A topological structure fast identification method for real-time operation of a power distribution network

By preprocessing multi-source data and improving WLS state estimation, combined with dynamic weight allocation and topology error calculation, the distribution network topology can be quickly identified, solving the problems of low accuracy and efficiency in existing technologies and realizing the need for real-time control.

CN122000891BActive Publication Date: 2026-07-24ELECTRIC POWER RES INST OF STATE GRID ZHEJIANG ELECTRIC POWER COMAPNY
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
ELECTRIC POWER RES INST OF STATE GRID ZHEJIANG ELECTRIC POWER COMAPNY
Filing Date
2026-04-10
Publication Date
2026-07-24

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Abstract

The application discloses a kind of topological structure fast identification methods for distribution network real-time operation, the method comprises: obtaining the multi-source measurement data of multiple data sources in distribution network, and the effective measurement data is obtained by pre-processing the multi-source measurement data;Based on the on-off state of switch equipment of distribution network, generate candidate topology set;Each candidate topology in the candidate topology set is estimated to obtain state estimation value;Calculate the topology error between the state estimation value of each candidate topology and the corresponding measurement value in the effective measurement data;Based on the topology error, filter out effective topology from candidate topology set as the operation topology of distribution network at current time.According to the scheme of the application, the accuracy and efficiency of distribution network topology identification are effectively improved.
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Description

Technical Field

[0001] The present invention relates to the technical field of distribution network topology structure identification, and specifically to a fast identification method for the topology structure for the real-time operation of the distribution network. Background Art

[0002] As a key link connecting the transmission network and users in the power system, the topology structure of the distribution network directly affects the accuracy of core regulation services such as fault location, load transfer, and power flow calculation. With the large-scale access of distributed power sources and the rapid growth of new loads, the topology structure of the distribution network has become increasingly complex, showing the characteristics of frequent switching and diverse states. Accurately and real-time grasping the actual operating topology of the distribution network is the basis for realizing advanced applications such as power flow calculation, fault location, and load transfer. Traditional topology identification methods relying on manual experience or offline modeling can no longer meet the real-time regulation requirements.

[0003] The existing distribution network faces the following challenges:

[0004] 1. Insufficient data sparsity and real-time performance: Compared with the transmission network, the distribution network has a lack of measurement points, and partially relies on high-precision devices such as synchronized phasor measurement units (PMUs). However, the deployment density of PMUs in the distribution network is low, making it difficult to comprehensively cover complex feeders. The measurement data collected by systems such as SCADA / AMI has a large granularity or poor real-time performance, resulting in traditional state estimation methods being difficult to accurately perform topology identification in distribution networks without redundant measurements.

[0005] 2. Topology dynamic changes: The switching of distributed power sources, the fluctuation of loads, and fault isolation and reconstruction operations make the topology structure of the distribution network change dynamically and frequently. Traditional topology identification methods relying on static switch information are prone to failure or delay.

[0006] 3. Algorithm efficiency: For complex feeders, the number of possible switch combinations is huge, resulting in the "combinatorial explosion" problem in topology reconstruction and identification. Traditional exhaustive methods or optimization algorithms are difficult to meet the timeliness requirements of the distribution network for minute-level rapid response. When the traditional weighted least squares method (WLS) is used for state estimation, the measurement weights are fixed, unable to adapt to the credibility differences of multi-source data in SCADA / AMI, and not optimized for the topology characteristics of complex feeders, making it difficult to balance the identification accuracy and speed.

[0007] Therefore, there is an urgent need for a method that can solve the problems of poor accuracy and low efficiency in the existing distribution network topology identification. Summary of the Invention

[0008] To solve the above technical problems of poor accuracy and low efficiency in the existing distribution network topology identification, the present invention provides a fast identification method for the topology structure for the real-time operation of the distribution network, so as to effectively improve the accuracy and efficiency of the distribution network topology identification.

[0009] To this end, the present invention adopts the following technical solution: A fast identification method for the topological structure for the real-time operation of a distribution network, which includes: obtaining multi-source measurement data of multiple data sources in the distribution network, and preprocessing the multi-source measurement data to obtain effective measurement data; generating a candidate topology set based on the on-off states of the switching devices in the distribution network, where the candidate topology set contains multiple candidate topologies; performing state estimation on each candidate topology in the candidate topology set to obtain state estimation values; the state estimation includes a calculation process based on the weighted least squares method, and its weight coefficient is determined according to the variance of the corresponding measurement data; calculating the topological error between the state estimation value of each candidate topology and the corresponding measured value in the effective measurement data; screening out effective topologies from the candidate topology set based on the topological error as the operating topology of the distribution network at the current moment.

[0010] Preferably, preprocessing the multi-source measurement data includes: removing abnormal data using the 3σ criterion; normalizing data with different dimensions; and complementing missing data using the linear interpolation method.

[0011] Preferably, generating the candidate topology set includes: dividing the complex feeder scenario into multiple partitions by region, and generating local candidate topologies for each partition; combining the local candidate topologies through the on-off combinations of the inter-region tie switches to form a global candidate topology set.

[0012] Preferably, the state estimation further includes: constructing a state estimation model, where the state estimation model includes the following elements: state variables: node voltage amplitude and phase angle; constraint conditions: power flow equations, branch power constraints, and equipment capacity limits.

[0013] Preferably, the calculation method of the weight coefficient is as follows:

[0014]

[0015] In the formula, is the weight coefficient of the i-th measurement data, is the variance of the i-th measurement data. The accuracy of state estimation is improved by dynamic weights.

[0016] Preferably, the calculation method of the topological error is as follows:

[0017]

[0018] In the formula, is the topological error, is the weight of the i-th measurement data, is the i-th actual measured value, is the i-th measured value calculated based on the state estimation result.

[0019] Preferably, the method further includes: performing power flow calculation verification on the screened effective topology; in response to passing the verification, confirming the effective topology as the operating topology at the current moment; in response to failing the verification, selecting the topology with the second smallest topological error from the remaining candidate topologies as the new effective topology and performing power flow calculation verification until the verification passes.

[0020] Preferably, the method further includes: continuously collecting the multi-source measurement data, and repeatedly executing all the steps in one or more of the foregoing technical solutions to achieve dynamic update of the distribution network operating topology.

[0021] Preferably, the determination of the weight coefficient further includes: assigning a weight coefficient with a value range of 0.8 to 1.0 to the SCADA system data; assigning a weight coefficient with a value range of 0.6 to 0.9 to the AMI system data.

[0022] Preferably, screening out the effective topology from the candidate topology set includes: determining the candidate topology with the smallest topological error as the effective topology.

[0023] The beneficial effects of the present invention are as follows: According to the solution of the present invention, based on multi-source system data, without the need to deploy additional high-precision monitoring equipment, it can be directly applied to complex feeder scenarios. The combinatorial explosion problem is solved by generating candidate topologies by partitioning, the search range is reduced by eliminating invalid topology combinations, and the state estimation efficiency is improved by combining the improved WLS to achieve rapid identification of the topological structure and meet the real-time regulation requirements. The present invention also optimizes the WLS algorithm by adopting dynamic weight assignment to adapt to the credibility differences of multi-source data, and combines the effectiveness verification step to ensure the accuracy and security of the identification results.

[0024] Furthermore, the present invention supports continuous update based on real-time data, can quickly adapt to the dynamic changes of the distribution network topology, and provides real-time and reliable topological support for services such as fault handling and load transfer.

[0025] Furthermore, the present invention also quickly locks the true topology from the candidate set by using the principle of error minimization, and its calculation efficiency is higher than traditional topology identification models based on complex optimization or deep learning, and can meet the requirements of the distribution network for real-time update and rapid response. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] By reading the following detailed description with reference to the accompanying drawings, the above and other objects, features and advantages of the exemplary embodiments of the present invention will become readily understood. In the drawings, several embodiments of the present invention are shown in an exemplary and non-limiting manner, and the same or corresponding reference numerals represent the same or corresponding parts, wherein:

[0027] Figure 1It is a flowchart showing a method for quickly identifying the topology structure for the real-time operation of a distribution network according to an embodiment of the present invention;

[0028] Figure 2 It is a schematic diagram showing the process of identifying the topology structure of a certain power grid by applying the method of the present invention. Detailed implementation manners

[0029] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative efforts shall fall within the protection scope of the present invention.

[0030] Next, the detailed implementation manners of the present invention will be described in detail in conjunction with the accompanying drawings.

[0031] Figure 1 It is a flowchart showing a method 100 for quickly identifying the topology structure for the real-time operation of a distribution network according to an embodiment of the present invention.

[0032] As Figure 1 shown, at step S101, multi-source measurement data of multiple data sources in the distribution network is obtained, and the multi-source measurement data is preprocessed to obtain effective measurement data. In some embodiments, real-time measurement data such as branch currents and key node voltages of the distribution network are collected through the SCADA system, and user-side voltage and current data are collected through the AMI system, and a multi-source measurement data set is formed by integration. The preprocessing of the multi-source measurement data includes: abnormal data is excluded using the 3σ criterion to avoid interference of abnormal data on the recognition result. Normalization processing is performed on data with different dimensions. For example, voltage and current data with different dimensions can be normalized to unify the data range. In response to data missing problems, the linear interpolation method is used to complete the missing data to ensure the integrity of the input data.

[0033] At step S102, a candidate topology set is generated based on the on / off states of the distribution network switchgear. The candidate topology set contains multiple candidate topologies. In some embodiments, generating the candidate topology set includes: dividing the complex feeder scenario into multiple partitions by region and generating local candidate topologies for each partition; combining the local candidate topologies through the on / off combinations of the inter-region tie switches to form a global candidate topology set. Specifically, based on the physical characteristics and on / off constraints of the distribution network switchgear (including sectionalizing switches and tie switches), all possible switch on / off combinations are traversed. Combining with the core requirement of radial operation of the distribution network, invalid combinations that do not conform to safety rules such as closed-loop operation and isolated nodes are excluded to generate the candidate topology set. For complex feeder scenarios, candidate topologies for each partition are generated according to the feeder partitions, and then a global candidate topology set is formed through the on / off combinations of the inter-region tie switches, narrowing the search scope and improving the generation efficiency.

[0034] In an application scenario, all operable switches (including sectionalizing switches and tie switches) in the distribution network can be combined, and based on all possible "on" or "off" combination states, a candidate topology set that satisfies the radial operation constraints is generated. Constraint filtering is performed on the candidate topologies in the candidate topology set. For example, the candidate topologies can be preliminarily filtered to exclude topologies that obviously do not meet the grid operation safety constraints (such as voltage over-limit and line overload).

[0035] At step S103, state estimation is performed on each candidate topology in the candidate topology set to obtain state estimation values. State estimation includes a calculation process based on the weighted least squares method, and its weight coefficients are determined according to the variances of the corresponding measurement data.

[0036] In some embodiments, state estimation also includes constructing a state estimation model. For each topology in the candidate topology set, using its network structure and known line parameters, its corresponding state estimation model is constructed. Specifically, the state estimation model includes the following elements: State variables: node voltage amplitude and phase angle. Constraint conditions: power flow equations, branch power constraints, equipment capacity limits, etc.

[0037] In this invention, an improved weighted least squares method (WLS) is adopted. The improvement lies in: dynamically allocating weights according to the measurement accuracy and credibility of SCADA / AMI data. The data of the SCADA system is assigned a higher initial weight due to its high measurement frequency and high accuracy, and the data of the AMI system is adaptively adjusted according to the transmission stability. Using the real-time collected SCADA / AMI measurement data as input, state estimation of the topology is performed to obtain an estimated state vector (such as node voltage phasor). The improved WLS aims to optimize the convergence and accuracy of the traditional WLS in the face of sparse measurements and low redundancy in the distribution network.

[0038] The calculation method of the weight coefficient is as follows:

[0039]

[0040] Wherein, is the weight coefficient of the i-th measurement data, is the variance of the i-th measurement data. The accuracy of state estimation is improved by dynamic weights.

[0041] In an application scenario, the determination of the weight coefficient further includes setting it to a corresponding range. Specifically, a weight coefficient with a value range of 0.8 to 1.0 is assigned to the SCADA system data; a weight coefficient with a value range of 0.6 to 0.9 is assigned to the AMI system data.

[0042] In an application scenario, another improvement point of the improved weighted least squares method in the present invention is to analyze historical data, weather factors, etc. through short-term load forecasting or generative adversarial network (GAN) to generate power data in areas without installed measurement facilities as "pseudo measurements" to fill the data gap, thereby solving the problem that traditional WLS state estimation highly depends on redundant real-time measurement data. Among them, data augmentation can also utilize data augmentation techniques (such as GAN) to generate sufficient, reasonable and evenly distributed amplified data based on limited samples, enabling the WLS algorithm to still perform effective state estimation when facing scarce measurement data, and significantly improving the observability of the distribution network.

[0043] The improved WLS in the present invention adopts a dynamic weight adjustment strategy. It assigns different weight values according to the reliability of the data source (for example, the reliability of SCADA real-time data is higher than that of pseudo measurements). This ensures that in the estimation calculation, high-reliability data plays a dominant role, avoiding low-quality data (such as pseudo measurements with large errors) from interfering with the extreme value estimation of the objective function through the same weight. Through dynamic weights, the linear power flow equation (physical constraint) and the pseudo measurement results are multimodally fused, further optimizing the accuracy and robustness of state estimation.

[0044] At step S104, calculate the topological error between the state estimation value of each candidate topology and the corresponding measured value in the effective measurement data. In some embodiments, the calculation method of the topological error is as follows:

[0045]

[0046] Wherein, is the topological error, is the weight of the i-th measurement data, is the i-th actual measured value, is the i-th measured value calculated based on the state estimation result.

[0047] In step S105, a valid topology is selected from the candidate topology set based on the topology error, and this valid topology is used as the operating topology of the distribution network at the current moment. In one application scenario, the candidate topology with the smallest topology error can be determined as the valid topology.

[0048] Furthermore, the method of the present invention further includes: performing power flow calculation verification on the selected effective topology; in response to passing the verification, confirming that the effective topology is the running topology at the current moment; in response to failing the verification, selecting the topology with the second smallest topology error from the remaining candidate topologies as a new effective topology and performing power flow calculation verification until the verification passes.

[0049] In addition, the multi-source measurement data can be continuously collected, and the above steps S101 to S105 can be repeatedly executed to achieve dynamic updates of the distribution network operation topology.

[0050] This invention transforms the objective function of WLS (i.e., the weighted sum of squared residuals) into a criterion for topology identification. It does not assume a fixed topology, but instead performs state estimation for each candidate topology in the candidate topology set. By calculating and comparing the measurement residuals (estimation errors) under different topology structures, the topology with the smallest residual is selected as the current actual operating topology. This improved application method based on residuals allows the algorithm to quickly verify the consistency of the topology using real-time cross-sectional voltage and current data, thereby adapting to dynamic changes in the distribution network topology.

[0051] The invention will now be described in detail in conjunction with specific application scenarios. Figure 2 This is a schematic diagram illustrating the process 200 of identifying a power grid topology using the method of the present invention.

[0052] like Figure 2 As shown, in step S201, data acquisition and preprocessing take place.

[0053] Real-time measurement data such as branch currents and key node voltages in the distribution network are collected through a SCADA system, while user-side voltage and current data are collected through an AMI system, integrating them to form a multi-source measurement dataset. The 3σ criterion is used to identify and remove outliers from the data to avoid interference with the identification results. Voltage and current data of different dimensions are normalized to unify the data range. To address the issue of missing data, linear interpolation is used to complete the missing data, ensuring the integrity of the input data.

[0054] Furthermore, this invention addresses the challenges of time alignment, high sparsity, and significant noise interference in multi-source heterogeneous data, which hinders the convergence of traditional deterministic equation-based methods (such as network-wide state estimation). By treating the voltage measurement data of each node as a time-series vector, the linear correlation between two node voltage vectors is quantified by calculating the Pearson correlation coefficient. Based on the correlation level and a set threshold, the voltage fluctuation trend of nodes within a certain time window is recorded. This approach, by setting a threshold, identifies highly correlated nodes as physically connected, thereby rapidly constructing the topology and effectively handling noise and latency issues in multi-source heterogeneous data.

[0055] In step S202, a candidate topology set is generated.

[0056] Based on the physical characteristics and on / off constraints of distribution network switchgear (including sectionalizing switches and tie switches), all possible on / off combinations are traversed. Considering the core requirements of radial operation of the distribution network, invalid combinations that do not comply with safety rules, such as those involving closed-loop operation or isolated nodes, are eliminated, generating a candidate topology set.

[0057] For complex feeder scenarios, candidate topologies for each feeder partition are generated, and then a global candidate topology set is formed by combining the on and off states of inter-regional interconnection switches, which narrows the search range and improves generation efficiency.

[0058] Candidate topologies are initially filtered to exclude those that clearly do not meet the safety constraints of power grid operation, such as those with voltage exceeding limits or line overload.

[0059] In step S203, the WLS state estimation is improved.

[0060] For each candidate topology, a corresponding distribution network state estimation model is constructed. State variables are selected as node voltage magnitude and phase angle, and constraints include power flow equations, branch power constraints, and equipment capacity limitations. An improved weighted least squares method is used to solve the model. The improvement lies in: dynamically assigning weights based on the measurement accuracy and reliability of SCADA / AMI data. SCADA system data receives a higher initial weight due to its high measurement frequency and accuracy, while AMI system data has its weights adaptively adjusted based on transmission stability. The weight coefficients are calculated in real-time using the variance of the measurement data, as shown in the following formula:

[0061]

[0062] In the formula, The weight of the i-th measurement data. Let be the variance of the i-th measurement data. Dynamic weighting is used to improve the accuracy of state estimation.

[0063] In step S204, topology error is calculated and filtered.

[0064] Calculate the error index between the state estimate of each candidate topology and the preprocessed valid input data. This error index can be expressed as a weighted sum of squares, i.e., the topology error, and its formula is as follows:

[0065]

[0066] In the formula, For topological error, The weight of the i-th measurement data. For the i-th actual measurement value, This is the i-th measurement value calculated based on the state estimation results.

[0067] In step S205, topology validity is verified and updated in real time.

[0068] Power flow calculations are performed on the selected effective topologies to verify whether they meet the radial operation requirements, whether the branch current exceeds the limit, and whether the node voltage is within the allowable range. If they do not meet the requirements, the candidate topology with the second smallest error is re-selected and verified until an effective topology that meets the constraints is obtained.

[0069] In some embodiments, the optimal topology can also be selected by error comparison. Specifically, the state estimation errors of all topologies in the candidate topology set are compared. The topology with the smallest error is selected as the effective operating topology of the distribution network at the current time.

[0070] The method of this invention is suitable for real-time updates of SCADA / AMI real-time measurement data. By continuously collecting SCADA / AMI real-time data and repeating the above steps, the topology structure is dynamically updated in real time, adapting to dynamic changes in distribution network switching operations, equipment commissioning and decommissioning, and other scenarios. In one application scenario, at the next sampling time or when a potential change occurs in the distribution network switching status, steps S101 to S105 are automatically triggered to quickly re-identify the current topology. This method can be used to solve the dynamic topology identification problem of feeders with complex topologies, providing accurate network structure information for the real-time operation, fault handling, and load transfer of the distribution network.

[0071] Taking a complex feeder system of a 10kV distribution network as an example, the system includes 3 feeders, 20 nodes, 15 sectional switches, and 3 tie switches. The SCADA system has a sampling frequency of 5 minutes / time, and the AMI system is connected to 12 user-side measurement nodes.

[0072] The method of this invention for topology identification includes the following steps:

[0073] Data acquisition and preprocessing: Collect SCADA / AMI voltage and current data within 1 hour, remove 2 outlier data points using the 3σ criterion, normalize the voltage (kV level) and current (A level) data, and use linear interpolation to complete 3 missing data points;

[0074] Candidate topology set generation: Based on the on / off constraints, an initial set of 86 candidate topologies is generated through traversal. 32 invalid topologies, such as those with closed-loop operation and isolated nodes, are removed, resulting in 54 valid candidate topologies.

[0075] Improved WLS state estimation: Construct a state estimation model for each candidate topology, and assign weight coefficients based on the variance of the measurement data. The weight coefficients for SCADA data range from 0.8 to 1.0, and the weight coefficients for AMI data range from 0.6 to 0.9.

[0076] Topology error calculation and screening: Calculate the error index of each candidate topology, and screen the topology with the smallest error as the effective topology. The error index is 0.032.

[0077] Validity verification and real-time updates: Power flow calculations are performed to verify the valid topology. Node voltage deviations are all within ±5%, and branch currents do not exceed limits. Real-time data is continuously collected, and the topology identification results are updated every 5 minutes to dynamically track topology changes caused by switching operations.

[0078] Tests showed that the topology identification method of this invention takes an average of 8 seconds and has an accuracy rate of 98.5%, which can meet the timeliness and accuracy requirements of real-time control of power distribution networks.

[0079] While this specification has shown and described numerous embodiments of the invention, it will be apparent to those skilled in the art that such embodiments are provided by way of example only. Many modifications, alterations, and alternatives will occur to those skilled in the art without departing from the spirit and essence of the invention. It should be understood that various alternatives to the embodiments of the invention described herein may be employed in the practice of this invention.

Claims

1. A method for rapid topology identification in real-time operation of distribution networks, characterized in that, include: Acquire multi-source measurement data from multiple data sources in the power distribution network, and preprocess the multi-source measurement data to obtain effective measurement data; The multi-source measurement data refers to real-time measurement data collected by the SCADA system and user-side data collected by the AMI system. A candidate topology set is generated based on the on / off status of the distribution network switching equipment, and the candidate topology set contains multiple candidate topologies; State estimation is performed on each candidate topology in the candidate topology set to obtain a state estimate value; the state estimation includes a calculation process based on weighted least squares, and the weight coefficients are determined according to the variance of the corresponding measurement data; Calculate the topology error between the state estimate of each candidate topology and the corresponding measurement value in the valid measurement data; Based on the topology error, a valid topology is selected from the candidate topology set and used as the operating topology of the distribution network at the current moment.

2. The method for rapid topology identification for real-time operation of distribution networks according to claim 1, characterized in that, Preprocessing of the multi-source measurement data includes: The 3σ criterion was used to remove outlier data. Normalize data of different dimensions; and Missing data were filled in using linear interpolation.

3. The method for rapid topology identification for real-time operation of distribution networks according to claim 1, characterized in that, The generation of candidate topology sets includes: The complex feeder scenario is divided into multiple partitions according to the region, and local candidate topologies for each partition are generated. The local candidate topologies are combined by switching the inter-regional communication switches on and off to form a global candidate topology set.

4. The method for rapid topology identification for real-time operation of distribution networks according to claim 1, characterized in that, The state estimation also includes: Construct a state estimation model, which includes the following elements: State variables: node voltage magnitude and phase angle; constraints: power flow equations, branch power constraints, and equipment capacity limits.

5. The method for rapid topology identification for real-time operation of distribution networks according to claim 1, characterized in that, The weighting coefficients are calculated as follows: In the formula, The weighting coefficient for the i-th measurement data is... Let be the variance of the i-th measurement data.

6. The method for rapid topology identification for real-time operation of distribution networks according to claim 1, characterized in that, The topology error is calculated as follows: In the formula, For topological error, The weight of the i-th measurement data. For the i-th actual measurement value, This is the i-th measurement value calculated based on the state estimation results.

7. The method for rapid topology identification for real-time operation of distribution networks according to claim 1, characterized in that, The method further includes: Power flow calculations were performed to verify the selected valid topologies; Upon successful verification, the valid topology is confirmed as the running topology at the current moment; In response to a failed verification, the topology with the second smallest topology error is selected from the remaining candidate topologies as a new valid topology, and power flow calculation is performed for verification until the verification passes.

8. The method for rapid topology identification for real-time operation of distribution networks according to any one of claims 1 to 7, characterized in that, The method further includes: The multi-source measurement data is continuously collected, and all steps of the rapid identification method for real-time operation of distribution networks according to any one of claims 1 to 7 are repeatedly executed to achieve dynamic updating of the operation topology of the distribution network.

9. The method for rapid topology identification for real-time operation of distribution networks according to claim 1, characterized in that, The determination of the weighting coefficients also includes: The SCADA system data is assigned a weight coefficient ranging from 0.8 to 1.0; the AMI system data is assigned a weight coefficient ranging from 0.6 to 0.

9.

10. The method for rapid topology identification for real-time operation of distribution networks according to claim 1, characterized in that, Selecting valid topologies from the candidate topology set includes: The candidate topology with the smallest topology error is determined as the effective topology.