses and enabling power transmission.

[0085] Edge direction: Construct bidirectional edges. This is because power flow can flow bidirectionally during normal operation (although the direction is determined at any given moment), which is fundamentally different from communication networks and transportation networks.

[0086] S1-2: Definition of weights:

[0087] Instead of using unweighted graphs or simple geographical distance as weights, we introduce weights closely related to electrical characteristics. Several preferred schemes exist for defining edge weights; one can be selected based on the evaluation focus:

[0088] Option 1 (Reflecting the difficulty of power flow transmission): Use the per-unit reactance of the branch as the weight. In high-voltage power grids, reactance is much larger than resistance and is the dominant parameter that determines the power flow distribution (proportional to the phase angle difference) and system stability; the smaller the reactance, the shorter the electrical distance of the path, the easier it is for power flow to pass through, and the stronger its connection effect on the topology.

[0089] Option 2 (Reflecting Line Transmission Capacity): The reciprocal of the line's rated capacity (or thermal stability limit) is used as the weight. The reciprocal of the capacity reflects the "cost" or "scarcity" of power transmission per unit. The larger the capacity of the line, the smaller its reciprocal weight, indicating that the line has a stronger transmission capacity and is less important when handling power flow (because of its large margin); conversely, the smaller the capacity of the line, the higher its weight, indicating that it is more vulnerable.

[0090] Option 3 (Reflecting Real-Time Operational Status): Using a function of the current line load rate as dynamic weights. This option upgrades the model from static to dynamic. The higher the load rate, the more critical the line, and the greater its weight should be. This option is more suitable for online risk assessment.

[0091] S1-3: The degree centrality index is calculated as follows: for node i, the degree centrality index is the number of edges connected to that node.

[0092] Specifically, step S2: Based on the degree centrality index, nodes whose degree centrality index meets the preset reliability standard are selected as candidate key nodes, including:

[0093] S2-1: The number of branches directly connected to a node serves as a degree centrality indicator, quantifying structural connectivity. In a power network, this corresponds to the number of incoming and outgoing lines to substations or the density of tie lines. Typically, nodes with high degree centrality bear more power transmission tasks; for example, hub substations usually have six or more incoming and outgoing lines.

[0094] In this embodiment, only nodes with a degree centrality index of ≥3 can meet the power supply reliability standard and be considered as candidate critical nodes.

[0095] Optional, S2-2: Static structural inspection:

[0096] Perform static structure checks on the nodes and edges in the weighted bidirectional graph model of the power grid, requiring them to meet the N-1 criterion, and remove the nodes and edges in the weighted bidirectional graph model of the power grid that fail the static structure check.

[0097] Basic topology indicators reflect the static network structure. Static structure verification ensures that the selected candidate critical nodes have a certain degree of power supply reliability, allowing subsequent evaluations to focus more on the truly engineering-significant "critical" nodes in the power grid, thus enhancing the practical guiding value of the analysis results.

[0098] If a node or edge does not meet the N-1 criterion, it means that after a component (such as a line, transformer, generator, etc.) fails or disconnects, the system may not be able to maintain stable operation or normal power supply, posing risks of overload, voltage / frequency exceeding limits, or even power outages. This necessitates increasing equipment redundancy and optimizing the power grid structure, which may lead to structural changes at that location and potentially cause invalid calculations. Furthermore, if the component is relatively weak, it is easily identified as a candidate critical node, leading to incorrect identification later.

[0099] In addition, if a node or edge does not meet the N-1 criterion, a corresponding prompt message needs to be generated to alert technical personnel that this is a weak point that needs special attention.

[0100] Optional, S2-3: Dynamic structural inspection:

[0101] Based on the power grid weighted bidirectional graph model, the nodes are dynamically structured and the proportion of each node that passes through all shortest paths is statistically analyzed, i.e., the electrical current betweenness. Nodes whose proportion of passing through all shortest paths is higher than a preset value are added as candidate key nodes and merged with the original candidate key nodes to remove duplicates.

[0102] The information control capability is characterized by the proportion of all shortest paths passing through this node, i.e., the electrical current betweenness. The electrical current betweenness of node i... The formula is:

[0103] ;

[0104] In the formula, Represents a node and The number of shortest paths between them. Represents a node and Let G be the number of paths between nodes i that pass through node i, and G be the set of nodes in the weighted bidirectional graph model of the power grid. In complex network theory, the length of any path between node pairs is the sum of the weights of all lines traversed by that path; the shortest path is the path with the minimum sum of weights.

[0105] Nodes with high electrical current betweenness numbers act as essential power flow channels in power systems. Identifying "structural holes" in the network, such as critical channels in inter-regional power projects, dynamically reflects the network's operational status. Electrical current betweenness numbers effectively characterize the pivotal role of nodes or edges in global power flow transmission, providing a theoretical basis for identifying lines and nodes undertaking important power transmission tasks. This enables supplementary identification of candidate critical nodes, preventing the appearance of critical nodes with few connected edges but special locations. Furthermore, it allows for accurate identification of hidden critical nodes through subsequent comprehensive criticality indices.

[0106] Specifically, in step S3, for the candidate key nodes, weighting parameters are set based on the node voltage level, and the degree centrality index is weighted to obtain the weighted degree centrality index, including:

[0107] The weighted parameters, constructed based on node voltage levels, assign a value of 1.0 to 345kV topology nodes, 0.7 to 161kV, 0.4 to 69kV, and 0.1 to 22 / 11kV nodes. This conforms to the voltage classification standard of DL / T 5429 "Technical Specification for Power System Design".

[0108] The weighted parameters of the nodes are set based on the node voltage level;

[0109] Weighted degree centrality index WDC i The calculation formula is:

[0110]

[0111] Among them, w i k represents the weighted parameter of node i. i This represents the number of edges connected to node i.

[0112] Weighting parameters are set according to the voltage classification standards in the power system design code, incorporating the key electrical characteristic of voltage level into the degree centrality index. Voltage level is positively correlated with power supply range. After setting weighting parameters, the differences in equipment importance are quantified; the higher the voltage level, the more critical the nodes and lines are.

[0113] Specifically, step S4: Use the PageRank algorithm to evaluate the degree to which each node is referenced by other nodes, and obtain the PageRank value of the candidate key nodes, including:

[0114] The PageRank algorithm, a core algorithm of the Google search engine, is used to evaluate the degree to which a node is referenced by other nodes. It characterizes the voltage support capability and power interaction strength of key components, overcoming the unidirectional defect of traditional centrality indicators.

[0115] Construct a probability transition matrix M, whose elements M ij This represents the probability of moving from node j to node i.

[0116]

[0117] in: This represents the transition weight of the edge from node j to node i; It is the sum of the transition weights of all outgoing edges from node j; It can be simply set to 1 (unweighted), or taken as the reciprocal of the per-unit reactance of the line (the result after normalization of the reference impedance), representing the ease of power flow transmission, so that strong connections correspond to high weights. The denominator is the sum of the transfer weights of all outgoing edges of node j, achieving normalization.

[0118] Assign an initial PageRank value to each node, with all nodes having the same initial value; typically set to 1 / N, where N is the total number of nodes.

[0119] The initial PageRank values ​​of all nodes constitute the initial PageRank value vector R(0), which is solved using the following power iteration formula:

[0120] ;

[0121] Where: R(t) is the PageRank value vector after the t-th iteration, M T This is the transpose of the transition matrix M, where α is the damping factor, typically taken as 0.85;

[0122] The power iteration formula indicates that there is a probability α of power transfer along the line in the system, and a probability of (1-α) of random jump to any node in the network (simulating power balancing or global coupling), where e is a column vector with all elements equal to 1, and N is the total number of nodes in the network. The vector is a uniformly distributed vector for random jumps;

[0123] Iterative calculation until , Given a preset tolerance, the final R is obtained. i This is the PageRank value of node i.

[0124] The PageRank algorithm is used to evaluate node importance, overcoming the one-way limitation of traditional centrality indicators. Through iterative calculation, it can accurately measure the degree to which a node is "referenced" or depended on by other nodes in the global network, effectively identifying the "core" hubs of global power transmission. Furthermore, by flexibly defining edge weights, the model can dynamically adjust according to different evaluation focuses (such as electrical distance, transmission capacity, and real-time operating status), demonstrating strong engineering practicality and scalability.

[0125] Specifically, in step S5, a comprehensive criticality index is generated, and all candidate critical nodes are ranked according to the comprehensive criticality index to obtain the critical hub identification result, including:

[0126] S5-1: For a node i, its comprehensive criticality index CI i The calculation is as follows:

[0127]

[0128] in: and These are the weighted degree centrality and PageRank value of node i after min-max normalization, respectively. θ is the fusion weight coefficient, ranging from [0,1]. It reflects the trade-off between local direct influence (represented by weighted degree centrality WDC) and global network embedding (represented by PageRank value). If θ=0.7, it indicates a greater emphasis on the direct connection strength of nodes (intuitively in engineering). If θ=0.5, it indicates that both are equally important. This parameter can be determined through expert experience or historical data inversion.

[0129] The minimum-maximum normalization formula is: , where X i This represents the i-th element of set X. Representing element X i The normalized result is given by min(X), which represents the minimum value of set X, and max(X), which represents the maximum value of set X.

[0130] S5-2: Based on the above formula, calculate the comprehensive criticality index (CI) of all nodes in the network. i All nodes are sorted by CI i The values ​​are sorted from largest to smallest, and a recognition threshold is set to identify the key hubs.

[0131] Setting an identification threshold to identify key hubs typically employs one of the following two methods:

[0132] Top-K method: Select the top K nodes (e.g., the top 10) as key hubs.

[0133] Threshold method: Set a threshold (like =0.1), identify all nodes greater than the threshold as critical hubs.

[0134] By introducing adjustable fusion weight coefficients, this invention can flexibly balance the local direct influence of nodes (reflected by weighted degree centrality) and the global network embedding degree (reflected by PageRank value). This allows the identification results to be customized according to different engineering needs, achieving comprehensive and accurate ranking of key hubs, and providing a clear and quantitative basis for subsequently formulating differentiated prevention and control strategies.

[0135] S5-3: Output the key hub identification results:

[0136] The algorithm process ends, and the key hub identification results are output.

[0137] The method of this invention can reveal "hidden" weaknesses: by employing a comprehensive assessment that integrates multi-dimensional information, this invention can discover "hidden" key points that are easily overlooked in traditional single-indicator analysis. This invention can accurately capture these structural risks, providing unprecedented depth of insight for power grid security defense.

[0138] The method of this invention can guide differentiated security control strategies: the identification results directly correspond to different prevention and control measures. Critical hubs need to be given priority protection, and stability control schemes to prevent power flow transfer overload need to be developed.

[0139] The method of this invention can automate and objectify the analysis process, and has strong engineering applicability and scalability:

[0140] (1) This method can be directly implemented based on data in the power grid energy management system (EMS) or common model data (CIM / G) format. It has high computational efficiency, is easy to integrate into existing power grid analysis platforms, forms a closed loop from data to decision, and has strong applicability.

[0141] (2) Good scalability: The analysis framework provided by this invention has good openness. In the future, it can be further integrated with more diverse safety constraint indicators such as voltage stability and transient stability, or combined with artificial intelligence algorithms for predictive safety assessment, with huge expansion potential.

[0142] Based on the improved PageRank algorithm, this method retains the convergence guarantee of the original algorithm while constructing an iterative solution mechanism suitable for large-scale power systems by introducing actual physical constraints and operational boundary conditions of the power system. This mechanism can fully utilize power grid data resources and achieve efficient computation while ensuring identification accuracy. It is suitable for real-time or near-real-time evaluation scenarios of provincial and above-scale power grids and has good engineering application prospects.

[0143] Example 2:

[0144] This embodiment provides a method for identifying critical hubs in a power system based on degree centrality and density, the process of which is as follows: Figure 1 As shown, it includes the following steps:

[0145] Step S1: Construct a power grid weighted bidirectional graph model of the power system to be evaluated, and calculate the degree centrality index of the nodes based on the power grid weighted bidirectional graph model;

[0146] Step S2: Based on the degree centrality index, select nodes whose degree centrality index meets the preset reliability standard as candidate key nodes;

[0147] Step S3: For the candidate key nodes, set weighting parameters based on the node voltage level, and perform weighting processing on the degree centrality index to obtain the weighted degree centrality index;

[0148] Step S4: Use the PageRank algorithm to evaluate the degree to which each node is referenced by other nodes, and obtain the PageRank value of the candidate key nodes;

[0149] Step S5: Combine the weighted degree centrality index with the PageRank value to generate a comprehensive criticality index, and sort all candidate critical nodes according to the comprehensive criticality index to obtain the critical hub identification results.

[0150] Test System: The internationally recognized standard test system—the IEEE 39-bus system—is adopted. This system comprises 39 buses (nodes), 10 generators, 46 AC transmission lines, and transformers (edges), representing a typical medium-to-large regional power grid model. Figure 2 As shown.

[0151] Step S1: Construct a weighted bidirectional graph model.

[0152] (1) Abstract the 39 busbars into 39 nodes.

[0153] (2) Abstract the 46 branches into 46 edges.

[0154] (3) Assign weights to each edge.

[0155] Step S2: Based on the degree centrality index, select nodes whose degree centrality index meets the preset reliability standard as candidate key nodes;

[0156] Assuming power exchange exists between all node pairs (or exchange weights are set based on generation / load capacity), calculate the electrical current betweenness of each branch. Nodes whose proportion of those passing through all shortest paths exceeds a preset value are added as candidate critical nodes and merged with the original candidate critical nodes to remove duplicates.

[0157] Step S3: For the candidate key nodes, set weighting parameters based on the node voltage level, and perform weighting processing on the degree centrality index to obtain the weighted degree centrality index;

[0158] The weighted parameters, constructed based on node voltage levels, assign a value of 1.0 to 345kV topology nodes and lines, 0.7 to 161kV, 0.4 to 69kV, and 0.1 to 22 / 11kV. These weighted parameters conform to the voltage classification standards of DL / T 5429 "Technical Specification for Power System Design".

[0159] Step S4: Use the PageRank algorithm to evaluate the degree to which each node is referenced by other nodes, and obtain the PageRank value of the candidate key nodes;

[0160] Step S5: Combine the weighted degree centrality index with the PageRank value to generate a comprehensive criticality index, and sort all candidate critical nodes according to the comprehensive criticality index to obtain the critical hub identification results.

[0161] The comprehensive criticality index of all 46 branches and 39 nodes was ranked.

[0162] Output:

[0163] Nodes such as 4, 16, 21, and 3 are typically hub substations that connect multiple important transmission lines. They are local power aggregation points and are identified as critical hubs.

[0164] Example effect:

[0165] This embodiment verifies that the method of the present invention successfully identifies key hubs in the IEEE 39-node system, such as nodes 4, 16, 21, and 3, which are bottlenecks in the global power flow.

[0166] Example 3:

[0167] This embodiment provides a power system critical hub identification system based on degree centrality and density, including a processor and a memory. The memory stores a computer program, and the processor executes the computer program to implement the method described in Embodiment 1.

[0168] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0169] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0170] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0171] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0172] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for identifying critical hubs in a power system based on degree centrality and density, characterized in that, include: Step S1: Construct a power grid weighted bidirectional graph model of the power system to be evaluated, and calculate the degree centrality index of the nodes based on the power grid weighted bidirectional graph model; Step S2: Based on the degree centrality index, select nodes whose degree centrality index meets the preset reliability standard as candidate key nodes; Step S3: For the candidate key nodes, set weighting parameters based on the node voltage level, and perform weighting processing on the degree centrality index to obtain the weighted degree centrality index; Step S4: Use the PageRank algorithm to evaluate the degree to which each node is referenced by other nodes, and obtain the PageRank value of the candidate key nodes; Step S5: Combine the weighted degree centrality index with the PageRank value to generate a comprehensive criticality index, and sort all candidate critical nodes according to the comprehensive criticality index to obtain the critical hub identification results; In step S4, the PageRank algorithm is used to evaluate the degree to which each node is referenced by other nodes to obtain the PageRank value of the candidate key nodes, including: Construct a probability transition matrix M, whose elements M ij This represents the probability of transitioning from node j to node i: ； in: This represents the transition weight of the edge from node j to node i; It is the sum of the transition weights of all outgoing edges from node j; It is taken as the reciprocal of the per-unit reactance of the line, representing the ease or difficulty of power flow transmission; Assign an initial PageRank value to each node. All nodes have the same initial value, which is 1 / N, where N is the total number of nodes. The initial PageRank values ​​of all nodes constitute the initial PageRank value vector R(0), which is solved using the following exponential iteration formula: ； Where: R(t+1) is the PageRank value vector after the (t+1)th iteration, R(t) is the PageRank value vector after the tth iteration, and M... T Let M be the transpose of the transition matrix, and α be the damping factor; The power iteration formula indicates that there is a probability α of power transfer along the path in the system, and a probability of (1-α) of random jump to any node in the network, where e is a column vector with all elements equal to 1, and N is the total number of nodes in the network. The vector is a uniformly distributed vector for random jumps; Iterative calculation until , Given a preset tolerance, the final R is obtained. i This is the PageRank value of node i.

2. The method for identifying critical hubs in a power system based on degree centrality and density according to claim 1, characterized in that, In step S1, the method for constructing a weighted bidirectional graph model of the power grid to be evaluated includes: A weighted bidirectional graph model of the power system to be evaluated is constructed, where nodes correspond to buses in the power system, edges correspond to transmission lines and transformer branches, and edge weights are defined based on electrical characteristics.

3. The method for identifying critical hubs in a power system based on degree centrality and density according to claim 2, characterized in that, In step S1, the degree centrality index is calculated as follows: for node i, the degree centrality index is the number of edges connected to that node.

4. The method for identifying critical hubs in a power system based on degree centrality and density according to claim 1, characterized in that, In step S2, nodes with a degree centrality index greater than or equal to 3 are selected as candidate key nodes that meet the preset reliability criteria.

5. The method for identifying critical hubs in a power system based on degree centrality and density according to claim 1, characterized in that, The method further includes: Static structure checks are performed on the nodes and edges in the weighted bidirectional graph model of the power grid, and nodes and edges that fail the static structure check are removed. The static structure test is to check whether it meets the N-1 criterion.

6. The method for identifying critical hubs in a power system based on degree centrality and density according to claim 1, characterized in that, In step S3, weighting parameters are set based on node voltage levels, and the degree centrality index is weighted to obtain a weighted degree centrality index, including: The weighted parameters of the nodes are set based on the node voltage level; Weighted degree centrality index WDC i The calculation formula is: ； Among them, w i k represents the weighted parameter of node i. i This represents the number of edges connected to node i.

7. The method for identifying critical hubs in a power system based on degree centrality and density according to claim 6, characterized in that, The weighted parameters of the nodes are set based on the node voltage level, including: For nodes with a voltage level of 345kV and above, the weighting parameter is 1.0; for nodes with a voltage level of 161kV, the weighting parameter is 0.7; for nodes with a voltage level of 69kV, the weighting parameter is 0.4; and for nodes with a voltage level of 22kV or 11kV, the weighting parameter is 0.

1.

8. The method for identifying critical hubs in a power system based on degree centrality and density according to claim 1, characterized in that, In step S5, a comprehensive criticality index is generated, and all candidate critical nodes are ranked according to the comprehensive criticality index to obtain the critical hub identification result, including: For a node i, its comprehensive criticality index CI i The calculation is as follows: ； in: and These are the weighted degree centrality and PageRank value of node i after min-max normalization, respectively, and θ is the fusion weight coefficient, with a value range of [0,1]. Based on the above formula, calculate the comprehensive criticality index (CI) of all nodes in the network. i All nodes are sorted by CI i The values ​​are sorted from largest to smallest, and a recognition threshold is set to identify the key hubs.

9. A power system critical hub identification system based on degree centrality and density, characterized in that, It includes a processor and a memory, the memory storing a computer program, and the processor executing the computer program to implement the method as described in any one of claims 1 to 8.

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