Method for determining key section and strong correlation section based on improved matrix aggregation algorithm

Abstract

The application provides a kind of key section and strong correlation section determination method based on improved matrix aggregation algorithm, and relates to power grid operation technical field.The system topology is obtained from node system diagram, the line connection and power flow direction information are collected in the topology structure, the improved adjacency matrix is obtained, the matrix distance index is defined and its minimum value is calculated, the adjacency matrix is aggregated by matrix operation, and the topology distribution closest to the main diagonal line of matrix element is obtained;The partitioned topology structure is partitioned, and the connecting line between the partitions is used as the section transmission line, and the initial transmission section that meets the transmission section condition is obtained by screening;The improved comprehensive index composed of branch opening distribution factor and line load rate is established as a criterion to determine the key transmission section;Finally, the power flow transfer impact of the disconnected line on other lines is quantified, the transfer proportion between multiple transmission sections is quantified, the correlation between multiple key sections is obtained, and the strong correlation section is determined.

Description

Technical Field

[0001] This invention relates to the field of power grid operation technology, and in particular to a method for determining key sections and strongly correlated sections based on an improved matrix aggregation algorithm. Background Technology

[0002] Real-time, accurate, and meticulous monitoring of the power grid by operators is conducive to the stable operation of the distribution network system, reduces the problem of missing critical lines, and avoids cascading accidents.

[0003] Currently, research on using adjacency matrix aggregation algorithms to screen power grid topologies is presented in the article "Research on Transmission Section Identification Method and Section Transmission Limit Based on Topology Aggregation" (pp. 33-42), Volume 50, Issue 5, 2022, *Power System Protection and Control*. This article proposes using a power grid topology aggregation algorithm to search for critical transmission sections. By performing a simple matrix transformation on the adjacency matrix, neighboring nodes in the topology are aggregated to the vicinity of the main diagonal of the adjacency matrix. A rapid search for power grid transmission sections is then performed on the transformed adjacency matrix, and critical transmission sections are identified using power flow distribution factors. Research on fundamental methods for determining strongly correlated sections using line power flow transfer impacts is presented in the article "Identification Method of Critical Transmission Sections Based on Improved GN Algorithm" (pp. 70-76), Volume 49, Issue 9, 2021, *Power Grid Analysis and Research*.

[0004] Current methods for analyzing critical transmission sections mainly revolve around two aspects: methods for identifying target sections within power grid zones and methods for screening lines based on the impact of power flow transfer. Pre-zone methods, which divide the power grid structure into zones based on operator experience or some logic, search for nearby branches within these zones, identifying those that meet certain criteria as critical branches. However, the search scope is limited to within a zone, failing to identify critical lines between zones, thus leading to the omission of critical transmission sections. Many studies employ index-based screening methods, using single indicators such as transmission betweenness or load factor as criteria for screening critical lines, without comprehensive consideration, lacking a holistic approach. Betweenness, in particular, has significant limitations. Methods involving improved algorithms or Laplace matrix transformations suffer from algorithmic drawbacks or may result in incorrect or missed selections, and many researchers lack verification of the section results after the search is completed. Existing methods for identifying critical transmission sections are not straightforward enough; existing methods relying on matrix transformations are prone to incorrect or missed selections, and after obtaining the critical transmission sections, there is no further analysis of related issues.

[0005] Regarding methods for identifying strongly correlated transmission sections using line power flow transfer impacts, the article "A Method for Identifying Critical Transmission Sections of Power Grids Based on an Improved GN Algorithm" uses entropy theory to define the sensitivity of the system state to line disconnection as a criterion for judging the criticality of the line. Further analysis of the transfer degrees between lines, between lines and sections, and between sections can reveal the correlation between multiple sections. Existing methods for determining the correlation between critical transmission sections mostly rely on approximate hierarchical classifications or human experience; methods that systematically determine the correlation between sections based on data are relatively vague. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a method for determining key sections and strongly correlated sections based on an improved matrix aggregation algorithm.

[0007] A method for determining key sections and strongly correlated sections based on an improved matrix aggregation algorithm, specifically including the following steps:

[0008] Step 1: Use the adjacency matrix aggregation algorithm to search for the initial cross-section of the power distribution network system;

[0009] Step 1.1: Construct an improved adjacency matrix;

[0010] Establish a power distribution network topology G(V,E), assuming the power distribution network system has n nodes and m buses, where V = {v1, v2, ..., v...} n}, E={e1,e2,…,e m}, v n For node numbering, e m For a graph G with n nodes, its adjacency matrix is ​​an n×n symmetric matrix, numbered as branches. Taking into account the power flow direction of the branches, an improved adjacency matrix A is constructed for the topology graph. The element a in the improved adjacency matrix is ​​defined. ij Let represent the power flow relationship from node i to node j, which characterizes the direction of power flow transmission between lines in the topology, as shown in Equation (1).

[0011]

[0012] The improved adjacency matrix A is then expressed as in equation (2).

[0013]

[0014] In the formula, a ij To improve the elements in the i-th row and j-th column of the adjacency matrix, when node i and node j are directly connected, i.e., there is an edge e m If an element exists, its value is not 0. When the active power flow direction is from node i to node j, the element value is 1; otherwise, it is -1. If there is no direct connection between node i and node j, i.e., no edge e, the element value is 1. mIf it exists, the element's value is 0.

[0015] Step 1.2: Aggregate the adjacency matrix using matrix operations;

[0016] a ij The distance from the coordinates of a given point to the main diagonal is defined as the distance index. The objective function of the distance index is to shorten the sum of distances between all elements within the matrix.

[0017]

[0018] In the formula, n and m are the superscript and subscript of the system node in the matrix, respectively, and V L It is the set of node pairs in the system that have directly connected edges, i.e., the set of non-zero elements of the matrix.

[0019] Step 1.3: Determine the conditions for power grid zoning;

[0020] Step 1.3.1: The number of nodes within a partition and the number of lines between partitions meet the actual requirements of the project. The number of nodes within a partition meets the minimum requirement determined by the system scale, as shown in the following formula:

[0021]

[0022] In the formula, numZ is the number of non-zero elements in the power grid partition, x is the corresponding partition number, numS is the number of non-zero elements in the partition submatrix, y is its corresponding partition number, and N is the number of non-zero elements in the partition submatrix. Z N S These are the set values.

[0023] Step 1.3.2: Determine the connectivity of the lines in the divided region, and use the Warshall algorithm to generate a new matrix on its adjacency matrix;

[0024] The specific method for generating a new matrix is ​​as follows: Starting from the first column, for each node, find all nodes with directed edges to this node, that is, the nodes in the row where the element in the column is 1. Then, logically add the row where these nodes are located to the row where the current node is located, and use this as the new row where these nodes are located, that is, add new directed edges. After generating a new matrix, if all the matrix elements are 1, it means that there is a path between each point, that is, the lines are connected. Retain the connected power grid partitions and remove the partitions where the actual power grid lines are not connected due to matrix operations.

[0025] Step 1.3.3: Perform a consistency judgment on the power flow transmission direction for the remaining power grid partitions; based on the directionality of the improved adjacency matrix A, after obtaining each partition of the power grid, directly select and retain partitions that meet the power flow consistency characteristics in the matrix. Specifically, partitions in the submatrix where all non-zero elements are in the same direction are considered to satisfy the cross-sectional power flow direction consistency.

[0026] Step 1.3.4: Search for a set of partitioned lines that satisfy the cut set property and meet the conditions in steps 1.3.1-1.3.3, and output them as the initial transmission section of the system.

[0027] The cut set property is that a cut set is a set of branches, which is the set of branches that pass through a closed surface after the graph is divided into two parts. If any branch is removed, the graph will be connected again.

[0028] Step 2: Determine the critical transmission section using improved comprehensive indicators; combine the branch breakage distribution factor with the line load rate as a comprehensive indicator to assess the criticality of the line, and determine the critical transmission section from both the breadth and depth of the line's impact.

[0029] Step 2.1: Calculate the branch discontinuity distribution factor;

[0030] The branch failure distribution factor is the proportion of power flow transferred to other branches after a branch failure. For example, the branch failure distribution factor of branch l1 after branch l2 fails is calculated using the following formula:

[0031]

[0032] In the formula, X l1-l2 X is the mutual impedance between branches l1 and l2. l2-l2 For its self-impedance, x l1 With x l2 These are the reactances of branches l1 and l2, respectively.

[0033]

[0034]

[0035] In the formula, M l1 Let l1 be the node-branch association vector, with two non-zero elements, +1 and -1, only at the corresponding positions of the two endpoints, i and j. For M l1 X is the transpose of B0, and B0 is an N-order susceptance matrix.

[0036] The lines within the initial transmission section are disconnected sequentially, and the branch interruption distribution factor for each line is calculated.

[0037] Step 2.2: Calculate the line load rate;

[0038] In the line load factor, the power flow change caused to branch l1 after branch l2 is disconnected within the cross section is:

[0039]

[0040] The power flow load factor of branch l1 after branch l2 is disconnected is:

[0041]

[0042] In the formula, P l1 For the initial power flow of branch l1, S represents the change in power flow caused by the disconnection of branch l2 on branch l1. l1 This represents the maximum transmission power of branch l1.

[0043] Step 2.3: Combine the branch line breakage distribution factor with the line load rate as a comprehensive indicator to evaluate the criticality of the line; the comprehensive indicator is judged from both the breadth and depth of the line's impact, and the calculation formula is as follows:

[0044] λ l1-l2 =aD l1-l2 +bR l1 (10)

[0045] In the formula, λ l1-l2 As a comprehensive index for evaluating the criticality of branch l2, a and b are weight coefficients, both greater than 0, and a+b=1;

[0046] Step 2.4: Identify key transmission sections;

[0047] The minimum values ​​of the branch breakage distribution factor D, the line load rate R, and the weighting coefficient are determined to obtain the criteria for improving the comprehensive index.

[0048] Using the minimum threshold λ of the comprehensive index min As a criterion for evaluating key transmission sections, the minimum threshold for improving the comprehensive index is: λ min = aD + bR, after calculating the improved comprehensive index of the line within the initial transmission section, it will be found that λ ≥ λ min The transmission section to which the line belongs is designated as the critical transmission section. If the line index does not meet the minimum threshold λ, the section is determined to be a non-critical transmission section until all initial transmission sections are identified and the critical transmission sections are output.

[0049] Step 3: Analyze the correlation between transmission sections and determine the strongly correlated sections; specifically, this includes the impact of power flow transfer and the degree of correlation between sections.

[0050] The power flow transfer impact refers to the power flow transfer impact on other cross-section lines caused by line failure. That is, when line l fails, the power flow impact E on line k is defined as follows: l→k for:

[0051]

[0052] In the formula, Gij B ij These are the equivalent conductance and susceptance of line k, respectively; U i U j Let U be the voltage amplitudes at nodes i and j at both ends of line k, respectively, and U be the voltage amplitudes at nodes i and j at both ends of line k. ij =U i -U j The voltage phase difference between the two ends of line k is δ. ij =δ i -δ j ;P ij and Q ij These represent the active and reactive power flow values ​​for line k, respectively. and δ represents the initial steady-state value of the corresponding variable; ij U ij P ij Q ij These are the measured values ​​of the corresponding variables after the fault occurred.

[0053] The sum of the power flow impacts E caused by the disconnection of line l in section TS1 on all lines in section TS2 is... TS1→TS2 for:

[0054]

[0055] In the formula, M represents the total number of lines in section TS2;

[0056] Therefore, the ratio of the impact of the operating state of line l within section TS1 on section TS2 to that of all sections is:

[0057]

[0058] In the formula, E TS1→TS The β value represents the power flow impact of a line fault within section TS1 on the entire section. The larger the β value, the more sensitive section TS2 is to power fluctuations in line l, and the greater the sensitivity, the easier it is to cause cascading accidents to spread. The smaller the β value, the less the section TS2 is affected by fluctuating power flow.

[0059] The degree of correlation Z between the cross sections is defined as:

[0060]

[0061] In the formula, N is the total number of lines in section TS1; the value of N represents the proportion of power flow impact caused by the power fluctuations in section TS1 caused by section TS2; the magnitude of the value of N defines the degree of correlation between sections, so sections with an N value greater than the set value are identified as strongly correlated sections.

[0062] The beneficial effects of adopting the above technical solution are as follows:

[0063] This invention provides a method for determining key transmission sections and strongly correlated sections based on an adjacency matrix aggregation algorithm, with the following beneficial results:

[0064] 1. An aggregation algorithm based on an improved adjacency matrix is ​​proposed. In the aggregated topology, partitions that meet the transmission section conditions are searched, and the tie lines between partitions are used as transmission section lines. The initial transmission section is then output. This method directly searches for power grid partitions in the aggregated topology, and the power flow consistency is filtered more intuitively, rather than pre-partitioning based on the experience of operators or previous partitioning cases, thus avoiding the problem of missed selection caused by pre-partitioning.

[0065] 2. The proposed improved comprehensive index based on branch breakage distribution factor and line load rate has the multifaceted ability to identify critical lines. It determines the critical transmission sections from both the breadth and depth of the line's impact, and takes a more comprehensive approach in the identification process.

[0066] 3. Finally, the proposed quantitative algorithm for the correlation between multiple sections reflects the stability of the power flow in other key sections when the line in a certain key section changes. By analyzing the correlation between multiple sections, it can also play a key monitoring role when operators adjust the operation mode and avoid cascading accidents. Attached Figure Description

[0067] Figure 1 This is an improved adjacency matrix diagram of IEEE-14 nodes in an embodiment of the present invention;

[0068] Figure 2 This is the aggregated adjacency matrix in this embodiment of the invention;

[0069] Figure 3 This is a schematic diagram of power grid partitioning in an embodiment of the present invention;

[0070] Figure 4 This is a flowchart illustrating the determination of the initial power transmission section in an embodiment of the present invention;

[0071] Figure 5 This is a flowchart illustrating the determination of key power transmission sections in an embodiment of the present invention. Detailed Implementation

[0072] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0073] A method for determining key sections and strongly correlated sections based on an improved matrix aggregation algorithm, specifically including the following steps:

[0074] Step 1: Use the adjacency matrix aggregation algorithm to search for the initial cross-section of the power distribution network system;

[0075] Step 1.1: Construct an improved adjacency matrix

[0076] Establish a power distribution network topology G(V,E), assuming the power distribution network system has n nodes and m buses, where V = {v1, v2, ..., v...} n}, E={e1,e2,…,e m}, v n For node numbering, e m For a graph G with n nodes, its adjacency matrix is ​​an n×n symmetric matrix, numbered as branches. Taking into account the power flow direction of the branches, an improved adjacency matrix A is constructed for the topology graph. The element a in the improved adjacency matrix is ​​defined. ij Let represent the power flow relationship from node i to node j, which characterizes the direction of power flow transmission between lines in the topology, as shown in Equation (1).

[0077]

[0078] The improved adjacency matrix A is then expressed as in equation (2).

[0079]

[0080] In the formula, a ij To improve the elements in the i-th row and j-th column of the adjacency matrix, when node i and node j are directly connected, i.e., there is an edge e m If an element exists, its value is not 0. When the active power flow direction is from node i to node j, the element value is 1; otherwise, it is -1. If there is no direct connection between node i and node j, i.e., no edge e, the element value is 1. m If a line exists, its value is 0. Taking IEEE-14 nodes as an example, ignoring the values ​​of unconnected lines, the adjacency matrix is ​​improved as follows: Figure 1 As shown.

[0081] Step 1.2: Aggregate the adjacency matrix using matrix operations;

[0082] a ij The distance from the main diagonal to the current coordinate is defined as the distance index. Shortening the sum of distances between elements in the matrix highlights the connections between nodes, facilitating the zoning of power grids by classifying closely connected lines as intra-regional lines and sparse lines connecting two regions as cross-sections. The objective function for the distance index is:

[0083]

[0084] In the formula, n and m are the superscript and subscript of the system node in the matrix, respectively, and V LLet be the set of directly connected node pairs in the system, i.e., the set of non-zero elements in the matrix. Minimizing the objective function indicates that the elements in the matrix are most tightly clustered along the main diagonal, closely resembling the complex network characteristics of a power grid community structure. Taking IEEE-14 nodes as an example, the aggregated adjacency matrix is ​​as follows: Figure 2 As shown.

[0085] Step 1.3: Determine the conditions for power grid zoning;

[0086] After the matrix elements are transformed and converged according to the aggregation algorithm, the order of the elements in the aggregated matrix changes.

[0087] Step 1.3.1: The number of nodes within a partition and the number of lines between partitions meet the actual requirements of the project. The number of nodes within a partition meets the minimum requirement determined by the system scale, as shown in the following formula:

[0088]

[0089] In the formula, numZ is the number of non-zero elements in the power grid partition, x is the corresponding partition number, numS is the number of non-zero elements in the partition submatrix, y is its corresponding partition number, and N is the number of non-zero elements in the partition submatrix. Z N S These are the set values.

[0090] For the IEEE-14 node system, operators, based on grid scale and experience, set the number of nodes within a search partition to be no less than 4, and the number of lines between partitions to be no more than 4. This is represented in the adjacency matrix as having no less than 4 non-zero elements within the partitioned region, and the number of non-zero elements within the remaining region (i.e., the submatrix) after removing the partition from the row containing the partitioned region. The grid partitioning is then performed as follows: Figure 3 As shown.

[0091] Step 1.3.2: Determine the connectivity of the lines in the divided region, and use the Warshall algorithm to generate a new matrix on its adjacency matrix;

[0092] The specific method for generating the new matrix is ​​as follows: Starting from the first column, for each node, find all nodes with directed edges to this node, that is, the nodes in the row where the element of this column is 1. Then, logically add the row where these nodes are located to the row where the current node is located, and use this as the new row where these nodes are located, that is, add new directed edges. This reflects that if these nodes do not have directed edges to other nodes, but have directed edges to this node, and can indirectly reach other nodes through this node, according to the definition of transitive closure, these nodes must have a directed edge to other nodes. After generating the new matrix, if all matrix elements are 1, it means that there is a path between each point, that is, the lines are connected. Retain the connected power grid partitions and remove the partitions where the actual power grid lines are not connected due to matrix operations.

[0093] Step 1.3.3: Perform a consistency judgment on the power flow transmission direction for the remaining power grid partitions; based on the directionality of the improved adjacency matrix A, after obtaining each partition of the power grid, directly select and retain partitions that meet the power flow consistency characteristics in the matrix. Specifically, partitions in the submatrix where all non-zero elements are in the same direction are considered to satisfy the cross-sectional power flow direction consistency.

[0094] Step 1.3.4: Search for a set of partitioned lines that satisfy the cut-set property and meet the conditions in steps 1.3.1-1.3.3, and output this set as the initial transmission section of the system. The flowchart is as follows: Figure 4 As shown.

[0095] The cut set property is that a cut set is a set of branches, which is the set of branches that pass through a closed surface after the graph is divided into two parts. If any branch is removed, the graph will be connected again.

[0096] Step 2: Determine the critical transmission section using improved comprehensive indicators; combine the branch breakage distribution factor with the line load rate as a comprehensive indicator to assess the criticality of the line, and determine the critical transmission section from both the breadth and depth of the line's impact.

[0097] Step 2.1: Calculate the branch discontinuity distribution factor;

[0098] The branch failure distribution factor is the proportion of power flow transferred to other branches after a branch failure. For example, the branch failure distribution factor of branch l1 after branch l2 fails is calculated using the following formula:

[0099]

[0100] In the formula, X l1-l2 X is the mutual impedance between branches l1 and l2. l2-l2 For its self-impedance, x l1 With x l2 These are the reactances of branches l1 and l2, respectively.

[0101]

[0102]

[0103] In the formula, M l1 Let l1 be the node-branch association vector, with two non-zero elements, +1 and -1, only at the corresponding positions of the two endpoints, i and j. For M l1 X is the transpose of B0, and B0 is an N-order susceptance matrix.

[0104] The lines within the initial transmission section are disconnected sequentially, and the branch interruption distribution factor for each line is calculated.

[0105] Step 2.2: Calculate the line load rate;

[0106] In the line load factor, the power flow change caused to branch l1 after branch l2 is disconnected within the cross section is:

[0107]

[0108] The power flow load factor of branch l1 after branch l2 is disconnected is:

[0109]

[0110] In the formula, P l1 For the initial power flow of branch l1, S represents the change in power flow caused by the disconnection of branch l2 on branch l1. l1 This represents the maximum transmission power of branch l1.

[0111] Line load factor reflects both the line's load-bearing capacity and its safety margin. A high load factor or a line that is heavily loaded indicates that if one line in a section breaks, it will have a significant impact on other lines, and the fault will directly threaten the safe and stable operation of the power grid.

[0112] Step 2.3: Combine the branch breakage distribution factor with the line load rate as a comprehensive indicator to evaluate the criticality of the line;

[0113] The comprehensive index assesses both the breadth and depth of the impact of the railway line, providing a more comprehensive identification of critical lines. The calculation formula is:

[0114] λ l1-l2 =aD l1-l2 +bR l1 (10)

[0115] In the formula, λ l1-l2 The comprehensive index for evaluating the criticality of branch l2 is a, b, which are weight coefficients, both greater than 0, and a+b=1; the values ​​of a and b can be determined by the power grid operation requirements or can be calculated by the entropy weight method.

[0116] λ l1-l2 The larger the value, the greater the power flow to nearby branches after the line is disconnected, and the easier it is to cause line overload and overload. The impact on other lines after the disconnection is more profound. The area and degree of impact after the fault need to be paid attention to by the control personnel. Therefore, it is selected as a comprehensive improvement indicator for evaluating the criticality of the line.

[0117] Step 2.4: Identify key transmission sections;

[0118] Since both the standardized branch breakage distribution factor D and the line load rate R are between 0 and 1, the weighted sum of the two still results in λ being between 0 and 1. To effectively screen more important lines and avoid omissions, the minimum values ​​of the branch breakage distribution factor D, the line load rate R, and the weighting coefficients are determined to obtain the criteria for improving the comprehensive index.

[0119] Using the minimum threshold λ of the comprehensive index min As a criterion for evaluating key transmission sections, the minimum threshold for improving the comprehensive index is: λ min = aD + bR, after calculating the improved comprehensive index of the line within the initial transmission section, it will be found that λ ≥ λ min The transmission section to which the line belongs is designated as the critical transmission section. If the line index does not meet the minimum threshold λ, the section is determined to be a non-critical transmission section until all initial transmission sections are identified and the critical transmission sections are output.

[0120] In this embodiment, the analysis of the interruption distribution factor D can be determined according to actual requirements. Its setting range is generally 0.2 to 0.3. This invention takes the median value of 0.25. This value is to improve the adaptability of the algorithm to various power grids. According to the practical operation experience of the power grid, when the safety margin of the line is less than 0.3, it needs to be monitored closely to prevent the line from collapsing. Therefore, the line load rate R is set to 0.7.

[0121] However, during power grid operation and dispatching, dispatchers often pay more attention to the magnitude of the existing power flow on the lines relative to the transmission limit, i.e., the line load level. Therefore, this invention uses a = 0.4 and b = 0.6, indicating that the line load rate R weighting coefficient is 0.6, which is 1 / 2 higher than the branch breakage distribution factor D. The minimum threshold λ of the comprehensive index is used. min As a criterion for evaluating key transmission sections, the minimum threshold for improving the comprehensive index is:

[0122] λ min =aD+bR=0.4×0.25+0.6×0.7=0.52

[0123] After calculating the improved comprehensive index of the lines within the initial transmission section, transmission sections with λ ≥ 0.52 are designated as critical transmission sections. If a line's index does not meet the minimum threshold λ, the section is determined to be a non-critical transmission section. This process continues until all initial transmission sections are identified, and the critical transmission sections are output. The flowchart is as follows. Figure 5 As shown.

[0124] Step 3: Analyze the correlation between transmission sections and determine the strongly correlated sections; specifically, this includes the impact of power flow transfer and the degree of correlation between sections.

[0125] The power flow transfer impact refers to the power flow transfer impact on other cross-section lines caused by line failure. That is, when line l fails, the power flow impact E on line k is defined as follows: l→k for:

[0126]

[0127] In the formula, G ij B ij These are the equivalent conductance and susceptance of line k, respectively; U i U j Let U be the voltage amplitudes at nodes i and j at both ends of line k, respectively, and U be the voltage amplitudes at nodes i and j at both ends of line k. ij =U i -U j The voltage phase difference between the two ends of line k is δ. ij =δ i -δ j ;P ij and Q ij These represent the active and reactive power flow values ​​for line k, respectively. and δ represents the initial steady-state value of the corresponding variable; ij U ij P ij Q ij These are the measured values ​​of the corresponding variables after the fault occurred.

[0128] The sum of the power flow impacts E caused by the disconnection of line l in section TS1 on all lines in section TS2 is... TS1→TS2 for:

[0129]

[0130] In the formula, M represents the total number of lines in section TS2;

[0131] Therefore, the ratio of the impact of the operating state of line l within section TS1 on section TS2 to that of all sections is:

[0132]

[0133] In the formula, E TS1→TS The β value represents the power flow impact of a line fault within section TS1 on the entire section. The larger the β value, the more sensitive section TS2 is to power fluctuations in line l, and the greater the sensitivity, the easier it is to cause cascading accidents to spread. The smaller the β value, the less the section TS2 is affected by fluctuating power flow.

[0134] The degree of correlation Z between the cross sections is defined as:

[0135]

[0136] In the formula, N is the total number of lines in section TS1; the value of N represents the proportion of power flow impact caused by the power fluctuation of section TS1 caused by section TS2; the magnitude of the value of N defines the degree of correlation between sections. Considering that the number of sections determined in actual engineering is not large, sections with N values ​​greater than the set value are identified as strongly correlated sections that need to be considered for control methods.

[0137] The above description is merely a preferred embodiment of this disclosure and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in the embodiments of this disclosure is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-described inventive concept. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features with similar functions disclosed in the embodiments of this disclosure.

Claims

1. A method for determining key sections and strongly correlated sections based on an improved matrix aggregation algorithm, characterized in that, Includes the following steps: Step 1: Use the adjacency matrix aggregation algorithm to search for the initial cross-section of the power distribution network system; Step 1 specifically includes the following steps: Step 1.1: Construct an improved adjacency matrix; Establish a power distribution network topology G(V,E), assuming the power distribution network system has n nodes and m buses, where V={v1,v2,…,v…} n }, E={e1,e2,…,e m }, v n For node numbering, e m For a graph G with n nodes, its adjacency matrix is ​​an n×n symmetric matrix, numbered as branches. Taking into account the power flow direction of the branches, an improved adjacency matrix A is constructed for the topology graph. The element a in the improved adjacency matrix is ​​defined. ij Let i be the power flow relationship from node i to node j, which represents the power flow transmission direction between lines in the topology, as shown in equation (1). （1）； The improved adjacency matrix A is then expressed as in equation (2); （2）； In the formula, a ij To improve the elements in the i-th row and j-th column of the adjacency matrix, when node i and node j are directly connected, i.e., there is an edge e m If an element exists, its value is not 0. When the active power flow direction is from node i to node j, the element value is 1; otherwise, it is -1. If there is no direct connection between node i and node j, i.e., no edge e, the element value is 1. m If it exists, the element's value is 0; Step 1.2: Aggregate the adjacency matrix using matrix operations; a ij The distance from the coordinates of a given point to the main diagonal is defined as the distance index. The objective function of the distance index is to shorten the sum of distances between all elements within the matrix. （3）； In the formula, n and m are the superscript and subscript of the system node in the matrix, respectively, and V L It is the set of node pairs in the system that have directly connected edges, i.e., the set of non-zero elements of the matrix; Step 1.3: Determine the conditions for power grid zoning; Step 1.3 specifically includes the following steps: Step 1.3.1: The number of nodes within a partition and the number of lines between partitions meet the actual requirements of the project. The number of nodes within a partition meets the minimum requirement determined by the system scale, as shown in the following formula: （4）； In the formula, numZ is the number of non-zero elements in the power grid partition, x is the corresponding partition number, numS is the number of non-zero elements in the partition submatrix, y is its corresponding partition number, and N is the number of non-zero elements in the partition submatrix. Z N S These are the set values; Step 1.3.2: Determine the connectivity of the lines in the divided region, and use the Warshall algorithm to generate a new matrix on its adjacency matrix; The specific method for generating a new matrix is ​​as follows: Starting from the first column, for each node, find all nodes with directed edges to this node, that is, the nodes in the row where the element of this column is 1. Then, logically add the row where these nodes are located to the row where the current node is located, and use this as the new row where these nodes are located, that is, add new directed edges. After generating a new matrix, if all the elements of the matrix are 1, it means that there is a path between each point, that is, the lines are connected. Retain the connected power grid partitions and remove the partitions where the actual power grid lines are not connected due to matrix operations. Step 1.3.3: Perform a consistency judgment on the power flow transmission direction for the remaining power grid partitions; Based on the directionality of the improved adjacency matrix A, after obtaining each partition of the power grid, directly select and retain partitions that meet the power flow consistency characteristics in the matrix. Specifically, partitions in the submatrix where all non-zero elements are in the same direction are considered to satisfy the cross-sectional power flow direction consistency. Step 1.3.4: Search for a set of partitioned lines that satisfy the cut set property and meet the conditions in steps 1.3.1-1.3.3, and output them as the initial transmission section of the system; The cut set property is that a cut set is a set of branches, which is the set of branches that pass through a closed surface after the graph is divided into two parts. If any branch is removed, the graph will be connected again. Step 2: Determine key transmission sections using improved comprehensive indicators; combine branch breakage distribution factor with line load rate as a comprehensive indicator to assess the criticality of the line, and determine key transmission sections from both the breadth and depth of the line's impact. Step 3: Analyze the correlation between transmission sections and determine the strongly correlated sections, specifically including the impact of power flow transfer and the degree of correlation between sections.

2. The method for determining key sections and strongly correlated sections based on an improved matrix aggregation algorithm according to claim 1, characterized in that, Step 2 specifically includes the following steps: Step 2.1: Calculate the branch discontinuity distribution factor; The branch disconnection distribution factor is the proportion of power flow transferred to other branches after a branch disconnection. The branch disconnection distribution factor of branch l1 after branch l2 is disconnected is calculated using the following formula: （5）； In the formula, The mutual impedance between branches l1 and l2, Its self-impedance, and These are the reactances of branches l1 and l2, respectively; （6）； （7）； In the formula, Let l1 be the node-branch association vector, with two non-zero elements, +1 and -1, only at the corresponding positions of the two endpoints, i and j. for X is the transpose of B0, and B0 is an N-order susceptance matrix. The lines within the initial transmission section are disconnected sequentially, and the branch interruption distribution factor of each line is calculated. Step 2.2: Calculate the line load rate; In the line load factor, the power flow change caused to branch l1 after branch l2 is disconnected within the cross section is: （8）； The power flow load factor of branch l1 after branch l2 is disconnected is: （9）； In the formula, For the initial power flow of branch l1, This represents the change in power flow caused by the disconnection of branch l2 on branch l1. This represents the maximum transmission power of branch l1; Step 2.3: Combine the branch breakage distribution factor with the line load rate as a comprehensive indicator for evaluating the criticality of the line; The comprehensive index is judged from both the breadth and depth of the line's impact, and the calculation formula is as follows: （10）； In the formula, As a comprehensive index for evaluating the criticality of branch l2, a and b are weight coefficients, both greater than 0, and a+b=1; Step 2.4: Determine the key transmission sections; The minimum values ​​of the branch breakage distribution factor D, the line load rate R, and the weighting coefficient are determined to obtain the criteria for improving the comprehensive index.

3. The method for determining key sections and strongly correlated sections based on an improved matrix aggregation algorithm according to claim 2, characterized in that, The criterion mentioned in step 2.4 is specifically the minimum threshold of the comprehensive index. As a criterion for evaluating key transmission sections, the minimum threshold for improving the comprehensive index is: After calculating the comprehensive improvement index of the line within the initial transmission section, there will be... The transmission section to which the line belongs is designated as the critical transmission section; if the line's specifications do not meet the requirements... If the minimum threshold is reached, the section is determined to be a non-critical transmission section. This process continues until all initial transmission sections are identified, and then the critical transmission sections are output.

4. The method for determining key sections and strongly correlated sections based on an improved matrix aggregation algorithm according to claim 1, characterized in that, In step 3, the power flow transfer impact refers to the power flow transfer impact of line failure on other cross-section lines. That is, when line l fails, the power flow impact on line k is defined. for: （11）； In the formula, , These are the equivalent conductance and susceptance of line k, respectively; , Let i and j be the voltage amplitudes at nodes i and j at the two ends of line k, respectively. The voltage phase difference between the two ends of line k is ; and These represent the active and reactive power flow values ​​for line k, respectively. , , and These are the initial steady-state values ​​of the corresponding variables; , , , These are the measured values ​​of the corresponding variables after the fault occurred; The sum of the power flow impacts caused by the disconnection of line l in section TS1 on all lines in section TS2 is... for: （12）； In the formula, M represents the total number of lines in section TS2; Therefore, the ratio of the impact of the operating state of line l within section TS1 on section TS2 to that of all sections is: （13）； In the formula, The power flow impact on the entire cross section caused by a line fault within section TS1. The larger the value, the more sensitive section TS2 is to power fluctuations of line l, and the greater the sensitivity, the easier it is to cause cascading accidents to spread; the smaller the value, the less impact section TS2 is on power fluctuations.

5. The method for determining key sections and strongly correlated sections based on an improved matrix aggregation algorithm according to claim 4, characterized in that, The degree of correlation between cross sections mentioned in step 3 is defined as Z: （14）； In the formula, N is the total number of lines in section TS1; the value of N represents the proportion of power flow impact caused by the power fluctuations in section TS1 caused by section TS2; the magnitude of the value of N defines the degree of correlation between sections, so sections with an N value greater than the set value are identified as strongly correlated sections.

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