Low-voltage transformer area topology reconstruction method based on synchronous measurement data

Abstract

The invention provides a low-voltage transformer area topology reconstruction method based on synchronous measurement data, and the method comprises the steps: obtaining a voltage fluctuation propagation delay value of each group in a hierarchical grouping set, recognizing a delay minimum path, and obtaining a preliminary connection path diagram; according to the preliminary connection path diagram, optimizing the processing path, analyzing the difference of recovery durations among nodes in the tree topology structure, and optimizing the connection strength of the tree topology structure by adopting a dynamic weight adjustment mode to obtain an optimized tree topology structure; extracting an inter-node distance value through the optimized tree topology structure, matching the distance value with an actual connection relationship, identifying an unmatched item by adopting error analysis and iteratively adjusting node grouping, and determining electrical distance distribution; and obtaining the connection strength value of each node in the electrical distance distribution, constructing the connection relation of each node, filtering the noise influence through data filtering processing, and obtaining a precise connection relation graph.

Description

Technical Field

[0001] This invention relates to the field of information technology, and in particular to a method for topology reconstruction of low-voltage distribution areas based on synchronous measurement data. Background Technology

[0002] Low-voltage distribution area topology reconfiguration is a crucial step in smart distribution network construction, directly impacting power system operational efficiency and fault diagnosis capabilities. Accurately identifying the connections between nodes in the distribution network can optimize power dispatch, improve power supply reliability, and reduce maintenance costs. Research in this area is critical for driving energy transition and achieving efficient power management. However, existing methods often face the challenge of accurately capturing dynamic changes when dealing with complex low-voltage distribution area topologies, especially in scenarios with frequent load switching, making real-time and accurate network structure reconfiguration difficult. Current solutions typically rely on post-processing of measurement data, attempting to infer node connections by correcting time deviations at various measurement points. However, due to insufficient time synchronization accuracy of measurement equipment, this method often fails to accurately reflect the instantaneous propagation process of voltage changes when facing rapid load changes. The start time and recovery duration of voltage changes are difficult to align precisely across different nodes, leading to deviations in topology inference results. This limitation restricts the applicability of existing methods in dynamic load scenarios, especially in low-voltage distribution areas with frequent load switching and complex electrical distances. In low-voltage distribution areas, voltage fluctuations caused by load switching exhibit a cascading effect. The propagation delay and recovery time of voltage changes are key indicators of the electrical distance and connection strength between nodes. However, due to insufficient time synchronization accuracy of measuring equipment, the distribution information of voltage changes along the time axis is often distorted. For example, in a low-voltage distribution area, when a large load is suddenly disconnected, the starting time of voltage fluctuations at each node may be misaligned by milliseconds due to equipment clock deviations, making it impossible to accurately determine the electrical connection strength between nodes. Summary of the Invention

[0003] This invention provides a method for topology reconstruction of low-voltage distribution areas based on synchronous measurement data, mainly including: The system collects voltage value records of each node based on synchronous measurement data without time calibration from the measurement equipment, detects the start and end points of voltage fluctuations during dynamic load switching events, identifies the differences in start time and recovery time between nodes through relative time sequence comparison, and constructs a time difference data set. Based on the time difference data set, the nodes are grouped, and the similarity of the differences in start time and recovery time among the nodes in the group is evaluated by cluster analysis. Nodes with high similarity are classified into the same electrical distance level to generate a hierarchical group set. Extract the voltage fluctuation propagation delay value of each group from the hierarchical grouping set, identify the path with the minimum delay, and generate a preliminary connection path map; Based on the preliminary connection path diagram, the differences in recovery time between nodes in the tree topology are analyzed, and the connection strength is optimized by dynamic weight adjustment to generate the optimized tree topology. The distance values ​​between nodes are extracted from the optimized tree topology, matched with the actual connection relationships, and the node grouping is iteratively adjusted through error analysis to generate the electrical distance distribution. Node connection strength values ​​are extracted from the electrical distance distribution to construct connection relationships, and a precise connection relationship diagram is generated through data filtering. Based on the refined connection diagram, new voltage fluctuation data is monitored, and inconsistencies between the start time difference and the existing connection diagram are detected, triggering topology reconstruction and generating updated low-voltage distribution area topology reconstruction results.

[0004] Furthermore, the method involves collecting voltage value records from each node based on synchronous measurement data without time calibration from the measuring device, detecting the start and end points of voltage fluctuations during dynamic load switching events, identifying differences in start times and recovery times between nodes through relative time sequence comparison, and constructing a time difference data set, including: The high-frequency sampling module of the low-voltage distribution area measurement equipment acquires the voltage sampling sequence of each node, records the voltage value and sampling number, calculates the voltage change rate between adjacent sampling points, marks the sampling number where the voltage change rate exceeds the preset change rate threshold for three consecutive sampling points as the fluctuation start point, and continues to monitor until the voltage change rate is lower than the preset change rate threshold and remains stable for five sampling cycles, which is then marked as the fluctuation end point, generating a fluctuation period marking sequence for each node. The high-frequency sampling module samples at a preset sampling frequency. Based on the fluctuation period marker sequence, the sampling sequence number of the fluctuation start point of each node is extracted, the difference between the sampling sequence numbers of adjacent nodes is calculated as the relative time offset, the number of sampling points from the start point to the end point is calculated as the recovery time value, all node pairs are traversed, and a structured record containing the node pair identifier, the difference value of the start time and the difference value of the recovery time is generated, and the time difference data set is summarized.

[0005] Furthermore, based on the time difference data set, the nodes are grouped, and cluster analysis is used to evaluate the similarity of the differences in start time and recovery time among the nodes within the group. Nodes with high similarity are grouped into the same electrical distance level, generating a hierarchical grouping set, including: Extract the start time difference value and recovery time difference value of the node pair from the time difference data set, construct the difference feature vector, calculate the distance value between the difference vector of the node and the reference node using the Euclidean distance formula, and form a similarity distance matrix; Based on the similarity distance matrix, the K-means clustering algorithm is used to group the nodes, iteratively updating the cluster centers until the sum of distances is minimized, and generating node groups. The number of clusters in the K-means clustering algorithm is preset according to the typical hierarchical structure of the low-voltage distribution area. The average value of the difference feature vector within each group is calculated as the electrical distance feature identifier. The groups are sorted according to the difference values ​​at the start time to determine the electrical distance hierarchy order and assign a hierarchy number. Verify the difference in recovery time between nodes within the same level. If the difference exceeds the threshold, redistribute the nodes based on the difference vector distance between adjacent levels to generate a set of level groups.

[0006] Furthermore, the step of extracting the voltage fluctuation propagation delay value of each group from the hierarchical grouping set, identifying the path with the shortest delay, and generating a preliminary connection path map includes: Extract the average difference in the starting time of nodes within each group from the hierarchical grouping set, calculate the propagation delay between adjacent levels, take the minimum difference value as the typical propagation delay, and generate a delay value sequence. Based on the delay value sequence, starting from the transformer outlet node, the node connection with the smallest delay in the next level is identified, and the process is repeated until the last level to generate a set of minimum delay connection relationships. Based on the set of minimum delay connections, construct the connection path from the root node to the end node, record the node sequence and cumulative delay value, and generate a preliminary connection path graph.

[0007] Furthermore, based on the preliminary connection path diagram, the analysis of the recovery time differences between nodes in the tree topology, and the optimization of connection strength using dynamic weight adjustment to generate an optimized tree topology, includes: Recovery time data of adjacent node pairs are extracted from the preliminary connection path diagram. The mean and standard deviation of the recovery time of child nodes under the same parent node are calculated. Nodes with a difference exceeding twice the standard deviation are marked as abnormal recovery nodes. The ratio of normal to abnormal nodes is statistically analyzed to form a node recovery feature distribution map. Based on the node recovery feature distribution map, parent-child connection weight values ​​are assigned, the cumulative weight product from the root node to the end node is calculated, and weak connection paths exceeding the preset cumulative threshold are identified. The preset cumulative threshold is determined according to the scale of the low-voltage distribution area. For the weak connection path, search again for the parent node that minimizes the difference in recovery time of the child node in the same or higher level nodes, adjust the connection relationship, update the parent-child node mapping table, and generate an optimized tree topology.

[0008] Furthermore, the step of extracting distance values ​​between nodes from the optimized tree topology, matching actual connection relationships, iteratively adjusting node groupings through error analysis, and generating an electrical distance distribution includes: Traverse the nodes from the optimized tree topology, calculate the number of connection segments to the root node as the topological distance, extract the cumulative propagation delay value as the temporal distance, construct a two-dimensional distance vector, and generate a node distance matrix. Based on the node distance matrix, the number of branch levels in the actual connection relationship is compared to calculate the topology error, and error nodes that exceed the preset tolerance value are marked, where the topology error = |topology distance - actual number of branch levels|; The error node is re-evaluated and its level is adjusted according to the time distance and the average level of adjacent levels. The adjustment result of reducing the topology error is retained. The process is iterated until the error is within the tolerance range or reaches the preset iteration limit, and an electrical distance distribution is generated.

[0009] Furthermore, the step of extracting node connection strength values ​​from the electrical distance distribution, constructing connection relationships, and generating a refined connection relationship graph through data filtering processing includes: The connection strength value between parent and child nodes is extracted from the electrical distance distribution, and an initial connection relationship table is constructed based on the connection strength value, where the connection strength value = 1 / (difference in recovery time between parent and child nodes + 1); Based on the initial connection relationship table, identify noisy connections whose connection strength values ​​exceed the mean plus or minus two standard deviations, count the number of noisy connections, verify the rationality of node connection relationships, and generate a set of noisy connections. Based on the set of noisy connections, the noise connection strength values ​​are corrected and replaced with the average value of the normal connection strength values. Isolated noise connections are removed, and an accurate connection relationship graph is generated. Here, an isolated noise connection refers to a connection where all connections of the node are marked as noise and no normal connection strength reference value can be found.

[0010] Furthermore, the step of monitoring new voltage fluctuation data based on the refined connection diagram, detecting inconsistencies between the start time difference and the existing connection diagram, triggering topology reconstruction, and generating updated low-voltage distribution area topology reconstruction results includes: Based on the refined connection diagram, monitor the voltage fluctuations of each node, record the start time and recovery time of the new load switching event, calculate the difference in start time between node pairs, subtract the historical difference value in the refined connection diagram, and generate a difference deviation sequence. Based on the difference deviation sequence, the first quartile, the third quartile, and the interquartile range of the difference deviation are calculated using the box plot method. If the deviation exceeds a preset value, it is determined to be an abnormal deviation. The number of abnormal node pairs is counted. If it exceeds the proportion threshold, topology reconstruction is triggered. The proportion threshold is determined according to the scale of the low-voltage distribution area. The time difference data set construction, node grouping, hierarchical division, path optimization and distance matching are re-executed to generate a new topology, update the refined connection relationship graph, record the changed nodes, and generate the updated low-voltage transformer area topology reconstruction result.

[0011] Furthermore, the time-calibration-free synchronous measurement data also includes: The measuring devices at each node do not rely on absolute timestamps; they only record the voltage value and the corresponding sampling sequence number. The synchronization is achieved by ensuring that the difference in sampling sequence numbers between adjacent nodes is less than or equal to a preset sampling period, thus achieving relative timing alignment. The sampling period is determined based on the high-frequency sampling module of the measuring device.

[0012] Furthermore, the optimization logic for the dynamic weight adjustment also includes: The adjusted tree topology must satisfy the tree structure constraints that each non-root node has one and only one parent node, the root node has no parent node, and the cumulative recovery time change on the path from each node to the root node before and after the adjustment must be within the allowable range. The allowable range is set based on the original cumulative recovery time.

[0013] The technical solutions provided by the embodiments of the present invention may include the following beneficial effects: This invention discloses a low-voltage distribution area topology reconstruction method based on synchronous measurement data. Addressing the voltage fluctuation characteristics under dynamic load switching scenarios in low-voltage distribution areas, it solves the operational problems of dynamic reconstruction of electrical distance distribution between nodes and topology structure. This invention collects voltage data from each node, detects the start and end points of fluctuations, and uses relative time-series comparison and cluster analysis to group nodes according to electrical distance levels, generating a preliminary connection path diagram. It then optimizes the tree-like topology structure through dynamic weight adjustment, extracts distance values ​​between nodes, matches actual connection relationships, and constructs a precise connection relationship diagram. For dynamic load scenarios, this invention updates voltage fluctuation data in real time, combines anomaly detection to identify inconsistencies, triggers topology reconstruction, and obtains the updated topology structure. This invention achieves accurate dynamic reconstruction of the low-voltage distribution area topology structure, effectively improving the efficiency and accuracy of power grid operation status monitoring and fault location, and providing technical support for intelligent power system management. Attached Figure Description

[0014] Figure 1 This is a flowchart of a low-voltage distribution area topology reconstruction method based on synchronous measurement data according to the present invention. Detailed Implementation

[0015] To further understand the content of this invention, a detailed description of the invention is provided in conjunction with the accompanying drawings and embodiments. The specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention. It should also be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0016] like Figure 1 This embodiment of a low-voltage distribution area topology reconstruction method based on synchronous measurement data may specifically include: S101. By collecting voltage value records of each node based on synchronous measurement data without time calibration from the measurement equipment, the starting point and ending point of voltage fluctuation of dynamic load switching events are detected. The difference in start time and recovery time between each node is identified by relative time sequence comparison, and a time difference data set is obtained.

[0017] Voltage sampling sequences for each node are acquired from the high-frequency sampling module of the low-voltage distribution area measurement equipment. During the acquisition process, the voltage value and corresponding sampling number of each node are recorded, and the voltage change rate between adjacent sampling points is calculated. When the voltage change rate of three consecutive sampling points exceeds a preset threshold, the sampling number is marked as the voltage fluctuation start point. Subsequent sampling data is continuously monitored until the voltage change rate decreases below the threshold and remains stable for five sampling cycles. The sampling number is then recorded as the fluctuation end point, forming a fluctuation period marking sequence for each node. Based on the fluctuation period marking sequence, the sampling number corresponding to the fluctuation start point of each node is extracted. The relative time offset is calculated by the difference in sampling numbers between adjacent nodes. If the starting sampling number of node A is N and that of node B is N+M, then the difference in the starting time of node B relative to node A is M sampling cycles. At the same time, the number of sampling points from the start point to the end point of each node is calculated as the recovery time value. All node pairs in the low-voltage distribution area are traversed to obtain the node pair identifier, the start time difference value, and the recovery time difference value. By integrating the start time difference value and recovery time difference value, a structured record containing three fields—node pair identifier, start time difference value, and recovery time difference value—is constructed. All records of node pairs are then aggregated to form a time difference data set.

[0018] Specifically, in one implementation, the low-voltage distribution area measurement equipment continuously monitors the voltage of each node through a built-in high-frequency sampling module. The sampling frequency is set to 1000 times per second to ensure that transient voltage changes caused by load switching can be captured. Each sampling point records the voltage amplitude at the current moment and the corresponding sampling number, forming a continuous voltage sampling sequence. The voltage change rate is obtained by dividing the voltage difference between two adjacent sampling points by the sampling time interval. When a high-power load at a node is suddenly disconnected, the voltage at that node and adjacent nodes will show a rapid rise.

[0019] Specifically, the preset threshold is determined based on the rated voltage and historical fluctuation data of the low-voltage distribution area, and is usually set to 2% of the rated voltage divided by the sampling period. When the voltage change rate of three consecutive sampling points exceeds this threshold, the system determines that this is the starting point of the voltage fluctuation and records the corresponding sampling number.

[0020] It should be noted that using three consecutive sampling points as the basis for judgment can effectively avoid misjudgments caused by single-point noise interference. The determination of the end point of fluctuation requires the voltage change rate to decrease below the threshold and maintain a stable state for five sampling cycles. This stability judgment ensures the integrity of the fluctuation process.

[0021] For example, in a low-voltage distribution area containing 20 measurement nodes, when the air conditioning load at node A suddenly shuts down, the voltage at node A begins to rise at sampling number 5000, while the voltage change is only detected at sampling number 5003 at node B, which is electrically closer to node A. There is a time skew of 3 sampling cycles between the two. By traversing all node pairs, the system calculates the difference in the start time between each pair, which reflects the propagation characteristics of voltage fluctuations in the low-voltage network. Simultaneously, the number of sampling points required for different nodes to recover from the onset of a fluctuation also varies; nodes with greater electrical distances often require longer recovery times.

[0022] Preferably, the structured record is stored in triplet form, including a node pair identifier field to uniquely identify the combination relationship between two nodes, a start time difference field to record the time offset in units of sampling period, and a recovery time difference field to record the difference in the number of sampling points during the recovery process of the two nodes. By summarizing all possible node pair combinations within the distribution area, a complete time difference data set is formed, which contains the spatiotemporal characteristics of the load switching event propagating throughout the low-voltage distribution area.

[0023] S102. Based on the time difference data set, the nodes are grouped. The similarity between the start time difference and recovery time difference of the nodes in the group is evaluated. Cluster analysis is used to classify nodes with high similarity into the same electrical distance level to determine the hierarchical group set.

[0024] The start-time difference and recovery-time difference values ​​of all node pairs are extracted from the time difference dataset to construct inter-node difference feature vectors. Each vector contains two dimensions corresponding to the start-time difference and recovery-time difference, respectively. The distance between any two nodes and the reference node is calculated by taking the square root of the sum of the squares of the differences in the two dimensions. If the distances of the difference vectors of two nodes relative to the reference node are close, it indicates that the two nodes are at similar electrical distance levels, forming a similarity distance matrix between nodes. Based on the similarity distance matrix, the K-means clustering algorithm is used to group all nodes. The number of clusters is set to a preset number of levels. The cluster center positions are iteratively updated until the sum of the distances from each node to its respective cluster center is minimized, obtaining the node grouping results. Within each group, the variance of the inter-node difference feature vectors is calculated. If the variance exceeds a preset threshold, the group is further divided to determine the final node grouping. Based on the final node grouping, the average value of each dimension of the difference feature vector of all nodes in each group is calculated as the electrical distance feature identifier of that group. The groups are then sorted according to the magnitude of the difference dimension values ​​at the start time in their feature identifiers to determine the electrical distance hierarchy from near to far, and each group is assigned a corresponding hierarchy number. Each group is labeled with this hierarchy number, and the recovery time difference between nodes within the same hierarchy is verified to be within a preset range. If the recovery time difference between a node and other nodes within the same hierarchy exceeds a threshold, the hierarchy is reassigned based on the difference feature vector distance between that node and adjacent hierarchy levels. After adjustment, a hierarchy group set is formed.

[0025] Specifically, in one implementation, the time difference dataset includes the difference in start time and recovery time between all node pairs within the low-voltage distribution area. These two dimensions reflect the propagation characteristics of voltage fluctuations in the network. During the construction of the difference feature vector, each node forms a two-dimensional vector relative to a selected reference node. The first dimension represents the difference in sampling sequence number of the voltage fluctuation start time between the node and the reference node, and the second dimension represents the difference in the number of sampling points required for both to recover to a steady state. The reference node is typically selected as the measurement point at the transformer outlet, as it is located at the root node position in the topology.

[0026] Specifically, the similarity distance matrix is ​​constructed using the Euclidean distance metric. For node i and node j, their difference feature vectors are Vi=[ti,ri] and Vj=[tj,rj], respectively, where t represents the difference in start time and r represents the difference in recovery time. The distance between the two nodes is calculated as d(i,j)=sqrt((ti-tj)²+(ri-rj)²). This distance metric comprehensively reflects the similarity of two nodes in terms of time response characteristics. The smaller the distance value, the closer the electrical characteristics of the two nodes are, and they are likely to be in the same power supply branch or have similar electrical distances. By traversing all node pairs, a symmetric similarity distance matrix is ​​formed, where each element represents the electrical similarity between the corresponding node pairs.

[0027] It's important to note that the K-means clustering algorithm first determines the initial locations of the cluster centers when grouping nodes. The initial cluster centers are determined by uniformly selecting k points in the difference feature vector space. The value of k is set based on the typical hierarchical structure of low-voltage substations, typically ranging from 3 to 5 levels. The algorithm iteratively optimizes the locations of the cluster centers. Each iteration consists of two steps: first, assigning each node to the group containing the nearest cluster center; second, recalculating the mean of the difference feature vectors of all nodes within each group as the new cluster center. This iterative process continues until the locations of the cluster centers no longer change significantly or the preset maximum number of iterations is reached.

[0028] In one possible implementation, variance calculation within a group is used to assess the clustering degree of nodes within that group. For a group G containing n nodes, its variance σ² is calculated as the average of the squared distances between the difference feature vectors of all nodes within the group and the cluster centers of that group. When the variance exceeds a preset threshold, it indicates that the electrical characteristics of the nodes within that group vary significantly, requiring secondary partitioning. Secondary partitioning uses the same clustering method but only applies to the nodes within that group, further dividing them into two subgroups, thereby improving the accuracy of the grouping.

[0029] For example, in a low-voltage distribution area containing 30 measurement nodes, K-means clustering is used to form four initial groups. The first group contains 8 nodes, mainly located on the main line near the transformer outlet, with their initial time difference values ​​concentrated in the range of 0 to 5 sampling periods. The second group contains 10 nodes, distributed on the first-level branch lines, with initial time difference values ​​ranging from 6 to 15 sampling periods. The third and fourth groups correspond to more distant electrical distance levels. The electrical distance characteristic of each group is obtained by calculating the average of the difference feature vectors of all nodes within the group; this average vector represents the typical time response characteristics of that level.

[0030] Preferably, the allocation of hierarchical numbers follows the principle of electrical distance from near to far. The sorting is mainly based on the numerical value of the difference in the starting time dimension in the characteristic identifier of each group. The smaller the difference in the starting time, the smaller the hierarchical number the group receives, indicating that its electrical distance is closer. This sorting method conforms to the physical propagation law of voltage fluctuations in the power distribution network, that is, the closer the node is to the disturbance source, the earlier it will sense the voltage change.

[0031] Understandably, the hierarchical assignment verification and adjustment mechanism can handle the assignment of boundary nodes. Some nodes may be located at the boundary of two hierarchies, with their electrical characteristics falling between the two levels. The verification process judges the rationality of the assignment by calculating the difference in recovery time between a node and other nodes in the same hierarchical level. If the recovery time of a node differs significantly from that of most nodes in the same hierarchical level, exceeding the preset tolerance range, its hierarchical assignment needs to be reassessed. Furthermore, the reassignment decision is based on the distance between the node and the differential feature vector of adjacent levels. The distance between the differential feature vector of the node and the cluster centers of the previous and next levels is calculated, and the level with the smaller distance is selected as the new assignment. This dynamic adjustment mechanism ensures that each node is assigned to the most suitable electrical distance level, improving the accuracy of topology reconstruction. After the adjustment, all nodes have clear hierarchical identifiers, forming a hierarchical grouping set that reflects the electrical distance distribution characteristics of the low-voltage distribution area.

[0032] In one embodiment, after a load switching event occurs in a low-voltage distribution area, four electrical distance levels are identified using the method described above. The first level includes 5 nodes at the transformer outlet and on the main line; the second level includes 12 nodes on the first-level branches; the third level includes 8 nodes on the second-level branches; and the fourth level includes 5 nodes for end users. This hierarchical division result closely matches the actual physical topology, verifying the effectiveness of the node grouping and hierarchical division method based on time difference characteristics.

[0033] S103. Obtain the voltage fluctuation propagation delay value of each group in the hierarchical grouping set, identify the path with the shortest delay, and obtain a preliminary connection path diagram.

[0034] The average difference in start time of all nodes within each group is extracted from the hierarchical grouping set. The propagation delay between adjacent hierarchical groups is calculated. By comparing the difference in start time from each node in the upper level to each node in the lower level, the minimum difference is taken as the typical propagation delay between the hierarchical pairs. This process is repeated for all adjacent hierarchical pairs to form a sequence of delay values ​​arranged hierarchically. Based on this sequence of delay values, the node connection pair with the minimum delay in the lower level is identified within each level. Starting from the transformer outlet node, a connection is established with the node with the minimum delay value in the next lower level. This process is repeated for the connected node, selecting the node with the minimum delay in the next lower level, and so on until the last level, obtaining a set of minimum delay connection relationships across levels. Using this set of minimum delay connection relationships, connection paths from the transformer outlet node to each end node are constructed. The node sequence and cumulative delay value on each path are recorded, generating a preliminary connection path map containing node identifiers, upper-level node identifiers, and path delay values.

[0035] Specifically, in one implementation, the hierarchical grouping set has divided all nodes in the low-voltage distribution area into different levels according to electrical distance, with each level representing a group of nodes with similar electrical characteristics. The extraction process of the average start time difference involves statistically processing the time characteristics of all nodes within each group, and obtaining the typical time response value of the group by calculating the sum of the start time differences of the nodes within the group relative to the reference point and dividing it by the number of nodes.

[0036] Specifically, calculating the propagation delay between adjacent levels requires comparing nodes in both levels one by one. For levels k and (k+1), the difference in start time between each node in level k and each node in level (k+1) is iterated, and the minimum value is selected as the typical propagation delay between the two levels. This minimum value selection strategy reflects the physical characteristic of voltage fluctuations propagating along the shortest electrical path in the network. By performing this operation on all adjacent level pairs, a sequence of delay values ​​arranged in hierarchical order is formed, which describes the temporal characteristics of voltage fluctuations propagating from the transformer outlet to the end layer by layer.

[0037] It should be noted that the identification of minimum delay connections adopts a layer-by-layer approach. The transformer outlet node, as the power supply starting point for the entire low-voltage distribution area, first calculates the delay values ​​from it to all nodes in the second level, and selects the node with the smallest delay to establish a parent-child connection. For second-level nodes with established connections, the delays to each node in the third level are calculated, and the node with the smallest delay is again selected for connection. This greedy selection strategy ensures that the optimal connection scheme is chosen at each step. Although it does not guarantee global optimality, it can quickly obtain a reasonable topology in practical applications.

[0038] For example, in a certain low-voltage distribution area, there are 5 candidate nodes from the transformer outlet node to the second level, with delay values ​​of 3, 5, 4, 7, and 6 sampling periods, respectively. The algorithm selects the node with a delay of 3 sampling periods to establish a connection. When the selected node expands to the third level, there are 8 candidate nodes to choose from, and the node with the smallest delay value is selected for connection after comparison.

[0039] Preferably, the initial connection path diagram is stored using a tree data structure. Each node record contains three key fields: a unique identifier for the node itself, the identifier of its parent node, and the cumulative delay value from the root node to that node. The cumulative delay is obtained by accumulating the delay values ​​of each path segment layer by layer, reflecting the electrical distance position of the node in the entire power distribution network. This structured path diagram provides basic data support for subsequent topology optimization and anomaly detection.

[0040] S104. Based on the preliminary connection path diagram, optimize the processing path, analyze the differences in recovery time between nodes in the tree topology, and optimize the connection strength of the tree topology using a dynamic weight adjustment method to obtain the optimized tree topology.

[0041] Recovery time data for adjacent node pairs on each path is extracted from the initial connection path graph. The mean and standard deviation of the recovery time of all child nodes under the same parent node are calculated. If the difference between the recovery time of a child node and the mean exceeds twice the standard deviation, the node is marked as an abnormal recovery node. The ratio of normal recovery nodes to abnormal recovery nodes under each parent node is counted to form a node recovery feature distribution map. Based on the node recovery feature distribution map, each parent-child connection is assigned a weight value, which is equal to the ratio of the child node's recovery time to the parent node's recovery time. The cumulative weight product from the root node to each end node is calculated by traversing all paths. If the cumulative weight product exceeds a threshold determined according to the transformer area size, the path is identified as a weak connection path, and a set of weak connection paths that need adjustment is obtained. Using the set of weak connection paths, alternative parent nodes are re-searched for nodes on the weak connection paths. The node that minimizes the difference in child node recovery time is selected as the new parent node at the same level or the next higher level. The connection relationship is adjusted while maintaining the tree structure, and the parent-child node mapping table is updated to obtain the adjusted topology connection graph. Using the adjusted topology graph, verify whether each node has only one parent node and the root node has no parent node. Calculate the cumulative recovery time change on the path from each node to the root node before and after the adjustment. If all nodes satisfy the tree structure constraint and the cumulative recovery time change is within the allowable range, then the current topology is determined to be the optimized tree topology structure.

[0042] Specifically, in one implementation, the construction of the node recovery characteristic distribution map is based on statistical analysis of the recovery time of each node in the preliminary connection path map. Recovery time refers to the number of sampling periods a node experiences from the detection of a voltage fluctuation to the voltage returning to a stable state. Theoretically, the recovery times of all child nodes under the same parent node should be similar because they are located at similar electrical distances. By calculating the mean and standard deviation of these child node recovery times, the consistency of nodes within the group can be quantitatively assessed. The standard deviation reflects the dispersion of the recovery time; when the recovery time of a child node deviates from the mean by more than twice the standard deviation, it indicates that the node may have special load characteristics or connection anomalies and needs to be marked as an abnormal recovery node for focused attention.

[0043] Specifically, the weight values ​​are calculated using a ratio method to quantify the electrical correlation strength between parent and child nodes. The ratio of the child node's recovery time to the parent node's recovery time reflects the attenuation characteristics of voltage fluctuations propagating from the parent node to the child node. Normally, this ratio should be close to 1, indicating similar recovery characteristics between parent and child nodes. When the ratio deviates significantly from 1, it suggests that there may be long power supply lines or large impedances between parent and child nodes, leading to differences in voltage recovery characteristics. The cumulative weight product is calculated starting from the root node, multiplying the weight values ​​of each segment layer by layer along each path. The final cumulative value reflects the electrical transmission characteristics of the entire path. The threshold determination needs to consider the size of the transformer substation and the topology depth. Typically, the threshold for large transformer substations is set relatively high because the longer paths naturally increase the cumulative weight.

[0044] It is important to note that identifying weak connection paths is crucial for topology optimization. These paths typically exhibit abnormally high cumulative weight products, meaning that multiple connection segments along the path have large weight values, reflecting a significant change in voltage recovery characteristics during propagation. The existence of weak connection paths can be caused by various factors, including increased impedance due to line aging, exacerbated voltage drops due to uneven load distribution, or connection errors during initial topology construction. Identifying these weak connection paths provides clear optimization targets for subsequent topology adjustments, allowing resources to be focused on improving weak links in the network.

[0045] For example, in a low-voltage distribution area containing 50 measurement nodes, the preliminary connection path map showed that the cumulative weight product of 8 paths exceeded the threshold. Analysis of these weak connection paths revealed that the problems of 5 of these paths were mainly concentrated in the connection segments from the third to the fourth level, indicating that the topology of this area needs to be optimized.

[0046] In one possible implementation, the search for alternative parent nodes employs a local optimization strategy. For each node on a weakly connected path, the algorithm searches for potential alternative parent nodes among nodes at the same or higher level. The evaluation criterion for the search is minimizing the difference in recovery time between the child node and the new parent node, which ensures that the adjusted connection better reflects the actual electrical relationships. Limiting the search to adjacent levels is based on the physical constraints of low-voltage substations; connections spanning multiple levels are rare in practice. Once a more suitable parent node is found, the parent-child node mapping table is updated, and it is necessary to check whether the adjustment will lead to loops, ensuring that the tree structure is always maintained.

[0047] Preferably, the adjusted topology graph needs to undergo a rigorous verification process. Verification of tree structure constraints includes checking whether each non-root node has one and only one parent node, whether the root node has no parent node, and whether there are isolated nodes or loops. These constraints are fundamental requirements of tree topologies; violating any one of them will lead to logical errors in the topology structure.

[0048] Understandably, the change in cumulative recovery time reflects the actual effect of the topology adjustment. By comparing the cumulative recovery time on the path from each node to the root node before and after the adjustment, the degree of improvement can be quantitatively assessed. Ideally, the adjusted cumulative recovery time should decrease, indicating a more reasonable electrical distance between nodes and transformers. The allowable range needs to take into account measurement errors and normal load fluctuations, and is typically set to 10% to 20% of the original cumulative recovery time.

[0049] For example, after topology optimization, six of the original eight weak connection paths in a low-voltage distribution area were improved, with their cumulative weight products decreasing below a threshold. The remaining two paths could not be further optimized due to physical line limitations, but their cumulative recovery times remained within acceptable limits. The average cumulative recovery time for the entire distribution area decreased by 15%, indicating that the topology optimization was effective. Furthermore, the optimized tree topology provides an accurate network model for the operation and management of the low-voltage distribution area. This structure clearly shows the power supply relationships and electrical distance distribution between nodes, facilitating fault location, load balancing, and network expansion.

[0050] S105. Extract the distance values ​​between nodes through the optimized tree topology, match the distance values ​​with the actual connection relationship, use error analysis to identify mismatches and iteratively adjust the grouping of nodes to determine the electrical distance distribution.

[0051] The optimized tree topology is traversed, and the number of connection segments along the path from the node to the root node is calculated as the topological distance. Simultaneously, the cumulative propagation delay along this path is extracted as the temporal distance. A two-dimensional distance vector containing both topological and temporal distances is constructed for each node, and the distance vectors of all nodes are aggregated to form a node distance matrix. Based on this node distance matrix, the actual connection relationships recorded in the low-voltage distribution area circuit diagram are obtained. The topological distance of each node is compared with the number of branch levels to the transformer in the circuit diagram, and the difference between the two is calculated as the topological error. If the topological error exceeds a preset tolerance value, the node is marked as an error node. All error nodes and their error values ​​are counted to form an error node set. Using this error node set, the level of each error node is reassessed. Based on the node's temporal distance value and the hierarchical affiliation of adjacent nodes, the level is reassigned by comparing the node with the average temporal distance of each level. After adjustment, the node's topological distance is recalculated. If the new topological error is less than the original error, the adjustment result is retained, resulting in the iteratively adjusted node level allocation; otherwise, the original level affiliation is restored, completing one round of iterative adjustment. Using the iteratively adjusted node hierarchy allocation, the error calculation and hierarchy adjustment process is repeated until the topology error of all nodes is within the tolerance range or reaches the preset iteration upper limit. The number of nodes and average time distance of each level are counted to determine the electrical distance distribution.

[0052] Specifically, in one implementation, the construction of the node distance matrix needs to consider both topological structure and temporal characteristics. The topological distance is obtained by traversing the tree structure using a depth-first search algorithm, starting from each node and traversing upwards to the root node, recording the number of connection segments traversed. This value directly reflects the node's hierarchical position in the power distribution network; the topological distance to the root node is 0, the topological distance to a child node directly connected to the root node is 1, and so on. The temporal distance is calculated by accumulating the propagation delay values ​​of each segment along the same path; these delay values ​​have already been obtained through voltage fluctuation analysis in the preceding steps. The construction of the two-dimensional distance vector ensures that each node has a unique location identifier, encompassing both structural and electrical characteristic information.

[0053] Specifically, the actual connection relationships are typically obtained from the design drawings of the low-voltage distribution area or the line files in the operation and maintenance management system. These records contain physical connection information from the transformer to each distribution box, and from the distribution box to the user's meter box, clearly indicating the number of branch levels for each node in the actual line. The number of branch levels refers to the number of branches required to reach the node from the transformer outlet. Theoretically, the topology distance obtained through topology reconstruction should be consistent with the actual number of branch levels. However, due to measurement errors, load changes, or deviations in the initial topology construction, there are often differences between the two. The topology error is calculated using a simple difference method. When the difference between the topology distance of a node and the actual number of branch levels exceeds the tolerance value, it indicates that the topology location of that node may be incorrect and needs to be adjusted.

[0054] It's important to note that the core of hierarchical reassessment lies in finding the correct affiliation of nodes. For each error node, the algorithm first extracts its time distance value, then calculates the average time distance across all levels. The average time distance is the arithmetic mean of the time distances of all normal nodes within that level, representing the typical electrical characteristics of that level. By comparing the time distance of the error node with the average time distance of each level, it's possible to determine which level the node is more likely to belong to. The degree of proximity is measured using the absolute difference, and the level with the smallest difference is selected as the node's new affiliation. Simultaneously, the hierarchical relationship between adjacent nodes must be considered to avoid logical errors such as a child node being at a higher level than its parent node.

[0055] For example, in a certain iterative adjustment, a node originally assigned to the third level had a topological distance of 3, but its actual branch level was 2, resulting in a topological error of 1 unit. Analysis revealed that the node's time distance was 15 sampling periods, while the average time distance for the second level was 14 sampling periods, and for the third level, it was 22 sampling periods. Clearly, the node's time characteristics were closer to those of the second level, so it was reassigned to the second level. After adjustment, the topological distance was recalculated, and the new topological distance became 2, consistent with the actual branch level, reducing the topological error to 0.

[0056] In one possible implementation, the convergence criterion for the iterative process employs a dual standard. The first standard is that the topology error of all nodes is within the tolerance range, typically set to 1, allowing the topology distance to differ from the actual branch level by one level. This tolerance setting considers special connection situations that may exist in actual lines, such as the presence of emergency power supply lines or ring main units. The second standard is reaching a preset iteration limit, usually set to 10 times, to prevent the algorithm from falling into an infinite loop. After each iteration, the number of erroneous nodes and the total error value are counted. If the improvement in two consecutive iterations is less than a preset threshold, the iteration can be terminated early.

[0057] Preferably, determining the electrical distance distribution includes not only statistical analysis of the number of nodes at each level, but also extraction of level characteristics. The average time distance at each level reflects the typical transmission delay of that level, and the standard deviation reflects the dispersion of nodes within that level. The distance difference between levels reflects the electrical spacing between adjacent levels. These statistical information collectively constitute the electrical distance distribution characteristics of the low-voltage distribution area, providing a quantitative basis for network optimization and fault diagnosis.

[0058] Understandably, through multiple rounds of iterative adjustments, the hierarchical assignment of nodes gradually becomes more reasonable, and the matching degree between the topology and actual physical connections continuously improves. A certain low-voltage distribution area contains 60 measurement nodes, and in the initial topology, 12 nodes had topology errors. After five rounds of iterative adjustments, the number of error nodes was reduced to three, and the errors of these three nodes were all within the tolerance range. The final determined electrical distance distribution shows that the first level contains 5 nodes, the second level has 18 nodes, the third level has 25 nodes, and the fourth level has 12 nodes, exhibiting a typical tree-like expansion characteristic. Furthermore, the determined electrical distance distribution can intuitively demonstrate the power supply structure characteristics of the low-voltage distribution area, identify weak links and optimization space in the network, and provide a scientific basis for subsequent network transformation and expansion planning.

[0059] S106. Obtain the connection strength values ​​of each node in the electrical distance distribution, construct the connection relationship of each node, filter out the noise influence through data filtering, and obtain an accurate connection relationship diagram.

[0060] The connection strength value between each node and its parent node is extracted from the electrical distance distribution. The connection strength value is equal to the reciprocal of the difference in recovery time between the parent and child nodes. All parent-child node pairs are traversed to construct an initial connection relationship table containing node identifiers, parent node identifiers, and connection strength values. A smaller difference indicates a larger connection strength value and a tighter connection. Based on this initial connection relationship table, records with abnormal connection strength values ​​are identified. If the connection strength value is lower than the mean of all strength values ​​minus two standard deviations or higher than the mean plus two standard deviations, it is marked as a noisy connection. The number of noisy connections for each node is counted. For nodes with more than a preset number of noisy connections, their connection relationships with other nodes are checked to see if they are within a reasonable range, thus obtaining a set of noisy connections to be filtered. Using this set of noisy connections, the connection strength values ​​marked as noisy are corrected by replacing the noise values ​​with the average of the other normal connection strength values ​​for that node. The strength values ​​in the connection relationship table are updated, and isolated noisy connection records for which no normal reference value can be found are removed, resulting in a refined connection relationship graph.

[0061] Specifically, in one implementation, the connection strength value is calculated based on the relative relationship between the recovery times of the parent and child nodes. The recovery time difference is obtained by subtracting the parent node's recovery time from the child node's recovery time; this difference reflects the time delay characteristic of voltage fluctuations propagating from the parent node to the child node. The connection strength value is defined as the reciprocal of this difference plus an offset constant, the introduction of which avoids calculation anomalies when the difference is zero. The smaller the difference, the tighter the electrical coupling between the parent and child nodes, and the larger the corresponding connection strength value.

[0062] Specifically, the initial connection table uses a triplet structure to store each connection entry. Node identifiers employ a unique numbering system within the low-voltage distribution area, typically corresponding to the actual meter box number or distribution box number. The parent node identifier points to the upstream power supply node of that node, with the parent node identifier of the root node set to null. Connection strength values ​​are retained to three decimal places to ensure the accuracy of subsequent analysis.

[0063] It should be noted that noisy connections are identified using outlier detection methods from statistics. First, the mean and standard deviation of all connection strength values ​​are calculated; these two statistics describe the central tendency and dispersion of connection strength. According to the 3σ rule of the normal distribution, more than 99.7% of normal data should fall within the range of the mean plus or minus three standard deviations. In practical applications, two standard deviations are used as the criterion, which effectively identifies outliers while avoiding excessive removal of boundary data.

[0064] For example, if the mean connection strength value of a low-voltage distribution area is 0.85 and the standard deviation is 0.12, then the normal range is 0.61 to 1.09. When the strength value of a connection is 0.45, which is below the lower limit of 0.61, it is marked as a noisy connection. For nodes with multiple noisy connections, it is necessary to further verify the rationality of their connection relationships to avoid misjudging normal but unusual connection situations.

[0065] Preferably, the noise value correction uses the neighborhood averaging method. For a connection strength value marked as noise, other connection strength values ​​of the node that are not marked as noise are extracted, and the arithmetic mean of these normal values ​​is calculated as the replacement value. This method maintains the local consistency of node connection characteristics. If all connections of a node are marked as noise, the node is identified as an isolated noise node, its connection records are removed from the relation table, and its topological position needs to be re-determined through other methods.

[0066] In one embodiment, after noise filtering, the distribution of connection strength values ​​in the refined connection graph is more concentrated, and the number of abnormal connections is reduced from the initial 15 to 2, thereby improving the reliability and accuracy of the topology.

[0067] S107. Based on the precise connection diagram, update the new voltage fluctuation data under the dynamic load scenario in real time, use anomaly detection to identify the difference in the start time of the new data and the inconsistency with the existing connection diagram, and trigger the topology reconstruction process to obtain the updated low-voltage distribution area topology reconstruction results.

[0068] Based on the refined connection diagram, the voltage values ​​of each node in the low-voltage distribution area are continuously monitored. When a voltage fluctuation caused by a new load switching event is detected, the start time and recovery time of the fluctuation for each node are recorded. The difference in the start time of each node pair in the new data is calculated. The historical difference value of the corresponding node pair in the refined connection diagram is subtracted from the new difference value to obtain the difference deviation sequence. The box plot method is used to identify outliers in the difference deviation sequence. The first quartile and third quartile of all deviations are calculated. The interquartile range is equal to the third quartile minus the first quartile. If the deviation of a node pair exceeds the third quartile plus the interquartile range multiplied by a preset coefficient, it is determined to be an abnormal deviation. The number of abnormally deviated node pairs is counted. If the number exceeds a preset proportion of the total number of node pairs, the topology reconfiguration flag is set to true. Based on the state where the topology reconstruction flag is true, the processing flow of the aforementioned steps is invoked, including the iterative processes of constructing the time difference data set, node grouping, hierarchical division, path optimization, and distance matching. Topology identification is re-executed based on newly acquired voltage fluctuation data to obtain a new topology structure. The new topology is compared with the original topology to identify changed connection relationships. Using these changed connection relationships, the corresponding node connection records in the refined connection relationship graph are updated, stable connections that have not changed are retained, newly identified connection relationships are merged, and the update time and list of changed nodes are recorded to form the updated low-voltage distribution area topology reconstruction result.

[0069] Specifically, in one implementation, the dynamic update mechanism for the low-voltage distribution area topology is based on continuous monitoring and real-time analysis of voltage fluctuation characteristics. A precise connection diagram serves as a reference, storing the standard connection relationships and time characteristic parameters between nodes in the distribution area under normal operating conditions. When new load switching, line reconnection, or equipment failure occurs in the low-voltage distribution area, it causes changes in the voltage fluctuation pattern. These changes can be identified promptly by comparing them with the reference. The deviation is calculated using the absolute difference method, that is, subtracting the standard difference value of the corresponding node pair in the historical record from the newly acquired difference value at the starting time. The resulting deviation reflects the degree of deviation between the current topology and the standard topology.

[0070] Specifically, box plots, as a classic statistical anomaly detection method, exhibit good robustness in identifying outliers. The first quartile represents the value at the 25th percentile after sorting all deviation data from smallest to largest, and the third quartile represents the value at the 75th percentile. The difference between the two is the interquartile range, reflecting the dispersion of the data. The preset coefficient is usually set to 1.5, a commonly used outlier criterion in statistics. When the deviation of a node pair exceeds the third quartile plus 1.5 times the interquartile range, it means that the deviation significantly deviates from the normal range, likely due to an actual change in the topology rather than measurement error.

[0071] It's important to note that the design of the topology reconfiguration trigger mechanism needs to balance sensitivity and stability. If the triggering conditions are too lenient, it will lead to frequent and unnecessary reconfigurations, consuming significant computational resources; if the conditions are too strict, it may miss genuine topology changes, affecting the system's accuracy. The preset percentage is typically set considering the size and complexity of the distribution area. For large distribution areas with more than 50 nodes, the percentage can be set to 10%, meaning reconfiguration is triggered when the number of abnormally deviating node pairs exceeds 10% of the total. For small distribution areas, the percentage can be appropriately increased to 15% or 20% to avoid false triggers caused by individual anomalies. When the topology reconfiguration flag is set to true, it indicates that the system determines the current topology structure has likely undergone substantial changes, requiring a complete reconfiguration of the topology.

[0072] For example, during normal operation of a low-voltage distribution area, the difference in start time between node A and node B remains stable at 8 sampling periods. After a line reconnection, newly acquired data shows that this difference becomes 12 sampling periods, with a deviation of 4 sampling periods. If the calculated third quartile is 2 and the interquartile range is 1, then the anomaly detection threshold is 2 + 1.5 × 1 = 3.5. Since the deviation of 4 exceeds the threshold of 3.5, this node pair is marked as having an abnormal deviation.

[0073] In one possible implementation, the process of re-performing topology identification does not simply repeat the aforementioned steps, but rather performs incremental updates using existing partial information. The system first identifies which nodes' connections may have changed; these nodes are typically those involved in abnormally deviating node pairs. Then, it focuses on regrouping and hierarchically classifying these nodes and their adjacent nodes, while maintaining the original topological positions of stable nodes that are not affected. This incremental update method significantly reduces computational load and improves system response speed. The comparison between the old and new topologies is achieved by comparing connections one by one. Each connection includes three elements: parent node, child node, and connection strength; any change in any of these elements is considered a change in the connection.

[0074] Preferably, the list of changed nodes is recorded in a time-series format, with each topology update recording the update time, change type, involved nodes, and reason for the change. Change types include adding connections, deleting connections, and modifying connection strength. This detailed change record provides crucial historical data support for subsequent topology evolution analysis and fault diagnosis.

[0075] Understandably, the updated low-voltage distribution area topology reconfiguration results not only include the latest network structure information but also retain the trajectory of topology changes. By analyzing these change trajectories, weak links and frequently changing areas within the distribution area can be identified, providing guidance for network optimization and equipment maintenance. After a month of continuous monitoring, a certain low-voltage distribution area triggered five topology reconfigurations, three of which were due to temporary load connections and two were due to emergency adjustments following line faults. Analysis of these reconfiguration records revealed frequent changes in the downstream connections of a certain distribution box; further inspection revealed loose wiring terminals in the distribution box. Furthermore, the implementation of the dynamic update mechanism allows the low-voltage distribution area topology to adapt to real-time network changes, maintaining the accuracy and timeliness of topology information and providing reliable basic data support for intelligent management of the distribution network.

[0076] The above embodiments are merely one of the preferred embodiments of the present invention and should not be used to limit the scope of protection of the present invention. Any modifications or refinements made to the main design concept and spirit of the present invention that are not of substantial significance, but solve the same technical problem as the present invention, should be included within the scope of protection of the present invention.

Claims

1. A method for topology reconstruction of low-voltage distribution areas based on synchronous measurement data, characterized in that, include: The system collects voltage value records of each node based on synchronous measurement data without time calibration from the measurement equipment, detects the start and end points of voltage fluctuations during dynamic load switching events, identifies the differences in start time and recovery time between nodes through relative time sequence comparison, and constructs a time difference data set. Based on the time difference data set, the nodes are grouped, and the similarity of the differences in start time and recovery time among the nodes in the group is evaluated by cluster analysis. Nodes with high similarity are classified into the same electrical distance level to generate a hierarchical group set. Extract the voltage fluctuation propagation delay value of each group from the hierarchical grouping set, identify the path with the minimum delay, and generate a preliminary connection path map; Based on the preliminary connection path diagram, the differences in recovery time between nodes in the tree topology are analyzed, and the connection strength is optimized by dynamic weight adjustment to generate the optimized tree topology. The distance values ​​between nodes are extracted from the optimized tree topology, matched with the actual connection relationships, and the node grouping is iteratively adjusted through error analysis to generate the electrical distance distribution. Node connection strength values ​​are extracted from the electrical distance distribution to construct connection relationships, and a precise connection relationship diagram is generated through data filtering. Based on the refined connection diagram, new voltage fluctuation data is monitored, and inconsistencies between the start time difference and the existing connection diagram are detected, triggering topology reconstruction and generating updated low-voltage distribution area topology reconstruction results.

2. The low-voltage distribution area topology reconstruction method based on synchronous measurement data according to claim 1, characterized in that, The method involves collecting voltage value records from each node based on synchronous measurement data without time calibration from the measuring device, detecting the start and end points of voltage fluctuations during dynamic load switching events, identifying differences in start times and recovery times between nodes through relative time sequence comparison, and constructing a time difference data set, including: The high-frequency sampling module of the low-voltage distribution area measurement equipment acquires the voltage sampling sequence of each node, records the voltage value and sampling number, calculates the voltage change rate between adjacent sampling points, marks the sampling number where the voltage change rate exceeds the preset change rate threshold for three consecutive sampling points as the fluctuation start point, and continues to monitor until the voltage change rate is lower than the preset change rate threshold and remains stable for five sampling cycles, which is then marked as the fluctuation end point, generating a fluctuation period marking sequence for each node. The high-frequency sampling module samples at a preset sampling frequency. Based on the fluctuation period marker sequence, the sampling sequence number of the fluctuation start point of each node is extracted, the difference between the sampling sequence numbers of adjacent nodes is calculated as the relative time offset, the number of sampling points from the start point to the end point is calculated as the recovery time value, all node pairs are traversed, and a structured record containing the node pair identifier, the difference value of the start time and the difference value of the recovery time is generated, and the time difference data set is summarized.

3. The low-voltage distribution area topology reconstruction method based on synchronous measurement data according to claim 1, characterized in that, The process involves grouping nodes based on the time difference data set, evaluating the similarity of start time and recovery time differences among nodes within a group using cluster analysis, and classifying nodes with high similarity into the same electrical distance level to generate a hierarchical grouping set, including: Extract the start time difference value and recovery time difference value of the node pair from the time difference data set, construct the difference feature vector, calculate the distance value between the difference vector of the node and the reference node using the Euclidean distance formula, and form a similarity distance matrix; Based on the similarity distance matrix, the K-means clustering algorithm is used to group the nodes, iteratively updating the cluster centers until the sum of distances is minimized, and generating node groups. The number of clusters in the K-means clustering algorithm is preset according to the typical hierarchical structure of the low-voltage distribution area. The average value of the difference feature vector within each group is calculated as the electrical distance feature identifier. The groups are sorted according to the difference values ​​at the start time to determine the electrical distance hierarchy order and assign a hierarchy number. Verify the difference in recovery time between nodes within the same level. If the difference exceeds the threshold, redistribute the nodes based on the difference vector distance between adjacent levels to generate a set of level groups.

4. The low-voltage distribution area topology reconstruction method based on synchronous measurement data according to claim 1, characterized in that, The step of extracting the voltage fluctuation propagation delay value of each group from the hierarchical grouping set, identifying the path with the shortest delay, and generating a preliminary connection path map includes: Extract the average difference in the starting time of nodes within each group from the hierarchical grouping set, calculate the propagation delay between adjacent levels, take the minimum difference value as the typical propagation delay, and generate a delay value sequence. Based on the delay value sequence, starting from the transformer outlet node, the node connection with the smallest delay in the next level is identified, and the process is repeated until the last level to generate a set of minimum delay connection relationships. Based on the set of minimum delay connections, construct the connection path from the root node to the end node, record the node sequence and cumulative delay value, and generate a preliminary connection path graph.

5. The low-voltage distribution area topology reconstruction method based on synchronous measurement data according to claim 1, characterized in that, The step of analyzing the differences in recovery time between nodes in the tree topology based on the preliminary connection path diagram, optimizing the connection strength using dynamic weight adjustment, and generating an optimized tree topology includes: Recovery time data of adjacent node pairs are extracted from the preliminary connection path diagram. The mean and standard deviation of the recovery time of child nodes under the same parent node are calculated. Nodes with a difference exceeding twice the standard deviation are marked as abnormal recovery nodes. The ratio of normal to abnormal nodes is statistically analyzed to form a node recovery feature distribution map. Based on the node recovery feature distribution map, parent-child connection weight values ​​are assigned, the cumulative weight product from the root node to the end node is calculated, and weak connection paths exceeding the preset cumulative threshold are identified. The preset cumulative threshold is determined according to the scale of the low-voltage distribution area. For the weak connection path, search again for the parent node that minimizes the difference in recovery time of the child node in the same or higher level nodes, adjust the connection relationship, update the parent-child node mapping table, and generate an optimized tree topology.

6. The low-voltage distribution area topology reconstruction method based on synchronous measurement data according to claim 5, characterized in that, The process of extracting distance values ​​between nodes from the optimized tree topology, matching actual connection relationships, iteratively adjusting node groupings through error analysis, and generating an electrical distance distribution includes: Traverse the nodes from the optimized tree topology, calculate the number of connection segments to the root node as the topological distance, extract the cumulative propagation delay value as the temporal distance, construct a two-dimensional distance vector, and generate a node distance matrix. Based on the node distance matrix, the number of branch levels in the actual connection relationship is compared to calculate the topology error, and error nodes that exceed the preset tolerance value are marked, where the topology error = |topology distance - actual number of branch levels|; The error node is re-evaluated and its level is adjusted according to the time distance and the average level of adjacent levels. The adjustment result of reducing the topology error is retained. The process is iterated until the error is within the tolerance range or reaches the preset iteration limit, and an electrical distance distribution is generated.

7. The low-voltage distribution area topology reconstruction method based on synchronous measurement data according to claim 6, characterized in that, The step of extracting node connection strength values ​​from the electrical distance distribution, constructing connection relationships, and generating a precise connection relationship graph through data filtering processing includes: The connection strength value between parent and child nodes is extracted from the electrical distance distribution, and an initial connection relationship table is constructed based on the connection strength value, where the connection strength value = 1 / (difference in recovery time between parent and child nodes + 1); Based on the initial connection relationship table, identify noisy connections whose connection strength values ​​exceed the mean plus or minus two standard deviations, count the number of noisy connections, verify the rationality of node connection relationships, and generate a set of noisy connections. Based on the set of noisy connections, the noise connection strength values ​​are corrected and replaced with the average value of the normal connection strength values. Isolated noise connections are removed, and an accurate connection relationship graph is generated. Here, an isolated noise connection refers to a connection where all connections of the node are marked as noise and no normal connection strength reference value can be found.

8. The low-voltage distribution area topology reconstruction method based on synchronous measurement data according to claim 7, characterized in that, The process of monitoring new voltage fluctuation data based on the refined connection diagram, detecting inconsistencies between the starting time difference and the existing connection diagram, triggering topology reconstruction, and generating updated low-voltage distribution area topology reconstruction results includes: Based on the refined connection diagram, monitor the voltage fluctuations of each node, record the start time and recovery time of the new load switching event, calculate the difference in start time between node pairs, subtract the historical difference value in the refined connection diagram, and generate a difference deviation sequence. Based on the difference deviation sequence, the first quartile, the third quartile, and the interquartile range of the difference deviation are calculated using the box plot method. If the deviation exceeds a preset value, it is determined to be an abnormal deviation. The number of abnormal node pairs is counted. If it exceeds the proportion threshold, topology reconstruction is triggered. The proportion threshold is determined according to the scale of the low-voltage distribution area. The time difference data set construction, node grouping, hierarchical division, path optimization and distance matching are re-executed to generate a new topology, update the refined connection relationship graph, record the changed nodes, and generate the updated low-voltage transformer area topology reconstruction result.

9. The low-voltage distribution area topology reconstruction method based on synchronous measurement data according to claim 1, characterized in that, The time-calibration-free synchronous measurement data also includes: The measuring devices at each node do not rely on absolute timestamps; they only record the voltage value and the corresponding sampling sequence number. The synchronization is achieved by ensuring that the difference in sampling sequence numbers between adjacent nodes is less than or equal to a preset sampling period, thus achieving relative timing alignment. The sampling period is determined based on the high-frequency sampling module of the measuring device.

10. The low-voltage distribution area topology reconstruction method based on synchronous measurement data according to claim 1, characterized in that, The optimization logic for dynamic weight adjustment also includes: The adjusted tree topology must satisfy the tree structure constraints that each non-root node has one and only one parent node, the root node has no parent node, and the cumulative recovery time change on the path from each node to the root node before and after the adjustment must be within the allowable range. The allowable range is set based on the original cumulative recovery time.

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