A power system renormalization equivalent modeling method for fragile skeleton preservation

Abstract

The present application relates to a power system renormalization equivalent modeling method for fragile skeleton preservation in power system security analysis. In view of the problems of heavy calculation burden in large-scale power transmission network fragile branch identification, difficulty in maintaining risk-related skeleton structure in conventional equivalent modeling, and difficulty in tracing equivalent results to the original physical branch space, a comprehensive branch vulnerability index composed of branch power flow stress, post-fault overload severity and branch power flow medium array is constructed, and a composite diffusion weight is formed by combining electrical coupling strength, power flow stress and post-fault power flow redistribution strength. Based on the composite diffusion weight, a symmetric normalized diffusion Laplace is constructed, the optimal partition scheme is determined through spectral region division and Pareto frontier knee point criterion, and the key skeleton network is extracted; the Ward equivalent is performed with the skeleton nodes and regional representative nodes as the reserved objects, and the renormalization equivalent power grid is generated. Further, the coverage mapping of the renormalization equivalent power grid branch to the original power grid physical branch set is established, and the fragile branch preservation effect is evaluated through hit rate and average accuracy, so as to compress the power grid scale, improve the key skeleton preservation ability, fragile branch identification consistency and the implementability of large-scale power grid rapid risk screening.

Description

Technical Field

[0001] This invention belongs to the field of power system security analysis and equivalent modeling technology, specifically involving a power system renormalization equivalent modeling method for maintaining vulnerable skeletons. It is applicable to scenarios such as key skeleton network extraction, vulnerable branch identification, rapid risk screening, and equivalent network construction in large-scale transmission networks, regional interconnected networks, and power systems with multiple operating modes. Background Technology

[0002] With the continuous advancement of new power system construction, the scale of inter-regional power transmission is constantly expanding, and the proportion of renewable energy grid connection is continuously increasing, making the network scale, power flow distribution, and inter-regional electrical coupling relationships of power systems increasingly complex. Operational risks in large-scale transmission networks are typically not uniformly distributed, but rather concentrated in a small number of critical branches and interfaces that bear the main responsibilities for power transfer, post-fault power flow redistribution, and inter-regional interconnection. Rapidly identifying these risk-related key structural elements is crucial for power grid security analysis, operational risk screening, fault prevention and control, and operation and maintenance decision-making.

[0003] Existing methods for identifying vulnerable branches in power systems typically involve direct power flow calculations, sensitivity analyses, N-1 fault scans, or cascaded fault simulations based on the original power grid. While these methods can effectively reflect physical factors such as branch power flow, branch capacity, and post-fault power flow transfer, they involve significant computational loads under conditions of large-scale transmission networks, multiple operating modes, and multiple fault scenarios, hindering rapid online or near-online screening. Some identification methods based on complex network indicators or topology offer faster computation speeds, but they often fail to adequately reflect branch reactance, branch susceptance, branch load levels, source-load power transfer relationships, and post-fault power flow redistribution mechanisms.

[0004] To reduce the complexity of system analysis, power system network reduction and equivalent modeling methods are widely used in planning calculations, stability analysis, and simulation acceleration. Common methods include Ward's equivalent model, Kron's reduction, node aggregation, and regional partitioning equivalent model. These methods typically aim to improve boundary injection response, regional power flow characteristics, planning computation efficiency, or preserve node electrical responses, and can reduce the number of nodes and branches to some extent. However, for vulnerability analysis, the equivalent network not only needs to be smaller in size but also needs to retain as many backbone branches as possible that play a dominant role in risk propagation, power flow transfer, and inter-regional connections in the original power grid. If a small number of critical branches within a region are averaged or eliminated during the coarsening process, the equivalent network, although smaller in size, may not be able to maintain the set and ranking of vulnerable branches in the original power grid.

[0005] Existing coarse-grained methods based on topological clustering, geographic partitioning, or ordinary graph Laplacian often rely primarily on topological connectivity or distance relationships for region division, making it difficult to uniformly incorporate branch electrical coupling strength, operational power flow stress, and post-fault power flow redistribution intensity into the partitioning metrics. For critical backbone network analysis, region partitioning and equivalent modeling should simultaneously consider electrical parameters, current operating status, and fault response characteristics, rather than solely relying on geographic proximity or ordinary topological connectivity.

[0006] Furthermore, there is often a lack of coverage mapping between the original power grid and the equivalent power grid, oriented towards the physical branch space. The branches generated after equivalence may correspond to one or more physical branches in the original power grid, or they may be equivalent filler branches generated after eliminating non-retained nodes. Without a clear coverage mapping, it is difficult to trace the identification results of vulnerable branches in the equivalent network back to the original power grid equipment level, and it is also difficult to objectively evaluate whether the set of vulnerable branches before and after equivalence is consistent and whether the order is maintained.

[0007] Therefore, it is necessary to construct a power system renormalization equivalent modeling method oriented towards preserving the vulnerable skeleton. Under the conditions of a large number of branches, complex operating states, and significant power flow transfer after a fault in large-scale transmission networks, this method should comprehensively consider branch power flow stress, post-fault overload severity, source-load power transfer effect, electrical coupling strength, and post-fault power flow redistribution intensity. This would form a closed-loop modeling method that includes composite diffusion spectrum partitioning, key skeleton extraction, skeleton-preserving Ward equivalent modeling, and coverage mapping consistency evaluation. This would allow the original key skeleton structure of the power grid and the identification results of vulnerable branches to be preserved while compressing the network size. Summary of the Invention

[0008] The purpose of this invention is to address the problems of existing power system equivalent modeling methods, which often focus on ordinary scale compression or boundary response preservation without explicitly preserving risk-related skeleton structures; existing vulnerable branch identification methods suffer from heavy computational burdens in large-scale transmission networks and multi-fault scenarios; ordinary topology clustering struggles to reflect branch reactance, power flow stress, and post-fault power flow redistribution; and the difficulty in tracing the identification results of vulnerable branches in the equivalent network back to the original physical branch space. This invention proposes a power system renormalization equivalent modeling method oriented towards vulnerable skeleton preservation. This method constructs a comprehensive branch vulnerability index and a composite diffusion weight to transform vulnerability information and post-fault power flow redistribution information into spectral partitioning metrics. Based on the priority preservation of key skeleton nodes and skeleton branches, Ward equivalence is performed. Furthermore, a mapping is established from the renormalized equivalent grid branches to the original physical grid branch set, thus forming a closed-loop equivalent modeling method encompassing original grid modeling, vulnerability calculation, composite diffusion spectral partitioning, key skeleton extraction, skeleton-preserving Ward equivalence, and consistency evaluation.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] 1. Acquisition of Original Power Network Data and Construction of Original Power Network Model. Acquire the node set, branch set, branch reactance, branch susceptance, branch capacity, active power injection at nodes, generating nodes, load nodes, branch power flow, candidate branch fault set, and analysis parameters of the target power system. Based on the power flow model or linear sensitivity model, construct the original power network (OPN) and determine the operating status of each node and branch in the original power network.

[0011] 2. Calculation of branch vulnerability index. Based on the branch power flow stress, overload severity after branch fault, and the role of the branch in the source-load power transfer path of each branch in the original power grid OPN, the comprehensive branch vulnerability index of each branch is calculated, and the vulnerability ranking of the physical branches of the original power grid is formed based on the comprehensive branch vulnerability index.

[0012] 3. Construction of Composite Diffusion Weights and Diffusion Laplace. Composite diffusion weights are constructed based on branch electrical coupling strength, branch power flow stress, and post-fault power flow redistribution strength. A weighted adjacency matrix, a generalized degree matrix, and a symmetric normalized diffusion Laplace are then formed based on these composite diffusion weights.

[0013] 4. Spectral Region Division and Determination of Optimal Partition Scheme. Spectral embedding and clustering are performed on the low-order nontrivial eigenvectors of the symmetric normalized diffusion Laplacian. The structural complexity and linear sensitivity error are calculated for different numbers of candidate partitions. The optimal number of partitions and the optimal region division scheme are determined based on the Pareto front knee point between the structural complexity and the linear sensitivity error.

[0014] 5. Key Backbone Network Extraction. The key backbone network is extracted based on the optimal region division scheme. This key backbone network includes inter-regional connection branch endpoints, power generation nodes, high-load nodes, high-current-power-between-number nodes, intra-regional backbone branches, and inter-regional backbone connection branches. Intra-regional backbone branches are determined based on composite diffusion weights and backbone node connectivity requirements, while inter-regional backbone connection branches are determined based on inter-regional connection relationships between adjacent regions and composite diffusion weights.

[0015] 6. Generation of Ward equivalent and renormalized equivalent power grids with skeleton preservation. Regional representative nodes are selected, and the skeleton nodes in the key skeleton network and the regional representative nodes are used as the retention set. The remaining non-skeleton nodes are used as the elimination set. For the elimination set Perform Ward equivalence to generate a retainer set. The equivalent admittance matrix, equivalent injection vector, and renormalized equivalent power network (REPN) are mentioned.

[0016] 7. Coverage Mapping, Consistency Evaluation, and Result Output. A coverage mapping is established from the branches in the renormalized equivalent grid (REPN) to the physical branch set of the original grid (OPN). The vulnerable branch identification results obtained by sorting the branches in the REPN according to the comprehensive branch vulnerability index are backtracked to the OPN physical branch space. The consistency evaluation index of the vulnerable branch set is calculated, and the renormalized equivalent grid, key backbone network, vulnerable branch set, coverage mapping relationship, and consistency evaluation results are output.

[0017] Based on the above method, preferably, the integrated branch vulnerability index and composite diffusion weight are constructed in the following manner.

[0018] Calculate the branch flow stress index, the overload severity index after a branch fault, and the branch flow betweenness index based on the branch flow stress index, the branch flow fault severity index, and the branch flow betweenness index. Comprehensive branch vulnerability index:

[0019]

[0020] In the formula, branch road The comprehensive vulnerability index of branch lines, and These are the indexes of the nodes at both ends of the branch. Indicates that by node and nodes The connecting branches branch road Branch tidal current stress index, branch road Overload severity index after candidate branch failure branch road The branch power flow betweenness index, PFB stands for Branch Power Flow Betweenness. , and These are the vulnerability weighting coefficients corresponding to the branch power flow stress index, overload severity index, and branch power flow betweenness index, respectively.

[0021] The branch power flow stress index is determined based on the branch load rate and the branch active power flow amplitude; the overload severity index is determined based on the degree of branch overload caused by the linear power flow transfer relationship after a candidate branch failure; and the branch power flow betweenness index is determined based on the transmission effect of the branch in the power transfer path from the generation node to the load node. The vulnerability weight coefficient can be determined by combining physical prior weights and objective correction weights, whereby the objective correction weights are determined based on the dispersion and correlation of each index.

[0022] Calculate the branch based on the branch electrical coupling strength, branch power flow stress, and post-fault power flow redistribution intensity. Composite diffusion weight:

[0023]

[0024] In the formula, branch road The composite diffusion weight, branch road Electrical coupling strength index branch road Branch tidal current stress index, branch road The intensity index of power flow redistribution after a fault. , and These are the diffusion weighting coefficients corresponding to the electrical coupling strength index, branch power flow stress index, and post-fault power flow redistribution strength index, respectively.

[0025] The electrical coupling strength index is determined based on the branch reactance or branch susceptance, and the post-fault power flow redistribution strength index is determined based on the sensitivity of the Line Outage Distribution Factor (LODF) under candidate branch faults and the power flow of the faulted branch. The diffusion weight coefficient can be determined by combining physical prior weights and objectively corrected weights.

[0026] Preferably, a weighted adjacency matrix is ​​constructed based on the composite diffusion weights. and generalized degree matrix And construct a symmetric normalized diffusion Laplace:

[0027]

[0028] In the formula, For symmetric normalized diffusion Laplace, It is the identity matrix. The weighted adjacency matrix is ​​composed of composite diffusion weights. For generalized degree matrix, Generalized degree matrix A negative 1 / 2 power matrix. The weighted adjacency matrix. The generalized degree matrix is ​​used to characterize the composite diffusion connection strength between adjacent nodes in the original power grid OPN. The diagonal elements are obtained by accumulating the composite diffusion weights of the adjacent branches of the corresponding node.

[0029] Preferably, the symmetric normalized diffusion Laplace... Eigenvalue decomposition is performed, low-order nontrivial eigenvectors are selected to construct a spectral embedding matrix, and the spectral embedding matrix is ​​then subjected to row normalization and clustering to obtain the number of candidate partitions. The following is a regional partitioning scheme. This is applicable to different numbers of candidate partitions. Calculate the structural complexity and linear sensitivity error The linear sensitivity error is expressed as:

[0030]

[0031] In the formula, The number of candidate partitions, Number of candidate partitions The structural complexity below, Number of candidate partitions The linear sensitivity error is below. Number of candidate partitions The relative error of the power transfer distribution factor (PTDF) of the renormalized equivalent grid relative to the original grid. Number of candidate partitions The relative error of LODF of the renormalized equivalent grid relative to the original grid, where PTDF is the power transfer distribution factor and LODF is the line interruption distribution factor. After normalization... - In the plane, a non-dominated Pareto front is determined, and the number of partitions on the Pareto front that satisfy the knee criterion is taken as the optimal number of partitions. .

[0032] Preferably, based on the optimal number of partitions The corresponding regional division scheme retains the endpoints of inter-regional connecting branches, power generation nodes, high-load nodes, and high-current-between-number nodes as backbone nodes; within each region, backbone branches are constructed based on composite diffusion weights, and non-backbone leaf branches are cut off while maintaining the connectivity of backbone nodes; for inter-regional connecting branches between adjacent regions, inter-regional connecting branches whose composite diffusion weights meet preset priority conditions are retained to form a key backbone network.

[0033] Preferably, the skeleton nodes and region representative nodes are combined into a retention set. The remaining non-skeleton nodes are used to form a cancellation set. The node admittance matrix of the original power grid is divided according to the retention set. and elimination set The data is divided into blocks, and the equivalent admittance matrix and equivalent injection vector are calculated using Ward's equivalent method:

[0034]

[0035]

[0036] In the formula, For the reserved set The equivalent admittance matrix on, For the reserved set Equivalent injection vector on, For the reserved set With Reserved Set The admittance submatrix between For the reserved set With elimination set The admittance submatrix between To eliminate the collection With elimination set The admittance submatrix between To eliminate the collection With Reserved Set The admittance submatrix between For the reserved set Inject vectors into nodes on the node. To eliminate the collection Inject vectors into nodes on the node. Admittance submatrix The inverse matrix in the corresponding constrained subspace, The reserved set consists of skeleton nodes and region representative nodes. The elimination set consists of the remaining non-skeleton nodes. Using equations (5) and (6), the retention set is obtained while eliminating non-skeleton nodes. The equivalent admittance relation and equivalent injection relation.

[0037] Preferably, based on the equivalent admittance matrix The off-diagonal elements are used to generate the equivalent branches of the renormalized equivalent power grid (REPN), and each branch in the REPN is established. Overlay mapping to OPN physical branch set .when When there is only one OPN physical branch, the REPN branch and the OPN physical branch are determined to have a one-to-one coverage relationship; when When multiple OPN physical branches are included, the REPN branch and the OPN physical branch are determined to have a one-to-many coverage relationship; when When the set is empty, the REPN branch is determined to be an equivalent fill branch.

[0038] According to the coverage mapping The top branches in REPN are sorted by their comprehensive branch vulnerability index. The proportionally fragile branches are mapped back to the OPN physical branch space, and the hit rate is calculated:

[0039]

[0040] In the formula, For truncation ratio The hit rate is low. The cutoff ratio for the set of vulnerable branches. The top-ranked branches in the OPN are sorted by the comprehensive branch vulnerability index. Proportional physical branch set, The REPN is sorted by the comprehensive branch vulnerability index and then mapped by coverage. The first part obtained after mapping back to the OPN physical branch space The proportional branch set, REPN is the renormalized equivalent grid, and OPN is the original grid. For the branch index in REPN, REPN branch The corresponding OPN physical branch coverage set, ∩ is the set intersection operation, and |·| is the number of elements in the set.

[0041] The average precision (AP) is calculated based on the hit positions of the REPN vulnerable branch rankings in the OPN physical branch space after coverage mapping. The hit rate (HR) and average precision (AP) are used as consistency evaluation indicators for the preservation of the vulnerable branch set and ranking between OPN and REPN. AP is used to evaluate the degree to which the REPN vulnerable branch rankings preserve the ranking of the target vulnerable branch set of OPN after coverage mapping.

[0042] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the steps of the above-described power system renormalization equivalent modeling method for maintaining a fragile skeleton.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] (1) This invention improves the physical interpretability of key backbone branch identification by constructing a comprehensive branch vulnerability index, which incorporates branch power flow stress, overload severity after branch fault and the role of the branch in the source load power transfer path into a unified ranking framework.

[0045] (2) This invention encodes the branch electrical coupling strength, branch power flow stress and post-fault power flow redistribution strength into the spectral partition metric by constructing a composite diffusion weight and a symmetric normalized diffusion Laplace, thereby avoiding network coarsening based solely on geographical distance or ordinary topological connections.

[0046] (3) This invention determines the optimal number of partitions by using the Pareto front knee point criterion, achieving a trade-off between structural complexity and PTDF / LODF linear sensitivity error, so that the region partitioning scheme takes into account both the size of the equivalent network and the ability to maintain linear response.

[0047] (4) By prioritizing the retention of the endpoints of cross-regional interconnection branches, power generation nodes, high load nodes, high power flow betweenness nodes and backbone branches, this invention reduces the masking of risk-dominant branches by ordinary equivalent processes, enabling the equivalent network to retain key backbone structures that play an important role in power flow transfer and fault propagation.

[0048] (5) This invention uses skeleton-preserving Ward equivalents to compress non-skeleton nodes while maintaining the equivalent admittance relationship and injection response on the reserved set, so that the renormalized equivalent grid has both scale compression and electrical response consistency.

[0049] (6) By establishing a coverage mapping from REPN branches to OPN physical branch sets, the present invention enables the identification results of vulnerable branches in the equivalent network to be traced back to the original physical branch space, which facilitates the mapping of the equivalent network analysis results to actual power transmission equipment.

[0050] (7) This invention evaluates the effectiveness of maintaining the set of vulnerable branches and maintaining the order between OPN and REPN by using the hit rate HR and average accuracy AP, so that the renormalized equivalent modeling results can be quantitatively verified by cross-scale consistency index. Attached Figure Description

[0051] To more clearly illustrate the technical solution of the present invention, the embodiments of the present invention will be described in detail below with reference to the accompanying drawings, in which:

[0052] Figure 1 This is a schematic diagram of the overall process of power system renormalization equivalent modeling for maintaining a fragile skeleton, provided by an embodiment of the present invention.

[0053] Figure 2 A schematic diagram of Pareto knee selection for structural complexity and linear sensitivity error provided in an embodiment of the present invention;

[0054] Figure 3 A schematic diagram of the regional division and key skeleton topology mapping of the original power grid and the renormalized equivalent power grid provided in an embodiment of the present invention;

[0055] Figure 4 This is a schematic diagram of OPN-REPN cross-scale branch vulnerability coverage mapping provided in an embodiment of the present invention. Detailed Implementation

[0056] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the following embodiments are only for illustrating the present invention and are not intended to limit the present invention; various modifications or equivalent substitutions can be made to the following embodiments by those skilled in the art without departing from the spirit and substance of the present invention, and all such modifications or substitutions should fall within the protection scope of the present invention.

[0057] Example 1: Acquisition of raw power grid data and construction of raw power grid model

[0058] This embodiment targets large-scale transmission networks, regional interconnected networks, or typical test networks, acquiring the node set, branch set, branch reactance, branch susceptance, branch capacity, node active power injection, generating nodes, load nodes, branch power flow, candidate branch fault set, and analysis parameters of the target power system. The node set includes bus nodes participating in power flow calculation and equivalent modeling; the branch set includes transmission lines, transformer branches, or equivalent branches; the branch capacity includes branch thermal stability limits or operational limits; and the node active power injection includes generating active power output, load active power demand, and equivalent injection.

[0059] Based on the above data, an original power grid OPN is established. The OPN can be represented as a weighted network consisting of a set of nodes and a set of branches. The branch weights are determined by branch reactance, branch susceptance, branch power flow, branch capacity, and subsequent composite diffusion weights. Preferably, under DC power flow or linear power flow models, the node active power injection vector, node phase angle vector, and node admittance matrix satisfy a linear power flow relationship. For scenarios using a linearized AC power flow model, corresponding branch power flow and node injection response models can also be established based on linear sensitivity relationships.

[0060] After completing the OPN modeling, the active power flow, branch load factor, node injection, and distribution of generating and load nodes for each branch under a given operating mode are calculated or retrieved, forming a candidate branch fault set. The candidate branch fault set may include N-1 interruption faults of all branches, or it may be formed by filtering based on branch voltage level, operating limits, power flow load factor, or scope of operation and maintenance concern.

[0061] like Figure 1 As shown, the method of this invention starts with OPN modeling, and sequentially performs spectral partitioning, key skeleton network extraction, Ward isometry and coverage mapping, ultimately generating REPN and its cross-scale mapping relationship with OPN. Through the data acquisition and original power grid model construction of this embodiment, a unified data foundation can be provided for subsequent branch vulnerability index calculation, composite diffusion weight construction, and isometry network generation.

[0062] Example 2: Calculation of Branch Vulnerability Index

[0063] This embodiment calculates the comprehensive branch vulnerability index for each physical branch based on the OPN established in Embodiment 1. The comprehensive branch vulnerability index is used to measure the risk contribution of the branch in the current operating state, power flow redistribution after candidate faults, and source-load power transfer paths, and serves as a unified evaluation basis for the original power grid physical branch vulnerability ranking and the renormalized equivalent power grid vulnerable branch ranking.

[0064] First, the branch power flow stress index is calculated based on the branch's active power flow amplitude, rated capacity, or operating limit. The branch power flow stress index can be obtained by weighting the branch load rate and normalized power flow amplitude, and is used to characterize the branch's load level under the current operating mode. The higher the branch load rate, or the greater the active power flow carried by the branch, the higher the branch power flow stress index.

[0065] Secondly, the overload severity index after a branch failure is calculated based on the candidate branch failure set. Specifically, linear power flow transfer analysis is performed on the candidate failed branches. Based on LODF sensitivity or other linear power flow transfer relationships, the impact of each candidate branch failure on the power flow of other branches is calculated. When the power flow of a branch exceeds its capacity or operating limit after a failure, the overload severity index is accumulated according to the degree of capacity exceedance. The overload severity index is used to characterize the risk exposure of a branch in the power flow redistribution after a failure.

[0066] Next, the branch power flow betweenness index is calculated based on the power transfer path from the generation node to the load node. The branch power flow betweenness index is used to characterize the channel role of the branch in the source-load power transfer process. When a branch is located on multiple important source-load power transfer paths, or carries a large source-load transfer power, the corresponding branch power flow betweenness index is higher.

[0067] After normalizing the above indicators, the branch is calculated according to formula (1). The comprehensive branch vulnerability index. The vulnerability weighting coefficient. , and The ranking can be determined by using fixed physical prior weights or by combining physical prior weights with objectively corrected weights. The objectively corrected weights can be determined based on the dispersion and correlation of the branch power flow stress index, overload severity index, and branch power flow betweenness index on each branch, so as to reduce the influence of a single manual empirical weight on the ranking results.

[0068] The comprehensive branch vulnerability index obtained through this embodiment can form a vulnerability ranking result for OPN physical branches. This ranking result is used both for identifying vulnerable skeleton branches in the critical skeleton network and for subsequent coverage mapping consistency evaluation with the REPN vulnerable branch ranking result.

[0069] Example 3: Construction of Composite Diffusion Weights and Diffusion Laplace

[0070] This embodiment, based on Embodiments 1 and 2, constructs a composite diffusion weight for spectral region partitioning. This composite diffusion weight differs from ordinary topological adjacency weights; it simultaneously integrates branch electrical coupling strength, branch power flow stress, and post-fault power flow redistribution strength, enabling the region partitioning process to reflect the power grid's physical parameters, operating status, and fault response characteristics.

[0071] First, calculate the branch electrical coupling strength index based on branch reactance or branch susceptance. For transmission lines expressed as branch reactance, the smaller the branch reactance, the larger the corresponding branch susceptance, and the stronger the electrical coupling between nodes is generally. The absolute value of the branch susceptance or its normalized form can be used as the electrical coupling strength index.

[0072] Secondly, the branch tidal current stress index from Example 2 is used as the operating state component of the composite diffusion weight. This component is used to ensure that high-load branches have higher diffusion connectivity during spectral partitioning, thereby preventing high-load channels from being simply weakened during coarsening.

[0073] Next, the post-fault power flow redistribution intensity index is calculated based on the LODF sensitivity under candidate branch faults and the power flow of the faulted branch. This index characterizes the degree to which a branch participates in power flow transfer or experiences power flow redistribution under different fault scenarios. When a branch is significantly affected by power flow transfer in multiple fault scenarios, its post-fault power flow redistribution intensity index is higher.

[0074] After normalizing the above three types of indicators, the branch is calculated according to formula (2). Composite diffusion weight The diffusion weighting coefficient , and The weighting can be set based on the importance of three types of factors: electrical coupling, power flow stress, and power flow redistribution after a fault. Alternatively, it can be determined by combining physical prior weights with objective correction weights.

[0075] Based on the composite diffusion weights, a weighted adjacency matrix is ​​constructed. If there is a branch between node i and node j, then The corresponding element is taken as the composite diffusion weight of that branch; if there is no branch between node i and node j, the corresponding element is zero. Further, the composite diffusion weights of the adjacent branches of each node are summed to obtain the generalized degree matrix. The diagonal elements. Construct a symmetric normalized diffusion Laplace based on equation (3). .

[0076] The symmetric normalized diffusion Laplace constructed in this embodiment can reflect the slowly changing regional structure under composite diffusion weights through its low-order nontrivial eigenvectors. This means that nodes are not only topologically adjacent but also similar in terms of electrical coupling, power flow stress, and post-fault power flow transfer response. This provides a risk-related electrical similarity measure for subsequent spectral region partitioning.

[0077] Example 4: Spectral Region Division and Determination of Optimal Partition Scheme

[0078] This embodiment is based on the symmetric normalized diffusion Laplace obtained in Example 3. The process involves spectral region partitioning and determining the optimal partitioning scheme. This spectral region partitioning divides the nodes in the OPN into several regions, ensuring strong composite diffusion relationships between nodes within each region and connecting regions through a small number of inter-regional connection branches. This provides a partitioning basis for key backbone network extraction and backbone-preserving Ward equivalence.

[0079] First of all, Eigenvalue decomposition is performed to obtain eigenvalues ​​and their corresponding eigenvectors. After removing the eigenvectors corresponding to trivial eigenvalues, low-order non-trivial eigenvectors are selected to construct a spectral embedding matrix. Each row of the spectral embedding matrix corresponds to the representation of a node in the low-dimensional spectral space. Then, the spectral embedding matrix is ​​row-normalized, and clustering methods are used to cluster the nodes to obtain the number of candidate partitions. The following is a regional division scheme.

[0080] For each candidate partition number Based on the regional division results, cross-regional connecting branches are identified, and the structural complexity is calculated. Preferably, structural complexity Based on the number of candidate partitions The number of inter-regional connection branches, the number of inter-regional interfaces, or the complexity of the equivalent network structure are determined. The lower the structural complexity, the simpler the inter-regional connections of the corresponding REPN, and the smaller the equivalent network size.

[0081] Meanwhile, regarding the number of candidate partitions The obtained regional division scheme is used for equivalent trial calculations or linear sensitivity approximation evaluation, and the relative error of the power transfer distribution factor (PTDF) is calculated. Relative error of line breakage distribution factor (LODF) And according to equation (4), the larger of the two values ​​is taken as the linear sensitivity error. . The smaller the value, the stronger the ability of the REPN constructed under the candidate partitioning scheme to maintain the linear power flow response and post-fault power flow transfer response of the OPN.

[0082] like Figure 2 As shown, after normalization - In the plane, candidate partitioning schemes typically represent a trade-off between structural complexity and linear sensitivity error. When the number of partitions is small, the network compression is high, but the linear sensitivity error may be large; when the number of partitions is large, the linear sensitivity error decreases, but the structural complexity increases. This embodiment describes... - The non-dominated Pareto front is determined in the plane, and the optimal number of partitions is selected based on the knee criterion, which yields a better compromise. The knee point criterion can be achieved by methods such as the included angle of three adjacent points, the maximum discrete curvature, or the minimum distance from the ideal point.

[0083] The optimal number of partitions obtained through this embodiment The optimal region partitioning scheme can achieve a balance between the complexity of the iso-network and the preservation of linear sensitivity, avoiding the problem of the iso-network being too coarse or too fine due to artificially fixing the number of partitions.

[0084] Example 5: Key Backbone Network Extraction

[0085] This embodiment extracts the key backbone network based on the optimal region partitioning scheme obtained in Embodiment 4. The key backbone network is used to retain backbone nodes and backbone branches in the OPN that play an important role in cross-regional power exchange, source-load power transfer, and power flow redistribution after a fault.

[0086] First, inter-regional connection branches are identified according to the optimal regional division scheme, and the nodes at both ends of the inter-regional connection branches are used as skeleton nodes. The endpoints of the inter-regional connection branches undertake the functions of inter-regional power exchange and power flow transfer interface after a fault. If they are eliminated during the equivalence process, it may lead to insufficient representation of the dominant inter-regional channels.

[0087] Secondly, generating nodes and high-load nodes are designated as backbone nodes. Generating nodes and high-load nodes correspond to the main power injection points and main power absorption points, respectively, and directly influence the source-load power transfer path and power flow distribution. The high-load nodes can be determined based on load size, load proportion, or load importance level.

[0088] Secondly, high power flow betweenness nodes are designated as backbone nodes. High power flow betweenness nodes can be determined based on the branch power flow betweenness of their connected branches, the number of source-load paths the node occupies, or the node's location within a critical channel. These nodes have a strong mediating role in power transfer paths, and prioritizing their retention helps maintain the critical backbone structure.

[0089] After determining the skeleton nodes, skeleton branches are constructed within each region based on composite diffusion weights. Preferably, a maximum weight spanning tree or a skeleton subgraph satisfying the connectivity requirements of skeleton nodes can be constructed within the region using composite diffusion weights as edge weights, and non-skeleton leaf branches are pruned while maintaining the connectivity of skeleton nodes. In cases where multiple cross-regional connection branches exist between adjacent regions, cross-regional connection branches whose composite diffusion weights satisfy preset priority conditions are retained, for example, retaining one or more cross-regional connection branches with the largest composite diffusion weights.

[0090] like Figure 3 As shown, the region partitioning, skeleton nodes, and skeleton branches in OPN can be extracted and retained in REPN. Figure 3 The physical branches, skeleton branches, region representative nodes, and equivalent coupling branches in this invention collectively demonstrate the prioritization of key skeleton structures during network compression. The key skeleton network extracted through this embodiment can serve as an important retention target in subsequent Ward equivalence, reducing the masking of risk-dominant branches by conventional equivalence processes.

[0091] Example 6: Crescent-Preserving Ward Equivalent and Renormalized Equivalent Power Grid Generation

[0092] This embodiment, based on the key skeleton network extracted in Embodiment 5, performs skeleton-preserving Ward equivalence and generates REPN. The skeleton-preserving Ward equivalence is not innovative solely in its Ward equivalence; rather, it prioritizes the retention of key skeleton nodes, skeleton branches, and region representative nodes while performing algebraic elimination on the remaining non-skeleton nodes, thereby compressing the network size while maintaining the key skeleton structure.

[0093] First, a representative node is selected within each region. This representative node represents the equivalent connection port between the non-skeleton subnet within the region and the external reserved network. The representative node can be determined based on node load, node injection, connection relationship with skeleton nodes, composite diffusion weight, or electrical centrality within the region. For regions without suitable non-skeleton nodes, existing skeleton nodes can be selected as representative nodes based on the actual node structure.

[0094] Secondly, the skeleton nodes obtained in Example 5 and the region representative nodes are combined to form a retention set. The remaining non-skeleton nodes are used to form a cancellation set. Reserved set Used to construct the node set in REPN, and to eliminate the set. This is used for compression via Ward equivalence. This partitioning method preserves inter-regional link endpoints, generation nodes, high-load nodes, high power flow betweenness nodes, and regional representative nodes after equivalence, thereby maintaining the critical backbone network and main source-load ports.

[0095] Next, the node admittance matrix of OPN is arranged according to the retention set. and elimination set Divide into blocks to obtain , , and The admittance submatrix is ​​equal to the set of values, and the retention set is calculated according to equations (5) and (6). Equivalent admittance matrix on and equivalent injection vector Through this equivalence process, the set is eliminated. Non-skeleton nodes are algebraically eliminated, and their impact on electrical coupling and node injection between retained nodes is reduced to the equivalent admittance matrix and equivalent injection vector.

[0096] Then, based on the equivalent admittance matrix Off-diagonal elements generate REPN equivalent branches. For reserved nodes... and ,when When the corresponding off-diagonal elements satisfy the branch generation condition, a node is generated in REPN. With nodes The equivalent branches between them. These equivalent branches may be physical branches that are directly retained in the OPN, or they may be equivalent coupling branches generated by Ward's equivalence after eliminating non-skeleton nodes.

[0097] like Figure 3As shown, REPN retains skeleton nodes and region representative nodes at the node level, and skeleton branches and key physical branches at the branch level. It also reflects the indirect electrical coupling caused by node elimination through equivalent coupling branches. Compared with OPN, REPN generated by this embodiment has fewer nodes and branches, while retaining the key skeleton structure that dominates power flow transfer and risk propagation.

[0098] Example 7: Coverage Mapping, Consistency Evaluation, and Result Output

[0099] In this embodiment, after obtaining REPN in embodiment 6, an overlay mapping is established from REPN branches to the OPN physical branch set. Furthermore, a consistency evaluation was conducted on the preservation of the fragile branch set and the order preservation between OPN and REPN.

[0100] For each branch in REPN Determine the corresponding OPN physical branch coverage set. When REPN branch When formed by directly retaining a physical branch in OPN, This includes an OPN physical branch, confirming a one-to-one coverage relationship between the REPN branch and the OPN physical branch. When the REPN branch... When representing the equivalent results of several physical branches or paths within a region, It can contain multiple OPN physical branches, determining that the REPN branch and the OPN physical branches have a one-to-many coverage relationship. When the REPN branch... When a filler branch generated by Ward's equivalent cannot correspond to a specific set of OPN physical branches. If the set is empty, the REPN branch is determined to be an equivalent fill branch.

[0101] After establishing the coverage mapping, the comprehensive branch vulnerability index is calculated in both OPN and REPN. For OPN, the vulnerability ranking of each physical branch is obtained according to Equation (1), and the top-ranked branches are selected. Proportional physical branches as For REPN, the REPN branches are sorted by vulnerability according to equation (1), and the top ones are selected. Proportional branches, and through Mapping back to the OPN physical branch space yields Then calculate the hit rate according to formula (7). .

[0102] Furthermore, the average precision (AP) is calculated based on the hit positions in the OPN physical branch space after the REPN vulnerable branch ranking is overlaid and mapped. AP is calculated by averaging the current precision each time the target vulnerable branch set of OPN is hit in the ranking sequence, and the average of each hit position is applied, characterizing the degree to which the REPN ranking results maintain the ranking of the target vulnerable branch set of OPN.

[0103] like Figure 4 As shown, the vulnerability index of the REPN equivalent branch and the vulnerability index of its covered OPN physical branch can be displayed through a scatter plot relationship. Figure 4 The consistent and divergent regions are used to help illustrate the vulnerability correspondence between OPN and REPN. When the sample distribution is close to the diagonal reference line and the hit points are mainly concentrated in the consistent identification region, it indicates that REPN can better maintain the vulnerable branch set and ordering relationship in OPN after coverage mapping.

[0104] This embodiment ultimately outputs the renormalized equivalent grid, critical backbone network, vulnerable branch set, coverage mapping relationship, and consistency evaluation results. These consistency evaluation results include, but are not limited to, hit rate (HR), average accuracy (AP), node compression rate, branch compression rate, PTDF relative error, and LODF relative error. Through these outputs, grid operators or analysis programs can perform rapid risk screening on a smaller-scale REPN and trace the results back to the OPN physical branch space.

[0105] Example 8: Typical Case Verification

[0106] This embodiment uses a public transmission network example or a typical regional transmission system as an example to illustrate the application effect of the method of the present invention. The public transmission network example may include IEEE 118, ACTIVSg200, IEEE 300, ACTIVSg500, Poland3120sp, and Poland 3375wp, etc. For each example, the same baseline capacity, reference node settings, and operating conditions are used to obtain node load, generation output, branch reactance, branch capacity, and branch power flow, construct an OPN, and execute the renormalization equivalent modeling process of the present invention.

[0107] First, an OPN is established according to Example 1, and the comprehensive branch vulnerability index for each physical branch is calculated according to Example 2. Second, a composite diffusion weight and a symmetric normalized diffusion Laplace are constructed according to Example 3. Then, spectral regions are divided for different numbers of candidate partitions according to Example 4, and the structural complexity is calculated. and linear sensitivity error The optimal number of partitions is determined based on the Pareto front knee point. Next, the key backbone network was extracted and REPN was generated according to Examples 5 and 6. Finally, the coverage mapping was established and HR and AP were calculated according to Example 7.

[0108] In a preferred embodiment, the method of the present invention can be compared with ordinary Ward equivalence, ordinary Kron reduction, topology clustering-based reduction methods, and methods that retain only a single high-load branch. Evaluation metrics include node compression ratio, branch compression ratio, relative error of the equivalent admittance matrix, phase response error of retained nodes, relative error of PTDF, relative error of LODF, hit rate (HR), and average accuracy (AP). These metrics allow for evaluation of the method of the present invention from three aspects: network size reduction, electrical response preservation, and consistency of vulnerable branches.

[0109] In typical examples, REPN can maintain high consistency of vulnerable branch sets while reducing the number of nodes and branches. For example, in several public systems, REPN can achieve a certain proportion of node compression rate and branch compression rate; at the truncation ratio... With a 10% success rate, the hit rate (HR) and average accuracy (AP) between OPN and REPN can remain at a high level. The above examples demonstrate that the method of this invention is applicable to transmission networks of different sizes and structural characteristics, and can provide a compact and traceable equivalent network model for rapid vulnerability screening of large-scale power grids.

[0110] It should be noted that the calculation system and truncation ratio in this embodiment are different. The range of candidate partitions, weighting coefficients, fault sets, and evaluation index thresholds are all exemplary settings and are not intended to limit the scope of protection of this invention. For actual power grids, adjustments can be made based on system scale, operating mode, fault screening scope, and security analysis requirements.

[0111] Example 9 Computer-readable storage medium

[0112] This embodiment provides a computer-readable storage medium, which may be a read-only memory, random access memory, disk, optical disk, solid-state drive, or other medium capable of storing computer programs, and stores computer programs thereon. When the computer program is executed by a processor, it calls the node set, branch set, branch reactance, branch susceptance, branch capacity, node active power injection, generating nodes, load nodes, branch power flow, candidate branch fault set, and analysis parameters of the target power system, and executes the power system renormalization equivalent modeling method for maintaining a vulnerable skeleton according to the steps described in Embodiments 1 to 8.

[0113] During execution, the computer program first establishes the OPN and determines the operating status of nodes and branches; then it calculates the comprehensive branch vulnerability index and composite diffusion weight; next, it constructs the weighted adjacency matrix, generalized degree matrix, and symmetric normalized diffusion Laplace; then, it determines the optimal region partitioning scheme through spectral embedding, clustering, and the Pareto knee criterion; finally, it extracts the key backbone network, and uses the backbone nodes and region representative nodes as the retention set. The remaining non-skeleton nodes are used as the elimination set. The process involves performing Ward equivalence and generating REPN; finally, establishing a coverage mapping from REPN branches to the OPN physical branch set, calculating the hit rate HR and average accuracy AP, and outputting the renormalized equivalent grid, critical backbone network, vulnerable branch set, coverage mapping relationship, and consistency evaluation results.

[0114] It should be noted that the power flow model type, linear sensitivity calculation method, candidate branch fault set, candidate partition number range, clustering method, knee criterion, skeleton node screening threshold, number of skeleton branches retained, regional representative node selection method, weight coefficient, and truncation ratio involved in the various embodiments of the present invention are as follows: Consistency evaluation indicators and other parameters can be set according to different power grid structures, operating modes and security analysis needs, and are still within the scope of protection of this invention.

[0115] The specific embodiments of the present invention have been described in detail above. However, those skilled in the art should understand that various modifications or variations can be made to the present invention without departing from the spirit and scope of the claims, and all such modifications or variations should be considered to fall within the protection scope of the present invention.

Claims

1. A method for equivalent modeling of power system renormalization for maintaining a fragile skeleton, characterized in that, Includes the following steps: (1) Steps for modeling the original power grid and constructing branch features: Obtain the node set, branch set, branch reactance, branch susceptance, branch capacity, active power injection of the target power system, generation node, load node, branch power flow, candidate branch fault set and analysis parameters, establish the original power network (OPN) based on the power flow model or linear sensitivity model, determine the operating status of each node and branch in the original power network; and construct a comprehensive branch vulnerability index and composite diffusion weight based on the branch power flow stress, the overload severity after the branch fault, the role of the branch in the source-load power transfer path, the branch electrical coupling strength and the power flow redistribution strength after the fault. (2) Steps for determining composite diffusion spectrum partitioning and optimal partitioning: Based on the composite diffusion weights, a weighted adjacency matrix, a generalized degree matrix, and a symmetric normalized diffusion Laplace are formed. The low-order nontrivial eigenvectors of the symmetric normalized diffusion Laplace are spectral embedded and clustered. The structural complexity and linear sensitivity error are calculated for different candidate partition numbers. The optimal partition number and optimal region partitioning scheme are determined based on the Pareto front knee point between the structural complexity and the linear sensitivity error. (3) Key skeleton network extraction and Ward equivalent generation steps: Extract the key skeleton network according to the optimal regional division scheme. The key skeleton network includes the endpoints of cross-regional connection branches, power generation nodes, high load nodes, high power flow betweenness nodes, internal skeleton branches and cross-regional skeleton connection branches. Select a regional representative node, take the skeleton nodes in the key skeleton network and the regional representative node as the retention set K, take the remaining non-skeleton nodes as the elimination set E, perform Ward equivalence on the elimination set E, and generate the equivalent admittance matrix, equivalent injection vector and renormalized equivalent power network (REPN) on the retention set K. (4) Coverage mapping, consistency evaluation and result output steps: Establish the coverage mapping from the branches in the renormalized equivalent grid REPN to the physical branch set of the original grid OPN, backtrack the vulnerable branch identification results obtained by sorting the branches in REPN according to the comprehensive branch vulnerability index to the OPN physical branch space, calculate the consistency evaluation index of the vulnerable branch set, and output the renormalized equivalent grid, key backbone network, vulnerable branch set, coverage mapping relationship and consistency evaluation results.

2. The power system renormalization equivalent modeling method for maintaining a fragile skeleton as described in claim 1, characterized in that, In step (1), the comprehensive branch vulnerability index and the composite diffusion weight are constructed in the following manner: Based on the branch power flow stress index, the overload severity index after branch fault, and the branch power flow betweenness index, the comprehensive branch vulnerability index of branch ij is calculated: In the formula, Let be the comprehensive vulnerability index of branch ij, where i and j are the indices of the nodes at both ends of the branch, respectively. The branch tidal current stress index is given by branch ij. The overload severity index of branch ij after a candidate branch failure. The branch power flow betweenness index is given by branch ij. , and These are the vulnerability weighting coefficients corresponding to the branch power flow stress index, overload severity index, and branch power flow betweenness index, respectively. The branch power flow stress index is determined based on the branch load rate and the branch active power flow amplitude; the overload severity index is determined based on the degree of branch overload caused by the linear power flow transfer relationship after a candidate branch failure; and the branch power flow betweenness index is determined based on the transmission effect of the branch in the power transfer path from the generation node to the load node. Calculate the composite diffusion weight of branch ij based on the branch electrical coupling strength, branch power flow stress, and post-fault power flow redistribution intensity: In the formula, The composite diffusion weight of branch ij, The electrical coupling strength index of branch ij is given. The branch tidal current stress index is given by branch ij. The power flow redistribution intensity index is the post-fault power flow redistribution intensity of branch ij. , and These are the diffusion weighting coefficients corresponding to the electrical coupling strength index, the branch power flow stress index, and the post-fault power flow redistribution intensity index, respectively. The electrical coupling strength index is determined based on the branch reactance or branch susceptance, and the power flow redistribution strength index after the fault is determined based on the line interruption distribution factor sensitivity and the power flow of the faulted branch under the candidate branch fault. The vulnerability weight coefficient and the diffusion weight coefficient are determined by combining physical prior weights and objective correction weights. The objective correction weights are determined based on the dispersion and correlation of each index.

3. The power system renormalization equivalent modeling method for maintaining a fragile skeleton as described in claim 1, characterized in that, In steps (2) to (4), the composite diffusion spectrum partitioning, key skeleton extraction, Ward isometry, and coverage mapping evaluation are implemented in the following manner: Based on the composite diffusion weights, a weighted adjacency matrix W and a generalized degree matrix D are constructed, and a symmetric normalized diffusion Laplace is also constructed: In the formula, Let I be a symmetric normalized diffusion Laplace matrix, W be the identity matrix, W be the weighted adjacency matrix composed of composite diffusion weights, and D be the generalized degree matrix. It is a negative first power matrix of the generalized degree matrix D; The symmetric normalized diffusion Laplace Eigenvalue decomposition is performed, and low-order nontrivial eigenvectors are selected to construct a spectral embedding matrix. This matrix is ​​then subjected to row normalization and clustering to obtain a region partitioning scheme for the number of candidate partitions Q. For different numbers of candidate partitions Q, the structural complexity C(Q) and linear sensitivity error F(Q) are calculated. The linear sensitivity error is expressed as: In the formula, Q is the number of candidate partitions, C(Q) is the structural complexity with Q candidate partitions, and F(Q) is the linear sensitivity error with Q candidate partitions. Let be the relative PTDF error of the renormalized equivalent grid relative to the original grid under the candidate partition number Q. Let Q be the relative error of the LODF of the renormalized equivalent grid relative to the original grid, PTDF be the power transfer distribution factor, and LODF be the line interruption distribution factor. The non-dominated Pareto front is determined in the normalized C(Q)-F(Q) plane, and the number of partitions that satisfy the knee criterion on the Pareto front is taken as the optimal number of partitions Q*. According to the region division scheme corresponding to the optimal number of partitions Q*, the endpoints of cross-regional interconnection branches, power generation nodes, high-load nodes, and high-current-between-number nodes are retained as skeleton nodes; within each region, skeleton branches are constructed based on composite diffusion weights, and non-skeleton leaf branches are cut off while maintaining the connectivity of skeleton nodes; for cross-regional interconnection branches between adjacent regions, cross-regional interconnection branches whose composite diffusion weights meet preset priority conditions are retained to form a key skeleton network. The skeleton nodes and regional representative nodes are combined into a retention set K, and the remaining non-skeleton nodes are combined into an elimination set E. The node admittance matrix of the original power grid is divided into blocks according to the retention set K and the elimination set E, and the equivalent admittance matrix and equivalent injection vector are calculated by Ward's equivalent method. In the formula, To preserve the equivalent admittance matrix on set K, Injecting equal vectors into the hold set K. The admittance submatrix between retention sets K and K' is... To preserve the admittance submatrix between the set K and the elimination set E, The admittance submatrix between the elimination set E and the elimination set E' is... To eliminate the admittance submatrix between set E and retention set K, Inject vectors into the nodes on the hold set K. Inject vectors into the nodes of the elimination set E. Admittance submatrix The inverse matrix in the corresponding constrained subspace; According to the equivalent admittance matrix The off-diagonal elements are used to generate the equivalent branches of the renormalized equivalent power grid (REPN), and a covering mapping Ω(e) is established from each branch e in REPN to the set of physical branches in OPN. When Ω(e) contains only one physical branch in OPN, the REPN branch and the OPN physical branch are determined to have a one-to-one covering relationship; when Ω(e) contains multiple physical branches in OPN, the REPN branch and the OPN physical branch are determined to have a one-to-many covering relationship; when Ω(e) is an empty set, the REPN branch is determined to be an equivalent filling branch. Based on the coverage mapping Ω(e), the top ρ vulnerable branches in REPN, sorted by comprehensive branch vulnerability index, are mapped back to the OPN physical branch space, and the hit rate is calculated: In the formula, The hit rate is the cutoff percentage ρ, where ρ is the cutoff percentage for the set of vulnerable branches. This refers to the set of physical branches with the highest ρ proportion in the OPN, sorted by the comprehensive branch vulnerability index. is the set of the top ρ proportional branches obtained by sorting the branches in REPN according to the comprehensive branch vulnerability index and mapping them back to the OPN physical branch space through the coverage mapping Ω(e), ∩ is the set intersection operation, and |·| is the number of elements in the set; The average accuracy (AP) is calculated based on the hit position of the vulnerable branch sorting in the OPN physical branch space after coverage mapping. The hit rate (HR) and average accuracy (AP) are used as the consistency evaluation index for maintaining the vulnerable branch set and the vulnerable branch sorting between OPN and REPN.

4. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the equivalent modeling method for power system renormalization with fragile skeleton preservation as described in any one of claims 1 to 3.

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