Branch transient energy driven power grid key section identification method, device and system and medium

Abstract

The invention provides a branch transient energy-driven power grid key section identification method, device and system and a medium, and the method comprises the steps: firstly, calculating four dynamic indexes of branch total virtual kinetic energy, disturbance energy accumulation time, disturbance energy impact and high-frequency energy ratio in a transient fault interval, and representing the characteristics of branch disturbance intensity, response time sequence and the like in a fault; a CRITIC method is adopted to fuse index variability and conflict, and branch transient energy indexes are constructed through weighted normalization; calculating an improved edge betweenness to describe an energy propagation main path by taking an index reciprocal as an edge weight; a weighted graph is constructed on the basis, high betweenness edges are gradually removed through a GN splitting algorithm, partitioning is controlled in combination with a power flow direction consistency criterion, and a key section is identified when the modularity is optimal; and finally, analyzing a branch load flow coupling relationship in the section by using the branch breaking distribution factor, screening a final transient key section with obvious dynamic response and compact structure, and realizing accurate identification of the transient energy propagation path key channel.

Description

Technical Field

[0001] This invention relates to the field of critical section identification technology from the perspective of power system transients, specifically a method, device, system, and medium for identifying critical sections of a power grid driven by branch transient energy. Background Technology

[0002] With the development of modern power systems, grid operating conditions are becoming increasingly complex, and power systems face more transient disturbance risks. When encountering faults such as short circuits and tripping, the system frequency and power angle will fluctuate drastically, and energy will rapidly redistribute along branches, potentially inducing instability or regional disconnection. To improve the system's dynamic response capability and risk prevention level, it is necessary to accurately identify critical sections that are crucial to energy propagation paths and stability during transient processes, providing fundamental support for load shedding, section protection, and dynamic control measures.

[0003] Many current studies employ partitioning methods to identify critical sections. Some studies propose spectral clustering methods based on standard shear and safety risk indicators, constructing a power grid graph model through voltage-power flow joint weighting and using improved standard shear to achieve efficient partitioning. Based on this, they combine the over-limit risk value under N-1 faults to identify critical sections. Other studies use improved fuzzy C-means clustering methods, optimizing cluster centers before searching for sections and introducing power flow change factors and safety margins to form composite indicators, solving the problems of misselection and omission. These methods have good identification performance under stable operating conditions, but they are mostly based on steady-state characteristic quantities, including static power flow distribution, node voltage, or sensitivity indicators. However, they are difficult to characterize the dynamic disturbance characteristics experienced by branches after a fault occurs, and cannot reflect the differences in disturbance intensity, response timing, and energy form. Furthermore, commonly used graph partitioning algorithms that rely on the statistics of shortest paths between node pairs, such as the Girvan-Newman (GN) algorithm, do not consider the driving role of generators as the main energy source and ignore the dynamic changes in path edge weights with disturbance evolution, making it difficult for the identification results to truly reflect the energy bottleneck channels in transient processes. Although some dynamic identification methods introduce energy function indices, they are not effectively integrated with the network structure, and the graph partitioning results lack physical interpretability.

[0004] In identifying transient critical sections, some studies use the synchronizing force coefficient, which considers voltage magnitude and phase angle, to measure branch coupling strength, thereby selecting branches with strong disturbance responses, constructing energy propagation paths, and determining critical sections through index comparison. Other studies, based on the extended equal-area criterion, after screening for critical faults with small stability margins, extract branches with large power fluctuations as candidate sections, constructing connected path cut sets based on generator complementary groups, and determining their criticality by combining section power and stability boundary distance. While both approaches consider generator group partitioning or connectivity during path construction, they do not introduce an energy propagation driving mechanism with generator nodes as the source point. Furthermore, both rely primarily on cut set or path heuristic strategies for branch selection in section formation, making it difficult to ensure the structural integrity and regional independence of the sections. Summary of the Invention

[0005] To ensure the safe and stable operation of the power grid under transient fault conditions, this invention proposes a method, device, system, and medium for identifying critical sections of the power grid driven by branch transient energy. It integrates multi-dimensional dynamic indicators such as total virtual kinetic energy, disturbance energy accumulation time, disturbance energy impact, and high-frequency energy proportion into a unified branch transient energy indicator, fully revealing the disturbance intensity, response speed, and energy distribution characteristics of branches during transient processes. Then, after weighting and fusing each indicator using the CRITIC method, it is used to construct edge weights and guide the energy propagation path from generator nodes to all network nodes, thereby calculating the electrically meaningful improved edge betweenness number. Based on this, the network structure is gradually divided using the GN algorithm, and high-risk sections across modules are identified. Combined with the branch breakage distribution factor, critical sections with dynamic significance, structural representativeness, and close internal connections are further screened.

[0006] A method for identifying critical sections of a power grid driven by branch transient energy includes:

[0007] Step (1): Use the power system simulation software PSASP to simulate transient fault scenarios, record the power of each branch, the angular frequency at both ends of the branch, and the rated angular frequency of the system during the transient process, and construct a system disturbance response state dataset.

[0008] Step (2): Based on the system disturbance response state dataset, calculate four types of indicators that reflect the transient characteristics of the branch in the fault interval: total virtual kinetic energy of the branch, disturbance energy accumulation time, disturbance energy impact, and high-frequency energy ratio. Then, determine the weighting coefficients by the CRITI method and weight and fuse the four types of indicators into the branch transient energy index.

[0009] Step (3): Using the reciprocal of the branch transient energy index obtained in step (2) as the edge weight, calculate the shortest path between each node. The improved edge betweenness is calculated by limiting the path set to the shortest path from the generator node to other nodes.

[0010] Step (4): Based on the improved edge betweenness calculated in step (3), the GN splitting algorithm is executed iteratively to remove the edge with the highest betweenness to partition the power grid. During the partitioning process, the critical section is determined based on the connection relationship between the newly generated partition and the old partition, and the iteration is terminated based on the change in modularity.

[0011] Step (5): Analyze the degree of connection between the lines in the key sections selected in step (4) using the branch breakage distribution factor analysis, and screen out the sections with close line connections as the final key sections of the power grid.

[0012] Furthermore, in step (2), four types of indicators reflecting the transient characteristics of the branch are calculated in the fault interval: total virtual kinetic energy of the branch, disturbance energy accumulation time, disturbance energy impact, and high-frequency energy ratio. Specifically, these include:

[0013] 1) Calculate the total virtual kinetic energy of the branch: The total virtual kinetic energy of the branch is used to measure the total disturbance energy accumulated in the branch during the fault period. It reflects the overall disturbance intensity level of the branch and is an important basic indicator for identifying energy concentration areas. Its expression is:

[0014] ;

[0015] ;

[0016] In the formula, Indicates the first A side road, , and These represent the steady-state time, the fault clearing time, and the integration cutoff time, respectively. and These represent the active power of the branch before and after the fault, respectively. The rated angular frequency of the branch is and The angular frequencies at both ends of the branch;

[0017] 2) Calculate the disturbance energy accumulation time: The disturbance energy accumulation time measures the temporal concentration of energy injection into a branch during a transient process. A smaller value indicates earlier energy accumulation and a faster branch response. Its expression is:

[0018] ;

[0019] In the formula, Indicates a branch At any moment The cumulative value of disturbance energy, This indicates the selected cumulative energy percentage;

[0020] 3) Calculate the disturbance energy impact: The disturbance energy impact is used to measure the maximum instantaneous disturbance injection intensity experienced by a branch during a fault disturbance. Its expression is:

[0021] ; ;

[0022] In the formula, For the first The rate of disturbance energy injection into each branch;

[0023] 4) Calculation of High-Frequency Energy Ratio: The high-frequency energy ratio measures the proportion of high-frequency components in the disturbance energy. It reflects the rapid changes in disturbance propagation during the system response, effectively identifies branches severely affected by sudden disturbances, and uncovers non-stationary behavior characteristics in the system's dynamic process. The high-frequency energy ratio is obtained by wavelet transform and is defined as the ratio of the energy of the high-frequency detail layer to the energy of all detail layers after wavelet decomposition. The db4 wavelet is used for decomposition to extract the detail coefficient energy at each scale. Then, the ratio of the energy corresponding to the high-frequency scale to the total energy at all scales is calculated, and the result serves as a quantitative representation of the high-frequency energy ratio. The specific expression is:

[0024] a. The expression for the input signal is:

[0025] ;

[0026] b. Scaling function of db4 wavelet (Low frequency) and wavelet function (High frequency) is defined as follows:

[0027] The scaling function is:

[0028] ;

[0029] In the formula These are the coefficients of the db4 wavelet low-pass filter. In the db4 wavelet, , , , ;

[0030] The wavelet function is:

[0031] ;

[0032] In the formula These are the coefficients of the high-pass filter. This is the filter length;

[0033] c. During signal expansion, construct the following family of orthogonal functions:

[0034] ;

[0035] d. Arbitrarily square-integrable signals Expanded to:

[0036] ;

[0037] In the formula, The maximum decomposition scale, i.e., the total number of layers in the wavelet decomposition; The scale number used for high-frequency energy calculations; , This represents the number of sampling points for the original signal. They are the approximation coefficients and Detail factor;

[0038] e. Calculation of high-frequency energy proportion index:

[0039] ;

[0040] In the formula, Indicates the first The branch road in the Detail coefficients signal under layer wavelet decomposition Indicates the first The energy of the layer, The number of high-frequency layers selected. denoted as the total number of wavelet decomposition layers.

[0041] Furthermore, in step (2), the weighting coefficients are determined using the CRITI method, and the four types of indicators are weighted and fused into a branch transient energy indicator, specifically including:

[0042] a. Data preprocessing:

[0043] Considering the issues of inconsistent dimensions, skewed distribution, and significant numerical differences among the indicators, a logarithmic transformation operation is uniformly introduced before weighting:

[0044] ;

[0045] in Indicates the first The branch road in the The original values ​​under each indicator To avoid tiny positive numbers with a value of zero when taking the logarithm;

[0046] The results after logarithmic processing are normalized by range to obtain the standardized index matrix. :

[0047] ;

[0048] b. CRITIC weighted

[0049] Obtaining the normalized index matrix Then, the weights of each indicator are calculated based on the CRITIC method, specifically as follows:

[0050] First, calculate the standard deviation of each indicator to measure the degree of difference in the information content of that indicator:

[0051] ;

[0052] In the formula, For the first The average of the indicators, The number of samples for the indicator;

[0053] Then calculate the degree of conflict between the indicators:

[0054] ;

[0055] ;

[0056] In the formula, For any two indicators and Pearson correlation coefficient, , Indicates the first The branch road in the , The normalized value after the logarithm of each indicator , For the first , The average of the indicators, For the number of samples, The number of indicators;

[0057] Next, the variability and conflict level are combined to calculate the overall information content of each indicator. :

[0058] ;

[0059] Finally, the total information content is normalized to obtain the final weight. :

[0060] ;

[0061] Branch transient energy index obtained by weighting using the CRITIC method for:

[0062] ;

[0063] In the formula, , , , All were obtained using the CRITIC method.

[0064] Furthermore, in step (3), the branch is weighted using the reciprocal of the branch transient energy index calculated in step (2), and the th... The edge weights of each branch are as follows:

[0065] ;

[0066] And thus, the shortest path between all pairs of nodes is calculated:

[0067] ;

[0068] In the formula, Indicates all from arrive The set of feasible paths;

[0069] An improved edge betweenness function that more closely approximates the energy transfer process is obtained by limiting the path set to the distance from generator nodes to other nodes. The calculation formula is as follows:

[0070] ;

[0071] In the formula, Indicates the first A side road, For all generator nodes, For all nodes of the power grid, For nodes and The shortest path between them, Represents a node and Between them, a side road The number of shortest paths.

[0072] Furthermore, in step (4), the critical section is determined based on the connection relationship between the newly generated partition and the old partition during the partitioning process. The principle followed when determining the critical section is: if the new partition and the old partition are connected in a chain, then the newly generated inter-partition connection line is the critical section; if the new partition and the old partition are connected in a ring, then the newly generated connection line needs to be combined with the existing connection line to determine the critical section.

[0073] Furthermore, in step (4), the iteration is terminated based on the change in modularity, specifically including: introducing a modularity index to save computing resources; terminating the split after the modularity decreases by more than a threshold three times consecutively; and outputting the cross-section accumulated when the optimal modularity is obtained as the key cross-section. The calculation expression for modularity is:

[0074] (twenty three);

[0075] (twenty four);

[0076] In the formula, The sum of the weights of all branches. Weighted adjacency matrix The elements in the array, namely the path weights between nodes i and j, , They are nodes , The weighting degree.

[0077] Furthermore, in step (5), based on the key sections determined in step (4), a branch breakage distribution factor is introduced to finely screen the candidate sections. The branch breakage distribution factor between any two branches within a section is calculated one by one and the average value is taken. Sections with an average value that meets the standard are selected as the final key sections. The calculation formula is:

[0078] (25);

[0079] (26);

[0080] (27);

[0081] In the formula, , Branch roads , Reactance, To open the branch road The input reactance of the formed port, To open the branch road The formed port and any branch in the network The transfer reactance between the ports is formed. , Branch roads , The node association matrix, Let be the admittance matrix of the network.

[0082] A branch transient energy-driven power grid critical section identification device includes:

[0083] The system disturbance response state dataset construction module is used to simulate transient fault scenarios using the power system simulation software PSASP, record the power of each branch, the angular frequency at both ends of the branch, and the rated angular frequency of the system during the transient process, and construct the system disturbance response state dataset.

[0084] The branch transient energy index construction module is used to calculate four types of indicators that reflect the transient characteristics of the branch in the fault interval: total virtual kinetic energy, disturbance energy accumulation time, disturbance energy impact, and high-frequency energy ratio. Then, the weighting coefficients are determined by the CRITI method to weight and fuse the four types of indicators into a branch transient energy index.

[0085] An improved edge betweenness acquisition module is used to calculate the shortest path between nodes using the reciprocal of the branch transient energy index as the edge weight. The improved edge betweenness is calculated by limiting the path set to the shortest path from the generator node to other nodes.

[0086] The critical section screening module is used to partition the power grid by performing the GN splitting algorithm iteratively to remove the highest betweenness edge based on the calculated improved edge betweenness. During the partitioning process, the critical sections are determined according to the connection relationship between the newly generated partitions and the old partitions, and the iteration is terminated according to the change in modularity.

[0087] The critical section determination module is used to analyze the degree of connection between lines in the critical sections selected by the critical section screening module using the branch breakage distribution factor analysis, and to screen out the sections with close line connections as the final critical sections of the power grid.

[0088] A branch transient energy-driven critical section identification system for power grids includes: a computer-readable storage medium and a processor;

[0089] The computer-readable storage medium is used to store executable instructions;

[0090] The processor is used to read executable instructions stored in the computer-readable storage medium and execute the branch transient energy-driven power grid critical section identification method.

[0091] A non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the aforementioned method for identifying critical sections of a power grid driven by branch transient energy.

[0092] The beneficial effects of this invention are:

[0093] 1. In step (2) of this invention, considering that the response characteristics of branch transient energy during the fault process are characterized by drastic changes in disturbance intensity, significant differences in time distribution, and complex and variable frequency domain structure, a branch transient energy index system integrating multi-dimensional dynamic characteristics is proposed. This system covers four dimensions: total virtual kinetic energy, disturbance energy accumulation time, disturbance energy impact degree, and high-frequency energy proportion, which are used to characterize the energy intensity, duration, injection rate characteristics, and frequency domain components of the disturbances experienced by the branch, thereby achieving a comprehensive quantitative characterization of the branch dynamic behavior.

[0094] 2. In step (3) of this invention, to address the problems of neglecting the directionality of disturbance sources and lacking physical driving basis for path distribution in traditional edge betweenness algorithms, a set of shortest paths with generator nodes as source points is constructed, and a weighted network model with clear physical meaning is established using the reciprocal of the branch transient energy index as the edge weight. Based on this, the edge betweenness values ​​of each branch are recalculated, and an improved edge betweenness index that integrates the energy propagation mechanism is proposed, which can more realistically reflect the propagation trend and path bottlenecks of disturbances along the power grid topology.

[0095] 3. In step (4) of this invention, based on the improved edge betweenness result, a weighted undirected graph is constructed by assigning weights to each branch in the power grid diagram. The GN algorithm is used to iteratively remove the edge with the largest edge betweenness, thereby realizing the gradual splitting of the network structure. During the partitioning process, the key sections are determined based on the connection relationship between the newly generated partition and the old partition, thereby identifying the set of key sections that have both transient energy transmission characteristics and network structure bottleneck characteristics. Attached Figure Description

[0096] Figure 1 This is a flowchart of a method for identifying critical sections of a power grid driven by branch transient energy according to an embodiment of the present invention;

[0097] Figure 2 This is a flowchart of the GN splitting algorithm according to an embodiment of the present invention;

[0098] Figure 3 This is a schematic diagram of the partition connection method according to an embodiment of the present invention;

[0099] Figure 4 This is a schematic diagram of the IEEE 39-node standard computation example of an embodiment of the present invention;

[0100] Figure 5 This is a normalized heatmap of branch disturbance index according to an embodiment of the present invention;

[0101] Figure 6 This is a diagram showing the transient indicators of each branch in an embodiment of the present invention;

[0102] Figure 7 This is a graph showing the change in modularity according to an embodiment of the present invention;

[0103] Figure 8 This is a schematic diagram of the key section 1 in an embodiment of the present invention;

[0104] Figure 9 This is a schematic diagram of the key section 2 in an embodiment of the present invention;

[0105] Figure 10 This is a schematic diagram of the key section 3 in an embodiment of the present invention;

[0106] Figure 11 This is a schematic diagram of the key section 4 in an embodiment of the present invention;

[0107] Figure 12 This is a diagram of the instantaneous virtual kinetic energy curve of a branch in a key section of an embodiment of the present invention;

[0108] Figure 13 This is a graph of the instantaneous virtual kinetic energy of a typical branch.

[0109] Figure 14 This is a comparison diagram of the branch road and the ordinary branch road in the key section of the embodiment of the present invention. Detailed Implementation

[0110] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0111] The first aspect of this invention provides a method for identifying critical sections of a power grid driven by branch transient energy, comprising the following steps.

[0112] Step (1): Use the power system simulation software PSASP to simulate transient fault scenarios, record the power of each branch, the angular frequency at both ends of the branch, and the rated angular frequency of the system during the transient process, and construct a system disturbance response state dataset. Its specific representation is as follows:

[0113] A typical power grid model was constructed using the power system simulation software PSASP to simulate transient fault conditions. A typical fault scenario, such as a three-phase-to-ground short circuit in a branch, was arbitrarily set, and key parameters such as fault location, start and end times, and corresponding clearing strategies were configured to recreate the dynamic operation of the system under fault disturbances. Simultaneously, during the simulation, core dynamic quantities such as the time-series changes of active power in each branch, the angular frequencies of the nodes at both ends of the branch, and the system's rated angular frequency were recorded in real time. This constructed a disturbance dataset covering time-domain evolution, spatial structure, and system dynamic response characteristics, providing a solid data foundation for subsequent extraction of branch disturbance features and identification of key sections.

[0114] Step (2): Based on the system disturbance response state dataset, calculate four types of indicators reflecting the transient characteristics of the branch in the fault interval: total virtual kinetic energy of the branch, disturbance energy accumulation time, disturbance energy impact, and high-frequency energy proportion. Then, determine the weighting coefficients using CRITIC and weightedly fuse the four types of indicators into a branch transient energy index. Its specific representation is as follows:

[0115] 1) The total virtual kinetic energy index measures the intensity of energy accumulation experienced by a branch during a transient fault, reflecting the dynamic disturbance characteristics caused by the difference in angular frequencies between the two endpoints. This index reveals the branch's location and the strength of the disturbance during energy transmission, serving as an important basis for identifying energy concentration areas. Its calculation method is as follows: Within a set fault duration interval, the square of the difference between the angular frequencies of the two endpoints of the branch and the system's rated angular frequency is extracted, multiplied hourly by the branch's active power, and then integrated over time. The final integral value is used as the total virtual kinetic energy evaluation result for the branch. The specific expression is:

[0116] (1)

[0117] (2)

[0118] In the formula, For the first A side road, , and These represent the steady-state time, the fault clearing time, and the integration cutoff time, respectively. and These represent the active power of the branch before and after the fault, respectively. The rated angular frequency of the branch is and The angular frequencies at both ends of the branch are given.

[0119] 2) The disturbance energy accumulation time index is used to measure the temporal distribution characteristics of energy injection in a branch during a transient disturbance, reflecting the pace of the response process and the concentration of major energy injection points. This index is defined as the earliest time point at which the accumulated disturbance energy of a branch first reaches a specific proportion of the total virtual kinetic energy. It characterizes the speed of the branch's dynamic response and the order in which the disturbance dominates. A shorter response time indicates that the branch participates in the disturbance process earlier and has a stronger leading role in the energy propagation path. Its calculation method is as follows: construct a time accumulation curve of the branch's disturbance energy, set a proportion threshold, and extract the time point corresponding to the first attainment of that value as the evaluation result of the disturbance energy accumulation time. The specific expression is:

[0120] (3)

[0121] In the formula, This represents the cumulative disturbance energy of the branch at time t. This indicates the selected cumulative energy ratio.

[0122] 3) The disturbance energy impact index measures whether a branch experiences a short-term high-intensity energy injection during a fault disturbance, reflecting the concentration and instantaneous impact characteristics of the disturbance. This index can identify key branches with highly concentrated energy release and pulse characteristics, helping to reveal strong impact paths in disturbance propagation. Its calculation method is as follows: the maximum growth rate of total virtual kinetic energy per unit time during the fault period is statistically analyzed, and the ratio of this rate to the average growth rate is used as the index value. The larger the value, the more concentrated the energy release and the stronger the impact. The specific expression is:

[0123] (4)

[0124] (5)

[0125] In the formula, For the first The rate of disturbance energy injection into each branch.

[0126] 4) The high-frequency energy proportion index measures the proportion of high-frequency components in the disturbance energy, reflecting the rapid changes in the disturbance propagation process. This index can identify branches significantly affected by sudden disturbances and capture the implicit non-stationary characteristics in the system response. Its calculation method is as follows: The virtual kinetic energy time series curve is decomposed using Daubechies 4 (db4) wavelet transform to extract the energy corresponding to the high-frequency scale, and the ratio of this energy to the total energy at all scales is calculated as the high-frequency energy proportion index. The specific expression is:

[0127] a. The expression for the input signal is:

[0128] (6)

[0129] b. Scaling function of db4 wavelet (Low frequency) and wavelet function (High frequency) is defined as follows:

[0130] The scaling function is:

[0131] (7)

[0132] In the formula These are the coefficients of the db4 wavelet low-pass filter. In the db4 wavelet, , , , .

[0133] The wavelet function is:

[0134] (8)

[0135] In the formula These are the coefficients of the high-pass filter. This is the filter length.

[0136] c. During signal expansion, construct the following family of orthogonal functions:

[0137] (9)

[0138] d. Arbitrarily square-integrable signals It can be expanded as follows:

[0139] (10)

[0140] In the formula, The maximum decomposition scale, i.e., the total number of layers in the wavelet decomposition; The scale number used for high-frequency energy calculations; , This represents the number of sampling points for the original signal. They are the approximation coefficients and Detail factor.

[0141] e. Calculation of high-frequency energy proportion index:

[0142] (11)

[0143] In the formula, Indicates the first The branch road in the Detail coefficients signal under layer wavelet decomposition Indicates the first The energy of the layer, The number of high-frequency layers selected. denoted as the total number of wavelet decomposition layers.

[0144] 5) Four types of disturbance characteristic indicators reflect the dynamic behavior characteristics of branches in transient processes from different dimensions such as disturbance intensity, response time, energy injection rate, and frequency structure. The indicators show significant differences in numerical distribution and exhibit certain complementarity and correlation in physical meaning. Considering that relying solely on a single statistic (such as information entropy) is insufficient to comprehensively characterize the information independence and conflict degree among the indicators, the CRITIC method is used to weight each indicator. This method introduces a correlation coefficient between indicators based on standard deviation weighting to measure the relative independence and conflict intensity of the information contained in each indicator, thereby optimizing the rationality of weight allocation and the discriminative power. The specific expression is:

[0145] a. Data preprocessing:

[0146] Considering the issues of inconsistent dimensions, skewed distribution, and significant numerical differences among the indicators, a logarithmic transformation operation is uniformly introduced before weighting:

[0147] (12)

[0148] in Indicates the first The branch road in the The original values ​​under each indicator To avoid tiny positive numbers with a value of zero when taking the logarithm.

[0149] The results after logarithmic processing are normalized by range to obtain the standardized index matrix. :

[0150] (13)

[0151] b. CRITIC weighted

[0152] Obtaining the normalized index matrix Then, the weights of each indicator are calculated based on the CRITIC method, specifically as follows:

[0153] First, calculate the standard deviation of each indicator to measure the degree of difference in the information content of that indicator.

[0154] (14)

[0155] In the formula, For the first The average of the indicators, The number of samples for the indicator.

[0156] Then calculate the degree of conflict between the indicators:

[0157] (15)

[0158] (16)

[0159] In the formula, For any two indicators and Pearson correlation coefficient, , Indicates the first The branch road in the , The normalized value after the logarithm of each indicator , For the first , The average of the indicators, For the number of samples, The number of indicators.

[0160] Next, the variability and conflict level are combined to calculate the overall information content of each indicator. :

[0161] (17)

[0162] Finally, the total information content is normalized to obtain the final weight. :

[0163] (18)

[0164] Branch transient energy index obtained by weighting using the CRITIC method for:

[0165] (19)

[0166] In the formula, , , , All were obtained using the CRITIC method.

[0167] Step (3): Based on step (2), using the branch transient energy index as the edge weight, calculate the shortest path between all node pairs. The improved edge betweenness is calculated by limiting the path set to the set of shortest paths between the generator node and other nodes. Its specific representation is as follows:

[0168] First, the reciprocal of the transient energy index of each branch is used as the edge weight of each branch. ,Right now:

[0169] (20)

[0170] Thus, a weighted undirected graph model is constructed. ,in , Given a set of nodes and a set of branches, the shortest path between each node is calculated using a shortest path algorithm.

[0171] (twenty one)

[0172] In the formula, Indicates all from arrive The set of feasible paths.

[0173] Then, an improved edge betweenness index that better reflects the physical characteristics of transient disturbances is calculated, and its formula is as follows:

[0174] (twenty two)

[0175] In the formula, Indicates the first A side road, For all generator nodes, For all nodes of the power grid, For nodes and The shortest path between them, Represents a node and Between them, a side road The number of shortest paths.

[0176] Step (4): Based on step (3), the GN splitting algorithm is iteratively executed to remove the edge with the largest edge betweenness to partition the power grid, and key sections are selected during the partitioning process. The following section combines... Figure 2 Instructions for specific steps:

[0177] a. Limit the path set to the generator node to other nodes, and use the shortest path algorithm to calculate the shortest path by combining the weighted method based on the inverse of the branch transient energy. Based on the shortest path results, count the frequency of each edge in all shortest paths and calculate its edge intermediary value.

[0178] b. Select the branch with the largest edge-to-interval value from the current graph structure as a candidate edge to be disconnected.

[0179] c. Check whether the power flow direction of the branch to be disconnected is consistent with the power flow of the branch that has not yet formed a section. If they are consistent, disconnect the branch. If they are inconsistent, determine whether its power flow is much smaller than that of other branches. If it is much smaller, disconnect normally. Otherwise, set its edge betweenness to zero and return to step b.

[0180] d. Determine if a new partition has been formed. If a new valid partition has been created, determine the cross-section based on the current connection relationships between the partitions. The specific determination principle is: if the newly created partition is linked to the old partition in a chain (e.g., ... Figure 3 As shown in (a), the newly generated inter-division connection line is the critical section; if the new partition and the old partition are connected in a ring (as shown in (a)), then the newly generated inter-division connection line is the critical section; Figure 3 As shown in (b), the newly generated connecting lines need to be combined with the existing connecting lines to determine the critical sections. After the determination is completed, return to step a to continue the next round of iteration; if no new effective partitions are generated, return directly to step a to continue the next round of iteration.

[0181] e. After successfully disconnecting a branch, the newly formed partition structure needs to be evaluated, and the modularity Q value of the current state needs to be calculated. The calculation formula is as follows:

[0182] (twenty three)

[0183] (twenty four)

[0184] In the formula, The sum of the weights of all branches. Weighted adjacency matrix The elements in the array, namely the path weights between nodes i and j, , They are nodes , The weighting degree.

[0185] If the Q value does not decrease three times consecutively, proceed to the next step; if it decreases three times consecutively, it is considered that continuing to partition will destroy the network structure. In this case, the splitting should be stopped, and the cross section accumulated when the optimal modularity is output as the critical cross section.

[0186] Based on step (4), in step (5), the connection between lines in the selected critical sections is analyzed using the branch breakage distribution factor analysis, and sections with close line connections are selected as the final transient critical sections of the power grid. The specific manifestations are as follows:

[0187] For the candidate sections initially identified using the GN algorithm, the branch breakage distribution factor (BFD) values ​​between any two branches are calculated for each section. The average level of the BFD values ​​within each section is statistically analyzed. Branch combinations with close structural connections and significant power flow interactions are identified and retained as the final transient critical sections. (Branch breakage distribution factor) The calculation formula is:

[0188] (25)

[0189] (26)

[0190] (27)

[0191] In the formula, , Branch roads , Reactance, To open the branch road The input reactance of the formed port, To open the branch road The formed port and any branch in the network The transfer reactance between the ports is formed. , Branch roads , The node association matrix, Let be the admittance matrix of the network.

[0192] To verify the feasibility of the branch transient energy-driven method for identifying critical sections of the power grid, this paper uses the IEEE 39-bus standard example ( Figure 4 The simulation was verified using a 10-second timeframe. A three-phase short-circuit fault was randomly selected on a line (line 14-15 in this embodiment) and the faulty line was permanently disconnected 0.12 seconds after the fault occurred. The power flow and angular frequency changes of each branch during the system disturbance response were recorded using a power system simulation platform to obtain a disturbance dataset containing time series data. Based on this, the total virtual kinetic energy, disturbance energy accumulation time, disturbance energy impact, and four types of transient disturbance indices for each branch within the fault interval were calculated. The CRITIC method was used to weight and fuse these indices to construct a unified branch transient energy index. Using this index as edge weights, a weighted graph structure was constructed. The improved edge betweenness number was calculated, and the GN algorithm was used for network partitioning and critical section identification. Finally, the branch breakage distribution factor was used to screen out the final critical sections with close line connections.

[0193] 1) Four types of disturbance energy indicators for each line

[0194] Typical lines that perform well in various disturbance energy indices are selected to demonstrate their representative dynamic response characteristics. All data are processed using the aforementioned normalization method. See Table 1 for details.

[0195] Table 1 Disturbance Energy Indicators

[0196]

[0197] From Table 1 and Figure 5It can be seen that some branches exhibit significant virtual kinetic energy, indicating that they bear a strong energy transmission load during the fault process; some branches have a short energy accumulation time, demonstrating a rapid response capability to disturbances; and some branches show highly concentrated impact characteristics or significant high-frequency components, revealing that they may induce spike responses or frequency fluctuations during disturbance propagation. These indicators reflect the dynamic behavior characteristics of branches during transient processes from different perspectives, providing multidimensional evidence for the identification of critical sections.

[0198] 2) Transient energy index of CRITIC weighted fusion

[0199] The weights of each indicator calculated using CRITIC are shown in Table 2 below:

[0200] Table 2 Weights of each indicator

[0201]

[0202] Depend on Figure 6 The fusion index results show that there are significant differences in the comprehensive disturbance characteristics of each branch. Some branches have significantly higher fusion indices, indicating that they have strong disturbance response capabilities in multiple dimensions and possess high criticality and instability risks; while other branches have significantly lower fusion indices, indicating that they perform stably under fault disturbances.

[0203] 3) Results of key sections

[0204] The top ten line edge betweenness numbers in the first iteration are shown in Table 3 below:

[0205] Table 3. Partial Line Intermediateities

[0206]

[0207] The key sections selected are shown in Table 3 below:

[0208] Table 4 Key Sections

[0209]

[0210] 4) Key section analysis

[0211] To further verify the dynamic significance of the critical section, taking critical section 2 as an example, the lines it contains are compared with ordinary branches, and their instantaneous virtual kinetic energy response curves during the transient process are plotted respectively, as follows. Figure 12 and Figure 13As shown, it can be observed that critical branches respond rapidly after a fault occurs, with multiple high-frequency, high-amplitude peaks appearing in their virtual kinetic energy curves, indicating that these branches play the role of the main energy transmission channel during system disturbances. In contrast, the virtual kinetic energy curves of ordinary branches are generally flat, with a delayed response and a lack of obvious energy impact characteristics, indicating that they do not participate in the main energy coupling process and have weaker disturbance response capabilities.

[0212] Figure 14 Further comparison of the virtual kinetic energy of critical branches and ordinary branches shows that critical branches are significantly higher than ordinary branches in terms of disturbance response timing, frequency and intensity, verifying the accuracy and engineering practicality of the aforementioned index fusion and critical section identification strategy.

[0213] Meanwhile, some routes, despite exhibiting high weights in the disturbance energy index system, were not selected as critical section routes. For example, routes 21-22 in Table 3, with a weight of approximately 0.74, did not have a higher edge betweenness number in the first iteration than some routes with lower weights. This indicates that while they possess strong dynamic response characteristics or energy injection features in local regions, their relatively peripheral position in the global energy propagation path—meaning they appear less frequently in the shortest path set—prevents them from forming energy channels that penetrate the main structure. Consequently, their edge betweenness number is low during the iterative partitioning process, and the algorithm does not prioritize their identification and inclusion in the critical section set. Although these routes have some importance, they are more like local response units rather than core bottlenecks affecting the overall energy diffusion structure of the system. This phenomenon further verifies the effectiveness and screening capability of the path-driven critical section identification method proposed in this invention in balancing branch weights and topological connectivity.

[0214] 5) Selection of the final critical section by the branch road discontinuity distribution factor

[0215] The threshold for the branch breakage distribution factor is set to 0.2, i.e. The critical sections are selected as the final critical sections. For sections consisting of only a single branch, these sections are usually located in critical interconnection positions in the power grid structure, and their corresponding branches exhibit outstanding energy response characteristics or significant edge betweenness weights during transient disturbances. They can independently reflect the weak channels or disconnection risks of the system, and are typical structurally independent critical sections with clear engineering significance and physical interpretation basis. Therefore, they are included in the final set of critical sections. The branch failure distribution factors of each selected critical section are shown in Table 5 below:

[0216] Table 5 Final Key Sections

[0217]

[0218] Another aspect of the present invention provides a critical section identification device for power grid driven by branch transient energy, comprising:

[0219] The system disturbance response state dataset construction module is used to simulate transient fault scenarios using the power system simulation software PSASP, record the power of each branch, the angular frequency at both ends of the branch, and the rated angular frequency of the system during the transient process, and construct the system disturbance response state dataset.

[0220] The branch transient energy index construction module is used to calculate four types of indicators that reflect the transient characteristics of the branch in the fault interval: total virtual kinetic energy, disturbance energy accumulation time, disturbance energy impact, and high-frequency energy ratio. Then, the weighting coefficients are determined by the CRITI method to weight and fuse the four types of indicators into a branch transient energy index.

[0221] An improved edge betweenness acquisition module is used to calculate the shortest path between nodes using the reciprocal of the branch transient energy index as the edge weight. The improved edge betweenness is calculated by limiting the path set to the shortest path from the generator node to other nodes.

[0222] The critical section screening module is used to partition the power grid by performing the GN splitting algorithm iteratively to remove the highest betweenness edge based on the calculated improved edge betweenness. During the partitioning process, the critical sections are determined according to the connection relationship between the newly generated partitions and the old partitions, and the iteration is terminated according to the change in modularity.

[0223] The critical section determination module is used to analyze the degree of connection between lines in the critical sections selected by the critical section screening module using the branch breakage distribution factor analysis, and to screen out the sections with close line connections as the final critical sections of the power grid.

[0224] Another aspect of the present invention provides a critical section identification system for power grid driven by branch transient energy, comprising: a computer-readable storage medium and a processor;

[0225] The computer-readable storage medium is used to store executable instructions;

[0226] The processor is used to read executable instructions stored in the computer-readable storage medium and execute the branch transient energy-driven power grid critical section identification method described in the first aspect.

[0227] In another aspect, the present invention provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the branch transient energy-driven power grid critical section identification method described in the first aspect.

[0228] 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.

[0229] 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.

[0230] 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.

[0231] 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.

[0232] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for identifying critical sections of a power grid driven by branch transient energy, characterized in that, include: Step (1): Use the power system simulation software PSASP to simulate transient fault scenarios, record the power of each branch, the angular frequency at both ends of the branch, and the rated angular frequency of the system during the transient process, and construct a system disturbance response state dataset. Step (2): Based on the system disturbance response state dataset, calculate four types of indicators that reflect the transient characteristics of the branch in the fault interval: total virtual kinetic energy of the branch, disturbance energy accumulation time, disturbance energy impact, and high-frequency energy ratio. Then, determine the weighting coefficients by the CRITI method and weight and fuse the four types of indicators into the branch transient energy index. Step (3): Using the reciprocal of the branch transient energy index obtained in step (2) as the edge weight, calculate the shortest path between each node. The improved edge betweenness is calculated by limiting the path set to the shortest path from the generator node to other nodes. Step (4): Based on the improved edge betweenness calculated in step (3), the GN splitting algorithm is executed iteratively to remove the edge with the highest betweenness to partition the power grid. During the partitioning process, the critical section is determined based on the connection relationship between the newly generated partition and the old partition, and the iteration is terminated based on the change in modularity. Step (5): Analyze the degree of connection between the lines in the key sections selected in step (4) using the branch breakage distribution factor analysis, and screen out the sections with close line connections as the final key sections of the power grid.

2. The method for identifying critical sections of a power grid driven by branch transient energy according to claim 1, characterized in that: In step (2), four types of indicators reflecting the transient characteristics of the branch are calculated in the fault interval: total virtual kinetic energy of the branch, disturbance energy accumulation time, disturbance energy impact, and high-frequency energy ratio. Specifically, these include: 1) Calculate the total virtual kinetic energy of the branch: The total virtual kinetic energy of the branch is used to measure the total disturbance energy accumulated in the branch during the fault period. It reflects the overall disturbance intensity level of the branch and is an important basic indicator for identifying energy concentration areas. Its expression is: ； ； In the formula, Indicates the first A side road, , and These represent the steady-state time, the fault clearing time, and the integration cutoff time, respectively. and These represent the active power of the branch before and after the fault, respectively. The rated angular frequency of the branch is and The angular frequencies at both ends of the branch; 2) Calculate the disturbance energy accumulation time: The disturbance energy accumulation time measures the temporal concentration of energy injection into a branch during a transient process. A smaller value indicates earlier energy accumulation and a faster branch response. Its expression is: ； In the formula, Indicates a branch At any moment The cumulative value of disturbance energy, This indicates the selected cumulative energy percentage; 3) Calculate the disturbance energy impact: The disturbance energy impact is used to measure the maximum instantaneous disturbance injection intensity experienced by a branch during a fault disturbance. Its expression is: ； ； In the formula, For the first The rate of disturbance energy injection into each branch; 4) Calculation of High-Frequency Energy Ratio: The high-frequency energy ratio measures the proportion of high-frequency components in the disturbance energy. It reflects the rapid changes in disturbance propagation during the system response, effectively identifies branches severely affected by sudden disturbances, and uncovers non-stationary behavior characteristics in the system's dynamic process. The high-frequency energy ratio is obtained by wavelet transform and is defined as the ratio of the energy of the high-frequency detail layer to the energy of all detail layers after wavelet decomposition. The db4 wavelet is used for decomposition to extract the detail coefficient energy at each scale. Then, the ratio of the energy corresponding to the high-frequency scale to the total energy at all scales is calculated, and the result serves as a quantitative representation of the high-frequency energy ratio. The specific expression is: a. The expression for the input signal is: ； b. Scaling function of db4 wavelet (Low frequency) and wavelet function (High frequency) is defined as follows: The scaling function is: ； In the formula These are the coefficients of the db4 wavelet low-pass filter. In the db4 wavelet, , , , ; The wavelet function is: ； In the formula These are the coefficients of the high-pass filter. This is the filter length; c. During signal expansion, construct the following family of orthogonal functions: ； d. Arbitrarily square-integrable signals Expanded to: ； In the formula, The maximum decomposition scale, i.e., the total number of layers in the wavelet decomposition; The scale number used for high-frequency energy calculations; , This represents the number of sampling points for the original signal. They are the approximation coefficients and Detail factor; e. Calculation of high-frequency energy proportion index: ； In the formula, Indicates the first The branch road in the Detail coefficient signals under layer wavelet decomposition Indicates the first The energy of the layer, The number of high-frequency layers selected. denoted as the total number of wavelet decomposition layers.

3. The method for identifying critical sections of a power grid driven by branch transient energy according to claim 2, characterized in that: In step (2), the weighting coefficients are determined by the CRITI method, and the four types of indicators are weighted and fused into a branch transient energy indicator, which specifically includes: a. Data preprocessing: Considering the issues of inconsistent dimensions, skewed distribution, and significant numerical differences among the indicators, a logarithmic transformation operation is uniformly introduced before weighting: ； in Indicates the first The branch road in the The original values ​​under each indicator To avoid tiny positive numbers with a value of zero when taking the logarithm; The results after logarithmic processing are normalized by range to obtain the standardized index matrix. : ； b. CRITIC weighted Obtaining the normalized index matrix Then, the weights of each indicator are calculated based on the CRITIC method, specifically as follows: First, calculate the standard deviation of each indicator to measure the degree of difference in the information content of that indicator: ； In the formula, For the first The average of the indicators, The number of samples for the indicator; Then calculate the degree of conflict between the indicators: ； ； In the formula, For any two indicators and Pearson correlation coefficient, , Indicates the first The branch road in the , The normalized value after the logarithm of each indicator , For the first , The average of the indicators, For the number of samples, The number of indicators; Next, the variability and conflict level are combined to calculate the overall information content of each indicator. : ； Finally, the total information content is normalized to obtain the final weight. : ； Branch transient energy index obtained by weighting using the CRITIC method for: ； In the formula, , , , All were obtained using the CRITIC method.

4. The method for identifying critical sections of a power grid driven by branch transient energy according to claim 3, characterized in that: In step (3), the branch is weighted using the reciprocal of the branch transient energy index calculated in step (2), and the th... The edge weights of each branch are as follows: ； And thus, the shortest path between all pairs of nodes is calculated: ； In the formula, Indicates all from arrive The set of feasible paths; An improved edge betweenness function that more closely approximates the energy transfer process is obtained by limiting the path set to the distance from generator nodes to other nodes. The calculation formula is as follows: ； In the formula, Indicates the first A side road, For all generator nodes, For all nodes of the power grid, For nodes and The shortest path between them, Represents a node and Between them, a side road The number of shortest paths.

5. The method for identifying critical sections of a power grid driven by branch transient energy according to claim 1, characterized in that: In step (4), the critical section is determined based on the connection relationship between the newly generated partition and the old partition during the partitioning process. The principle followed when determining the critical section is: if the new partition and the old partition are connected in a chain, then the newly generated inter-partition connection line is the critical section; if the new partition and the old partition are connected in a ring, then the newly generated connection line needs to be combined with the existing connection line to determine the critical section.

6. The method for identifying critical sections of a power grid driven by branch transient energy according to claim 1, characterized in that: In step (4), the iteration is terminated based on the change in modularity. Specifically, this includes: introducing a modularity index to save computational resources; terminating the split after the modularity decreases by more than a threshold three times consecutively; and outputting the cross-section accumulated when the optimal modularity is achieved as the key cross-section. The expression for calculating modularity is: （23）； （24）； In the formula, The sum of the weights of all branches. Weighted adjacency matrix The elements in the array, namely the path weights between nodes i and j, , They are nodes , The weighting degree.

7. The method for identifying critical sections of a power grid driven by branch transient energy according to claim 1, characterized in that: In step (5), based on the key sections determined in step (4), the branch breakage distribution factor is further introduced to finely screen the candidate sections. The branch breakage distribution factor between any two branches within a section is calculated one by one and the average value is taken. Sections with an average value that meets the standard are selected as the final key sections. The calculation formula is: （25）； （26）； （27）； In the formula, , Branch roads , Reactance, To open the branch road The input reactance of the formed port, To open the branch road The formed port and any branch in the network The transfer reactance between the ports is formed. , Branch roads , The node association matrix, Let be the admittance matrix of the network.

8. A branch transient energy-driven power grid critical section identification device, characterized in that, include: The system disturbance response state dataset construction module is used to simulate transient fault scenarios using the power system simulation software PSASP, record the power of each branch, the angular frequency at both ends of the branch, and the rated angular frequency of the system during the transient process, and construct the system disturbance response state dataset. The branch transient energy index construction module is used to calculate four types of indicators that reflect the transient characteristics of the branch in the fault interval: total virtual kinetic energy, disturbance energy accumulation time, disturbance energy impact, and high-frequency energy ratio. Then, the weighting coefficients are determined by the CRITI method to weight and fuse the four types of indicators into a branch transient energy index. An improved edge betweenness acquisition module is used to calculate the shortest path between nodes using the reciprocal of the branch transient energy index as the edge weight. The improved edge betweenness is calculated by limiting the path set to the shortest path from the generator node to other nodes. The critical section screening module is used to partition the power grid by performing the GN splitting algorithm iteratively to remove the highest betweenness edge based on the calculated improved edge betweenness. During the partitioning process, the critical sections are determined according to the connection relationship between the newly generated partitions and the old partitions, and the iteration is terminated according to the change in modularity. The critical section determination module is used to analyze the degree of connection between lines in the critical sections selected by the critical section screening module using the branch breakage distribution factor analysis, and to screen out the sections with close line connections as the final critical sections of the power grid.

9. A branch transient energy-driven power grid critical section identification system, comprising: Computer-readable storage media and processors; The computer-readable storage medium is used to store executable instructions; The processor is used to read executable instructions stored in the computer-readable storage medium and execute the power grid critical section identification method driven by branch transient energy as described in any one of claims 1-7.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method for identifying critical sections of a power grid driven by branch transient energy as described in any one of claims 1-7.

Images