Power distribution network topology identification method considering intelligent electric meter and [mu] PMU measurement

Abstract

The invention discloses a power distribution network topology identification method considering an intelligent electric meter and mu PMU measurement. The method comprises the following steps: step 1, obtaining a network approximate admittance matrix by adopting the intelligent electric meter and mu PMU measurement data; 2, further approximating the admittance matrix in the step 1 by adopting an unscented Kalman filtering method to obtain a relatively accurate admittance matrix; 3, adding an explicit regularization item to the progressive graph convolutional network loss function in combination with the physical constraint of an admittance matrix; and 4, carrying out network global and local characteristic capture on the precise admittance matrix in the step 2 by adopting the progressive graph convolutional network improved in the step 3, and finally obtaining a required network admittance matrix. The invention aims to solve the problems of insufficient power distribution network topology identification precision and poor noise immunity in the prior art, and provides a topology identification method combining an intelligent electric meter and mu PMU measurement, so that efficient identification and parameter optimization of the power distribution network topology are realized.

Description

Technical Field

[0001] The present invention belongs to the fields of power systems and machine learning, and particularly relates to a method for identifying the topology of a distribution network considering the measurements of smart meters and μPMUs. Background Art

[0002] Due to the dynamic changes in the topology of the distribution network and the lack of accurate network parameters in some areas, existing methods are difficult to obtain high-precision topology information in a high-noise environment. Therefore, how to identify the topology of the distribution network is a key link in the state monitoring and control of the distribution network, and its accuracy directly affects the safety and efficiency of the power grid operation.

[0003] The patent with the application publication number CN116885841A proposes a method and system for obtaining distribution network topology identification data. This invention acquires the carrier signals detected by the distribution network detection terminal, performs structured processing on the carrier signals, and based on the processed carrier signals, combines a logic control algorithm to obtain a distribution network topology identification fusion data set. The patent with the application publication number CN118801331A proposes a method and system for identifying the topology and parameter identification of a distribution network without PMUs. This invention collects relevant data of the distribution network and constructs a power flow calculation equation model for the distribution system, uses linear regression to judge the connection status of nodes and calculate the admittance matrix of the lines, and performs iteration based on the judgment results and the admittance matrix to obtain the topology identification and parameter identification results. However, the above methods require a large amount of calculation and rely on a fixed network topology, and they show deficiencies when facing problems such as non-linear, non-Euclidean distributed data, and measurement noise.

[0004] In summary, the current research on the topology of the distribution network is not in-depth. Therefore, a method for identifying the topology of the distribution network considering the measurements of smart meters and μPMUs is proposed, which can better meet the accurate topology identification requirements in a complex distribution network environment. Summary of the Invention

[0005] The present invention aims to solve the problems of insufficient accuracy and poor noise resistance in the topology identification of the distribution network in the prior art. In response to this problem, a topology identification method combining smart meters and Micro-synchronous Phasor Measurement Units (μPMUs) is proposed to achieve efficient identification of the distribution network topology and parameter optimization.

[0006] To achieve the above invention purpose, the method of the present invention includes the following steps:

[0007] Step 1: Use the measurement data of smart meters and μPMUs to obtain an approximate network admittance matrix;

[0008] Step 2: Using the unscented Kalman filter method, further approximate the network approximate admittance matrix in Step 1 to obtain an accurate admittance matrix;

[0009] Step 3: Combining the physical constraints of the admittance matrix, add an explicit regularization term to the loss function of the progressive graph convolutional network to obtain an improved progressive graph convolutional network;

[0010] Step 4: Use the improved progressive graph convolutional network in Step 3 to capture the global and local characteristics of the network for the accurate admittance matrix in Step 2, obtain the required network admittance matrix, and deduce the connection relationship and topological structure of each node in the network from its dimension, the position and value of non-zero elements.

[0011] Further, Step 1 uses the measurement data of smart meters and μPMUs to obtain the network approximate admittance matrix, including:

[0012] Step 1-1: Obtain the network preliminary admittance matrix through smart meter data;

[0013] Step 1-2: Further approximate the network preliminary admittance matrix through μPMU measurement data to obtain the network approximate admittance matrix.

[0014] Further, Step 1-1 specifically includes:

[0015] Obtain the active power injection P i (k), reactive power injection Q i (k) and the voltage magnitude |V i |(k) of the i-th bus at the specified time k:

[0016]

[0017] where: P i,n and Q i,n are the nominal values of active power and reactive power respectively; |V i | is the nominal value of the voltage magnitude; and are the corresponding measurement noises respectively; σ L is the measurement uncertainty;

[0018] For nodes without smart meters, obtain pseudo-measurement values through estimation;

[0019] Obtain the network preliminary admittance matrix according to the measured data.

[0020] Further, Step 1-2 specifically includes:

[0021] Measure the magnitude |V i |(k) and phase θ of the voltage phasor on some buses through a small number of μPMUsi (k), and the current phasor |I of the current phasor on the busbar i at the specified moment k ij |(k):

[0022]

[0023] Where: |V i | n is the voltage amplitude of the busbar; θ i,n is the voltage phase angle; |I ij | n is the nominal value of the current; σ PMU is the measurement uncertainty of the μPMU;

[0024] According to the obtained voltage and current phasor data, further approximate it to obtain the network approximate admittance matrix G ij and B ij :

[0025]

[0026] Where: and are the conductance and susceptance matrices obtained by preliminary estimation respectively; θ ij is the voltage phase angle difference between the i-th node and the j-th node.

[0027] Furthermore, step 2 specifically includes:

[0028] Step 2-1: Define the state matrix and the measurement matrix:

[0029]

[0030] Where: x (k) and y (k) are the state matrix and the measurement matrix respectively; P (k) , Q (k) , |V| (k) , I f (k) and θ M (k) are the active power injection, reactive power injection, voltage amplitude, current phasor and voltage phase angle of the busbar at the moment k respectively;

[0031] Step 2-2: In the unscented Kalman filter framework, describe the dynamic changes of the system by constructing a state space model. The state space model represents the relationship between the power and voltage of each busbar through the following non-linear relationship, specifically as follows:

[0032]

[0033] Where: P i and Qi The active power and reactive power injections of the i-th node respectively;

[0034] Step 2-3: Generate a set of sigma points based on the estimated values of the current state. Each sigma point represents a possible state estimate, and the sigma points are propagated through the non-linear function of the system to calculate the measurement results corresponding to each sigma point;

[0035] Step 2-4: In each filtering, first predict the current state using the previous estimated value and measurement data. The prediction process is achieved by propagating the sigma points; compare the propagated sigma points with the actual measurement data to update the state estimate; calculate the difference between the predicted value and the actual measurement value, and correct it using the Kalman gain; after the unscented Kalman filter update, obtain the accurate admittance matrix, that is, obtain the estimates of conductance and susceptance in the more accurate admittance matrix, so as to provide more accurate network topology and parameter information.

[0036] Furthermore, Step 3 specifically includes:

[0037] Step 3 specifically includes:

[0038] Step 3-1: Adopt a progressive graph convolutional network to automatically learn the optimal network topology through its progressive mechanism. The progressive graph convolutional network dynamically adjusts from both the network depth and width. The specific feature update formula is as follows:

[0039]

[0040] In the formula: H (l) is the node feature matrix of the l-th layer; is the normalized adjacency matrix; W (l+1) is the weight matrix of the (l + 1)-th layer; σ is the non-linear activation function;

[0041] Step 3-2: Combine the physical constraints of the admittance matrix and add an explicit regularization term to the loss function of the progressive graph convolutional network. The total loss function expression is:

[0042]

[0043] In the formula: is the total loss; is the main task loss; is the symmetry constraint; is the row and column sum constraint; λ1, λ2 are regularization weights.

[0044] Furthermore, Step 4 specifically includes:

[0045] Step 4-1: Use the accurate admittance matrix estimated by the unscented Kalman filter as the graph input and input it into the improved progressive graph convolutional network;

[0046] Step 4-2: The improved progressive graph convolutional network updates the features of each node through multiple layers of graph convolution. Initially, the node feature matrix X contains voltage amplitudes and other network parameters. The expression of the graph convolution operation in the l-th layer is:

[0047]

[0048] where: H (l) is the node feature matrix of the l-th layer; is the normalized adjacency matrix; W (l) is the weight matrix of the l-th layer; σ is the non-linear activation function;

[0049] Step 4-3: By dynamically adjusting the depth and width of the network according to the performance of the task, in each layer, if adding new layers or blocks can improve the performance, the model gradually expands the network; if it cannot improve the performance, these layers or blocks are removed. The output of each layer is calculated through a linear transformation:

[0050] Y = H (l+1) O (9)

[0051] where: O is the output transformation matrix; Y is the finally output admittance matrix.

[0052] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0053] 1. To reduce the computational complexity, the present invention adopts a progressive structure optimization mechanism, which avoids unnecessary computational overhead while meeting the accuracy requirements; in each step of optimization, only the newly added part is trained and adjusted, greatly reducing the computational complexity and training time;

[0054] 2. To solve the obvious lack of robustness when facing incomplete or noisy data, the present invention combines the data of smart meters and micro - phasor measurement units, processes the measurement data of different devices through the unscented Kalman filter, realizes the efficient fusion and comprehensive utilization of multi - source data, and can still maintain a high parameter estimation accuracy even in the case of data missing or large measurement noise. Brief Description of the Drawings

[0055] The following further describes the present invention with reference to the drawings and embodiments:

[0056] Figure 1 is the flow chart of a method for identifying the topology of a distribution network considering smart meters and μPMU measurements according to an embodiment of the present invention;

[0057] Figure 2 It is the IEEE 33-node network structure diagram of the embodiment of the present invention;

[0058] Figure 3 It is the network identification error diagram of the IEEE 33 nodes by the algorithm of the embodiment of the present invention. Detailed implementation manners

[0059] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0060] The embodiment of the present invention provides a distribution network topology identification method considering smart meters and μPMU measurements, as Figure 1 shown, including the following steps:

[0061] Step 1: Use the measurement data of smart meters and μPMUs to obtain the network approximate admittance matrix;

[0062] Step 2: Use the unscented Kalman filter method to further approximate the admittance matrix in Step 1 to obtain a more accurate admittance matrix;

[0063] Step 3: Combine the physical constraints of the admittance matrix and add an explicit regularization term to the progressive graph convolutional network loss function;

[0064] Step 4: Use the improved progressive graph convolutional network in Step 3 to capture the global and local characteristics of the network for the accurate admittance matrix in Step 2 to obtain the required network admittance matrix, and deduce the connection relationship and topological structure of each node in the network through its dimension, the position and value of the non-zero elements.

[0065] In Step 1, the generation of the network approximate admittance matrix is mainly divided into two steps:

[0066] Step 1-1: First, obtain the active power injection, reactive power injection, and the voltage amplitude of the i-th bus at the specified time k through the smart meters installed at different nodes of the distribution network, which can be written as:

[0067]

[0068] In the formula: P i,n and Q i,n are the nominal values of active power and reactive power respectively; |V i | is the nominal value of the voltage amplitude; and are the corresponding measurement noises; σ L is the measurement uncertainty.

[0069] For nodes without smart meters installed, pseudo-measurement values are obtained through estimation, and the admittance matrix is initially constructed based on the measured data.

[0070] Step 1-2: Secondly, measure the magnitudes and phases of the voltage phasors on some buses and the current phasor of the current on bus i at a specified time k through a small number of μPMUs. It can be written as:

[0071]

[0072] In the formula: |V i | n is the voltage magnitude of the bus; θ i,n is the voltage phase angle; |I ij | n is the nominal value of the current; σ PMU is the measurement uncertainty of the μPMU.

[0073] Based on the obtained voltage and current phasor data, the network approximate admittance matrix G ij and B ij are further approximated and can be written as:

[0074]

[0075] In the formula: and are the conductance and susceptance matrices obtained from the preliminary estimation respectively; θ ij is the voltage phase angle difference between the i-th node and the j-th node.

[0076] In Step 2, the unscented Kalman filter method is used to further approximate the admittance matrix in Step 1 to obtain a more accurate admittance matrix. Specifically, in Step 2, since the measurement data from smart meters and μPMUs usually contain different degrees of noise and uncertainty, directly using these initial values may lead to incorrect topology identification results. Therefore, in order to improve the accuracy of parameter estimation, the probability method of the unscented Kalman filter is used to iteratively refine and estimate the network approximate admittance matrix obtained in Step 1. The unscented Kalman filter has significant advantages in capturing the nonlinear characteristics of variables, so selecting parameter variables with strong coupling has a good promoting effect on improving robustness. The specific steps are as follows:

[0077] Step 2-1: Define the state matrix and the measurement matrix, which can be written as:

[0078]

[0079] In the formula: x (k)and y (k) are the state matrix and the measurement matrix respectively; P (k) , Q (k) , |V| (k) , I f (k) and θ M (k) are the active power injection, reactive power injection, voltage magnitude, current phasor, and voltage phase angle of the bus at time k respectively.

[0080] Step 2-2: In the unscented Kalman filter framework, the dynamic changes of the system are described by constructing a state space model, and this model represents the relationship between the power and voltage of each bus through the following non-linear relationship, specifically as follows:

[0081]

[0082] In the formula: P i and Q i are the active power and reactive power injections of the i-th node respectively.

[0083] Step 2-3: The unscented transform is used to update the state of the non-linear system by generating "sigma points" to approximate the probability distribution of the state variables. First, a set of sigma points is generated based on the estimated value of the current state, and each sigma point represents a possible state estimate. Secondly, these sigma points are propagated through the non-linear function of the system to calculate the measurement results corresponding to each sigma point;

[0084] Step 2-4: In each filtering, first, the current state is predicted using the previous estimated value and measurement data, and this prediction process is achieved by propagating the sigma points. Secondly, the propagated sigma points are compared with the actual measurement data to update the state estimate. By calculating the difference between the predicted value and the actual measurement value and using the Kalman gain for correction. Finally, through the update step of the unscented Kalman filter, more accurate estimates of the conductance and susceptance in the admittance matrix are obtained, thus providing more accurate network topology and parameter information.

[0085] In Step 3, the improved progressive graph convolutional network is mainly divided into two steps:

[0086] Step 3-1: An incremental graph convolutional network is used to automatically learn the optimal topology of the network. Since the static graph convolutional network requires the pre-defined number of layers and width of the network, its fixed structure is difficult to adapt to complex practical problems. Moreover, as the depth of the network increases, the node features of the static graph convolutional network will have the problem of over-smoothing, resulting in the loss of the discriminative ability of node features and making it difficult to identify complex topologies. Therefore, in order to adapt to topologies of different complexities and reduce the risk of over-smoothing, an incremental graph convolutional network is adopted to automatically learn the optimal topology of the network through its progressive mechanism. The incremental graph convolutional network dynamically adjusts from both the network depth and width. The specific feature update formula can be written as:

[0087]

[0088] where: H (l) is the node feature matrix of the l-th layer; is the normalized adjacency matrix; W (l+1) is the weight matrix of the (l + 1)-th layer; σ is the non-linear activation function.

[0089] Step 3-2: Combining the physical constraints of the admittance matrix, an explicit regularization term is added to the loss function of the incremental graph convolutional network. Since the incremental graph convolutional network is a data-driven deep learning model, its output may not conform to physical laws, resulting in significant errors when dealing with noisy data. Therefore, in order to ensure the physical consistency of the output and improve the topology recognition accuracy, combining the physical constraints of the admittance matrix (i.e., symmetry constraint and row-column sum constraint), an explicit regularization term is added to the loss function of the incremental graph convolutional network for processing. The specific total loss function expression can be written as:

[0090]

[0091] where: is the total loss; is the main task loss; is the symmetry constraint; is the row-column sum constraint; λ1, λ2 are the regularization weights.

[0092] In step 4, the improved incremental graph convolutional network in step 3 is used to capture the global and local characteristics of the network for the accurate admittance matrix in step 2, obtaining the required network admittance matrix. Through its dimension, the position and value of non-zero elements, the connection relationship and topology of each node in the network are deduced. It mainly includes three steps:

[0093] Step 4-1: The accurate admittance matrix estimated by the unscented Kalman filter is used as the graph input and input into the incremental graph convolutional network model;

[0094] Step 4-2: The progressive graph convolutional network updates the features of each node through multiple layers of graph convolutions. Initially, the node feature matrix X can contain voltage magnitudes and other network parameters. The expression of the graph convolution operation at the l-th layer can be written as:

[0095]

[0096] where: H (l) is the node feature matrix at the l-th layer; is the normalized adjacency matrix; W (l) is the weight matrix at the l-th layer; σ is the non-linear activation function.

[0097] Through this feature aggregation and transformation, the progressive graph convolutional network gradually optimizes the node features, enabling the network to learn the optimal topology and parameters.

[0098] Step 4-3: By dynamically adjusting the depth and width of the network according to the performance of the task, in each layer, if adding new layers or blocks can improve the performance, the model gradually expands the network; if it cannot improve the performance, these layers or blocks are removed. The output of each layer is calculated through a linear transformation:

[0099] Y = H (l+1) O (9)

[0100] where: O is the output transformation matrix; Y is the final output admittance matrix.

[0101] Example:

[0102] To verify the effectiveness of the present invention, we select the standard IEEE 33-node test system as the analysis object. This system contains 33 nodes and has a relatively complex topology, which is suitable for verifying the application effect of the present invention. The specific structure is as Figure 2As shown. In this embodiment, by installing smart meters and μPMU devices at each node in the IEEE 33-node system, data such as voltage, current, and power of the nodes are collected. The following are some examples of the collected data: Node 1: The voltage amplitude is 1.05 p.u.; the current is -0.16 + j0.07 A; the power is 0.15 MW + j0.05 MVAR. Node 2: The voltage amplitude is 0.98 p.u.; the current is 0.12 - j0.06 A; the power is 0.08 MW - j0.02 MVAR. Using these collected data, a preliminary admittance matrix is calculated through network analysis methods. The preliminary admittance matrix is calculated based on the topological structure of the power grid and current-voltage information, and there are certain errors in the initial admittance matrix. The unscented Kalman filter is applied to optimize the preliminary admittance matrix. Assume that the initial admittance matrix of the power grid is Y, and its initial error is 6% (according to the measurement error). After UKF optimization, the admittance matrix error is reduced to 4%. Some data examples of the optimized admittance matrix are as follows: Preliminary calculation of Y 12 = 0.05 + j0.03. After optimization, Y 12 = 0.048 + j0.028. After optimization by the unscented Kalman filter, the accuracy of the admittance matrix is significantly improved, and the error is reduced from 5% to 4%. Then, a physical regularization term is added to the loss function of the progressive graph convolutional network to ensure that the optimized admittance matrix satisfies the physical constraints of the power grid. Finally, the progressive graph convolutional network captures the global and local characteristics of the optimized admittance matrix, and finally the required network admittance matrix is obtained. The specific identification results are as Figure 3 shown.

[0103] To comprehensively evaluate the performance of the method proposed in the present invention, taking the 33-node system as an example and without considering measurement errors, it is compared with the existing Lasso regression method, contract transformation method, and NR iteration method. The specific comparison results are shown in Table 1.

[0104] Table 1 Comparison results of different methods in the 33-node system (without errors)

[0105] Method Accuracy rate (%) Conductance g error (%) Susceptance b error (%) Computation time (seconds) Improved PGCN 98.5％ 4.2％ 3.7％ 15.2 Lasso regression method 90.3％ 8.6％ 8.3％ 18.6 Contract transformation method 92.4％ 7.2％ 7.6％ 20.4 NR iteration method 95.2％ 6.5％ 6.8％ 25.7

[0106] From the results, it can be seen that the improved progressive graph convolutional network method performs excellently in topology identification and conductance and susceptance estimation. The accuracy rate and error are better than other methods, and the calculation time is relatively short; the Lasso regression method and the contract transformation method have lower topology identification accuracy rates and larger estimation errors for conductance and susceptance; the NR iteration method performs well under standard conditions, but due to its dependence on good initial conditions, once the initial value is incorrect, it will lead to poor model convergence and longer calculation time.

[0107] To analyze the robustness of the method of the present invention under different measurement errors, taking the 33-node system as an example, considering the measurement errors, it is compared with the existing Lasso regression method, contract transformation method and NR iteration method. The specific comparison results are shown in Table 2.

[0108] Table 2 Comparison Results of Different Methods in 33-Node System (0-10% Error)

[0109]

[0110]

[0111] It can be seen from the results that for the progressive graph convolutional network method, under different voltage error ranges, the identification errors of conductance and susceptance are relatively low. Especially under higher error conditions, the error increase is the smallest, indicating that it can still maintain high accuracy under the influence of noise and data errors; for the Lasso regression method and the contract transformation method, when the voltage error is large, the error increase is large. Especially when the voltage error reaches 6%-10%, the identification errors of conductance and susceptance increase significantly, showing that they are more sensitive to measurement errors; although the NR iteration method performs well under certain error conditions, as the error increases, the errors gradually accumulate, resulting in an increase in the estimation errors of conductance and susceptance.

[0112] In summary, this embodiment verifies the effectiveness of the method of the present invention through the IEEE 33-node system. Specific data show that the admittance matrix optimized by the unscented Kalman filter and the progressive graph convolutional network has stronger robustness compared with the results of the existing methods under the same conditions, and can effectively reduce the accumulation of errors, and is particularly suitable for noise and uncertain data in the tasks of distribution network topology identification and parameter estimation. The method of the present invention shows obvious advantages in terms of accuracy, reliability and real-time performance compared with the traditional methods.

[0113] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: the specific implementation manners of the present invention can still be modified or equivalently replaced, and any modification or equivalent replacement without departing from the spirit and scope of the present invention shall be covered by the protection scope of the claims of the present invention.

Claims

1. A method for identifying the topology of a distribution network considering the measurements of smart meters and μPMUs, characterized in that, Including the following steps: Step 1: Obtain the network approximate admittance matrix using the measurement data of smart meters and μPMUs; Step 2: Use the unscented Kalman filter method to further approximate the network approximate admittance matrix in Step 1 to obtain the exact admittance matrix; Step 3: Combine the physical constraints of the admittance matrix, add an explicit regularization term to the loss function of the progressive graph convolutional network to obtain an improved progressive graph convolutional network; Step 4: Use the improved progressive graph convolutional network in Step 3 to capture the global and local characteristics of the network for the exact admittance matrix in Step 2, obtain the required network admittance matrix, and deduce the connection relationship and topological structure of each node in the network through its dimension, the position and value of non-zero elements.

2. Research on the method for identifying the topology of a distribution network considering the measurements of smart meters and μPMUs according to claim 1, characterized in that: Step 1 uses the measurement data of smart meters and μPMUs to obtain the network approximate admittance matrix, including: Step 1-1: Obtain the preliminary network admittance matrix through smart meter data; Step 1-2: Further approximate the preliminary network admittance matrix through μPMU measurement data to obtain the network approximate admittance matrix.

3. Research on the method for identifying the topology of a distribution network considering the measurements of smart meters and μPMUs according to claim 2, characterized in that: Step 1-1 specifically includes: The active power injection P is obtained from smart meters installed at different nodes of the distribution network i (k), the reactive power injection Q i (k), and the voltage magnitude |V i |(k) of the i-th bus at the specified time k: Where: P i,n and Q i,n are the nominal values of the active power and the reactive power respectively; |V i | is the nominal value of the voltage amplitude; and are the corresponding measurement noises respectively; σ L is the measurement uncertainty; For nodes without smart meters, obtain pseudo-measurement values through estimation; Obtain the preliminary network admittance matrix according to the measured data.

4. Research on the method for identifying the topology of a distribution network considering the measurements of smart meters and μPMUs according to claim 3, characterized in that: Step 1-2 specifically includes: Measure the magnitude |V i |(k) and phase θ i (k) of the voltage phasor on certain buses through a small number of μPMUs, and the current phasor |I ij |(k) on bus i at the specified time k: Where: |V i | n is the voltage amplitude of the busbar; θ i,n is the voltage phase angle; |I ij | n is the nominal value of the current; σ PMU is the measurement uncertainty of the μPMU; Based on the obtained voltage and current phasor data, further approximate them to obtain the network approximate admittance matrix G ij and B ij : Wherein: and are respectively the conductance and susceptance matrices obtained by preliminary estimation; θ ij is the voltage phase angle difference between the i-th node and the j-th node.

5. Research on the method for identifying the topology of a distribution network considering the measurements of smart meters and μPMUs according to claim 1, characterized in that: Step 2 specifically includes: Step 2-1: Define the state matrix and measurement matrix: where: x (k) and y (k) are the state matrix and the measurement matrix respectively; P (k) , Q (k) , |V| (k) , I f (k) and θ M (k) are the active power injection, reactive power injection, voltage magnitude, current phasor and voltage phase angle of the bus at time k respectively; Step 2-2: In the unscented Kalman filter framework, describe the dynamic changes of the system by constructing a state space model. The state space model represents the relationship between the power and voltage of each bus through the following nonlinear relationship, specifically as follows: Where: P i and Q i are the active power and reactive power injections at the i-th node, respectively; Step 2-3: Generate a set of sigma points based on the estimated value of the current state. Each sigma point represents a possible state estimate. The sigma points are propagated through the nonlinear function of the system to calculate the measurement results corresponding to each sigma point; Step 2-4: In each filtering, first predict the current state using the previous estimated value and measurement data. The prediction process is achieved by propagating the sigma points; compare the propagated sigma points with the actual measurement data to update the state estimate; calculate the difference between the predicted value and the actual measurement value, and use the Kalman gain for correction; after the unscented Kalman filter update, obtain the exact admittance matrix, that is, obtain the estimates of conductance and susceptance in a more accurate admittance matrix, so as to provide more accurate network topology and parameter information.

6. Research on the method for identifying the topology of a distribution network considering the measurements of smart meters and μPMUs according to claim 1, characterized in that: Step 3 specifically includes: Step 3-1: Use the progressive graph convolutional network to automatically learn the optimal network topology structure through its progressive mechanism. The progressive graph convolutional network dynamically adjusts from both the network depth and width. The specific feature update formula is as follows: Where: H (l) is the node feature matrix of the l-th layer; is the normalized adjacency matrix; W (l+1) is the weight matrix of the (l + 1)-th layer; σ is the non-linear activation function; Step 3-2: Combine the physical constraints of the admittance matrix, add an explicit regularization term to the loss function of the progressive graph convolutional network. The total loss function expression is: Wherein: is the total loss; is the main task loss; is the symmetry constraint; is the row and column sum constraint; λ1, λ2 are regularization weights.

7. Research on the method for identifying the topology of a distribution network considering the measurements of smart meters and μPMUs according to claim 1, characterized in that: Step 4 specifically includes: Step 4-1: Take the exact admittance matrix estimated by the unscented Kalman filter as the graph input and input it into the improved progressive graph convolutional network; Step 4-2: The improved progressive graph convolutional network updates the features of each node through multiple layers of graph convolution. Initially, the node feature matrix X contains voltage magnitudes and other network parameters. The expression of the graph convolution operation in the l-th layer is as follows: Where: H (l) is the node feature matrix of the l-th layer; is the normalized adjacency matrix; W (l) is the weight matrix of the l-th layer; σ is the non-linear activation function; Step 4-3: By dynamically adjusting the depth and width of the network according to the performance of the task, in each layer, if adding new layers or blocks can improve the performance, the model gradually expands the network; if it cannot improve the performance, these layers or blocks are removed. The output of each layer is calculated through a linear transformation: Y = H (l+1) O (9) In the formula: O is the output transformation matrix; Y is the final output admittance matrix.

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