Low-voltage transformer area topology modeling method and system based on hierarchical clustering

Abstract

The invention discloses a low-voltage transformer area topology modeling method and system based on hierarchical clustering, and the method comprises the steps: building a sensitivity relation between voltage and current, calculating a sensitivity coefficient of voltage to current, and calculating a sensitivity matrix according to the resistance value and reactance value of each line in transformer area topology; subtraction is carried out on the electrical quantity under the continuous time section, a sensitivity relational expression is converted, and an associated impedance matrix is obtained and comprises an associated resistance matrix and an associated reactance matrix; based on an improved hierarchical clustering algorithm, inputting an associated resistance matrix or an associated reactance matrix to generate a tree diagram; and identifying hidden nodes according to the tree diagram, determining a generation sequence of the hidden nodes and a subordinate connection relationship between the nodes, and constructing a transformer area topology. By implementing the method, not only can the correlated impedance between the end nodes be accurately calculated, but also all hidden nodes in the network can be identified based on the correlated impedance matrix and the network topology can be correctly deduced, high accuracy and robustness are shown, and the cost is low.

Description

Technical Field

[0001] The present invention relates to the technical field of low-voltage distribution network management, and in particular to a low-voltage distribution area topology modeling method and system based on hierarchical clustering. Background Art

[0002] As the terminal unit of the power system, the low-voltage distribution network has a complex and changeable structure, great safety hazards, low level of informatization, and has long adopted an open-loop management and operation mode of "maintenance by emergency" and "regular maintenance". With the aging of the distribution network and the access of new energy sources, such as distributed photovoltaics, these problems have become more urgent. Accurate topology and line parameter information is the cornerstone of the digitalization of the distribution network, but the current perception ability of the distribution network is limited. The topology and line parameter information in actual management mostly comes from planning documents, equipment ledgers and nameplate information, which are often missing and not updated in time.

[0003] Although a large amount of technical research and engineering practice has been devoted to the topology and line parameter identification of low-voltage substations, there are still many challenges: smart meters are the main source of measurement data, and their data need to complete topology and parameter identification without containing phase angle information; smart meters are usually only deployed at user nodes, which makes it difficult to determine the number and location of branch nodes; the access of distributed photovoltaics makes the power flow direction in the distribution network changeable and the voltage fluctuations intensify, which poses a severe challenge to the accuracy of the identification algorithm. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a low-voltage substation topology modeling method and system based on hierarchical clustering, which can accurately identify the low-voltage substation topology and line parameters under conditions such as no phase angle measurement information, missing branch node information, and voltage fluctuations and reverse and variable currents caused by distributed photovoltaic access.

[0005] To solve the above technical problems, as one aspect of the present invention, a low voltage area topology modeling method based on hierarchical clustering is provided, which comprises the following steps: Step S10, establishing a sensitivity relationship between voltage and current, calculating the sensitivity coefficient of voltage to current, and calculating a sensitivity matrix according to the resistance and reactance values ​​of each line segment in the substation topology; Step S11, subtracting the electrical quantities under continuous time sections, converting the sensitivity relationship, and obtaining the associated impedance matrix, including the associated resistance matrix and the associated reactance matrix; Step S12, based on the improved hierarchical clustering algorithm, inputting the associated resistance matrix or the associated reactance matrix to generate a dendrogram; Step S13, identifying hidden nodes according to the tree diagram, and determining the order of generating hidden nodes and the subordinate connection relationship between nodes, and constructing the station area topology.

[0006] Preferably, step S10 further includes: The angle between voltage and current is calculated by the power factor, and the sensitivity coefficient of voltage to current is obtained by combining the difference in voltage and current amplitudes.

[0007] Preferably, in step S11, it further includes: The elements in the sensitivity matrix are negated to obtain the associated resistance matrix and the associated reactance matrix. The associated impedance matrix is ​​formed by taking the elements in the associated resistance matrix as the real part and the elements at the corresponding positions in the associated reactance matrix as the imaginary part.

[0008] Preferably, in step S12, based on an improved hierarchical clustering algorithm, an associated resistance matrix or an associated reactance matrix is ​​input to generate a dendrogram, further comprising: Input the associated resistance matrix or associated reactance matrix as the initial input matrix; Initialize the association resistance matrix and distance matrix, and treat each user node as an independent cluster; The node cluster merging, association resistance matrix updating and distance matrix updating operations are performed cyclically until all user nodes are clustered into one cluster and a dendrogram is output.

[0009] Preferably, in step S13, the hidden nodes are identified according to the dendrogram, and the generation order of the hidden nodes and the subordinate connection relationship between the nodes are determined to construct the station area extension, further comprising: Initialize the node set; Find the first merged node in the dendrogram, determine the order of generating hidden nodes and the subordinate connection relationship between nodes; The hidden node generation and node set update operations are executed cyclically until the node set contains only one node, the connection between the distribution transformer outgoing line node and the distribution transformer node is established, the topology reconstruction is completed, and the topological structure diagram of the low-voltage distribution station area is drawn.

[0010] Accordingly, as another aspect of the present invention, a low voltage area topology modeling system based on hierarchical clustering is also provided, which comprises: A sensitivity relationship building module is used to build a sensitivity relationship between voltage and current, calculate the sensitivity coefficient of voltage to current, and calculate a sensitivity matrix; The module for obtaining the associated impedance matrix is ​​used to make a difference in the electrical quantities under the continuous time section, transform the sensitivity relationship, and obtain the associated impedance matrix; A hierarchical clustering processing module is used to input the correlation impedance matrix and generate a dendrogram based on an improved hierarchical clustering algorithm; The topology modeling module is used to identify hidden nodes according to the tree diagram, determine the generation order of hidden nodes and the subordinate connection relationship between nodes, and construct the station area topology.

[0011] Preferably, in the sensitivity relationship establishing module, the angle between the voltage and the current is calculated by the power factor, and the sensitivity coefficient of the voltage to the current is calculated in combination with the difference in the voltage and current amplitudes.

[0012] Preferably, in the associated impedance matrix obtaining module, the associated resistance matrix and the associated reactance matrix are obtained by taking the inverse of the elements in the sensitivity matrix, and the associated impedance matrix is ​​formed by taking the elements in the associated resistance matrix as the real part and the elements at the corresponding positions in the associated reactance matrix as the imaginary part.

[0013] Preferably, the hierarchical clustering processing module further comprises: An input matrix obtaining unit is used to input a correlation resistance matrix or a correlation reactance matrix as an initial input matrix; An initialization processing unit is used to initialize the association resistance matrix and the distance matrix, and regard each user node as an independent cluster; The dendrogram obtaining unit is used to cyclically execute node cluster merging, association resistance matrix updating and distance matrix updating operations until all user nodes are clustered into one cluster and output a dendrogram.

[0014] Preferably, the topology modeling module further comprises: A node set initialization unit, used to initialize a node set; A hidden node determination unit is used to find the first node to be merged in the dendrogram, determine the generation order of the hidden nodes and the subordinate connection relationship between the nodes; The topology reconstruction unit is used to cyclically execute hidden node generation and node set update operations until the node set contains only one node, establish the connection between the distribution transformer outgoing line node and the distribution transformer node, complete the topology reconstruction, and draw the topology structure diagram of the low-voltage distribution station area.

[0015] The implementation of the embodiments of the present invention has the following beneficial effects: The present invention provides a low-voltage area topology modeling method and system based on hierarchical clustering, which is especially aimed at the complex characteristics of single-phase low-voltage distribution network, such as no phase angle measurement, missing branch node information and dynamic changes caused by distributed photovoltaic access, to identify topology and line parameters. This method can not only accurately calculate the associated impedance between terminal nodes, but also identify all hidden nodes in the network based on the associated impedance matrix and correctly deduce the network topology, showing a high degree of accuracy and robustness, and has significant engineering application value.

[0016] In the embodiment of the present invention, only limited scalar data provided by the smart meter is needed to develop the solution, without the need for additional phase angle measurement information. This method can not only quickly obtain the associated impedance between the terminal nodes, but also effectively identify the hidden nodes in the network and deduce the topological structure, with fast calculation speed and accurate and reliable identification results.

[0017] In addition, the present invention does not have high requirements on the deployment density and distribution of the measurement devices. It only needs to deploy basic sensing devices on the transformer and user side to complete the identification task, which greatly reduces the investment cost. At the same time, the identification accuracy of this method is less affected by different measurement error distributions, showing good adaptability and stability, and providing strong support for the intelligent management and operation and maintenance of the distribution network. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, without paying creative labor, other drawings obtained based on these drawings still belong to the scope of the present invention. Figure 1 A schematic diagram of the main process of an embodiment of a low-voltage substation topology modeling method based on hierarchical clustering provided by the present invention; Figure 2 for Figure 1 A more detailed flowchart of step S12 and step S13; Figure 3 A schematic diagram of a single-phase low-voltage power distribution network topology in one embodiment of the present invention; Figure 4 A dendrogram generated by an improved hierarchical clustering algorithm in one embodiment of the present invention; Figure 5 A low voltage area topology modeling result in one embodiment of the present invention; Figure 6 A schematic structural diagram of an embodiment of a low voltage substation topology modeling system based on hierarchical clustering provided by the present invention; Figure 7 for Figure 6 The schematic diagram of the structure of the middle-level clustering processing module; Figure 8 for Figure 6 Schematic diagram of the structure of the topology modeling module. DETAILED DESCRIPTION

[0019] In order to make the objectives, technical solutions and advantages of the present invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings.

[0020] like Figure 1 FIG. 1 shows a schematic diagram of the main process of an embodiment of a low-voltage area topology modeling method based on hierarchical clustering provided by the present invention; and FIG. Figure 2As shown, in this embodiment, the method at least includes the following steps: Step S10, establishing a sensitivity relationship between voltage and current, calculating the sensitivity coefficient of voltage to current, and calculating a sensitivity matrix according to the resistance and reactance values ​​of each line segment in the substation topology; In step S10, the angle between the voltage and the current is calculated by the power factor, and the difference between the voltage and current amplitudes is combined to obtain the sensitivity coefficient of the voltage to the current.

[0021] Specifically, in a single-phase low-voltage distribution network, the sensitivity coefficient of voltage to current is defined as:

[0022] Where: and The operators are used to obtain the real and imaginary parts of the phasor respectively; and The sizes are The voltage and current amplitude matrix is is the number of loads on the phase under study, is the number of available samples; the matrix The angle between the load voltage and current is stored, which can be calculated based on the power factor; and are the differences between the voltage amplitude and current phasor at different (usually continuous) time sections; and is the sensitivity matrix.

[0023] set up Representation Node , The set of branches that are the common part of the complete path formed by each of them and the root node, then the matrix and The elements in can be calculated by the following formula:

[0024] Where: Matrix and The elements in are the resistance and reactance values ​​of each section of the line in the substation topology; and is the node label.

[0025] Step S11, subtracting the electrical quantities under continuous time sections, converting the sensitivity relationship, and obtaining the associated impedance matrix, including the associated resistance matrix and the associated reactance matrix; In step S11, by taking the inverse of the elements in the sensitivity matrix, an associated resistance matrix and an associated reactance matrix are obtained, and the elements in the associated resistance matrix are taken as the real part and the elements at the corresponding positions in the associated reactance matrix are taken as the imaginary part to form an associated impedance matrix.

[0026] Specifically, by subtracting the electrical quantities under continuous time sections, equation (1) can be transformed into:

[0027] Where: , , express The column vector of the measured values ​​sampled at each moment; , , express The column vector of the measurement values ​​sampled at the previous moment.

[0028] Sensitivity matrix and Taking the opposite of all elements in , we can get the associated resistance matrix and the associated reactance matrix ,by The elements in are real parts, with The elements at the corresponding positions in are the imaginary parts, which can form the associated impedance matrix , where the elements Node , The associated impedance between nodes is equal to , The sum of the impedances of the common parts of the complete paths formed by each node and the root node.

[0029] Step S12, based on the improved hierarchical clustering algorithm, inputting the associated resistance matrix or the associated reactance matrix to generate a dendrogram; In step S12, it further includes: Input the associated resistance matrix or associated reactance matrix as the initial input matrix; Initialize the association resistance matrix and distance matrix, and treat each user node as an independent cluster; The node cluster merging, association resistance matrix updating and distance matrix updating operations are performed cyclically until all user nodes are clustered into one cluster and a dendrogram is output.

[0030] Specifically, in the actual example, the following content needs to be included: a) Input matrix construction: The single-phase low-voltage distribution network of each user has an associated resistance matrix and the associated reactance matrix They are:

[0031] Where: , Node , The associated resistance and associated reactance between them.

[0032] Theoretically, both the associated resistance matrix and the associated reactance matrix can be used as inputs for subsequent steps. For ease of description, only the associated resistance is taken as an example. The associated reactance can be calculated synchronously using the same method.

[0033] b) Initialize the associated resistance matrix: execute Get a symmetric matrix , That is the initial correlation resistance matrix :

[0034] Where: For Node , The initial value of the associated resistance between.

[0035] c) Distance matrix initialization: define nodes , The initial resistance distance between , fill the initial distance matrix with the initial resistance distance :

[0036] d) Node cluster initialization: treat each user node as an independent cluster and obtain the initial node cluster set ,in Represented by the node Individually formed clusters.

[0037] e) Node cluster merging: Let The node cluster set before the next cycle is , are consecutive integers starting from 1. After the cycle starts, Find the two closest clusters and , merge them into a new cluster , so the current node cluster set is from Became .

[0038] f), Update the associated resistance matrix: Let The correlation resistance matrix before the second cycle is: , No. After the cycle starts, Delete the cluster and Related rows and columns, and add a new row and column to store the new cluster and The associated resistance between all clusters in is as follows: , ,in , Respectively represent After the second cycle and The associated resistance between clusters The associated resistance between itself and itself, according to this principle, the current associated resistance matrix can be changed from becomes .

[0039] g), distance matrix update: Let The distance matrix before the second cycle is , No. After the cycle starts, Delete the cluster and Related rows and columns, and add a new row and column to store the new cluster and The resistance distance between all clusters in is as follows: ,in Indicates After the second cycle and The resistance distance between them, according to this principle, the current distance matrix can be changed from becomes .

[0040] h) Loop through the "merge" and "update" operations in steps e) to g). When all user nodes are clustered into one cluster, stop the loop and output the tree diagram.

[0041] Step S13, identifying hidden nodes according to the tree diagram, and determining the order of generating hidden nodes and the subordinate connection relationship between nodes, and constructing the station area topology.

[0042] In step S13, it further includes: Initialize the node set; Find the first merged node in the dendrogram, determine the order of generating hidden nodes and the subordinate connection relationship between nodes; The hidden node generation and node set update operations are executed cyclically until the node set contains only one node, the connection between the distribution transformer outgoing line node and the distribution transformer node is established, the topology reconstruction is completed, and the topological structure diagram of the low-voltage distribution station area is drawn.

[0043] Specifically, in the improved hierarchical clustering algorithm, one cycle includes one cluster merge, and each merge is accompanied by the generation of hidden nodes or the inclusion of existing nodes into the generated hidden nodes. After the dendrogram is generated through the above steps a) to h), the following steps are continued to mine the information contained in the "merge" to determine the generation order of hidden nodes and the subordinate connection relationship between nodes: i) Node set initialization: Set the initial node set ,in Indicates User nodes.

[0044] j), Hidden node generation: Let the generation The node set before the hidden node is , are consecutive integers starting from 1, and we search for The first two nodes merged in The above merged to produce a cluster , then lock In range, in cluster The nodes participating in these mergers are considered to be all subordinate to the hidden nodes. , and that the tree diagram The position is the condensation point corresponding to the highest of these mergers, It is a height difference threshold that can be set freely. Experiments show that it is easier to get ideal results by taking a value between 0.004 and 0.005.

[0045] k), node set update: Delete the nodes belonging to hidden nodes Those nodes and add hidden nodes , so the current node set is from Became .

[0046] l) Loop through steps i) to k) when The loop stops when only one node is included. This node is the distribution transformer outgoing line node.

[0047] m) Establish the connection between the distribution transformer outgoing line node and the distribution transformer node, and the distribution transformer outgoing line node is directly subordinate to the distribution transformer node.

[0048] n) After obtaining the generation order of hidden nodes and the subordinate connection relationship between nodes, the topology reconstruction can be carried out from bottom to top to draw the topological structure diagram of the low-voltage distribution station area.

[0049] A more detailed flowchart of the above steps S12 and S13 can be found in Figure 2 shown.

[0050] The following combination Figures 3 to 5 A specific example is used to illustrate the specific application of the method provided by the present invention.

[0051] A real low-voltage distribution network in a city (such as Nanjing) is selected as a test sample to verify this method. The one-phase topology diagram of the network is shown in Figure 3 As shown in the figure, the sample data is collected at an interval of 15 minutes and a time span of 10 days. According to the ledger records and relevant literature, the true value of the line impedance is calculated, and the true value of the associated impedance matrix is ​​further obtained.

[0052] Firstly, the collected current, power and voltage data sets are used as input to obtain the associated resistance and associated reactance between each pair of end-user nodes. Then, based on the associated impedance matrix, an improved hierarchical clustering algorithm is used to generate Figure 4 Finally, all the hidden nodes in the network are identified by combining the dendrogram and the station area topology is constructed from bottom to top. The order of generating hidden nodes and the subordinate connection relationship between nodes are recorded in Table 1. According to Table 1, the following can be drawn: Figure 5 The topology diagram of the station area is shown.

[0053] Table 1. The order of hidden node generation and the subordinate connection relationship between nodes in the error-free scenario

[0054] In order to further explore the impact of different measurement error distributions on the proposed model, 0.2% and 0.5% Gaussian distribution errors are added to the current, power, and voltage data sets to form measurement sets, as shown in Table 2. They are input into the proposed model to obtain the associated impedance matrix and deduce the substation topology.

[0055] Table 2 Test scenario settings

[0056] The Robinson-Foulds (RF) distance is used to measure the distance between the topology identification result and the true topology. An RF distance of 0 indicates that the identification result is completely consistent with the true situation. The average impedance error is used to evaluate the accuracy of the associated impedance calculation. The average impedance error is divided into two parts: the average resistance error and the average reactance error. The average resistance error is equal to the mean absolute error (MAE) between the calculated associated resistance matrix and its true value, and the average reactance error is equal to the mean absolute error between the calculated associated reactance matrix and its true value. The accuracy of the associated impedance and topology identification under different test scenarios is shown in Table 3.

[0057] Table 3 Comparison of correlation impedance and topology identification accuracy under different test scenarios

[0058] like Figure 6 FIG. 1 is a schematic diagram showing a structure of an embodiment of a low voltage area topology modeling system based on hierarchical clustering provided by the present invention; and FIG. Figures 7 and 8 As shown, in this embodiment, the low-voltage area topology modeling system 1 based on hierarchical clustering at least includes: A sensitivity relationship establishing module 10 is used to establish a sensitivity relationship between voltage and current, calculate a sensitivity coefficient of voltage to current, and calculate a sensitivity matrix; The associated impedance matrix obtaining module 11 is used to make a difference in the electrical quantities under the continuous time section, transform the sensitivity relationship, and obtain the associated impedance matrix; A hierarchical clustering processing module 12 is used to input the associated impedance matrix and generate a dendrogram based on an improved hierarchical clustering algorithm; The topology modeling module 13 is used to identify hidden nodes according to the tree diagram, determine the generation order of hidden nodes and the subordinate connection relationship between nodes, and construct the substation area topology.

[0059] More specifically, in the sensitivity relationship establishing module 10, the angle between the voltage and the current is calculated by the power factor, and the sensitivity coefficient of the voltage to the current is calculated in combination with the difference in the voltage and current amplitudes.

[0060] In the associated impedance matrix obtaining module 11, the associated resistance matrix and the associated reactance matrix are obtained by taking the inverse of the elements in the sensitivity matrix, and the associated impedance matrix is ​​formed by taking the elements in the associated resistance matrix as the real part and the elements at the corresponding positions in the associated reactance matrix as the imaginary part.

[0061] like Figure 7 As shown, in a specific example, the hierarchical clustering processing module further includes: An input matrix obtaining unit 120 is used to input a correlation resistance matrix or a correlation reactance matrix as an initial input matrix; An initialization processing unit 121 is used to initialize the association resistance matrix and the distance matrix, and regard each user node as an independent cluster; The dendrogram obtaining unit 122 is used to cyclically perform node cluster merging, association resistance matrix updating and distance matrix updating operations until all user nodes are clustered into one cluster and output a dendrogram.

[0062] like Figure 8 As shown, in a specific example, the topology modeling module 13 further includes: A node set initialization unit 130, used to initialize a node set; A hidden node determination unit 131 is used to find the first merged node in the dendrogram, determine the generation order of the hidden nodes and the subordinate connection relationship between the nodes; The topology reconstruction unit 132 is used to cyclically perform hidden node generation and node set update operations until the node set contains only one node, establish the connection between the distribution transformer outgoing line node and the distribution transformer node, complete the topology reconstruction, and draw the topology structure diagram of the low-voltage distribution station area.

[0063] For more details, please refer to and combine the above Figures 1 to 5 The description is not repeated here.

[0064] The implementation of the embodiments of the present invention has the following beneficial effects: The present invention provides a low-voltage area topology modeling method and system based on hierarchical clustering, which is especially aimed at the complex characteristics of single-phase low-voltage distribution network, such as no phase angle measurement, missing branch node information and dynamic changes caused by distributed photovoltaic access, to identify topology and line parameters. This method can not only accurately calculate the associated impedance between terminal nodes, but also identify all hidden nodes in the network based on the associated impedance matrix and correctly deduce the network topology, showing a high degree of accuracy and robustness, and has significant engineering application value.

[0065] In the embodiment of the present invention, only limited scalar data provided by the smart meter is needed to develop the solution, without the need for additional phase angle measurement information. This method can not only quickly obtain the associated impedance between the terminal nodes, but also effectively identify the hidden nodes in the network and deduce the topological structure, with fast calculation speed and accurate and reliable identification results.

[0066] In addition, the present invention does not have high requirements on the deployment density and distribution of the measurement devices. It only needs to deploy basic sensing devices on the transformer and user side to complete the identification task, which greatly reduces the investment cost. At the same time, the identification accuracy of this method is less affected by different measurement error distributions, showing good adaptability and stability, and providing strong support for the intelligent management and operation and maintenance of the distribution network.

[0067] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, units, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product implemented 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.

[0068] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A unit of functionality specified in one or more boxes.

[0069] The above disclosure is only a preferred embodiment of the present invention, which certainly cannot be used to limit the scope of the present invention. Therefore, equivalent changes made according to the claims of the present invention are still within the scope of the present invention.

Claims

1. A low voltage area topology modeling method based on hierarchical clustering, characterized in that: The following steps are involved: Step S10, establishing a sensitivity relationship between voltage and current, calculating the sensitivity coefficient of voltage to current, and calculating a sensitivity matrix according to the resistance and reactance values ​​of each line segment in the substation topology; Step S11, subtracting the electrical quantities under continuous time sections, converting the sensitivity relationship, and obtaining the associated impedance matrix, including the associated resistance matrix and the associated reactance matrix; Step S12, based on the improved hierarchical clustering algorithm, inputting the associated resistance matrix or the associated reactance matrix to generate a dendrogram; Step S13, identifying hidden nodes according to the tree diagram, and determining the order of generating hidden nodes and the subordinate connection relationship between nodes, and constructing the station area topology.

2. The method according to claim 1, characterized in that Step S10 further includes: The angle between voltage and current is calculated by the power factor, and the sensitivity coefficient of voltage to current is obtained by combining the difference in voltage and current amplitudes.

3. The method according to claim 2, characterized in that In step S11, it further includes: The elements in the sensitivity matrix are negated to obtain the associated resistance matrix and the associated reactance matrix. The associated impedance matrix is ​​formed by taking the elements in the associated resistance matrix as the real part and the elements at the corresponding positions in the associated reactance matrix as the imaginary part.

4. The method according to claim 3, characterized in that In step S12, based on the improved hierarchical clustering algorithm, the associated resistance matrix or the associated reactance matrix is ​​input to generate a dendrogram, further comprising: Input the associated resistance matrix or associated reactance matrix as the initial input matrix; Initialize the association resistance matrix and distance matrix, and treat each user node as an independent cluster; The node cluster merging, association resistance matrix updating and distance matrix updating operations are performed cyclically until all user nodes are clustered into one cluster and a dendrogram is output.

5. The method according to claim 4, characterized in that In step S13, the hidden nodes are identified according to the tree diagram, and the generation order of the hidden nodes and the subordinate connection relationship between the nodes are determined to construct the station area extension, which further includes: Initialize the node set; Find the first merged node in the dendrogram, determine the order of generating hidden nodes and the subordinate connection relationship between nodes; The hidden node generation and node set update operations are executed cyclically until the node set contains only one node, the connection between the distribution transformer outgoing line node and the distribution transformer node is established, the topology reconstruction is completed, and the topological structure diagram of the low-voltage distribution station area is drawn.

6. A low voltage area topology modeling system based on hierarchical clustering, characterized in that: include: A sensitivity relationship building module is used to build a sensitivity relationship between voltage and current, calculate the sensitivity coefficient of voltage to current, and calculate a sensitivity matrix; The module for obtaining the associated impedance matrix is ​​used to make a difference in the electrical quantities under the continuous time section, transform the sensitivity relationship, and obtain the associated impedance matrix; A hierarchical clustering processing module is used to input the correlation impedance matrix and generate a dendrogram based on an improved hierarchical clustering algorithm; The topology modeling module is used to identify hidden nodes according to the tree diagram, determine the generation order of hidden nodes and the subordinate connection relationship between nodes, and construct the station area topology.

7. The system according to claim 6, characterized in that In the sensitivity relationship establishment module, the angle between voltage and current is calculated by the power factor, and the sensitivity coefficient of voltage to current is calculated by combining the difference in voltage and current amplitudes.

8. The system according to claim 7, characterized in that In the associated impedance matrix obtaining module, the associated resistance matrix and the associated reactance matrix are obtained by taking the inverse of the elements in the sensitivity matrix. The associated impedance matrix is ​​formed by taking the elements in the associated resistance matrix as the real part and the elements at the corresponding positions in the associated reactance matrix as the imaginary part.

9. The system according to claim 8, characterized in that The hierarchical clustering processing module further comprises: An input matrix obtaining unit is used to input a correlation resistance matrix or a correlation reactance matrix as an initial input matrix; An initialization processing unit is used to initialize the association resistance matrix and the distance matrix, and regard each user node as an independent cluster; The dendrogram obtaining unit is used to cyclically execute node cluster merging, association resistance matrix updating and distance matrix updating operations until all user nodes are clustered into one cluster and output a dendrogram.

10. The system according to claim 9, characterized in that The topology modeling module further includes: A node set initialization unit, used to initialize a node set; A hidden node determination unit is used to find the first node to be merged in the dendrogram, determine the generation order of the hidden nodes and the subordinate connection relationship between the nodes; The topology reconstruction unit is used to cyclically execute hidden node generation and node set update operations until the node set contains only one node, establish the connection between the distribution transformer outgoing line node and the distribution transformer node, complete the topology reconstruction, and draw the topology structure diagram of the low-voltage distribution station area.

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