Unsupervised inference method and system for power distribution network topology structure

Abstract

The application relates to the technical field of power distribution networks, and provides a power distribution network topology structure unsupervised inference method and system.The method comprises the following steps: unsupervised training of a space-time graph convolution network model by using the unlabeled measurement time sequence data of nodes, and inference of the power distribution network topology structure by using the trained space-time graph convolution network model.The space-time graph convolution network model comprises a space-time graph encoder and a double-branch decoder, the double-branch decoder comprises a voltage reconstruction decoder and an edge prediction decoder, the voltage reconstruction decoder calculates predicted voltage according to a node space-time embedding feature vector, and the edge prediction decoder predicts a node in-edge probability according to the node space-time embedding feature vector.In the loss function of the space-time graph convolution network model, the voltage reconstruction loss is the error between the predicted voltage and the real voltage measurement value, and the physical consistency loss is determined according to the node in-edge probability under the current law constraint.The application realizes high-precision and high-efficiency topology inference without real topology labels.

Description

Technical Field

[0001] This invention relates to the field of power distribution network technology, and specifically to an unsupervised method and system for inferring the topology of a power distribution network. Background Technology

[0002] Distribution network topology inference refers to using the measurement data (such as voltage, current, power, etc.) of observable nodes in the power grid to infer their invisible physical connections. The existing known technical routes in this field mainly include the following categories: (1) State estimation method based on electrical model: This method is based on circuit theory (such as Kirchhoff's laws and Ohm's laws), substitutes the measurement data with the network topology and line parameters into the power flow equation, and verifies or identifies the topology by solving nonlinear equations or optimization problems. (2) Method based on statistical correlation: This method believes that nodes with close electrical distances have more similar statistical characteristics (such as Pearson correlation coefficient and mutual information) in their voltage, power and other measurement data. The similarity matrix of the measurement sequences between nodes is calculated, and the topology is constructed using algorithms such as minimum spanning tree. (3) Method based on intelligent optimization algorithm: This method models the topology inference problem as a combinatorial optimization problem, uses the degree of matching between the measurement data and the simulation data under the candidate topology as the fitness function, and uses genetic algorithms, particle swarm algorithms, etc. to search for the optimal topology structure.

[0003] Existing technical solutions for inferring distribution network topology based on intelligent optimization algorithms mainly fall into two categories: The first is a topology inference method based on supervised graph neural networks (GNNs). This method requires a large amount of measurement data with real topology labels to train the network model. However, in actual distribution networks, complete and accurate topology labels are often missing or outdated, and the cost of obtaining them is extremely high, making this method difficult to deploy and limiting its generalization ability. The second method is based on unsupervised physical models and optimization solutions. This method models topology inference as a nonlinear programming problem, identifying the topology by solving power flow equations or optimization objectives. This method has extremely high computational complexity, and the solution time increases exponentially with the number of nodes, making it difficult to meet real-time requirements. Furthermore, it is sensitive to measurement noise and missing data, exhibiting poor robustness.

[0004] In summary, in the existing technologies, supervised learning methods are limited by the data label bottleneck, while unsupervised physics optimization methods are constrained by model complexity and solution efficiency, and cannot achieve high-precision and high-efficiency topology inference without real topology labels. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides an unsupervised method and system for topology inference of power distribution networks. It adopts a framework that combines self-supervised learning with a spatiotemporal graph convolutional network model. It can achieve high-precision and high-efficiency topology inference using only easily obtainable node measurement time-series data without any real topology labels.

[0006] The first aspect of this invention provides an unsupervised method for inferring the topology of a power distribution network, comprising: Unsupervised training of the spatiotemporal graph convolutional network model is performed using unlabeled measurement time-series data from each node of the distribution network to obtain a trained spatiotemporal graph convolutional network model. The measurement time series data of the distribution network nodes to be inferred are input into the trained spatiotemporal graph convolutional network model. The distribution network topology is inferred through the spatiotemporal graph convolutional network model, and the distribution network topology map is output. The spatiotemporal graph convolutional network model includes: a spatiotemporal graph encoder and a dual-branch decoder; The spatiotemporal graph encoder includes a temporal convolutional layer and a spatial graph convolutional layer, which are used to extract spatiotemporal correlation features from measurement time series data and output node spatiotemporal embedding feature vectors. The dual-branch decoder includes a voltage reconstruction decoder and an edge prediction decoder. The voltage reconstruction decoder calculates the predicted voltage based on the node spatiotemporal embedding feature vector, and the edge prediction decoder predicts the node edge entry probability based on the node spatiotemporal embedding feature vector. The loss function of the spatiotemporal graph convolutional network model includes voltage reconstruction loss and physical consistency loss. The voltage reconstruction loss is the error between the predicted voltage and the actual voltage measurement value. The physical consistency loss is determined based on the node edge probability under the constraint of the node current law.

[0007] In this embodiment of the invention, the unsupervised inference method for distribution network topology further includes: Before inputting the measurement time-series data of the distribution network nodes to be inferred into the trained spatiotemporal graph convolutional network model, feature vectors of each node are constructed. The feature vector of the constructed node includes: Based on the preprocessed measurement time series data of each node, a feature vector is constructed for each node in each time slice; For a length of The time window will be used to determine the time window for each node. The feature vectors of each time slice are stacked into a feature matrix; The measurement timing data includes: voltage amplitude, voltage phase angle, active power, and reactive power; Each node's feature vector contains the original measurement values ​​from the measurement time series data, as well as multiple derived features, including: voltage change, sine and cosine values ​​of voltage phase angle, current amplitude calculated by active and reactive power approximation, and load factor calculated based on node capacity or historical maximum value.

[0008] In this embodiment of the invention, the spatial graph convolutional layer in the spatiotemporal graph encoder contains a learnable adjacency matrix; The initial value of the learnable adjacency matrix is ​​set as a matrix based on the correlation coefficient of node measurement data, and is updated during training through gradient descent.

[0009] In this embodiment of the invention, the spatial graph convolutional layer measures the potential connection strength between nodes through a learnable adjacency matrix. The current features of the nodes are linearly transformed, then weighted and summed according to the normalized weights of the learnable adjacency matrix, and finally updated through an activation function.

[0010] In this embodiment of the invention, the voltage reconstruction decoder includes a differentiable push-back simulation layer. The differentiable push-back simulation layer simulates voltage drop calculation based on linearized power flow according to the node spatiotemporal embedding feature vector and known node injected power data to obtain the predicted voltage.

[0011] In this embodiment of the invention, the physical consistency loss includes KCL constraint loss based on Kirchhoff's current law and radial constraint loss. The radial constraint loss avoids loops by penalizing non-zero elements in the power of the predicted adjacency matrix.

[0012] In this embodiment of the invention, the loss function further includes: edge prediction regularization loss; The edge prediction regularization loss introduces a regularization term to calculate the L1 norm of the probabilistic adjacency matrix.

[0013] In this embodiment of the invention, the unsupervised inference method for distribution network topology further includes: Before outputting the distribution network topology, the probability adjacency matrix representing the probability of nodes entering edges is binarized by applying a threshold to obtain a preliminary adjacency matrix. Then, a connected and acyclic radial network is generated using the minimum spanning tree algorithm or the parent node selection algorithm, which serves as the final distribution network topology.

[0014] In this embodiment of the invention, the unsupervised training of the spatiotemporal graph convolutional network model using measurement time-series data from each node of the distribution network includes: Step A: Preprocess the measurement time series data of each node in the distribution network, and construct an initial feature vector for each node in each time slice; Step B: Input the preprocessed measurement time series data into the spatiotemporal graph convolutional network model, and pass it through the spatiotemporal graph encoder and dual-branch decoder for forward propagation to obtain the predicted voltage and the probability adjacency matrix representing the probability of nodes entering edges. Step C: Calculate the voltage rebuilding loss and physical consistency loss, and calculate the total loss based on the voltage rebuilding loss and physical consistency loss; Step D: With the goal of minimizing the total loss, update the parameters of the spatiotemporal graph convolutional network model using the backpropagation algorithm; Step E: Repeat steps B through D until the rate of change of the total loss is less than the preset threshold.

[0015] A second aspect of the present invention provides an unsupervised inference system for distribution network topology, comprising: a spatiotemporal graph convolutional network model; The spatiotemporal graph convolutional network model is obtained through unsupervised training based on unlabeled measurement time-series data of each node in the distribution network. The spatiotemporal graph convolutional network model is used to infer the topology of the distribution network based on the input measurement time series data of the distribution network nodes to be inferred, and output the distribution network topology map. The spatiotemporal graph convolutional network model includes: a spatiotemporal graph encoder and a dual-branch decoder; The spatiotemporal graph encoder includes a temporal convolutional layer and a spatial graph convolutional layer, which are used to extract spatiotemporal correlation features from measurement time series data and output node spatiotemporal embedding feature vectors. The dual-branch decoder includes a voltage reconstruction decoder and an edge prediction decoder. The voltage reconstruction decoder calculates the predicted voltage based on the node spatiotemporal embedding feature vector, and the edge prediction decoder predicts the node edge entry probability based on the node spatiotemporal embedding feature vector. The loss function of the spatiotemporal graph convolutional network model includes voltage reconstruction loss and physical consistency loss. The voltage reconstruction loss is the error between the predicted voltage and the actual voltage measurement value. The physical consistency loss is determined based on the node edge probability under the constraint of the node current law.

[0016] In this embodiment of the invention, the unsupervised inference system for distribution network topology further includes: a feature construction module; The feature construction module is used to construct a feature vector for each node in each time slice based on the preprocessed measurement time-series data of each node; for a length of The time window will be used to determine the time window for each node. The feature vectors of each time slice are stacked into a feature matrix; The measurement timing data includes: voltage amplitude, voltage phase angle, active power, and reactive power; Each node's feature vector contains the original measurement values ​​from the measurement time series data, as well as multiple derived features, including: voltage change, sine and cosine values ​​of voltage phase angle, current amplitude calculated by active and reactive power approximation, and load factor calculated based on node capacity or historical maximum value.

[0017] In this embodiment of the invention, the spatial graph convolutional layer in the spatiotemporal graph encoder contains a learnable adjacency matrix; The initial value of the learnable adjacency matrix is ​​set as a matrix based on the correlation coefficient of node measurement data, and is updated during training through gradient descent.

[0018] In this embodiment of the invention, the spatial graph convolutional layer measures the potential connection strength between nodes through a learnable adjacency matrix. The current features of the nodes are linearly transformed, then weighted and summed according to the normalized weights of the learnable adjacency matrix, and finally updated through an activation function.

[0019] In this embodiment of the invention, the voltage reconstruction decoder includes a differentiable push-back simulation layer. The differentiable push-back simulation layer simulates voltage drop calculation based on linearized power flow according to the node spatiotemporal embedding feature vector and known node injected power data to obtain the predicted voltage.

[0020] In this embodiment of the invention, the physical consistency loss includes KCL constraint loss based on Kirchhoff's current law and radial constraint loss. The radial constraint loss avoids loops by penalizing non-zero elements in the power of the predicted adjacency matrix.

[0021] The above technical solution utilizes unlabeled measurement time-series data to construct a self-supervised (unsupervised) learning spatiotemporal graph convolutional network model through a spatiotemporal graph encoder and a dual-branch decoder. In the dual-branch decoder, the voltage reconstruction decoder calculates the predicted voltage based on the node spatiotemporal embedding feature vector, while the edge prediction decoder predicts the node's edge-entry probability based on the node's spatiotemporal embedding feature vector. The spatiotemporal graph convolutional network model is trained using "voltage reconstruction loss" as the primary driving signal, while also incorporating physical consistency loss based on node edge-entry probability under the constraint of the node current law. This enables direct and efficient inference of the unknown distribution network topology from the data. This invention does not rely on any real topology labels, nor does it require pre-constructing labeled simulated datasets. Instead, it utilizes only the actually acquired unlabeled measurement time-series data and trains the model through a self-supervised learning framework centered on "voltage reconstruction." The model, by forcing itself to learn the potential connections, can accurately reconstruct the observable voltage and indirectly infer the topology, achieving high-precision and high-efficiency topology inference without real topology labels.

[0022] Other features and advantages of the technical solution of the present invention will be described in detail in the following detailed embodiments section. Attached Figure Description

[0023] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings: Figure 1This is a flowchart of the unsupervised inference method for distribution network topology provided in an embodiment of the present invention; Figure 2 This is a flowchart illustrating the overall implementation of the unsupervised inference method for distribution network topology provided in this embodiment of the invention. Figure 3 This is a schematic diagram of the spatiotemporal graph convolutional network model provided in an embodiment of the present invention; Figure 4 This is an architecture diagram of the unsupervised inference system for distribution network topology provided in an embodiment of the present invention. Detailed Implementation

[0024] To make the technical solutions and advantages of the embodiments of the present invention clearer, the exemplary embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not an exhaustive list of all embodiments. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0025] As described in the background section, existing methods for inferring the topology of distribution networks based on intelligent optimization algorithms mainly include topology inference methods based on supervised graph neural networks (GNNs) and methods based on unsupervised physical models and optimization solutions.

[0026] Among them, the topology inference method based on supervised graph neural network (GNN) has the following typical implementation: (1) Data preparation: collect distribution network data or generate a large number of distribution network scenarios through simulation. Each scenario includes: node measurement time series data (voltage, power, etc.), and known and accurate topology labels (i.e., adjacency matrix); (2) Model construction and training: construct a graph neural network model. The model takes the measurement features of all nodes as input, aggregates neighbor information through message passing mechanism, and finally outputs a probability matrix representing the possibility of connection between nodes. The training of the model is a standard supervised learning process with the optimization objective of minimizing the difference between the predicted adjacency matrix and the real label (such as cross-entropy loss); (3) Inference: input the node measurement data of new and unknown topology into the trained model, and the model directly outputs the predicted topology. The core premise of this method is to have a large number of paired samples with accurate labels (scenario data, topology labels) for training. However, in real power grids, especially low-voltage distribution networks, complete and accurate topology connection files (i.e., tags) are often missing, outdated, or inconsistent with reality. This makes it extremely costly, or even impossible, to obtain sufficiently large and high-quality labeled data, which severely restricts the actual deployment and application of such supervised methods.

[0027] Another method based on unsupervised physical models and optimization solutions has the following typical implementation: (1) Problem modeling: Based on the physical laws of the power grid (such as branch power flow equations), a mathematical model is established. This model expresses the observed node measurement data (such as voltage amplitude difference, phase angle difference, and power) as a function of unknown topology connection variables and line parameters; (2) Optimization solution: The problem is formalized into a mixed integer nonlinear programming problem. The topology is represented by binary variables (0 / 1 represents connection or non-connection), and the line parameters are continuous variables. By designing specialized optimization algorithms (such as relaxation, decomposition, and heuristic search), the topology solution that minimizes the error between the model calculation value and the actual observation value is found under the premise of satisfying network constraints such as radial distribution; (3) Result output: After solving the optimization problem, the inferred topology connection relationship and the estimated value of the line parameters are obtained. Although this method does not require topology labels, its performance is heavily dependent on the accuracy of the established physical model and the efficiency of solving the optimization problem. The power flow equations of distribution networks are inherently nonlinear and nonconvex, making their optimization problems extremely complex and computationally time-consuming, thus failing to meet the requirements of real-time or near-real-time inference. Furthermore, the models are sensitive to measurement noise and missing data, easily getting trapped in local optima, resulting in poor stability and robustness of the inference results.

[0028] In existing technologies, supervised learning methods are limited by data labeling bottlenecks, while unsupervised physics optimization methods are constrained by model complexity and solution efficiency, and cannot achieve high-precision and high-efficiency topology inference without real topology labels.

[0029] This invention proposes an unsupervised inference method for distribution network topology using an unsupervised / self-supervised learning framework. It adopts a framework that combines self-supervised learning with a spatiotemporal graph convolutional network model. It can achieve high-precision and high-efficiency topology inference by using only easily obtainable node measurement time-series data and without any real topology labels.

[0030] This invention utilizes unlabeled measurement time-series data and constructs a self-supervised (unsupervised) learning spatiotemporal graph convolutional network model through a spatiotemporal graph encoder containing a learnable adjacency matrix and a dual-branch decoder. In the dual-branch decoder, the voltage reconstruction decoder calculates the predicted voltage based on the node spatiotemporal embedding feature vector, while the edge prediction decoder predicts the node's edge-entry probability based on the node's spatiotemporal embedding feature vector. The spatiotemporal graph convolutional network model is trained using "voltage reconstruction loss" as the primary driving signal, while also incorporating physical consistency loss based on node edge-entry probability under the constraint of the node current law. This enables direct and efficient inference of unknown distribution network topology from the data. This invention does not rely on any real topology labels, nor does it require pre-constructing labeled simulated datasets. Instead, it utilizes only the actually acquired unlabeled measurement time-series data and trains the model through a self-supervised learning framework centered on "voltage reconstruction." The model, by forcing itself to learn the latent connections, can accurately reconstruct the observable voltage and indirectly infer the topology, achieving high-precision and high-efficiency topology inference without real topology labels.

[0031] Figure 1 This is a flowchart of the unsupervised inference method for distribution network topology provided in an embodiment of the present invention. Figure 1 As shown, the unsupervised inference method for distribution network topology provided in this embodiment includes the following steps: S100: Unsupervised training of the spatiotemporal graph convolutional network model is performed using unlabeled measurement time-series data from each node of the distribution network until the loss function value of the spatiotemporal graph convolutional network model tends to stabilize, thus obtaining the trained spatiotemporal graph convolutional network model. S200 inputs the measurement time series data of the distribution network nodes to be inferred into the trained spatiotemporal graph convolutional network model, infers the distribution network topology through the spatiotemporal graph convolutional network model, and outputs the distribution network topology map.

[0032] The spatiotemporal graph convolutional network model includes a spatiotemporal graph encoder and a two-branch decoder. The spatiotemporal graph encoder comprises temporal convolutional layers and spatial graph convolutional layers, used to extract spatiotemporal correlation features from measurement time-series data and output node spatiotemporal embedding feature vectors. The two-branch decoder includes a voltage reconstruction decoder and an edge prediction decoder. The voltage reconstruction decoder calculates the predicted voltage based on the node spatiotemporal embedding feature vectors, while the edge prediction decoder predicts the node's edge input probability based on the node spatiotemporal embedding feature vectors.

[0033] Specifically, the spatial graph convolutional layer in the spatiotemporal graph encoder contains a learnable adjacency matrix. The learnable adjacency matrix is ​​initially set to a matrix based on the correlation coefficients of node measurement data and is updated during training via gradient descent.

[0034] Spatial graph convolutional layers learn adjacency matrices To measure the potential connection strength between nodes, the current features of the nodes are processed by a trainable weight matrix. After linear transformation, according to the learnable adjacency matrix The normalized weights are weighted and summed, and then the updated features are obtained through an activation function, thus achieving adaptive information aggregation without real topological priors.

[0035] Specifically, the voltage reconstruction decoder includes a differentiable push-back simulation layer. This differentiable push-back simulation layer can simulate voltage drop calculations based on linearized power flow without requiring precise line parameters, based on the node spatiotemporal embedding feature vector and known node injected power data, to obtain the predicted voltage. .

[0036] Specifically, the edge prediction decoder is implemented by a multilayer perceptron. Its input is the concatenation of the embedded feature vectors of any two nodes, and the output is mapped to a probability value between 0 and 1 by the sigmoid function. The probability values ​​of all node pairs formed by two nodes constitute the node edge probability.

[0037] The loss function of the spatiotemporal graph convolutional network model includes voltage reconstruction loss. and physical consistency loss Among them, voltage reconstruction loss For predicting voltage Error between actual voltage measurement and physical consistency loss It is determined based on the probability of incoming edges at nodes under the constraint of the node current law.

[0038] Physical consistency loss Including KCL constraint loss based on Kirchhoff's current law and radial constraint loss The formula for calculating KCL constraint loss is: ; in, Let be the probability adjacency matrix representing the probability of a node entering an edge. Middle node With nodes There is a probability that an edge exists between them. This indicates that the summation is performed for all non-roots ( )node.

[0039] Radial constraint loss Loops are avoided by penalizing non-zero elements in the powers of the predicted adjacency matrix. The total physical consistency loss is... ,in For weight hyperparameters.

[0040] Specifically, the loss function also includes edge prediction regularization loss. Predicting regularization loss A regularization term is introduced to calculate the L1 norm of the probabilistic adjacency matrix to prevent the spatiotemporal graph convolutional network model from outputting an overly dense or sparse connection structure.

[0041] Total loss of loss function Represented as: ,in , To balance the hyperparameters.

[0042] In a specific embodiment, the unsupervised inference method for distribution network topology further includes the following steps: before outputting the distribution network topology graph, the probability adjacency matrix representing the probability of node entry edges is processed. A threshold is applied to binarize the initial adjacency matrix, and then the minimum spanning tree algorithm or the parent node selection algorithm is used to generate a connected and acyclic radial network as the final distribution network topology.

[0043] In a specific embodiment, the unsupervised inference method for distribution network topology further includes the following steps: before inputting the measurement time-series data of the distribution network nodes to be inferred into the trained spatiotemporal graph convolutional network model (step S200), constructing the feature vectors of each node to be inferred. Alternatively, before performing unsupervised training on the spatiotemporal graph convolutional network model (step S100), constructing the feature vectors of each node in the distribution network.

[0044] The specific process of constructing the feature vectors of nodes includes: based on the preprocessed measurement time series data of each node, constructing the feature vectors of each node... Slice at each time Construct a feature vector For a length of The time window will be used to determine the time window for each node. The feature vectors of each time slice are stacked into a feature matrix. , For feature dimension, This represents the set of real numbers. The measurement time-series data includes: voltage amplitude, voltage phase angle, active power, and reactive power. The feature vector of each node contains the original measurement values ​​from the measurement time-series data, as well as several derived features, including: voltage change, sine and cosine values ​​of the voltage phase angle (used to eliminate phase winding effects), current amplitude calculated through active and reactive power approximations, and load factor calculated based on node capacity or historical maximum values.

[0045] In step S100 above, the spatiotemporal graph convolutional network model is trained unsupervised using the measurement time-series data of each node in the distribution network, including the following steps: Step A: Preprocess the measurement time series data of each node in the distribution network, including timestamp alignment, outlier removal and missing value imputation, and construct an initial feature vector for each node in each time slice; Step B: Input the preprocessed measurement time-series data into the spatiotemporal graph convolutional network model, and pass it through the spatiotemporal graph encoder and dual-branch decoder for forward propagation to obtain the predicted voltage. The probability adjacency matrix represents the probability of an edge entering a node. ; Step C: Calculate voltage reconstruction loss and physical consistency loss and voltage reconstruction loss and physical consistency loss and edge prediction regularization loss Weighted summation yields the total loss; Step D: With the goal of minimizing the total loss, update all trainable parameters in the spatiotemporal graph convolutional network model through the backpropagation algorithm, including: the learnable adjacency matrix in the spatiotemporal graph encoder, the weights of the temporal convolutional layer and the spatial graph convolutional layer, and the weights of the dual-branch decoder. Step E: Repeat steps B through D until the rate of change of the total loss is less than the preset threshold.

[0046] The following section describes the overall implementation process of this invention in detail, covering model construction, training, and application. (Refer to...) Figure 2 The overall implementation process of the unsupervised inference method for distribution network topology includes the following steps: Step 1: Data Preprocessing and Feature Construction. This step transforms the raw measurement time-series data, which may contain noise and missing values, into normalized features suitable for model input. First, data cleaning and alignment are performed. For the measurement data of the N input nodes (such as voltage amplitude V, voltage phase angle θ, active power P, reactive power Q, etc.), timestamp alignment is performed, obvious outliers (such as values ​​exceeding the physical reasonable range) are removed, and short-term missing data are filled using methods such as linear interpolation. Second, node feature construction is performed. For each node i, at each time slice t, an initial feature vector is constructed. eigenvectors It includes not only the original measurements but also their derived features to more comprehensively reflect the node state. Multiple derived features enhance the characterization of the node state: voltage changes. The sine and cosine values ​​of the voltage phase angle and Current amplitude calculated using active and reactive power approximations and load factor calculated based on node capacity or historical maximum value. ,in, Let be the voltage magnitude of node i at time t. Let be the voltage magnitude of node i at time t-1. Let be the voltage phase angle of node i at time t. Let be the square of the active power of node i at time t. Let be the square of the reactive power of node i at time t. Let be the active power of node i at time t. This is the maximum active power limit for node i. Finally, for a node of length... The time window will be used to determine the time window for each node. The feature vectors of each time slice are stacked into a feature matrix. ( (as feature dimension), for use by subsequent models.

[0047] Step 2: Construct a spatiotemporal graph convolutional network model. Design a spatiotemporal graph convolutional network with an encoder-decoder structure, such as... Figure 3 As shown, the Spatiotemporal Graph Encoder (ST-GCN Encoder) includes a Temporal Convolutional Layer (TCN) and a Spatial Graph Convolutional Layer (GCN). The TCN extracts the temporal dependencies of each node, while the GCN aggregates information from potential neighboring nodes. The purpose of the ST-GCN Encoder is to encode the temporal features of each node, along with information from its potential neighboring nodes, into a high-level feature vector that contains spatiotemporal correlations. Since the network does not know the real neighbors (i.e., topology) in the early stages of training, it can adaptively discover and aggregate the most relevant node information in the feature space through learnable spatial graph convolution.

[0048] Temporal convolutional layers (TCNs) process the input feature matrix By independently applying one-dimensional convolution or dilated convolution, we can capture its own time patterns such as power fluctuations and voltage changes.

[0049] For a spatial graph convolutional layer (GCN), a learnable adjacency matrix is ​​defined. To measure the potential connection strength between nodes, during training, the current features of a node are linearly transformed, then weighted and summed according to the normalized weights of the learnable adjacency matrix, and finally activated to obtain the updated features. In the spatial graph convolutional layer, for a node... , its first The feature update formula for a layer is: ; in, For nodes In the The layer's output feature vector (updated embedded features); For activation functions; This represents the total number of nodes in the distribution network. It is a learnable adjacency matrix; Represents a learnable adjacency matrix The row-normalized version after softmax Line 1 Column elements represent nodes For nodes Normalized connection strength; For the first The trainable weight matrix of the layer is used to perform linear transformations on the input features; For nodes In the The input feature vector of the layer; This indicates that for all nodes The contributions are summed to achieve information aggregation.

[0050] During the initialization of physical perception, in order to accelerate training and guide the model, The initial values ​​are not completely random, but are set as a matrix based on the correlation coefficients of nodal measurement data, providing the model with a starting point that conforms to electrical intuition.

[0051] The dual-branch decoder consists of two parallel heads, each corresponding to one of the two self-supervised training objectives. Decoder head A is the edge predictor, taking any two nodes as input (e.g., node A). i ,node j Embedding vectors of the node pairs and Output node through a multilayer perceptron (MLP) i ,node j The probability that an edge exists between them. : ; The probabilities of all nodes having an edge form a probability adjacency matrix. This is the direct output of topology inference.

[0052] The decoder head B is a voltage reconstructor (self-supervised signal source) that receives the embedding vector H of all nodes and the known node injection power (P, Q), and predicts the voltage of each node based on the learned latent connections (implied in H).

[0053] Specifically, a lightweight, differentiable push-back simulation layer is designed. This layer combines the connectivity information embedded in the vector H (e.g., through a weight matrix generated by H) with physical laws (such as voltage drop calculation based on linearized power flow) to calculate the predicted voltage. This layer does not require precise line parameters; its purpose is to teach the model a mapping rule that approximates the power flow relationship. The differentiable forward-backward simulation layer reconstructs the power flow calculation process of the forward-backward method into a differentiable computational graph, enabling it to be used as a layer in a neural network. While maintaining physical consistency, it supports optimization of network parameters through gradient descent. The forward-backward method is a classic numerical method for calculating power flow in radial distribution networks. Differentiable means that the computational graph of the simulation process supports automatic differentiation, i.e., the gradient of the output with respect to the input can be efficiently calculated. This allows the entire simulation layer to be embedded into a deep learning model and trained end-to-end through backpropagation. The differentiable forward-backward simulation layer acts as a learnable, physical model-based module in the neural network for modeling the power flow process.

[0054] Step 3: Unsupervised Training and Loss Function Design. The training strategy and loss function were improved. During forward propagation, preprocessed batch data was input into the model to obtain the predicted voltage. The probability adjacency matrix represents the probability of an edge entering a node. In the multi-task loss function calculation process, a composite loss function L guides the model to learn a topology that conforms to physical laws. The composite loss function L consists of the following three parts: Voltage rebuilding loss Calculate the predicted voltage Compared with the actual measured voltage input The mean square error (MSE) between the voltage and the signal, as the core of the self-supervised signal, requires the model to learn the correct topology and correlations in order to accurately reconstruct the voltage. Voltage reconstruction loss. Represented as: ; Physical consistency loss Physical laws are introduced as soft constraints, and a loss term based on Kirchhoff's Current Law (KCL) and the characteristics of radial networks is defined. For each node (except the root node), the sum of the predicted edge probabilities should be close to 1 (approximately representing that there is one and only one parent node). Radial constraints encourage the final generated graph to be tree-like, which can be achieved by calculating the power of the predicted adjacency matrix and penalizing non-zero elements to avoid the occurrence of loops. Edge prediction regularization loss To prevent the model from predicting overly dense or sparse connections, a regularization term is added, such as encouraging... The overall sparsity (L1 norm). ; Total loss Represented as: ;in and These are hyperparameters used to balance the weights of various losses.

[0055] During backpropagation and parameter update, the total loss is calculated. Regarding all trainable parameters of the model (including the learnable adjacency matrix) The gradient of the parameters is calculated, and the parameters are updated using an optimizer (such as Adam).

[0056] Step 4: Topology Inference Application. Once the model training has converged, it can be used to perform topology inference on new scenes.

[0057] Input new data: Obtain measurement data of the new block of the target distribution network and perform the same preprocessing as in step one.

[0058] Forward inference: The processed data is input into the trained model, which runs the encoder and decoder head A (edge ​​predictor) and directly outputs the probability adjacency matrix. .

[0059] Post-processing: processing the probability adjacency matrix Binarization is performed using a threshold (e.g., 0.5) to obtain a preliminary adjacency matrix. Then, post-processing steps such as the minimum spanning tree algorithm or simple parent node selection (selecting the incoming edge with the highest probability) are used to ensure that the output topology satisfies the strict physical constraint of a radial distribution network, generating the final topology connection graph.

[0060] The above technical solution provides a novel model training framework that does not rely on real topological connectivity labels. Instead, its training objective is to enable the model to accurately reconstruct or predict observable node voltage measurements based on its inferred potential connectivity relationships. This is achieved through a differentiable voltage reconstruction decoder head, where the error between the predicted and actual measurements (voltage reconstruction loss) serves as the primary self-supervised signal driving model learning. This allows the model to be trained using massive amounts of readily available unlabeled historical running data.

[0061] Building upon the self-supervised loss (voltage reconstruction loss), explicit physical consistency constraints are introduced as part of the loss function. These constraints directly encode the inherent physical laws of the distribution network, such as node inflow constraints based on Kirchhoff's Current Law (KCL) and topological constraints ensuring a radial network structure. This loss function embeds domain knowledge into the data-driven model in a differentiable form, forcing the model to not only fit the data during learning but also adhere to fundamental circuit laws. This significantly improves the inference stability and interpretability of results under noisy data, avoiding physically infeasible solutions that might arise from purely data-driven methods.

[0062] This invention presents an encoder network specifically designed for distribution network measurement data. The network employs a cascaded structure of Temporal Convolutional Network (TCN) + Spatial Graph Convolutional Network (GCN) to simultaneously capture the temporal dynamics of node features and the potential spatial relationships between nodes. The spatial graph convolutional layer operates on a learnable adjacency matrix initialized with node feature correlations, which is optimized along with other model parameters during training. Temporal convolution addresses the problem of temporal dependency modeling; while the learnable spatial graph convolution enables the model to adaptively discover and aggregate electrically relevant node information without prior topological knowledge, providing high-quality feature representations for subsequent edge prediction and voltage reconstruction.

[0063] The spatiotemporal graph convolutional network model of this invention employs a dual-branch decoder. One branch (edge ​​predictor) directly outputs the connection probabilities between nodes; the other branch (voltage reconstructor) uses encoded features and known power data to predict node voltages through a lightweight, differentiable forward-backward process. The voltage reconstruction branch is the source of the self-supervised signal; the edge predictor branch is the interface for the final application output. Both share the features extracted by the same encoder, ensuring that the learned features simultaneously serve the goals of correlation mining and satisfying physical laws, thereby achieving unsupervised training and end-to-end inference.

[0064] Furthermore, during the inference stage of the spatiotemporal graph convolutional network model, a post-processing step based on the minimum spanning tree algorithm or the parent node selection algorithm is introduced for the probability adjacency matrix output by the model. This step forces the fuzzy probability output to be transformed into a strict, connected, and acyclic radial network, ensuring that the final generated topology meets the physical structural constraints of the power distribution network. This ensures that regardless of the probability distribution of the model output, the final engineering output is a physically valid topology, greatly improving the practicality and reliability of the technical solution.

[0065] By integrating unsupervised learning, spatiotemporal graph modeling, and physical constraints, the above technical solution achieves a robust and computationally efficient distribution network topology inference that does not rely on real labels.

[0066] Compared with existing technologies (supervised GNN and unsupervised physics optimization methods), the technical solution of this invention has the following advantages: (1) Get rid of label dependence: The self-supervised learning based on voltage reconstruction loss is adopted, which can train the model without any real topological labels, solves the problem of scarce labeled data, and greatly reduces the deployment threshold; (2) Extremely high computational efficiency: It transforms the complex mixed-integer nonlinear programming problem into end-to-end forward propagation, with inference speed reaching the millisecond level, meeting the requirements of real-time or near-real-time applications; (3) Strong robustness: The spatiotemporal graph convolutional encoder has denoising capabilities, and the physical constraint loss guides the model output to tend towards physically feasible solutions, and has good tolerance for measurement noise and missing data; (4) Physical interpretability: KCL and radial constraints are embedded in the training phase, and a connected acyclic network is forcibly generated in the post-processing. The output topology strictly conforms to the physical laws of the power distribution network, and the results are reliable. (5) Make full use of unlabeled historical data: The unsupervised paradigm can digest massive amounts of unlabeled measurement data, enabling the model to learn a wider range of operating conditions and has excellent generalization ability.

[0067] Figure 4 This is an architecture diagram of the unsupervised inference system for distribution network topology provided in an embodiment of the present invention. Figure 4 As shown, the unsupervised inference system for distribution network topology provided in this embodiment includes: a spatiotemporal graph convolutional network model, which is obtained through unsupervised training based on the measurement time-series data of each node in the distribution network. The spatiotemporal graph convolutional network model is used to infer the distribution network topology based on the input measurement time-series data of the nodes to be inferred, and outputs a distribution network topology map. The spatiotemporal graph convolutional network model includes: a spatiotemporal graph encoder and a dual-branch decoder. The spatiotemporal graph encoder includes a temporal convolutional layer and a spatial graph convolutional layer, used to extract spatiotemporal correlation features from the measurement time-series data and output node spatiotemporal embedding feature vectors. The dual-branch decoder includes: a voltage reconstruction decoder and an edge prediction decoder. The voltage reconstruction decoder calculates the predicted voltage based on the node spatiotemporal embedding feature vectors, and the edge prediction decoder predicts the node edge entry probability based on the node spatiotemporal embedding feature vectors. The loss function of the spatiotemporal graph convolutional network model includes voltage reconstruction loss and physical consistency loss. The voltage reconstruction loss is the error between the predicted voltage and the actual voltage measurement value, and the physical consistency loss is determined based on the node edge entry probability under the constraint of the node current law.

[0068] In a specific embodiment, the unsupervised inference system for the distribution network topology further includes a feature construction module. The feature construction module is used to construct a feature vector for each node in each time slice based on the preprocessed measurement time-series data of each node; for a given length of... The time window will be used to determine the time window for each node. The feature vectors of each time slice are stacked to form a feature matrix. The measurement time series data includes: voltage amplitude, voltage phase angle, active power, and reactive power; the feature vector of each node contains the original measurement values ​​in the measurement time series data as well as multiple derived features, including: voltage change, sine and cosine values ​​of voltage phase angle, current amplitude calculated by approximation of active and reactive power, and load factor calculated based on node capacity or historical maximum value.

[0069] In a specific embodiment, the spatial graph convolutional layer in the spatiotemporal graph encoder includes a learnable adjacency matrix. The initial value of the learnable adjacency matrix is ​​set as a matrix based on the correlation coefficients of node measurement data, and it is updated during training using gradient descent. The spatial graph convolutional layer measures the potential connection strength between nodes using the learnable adjacency matrix. After linear transformation, the current features of the nodes are weighted and summed according to the normalized weights of the learnable adjacency matrix, and then passed through an activation function to obtain the updated features.

[0070] In a specific embodiment, the voltage reconstruction decoder includes a differentiable push-back simulation layer. The differentiable push-back simulation layer simulates voltage drop calculation based on linearized power flow according to the node spatiotemporal embedding feature vector and known node injected power data to obtain the predicted voltage.

[0071] In a specific embodiment, the physical consistency loss includes the KCL constraint loss based on Kirchhoff's current law and the radial constraint loss. The radial constraint loss avoids loops by penalizing non-zero elements in the power of the predicted adjacency matrix.

[0072] The loss function of the spatiotemporal graph convolutional network model also includes edge prediction regularization loss. Edge prediction regularization loss introduces a regularization term that calculates the L1 norm of the probabilistic adjacency matrix to prevent the spatiotemporal graph convolutional network model from outputting an overly dense or sparse connection structure.

[0073] In a specific embodiment, the spatiotemporal graph convolutional network model applies a threshold to the probability adjacency matrix representing the probability of nodes entering edges to binarize it into a preliminary adjacency matrix, and uses the minimum spanning tree algorithm or the parent node selection algorithm to forcibly generate a connected and acyclic radial network as the final distribution network topology.

[0074] In a specific embodiment, the spatiotemporal graph convolutional network model undergoes unsupervised training, including the following steps: Step A: Preprocess the measurement time series data of each node in the distribution network. The preprocessing includes timestamp alignment, outlier removal, and missing value imputation. An initial feature vector is constructed for each node in each time slice. Step B: Input the preprocessed measurement time-series data into the spatiotemporal graph convolutional network model, and pass it through the spatiotemporal graph encoder and dual-branch decoder for forward propagation to obtain the predicted voltage. The probability adjacency matrix represents the probability of an edge entering a node. ; Step C: Calculate voltage reconstruction loss and physical consistency loss and voltage reconstruction loss and physical consistency loss and edge prediction regularization loss Weighted summation yields the total loss; Step D: With the goal of minimizing the total loss, update all trainable parameters in the spatiotemporal graph convolutional network model through the backpropagation algorithm, including: the learnable adjacency matrix in the spatiotemporal graph encoder, the weights of the temporal convolutional layer and the spatial graph convolutional layer, and the weights of the dual-branch decoder. Step E: Repeat steps B through D until the rate of change of the total loss is less than the preset threshold.

[0075] The technical details of the unsupervised inference system for distribution network topology provided in this embodiment can be understood by referring to the specific implementation details of the unsupervised inference method for distribution network topology described above. This unsupervised inference system for distribution network topology has the same technical effect as the unsupervised inference method for distribution network topology described above, and will not be described again here.

[0076] The present invention also provides an electronic device, including: a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the above-described unsupervised inference method for power distribution network topology.

[0077] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of the present invention can be implemented using various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0078] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0079] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0080] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0081] The optional embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the embodiments of the present invention are not limited to the specific details in the above embodiments. Within the scope of the technical concept of the embodiments of the present invention, various simple modifications can be made to the technical solutions of the embodiments of the present invention, and these simple modifications all fall within the protection scope of the embodiments of the present invention. Furthermore, it should be noted that the various specific technical features described in the above specific embodiments can be combined in any suitable manner without contradiction. As long as such combination does not violate the spirit of the embodiments of the present invention, it should also be considered as the content disclosed in the embodiments of the present invention.

Claims

1. An unsupervised method for inferring the topology of a power distribution network, characterized in that, include: Unsupervised training of the spatiotemporal graph convolutional network model is performed using unlabeled measurement time-series data from each node of the distribution network to obtain a trained spatiotemporal graph convolutional network model. The measurement time series data of the distribution network nodes to be inferred are input into the trained spatiotemporal graph convolutional network model. The distribution network topology is inferred through the spatiotemporal graph convolutional network model, and the distribution network topology map is output. The spatiotemporal graph convolutional network model includes: a spatiotemporal graph encoder and a dual-branch decoder; The spatiotemporal graph encoder includes a temporal convolutional layer and a spatial graph convolutional layer, which are used to extract spatiotemporal correlation features from the measurement time series data and output node spatiotemporal embedding feature vectors. The dual-branch decoder includes a voltage reconstruction decoder and an edge prediction decoder. The voltage reconstruction decoder includes a differentiable push-back simulation layer. The differentiable push-back simulation layer simulates the voltage drop calculation based on linearized power flow to obtain the predicted voltage according to the node spatiotemporal embedding feature vector and the known node injection power data. The edge prediction decoder predicts the node edge entry probability according to the node spatiotemporal embedding feature vector. The loss function of the spatiotemporal graph convolutional network model includes voltage reconstruction loss and physical consistency loss. The voltage reconstruction loss is the error between the predicted voltage and the actual voltage measurement value. The physical consistency loss is determined based on the node edge probability under the constraint of the node current law.

2. The unsupervised inference method for distribution network topology according to claim 1, characterized in that, The method further includes: Before inputting the measurement time-series data of the distribution network nodes to be inferred into the trained spatiotemporal graph convolutional network model, feature vectors of each node are constructed. Methods for constructing the feature vectors of nodes include: Based on the preprocessed measurement time series data of each node, a feature vector is constructed for each node in each time slice; For a length of The time window will be used to determine the time window for each node. The feature vectors of each time slice are stacked into a feature matrix; The measurement timing data includes: voltage amplitude, voltage phase angle, active power, and reactive power; Each node's feature vector contains the original measurement values ​​from the measurement time series data, as well as multiple derived features, including: voltage change, sine and cosine values ​​of voltage phase angle, current amplitude calculated by active and reactive power approximation, and load factor calculated based on node capacity or historical maximum value.

3. The unsupervised inference method for distribution network topology according to claim 1, characterized in that, The spatial graph convolutional layer in the spatiotemporal graph encoder contains a learnable adjacency matrix; The initial value of the learnable adjacency matrix is ​​set as a matrix based on the correlation coefficient of node measurement data, and is updated during training through gradient descent.

4. The unsupervised inference method for distribution network topology according to claim 3, characterized in that, The spatial graph convolutional layer measures the potential connection strength between nodes through a learnable adjacency matrix. After linear transformation, the current features of the nodes are weighted and summed according to the normalized weights of the learnable adjacency matrix, and then the updated features are obtained through an activation function.

5. The unsupervised inference method for distribution network topology according to claim 1, characterized in that, The physical consistency loss includes Kirchhoff's current law-based KCL constraint loss and radial constraint loss, which avoids loops by penalizing non-zero elements in the powers of the predicted adjacency matrix.

6. The unsupervised inference method for distribution network topology according to claim 1, characterized in that, The loss function further includes: edge prediction regularization loss; The edge prediction regularization loss introduces a regularization term to calculate the L1 norm of the probabilistic adjacency matrix.

7. The unsupervised inference method for distribution network topology according to claim 1, characterized in that, The method further includes: Before outputting the distribution network topology, the probability adjacency matrix representing the probability of nodes entering edges is binarized by applying a threshold to obtain a preliminary adjacency matrix. Then, a connected and acyclic radial network is generated using the minimum spanning tree algorithm or the parent node selection algorithm, which serves as the final distribution network topology.

8. The unsupervised inference method for distribution network topology according to claim 2, characterized in that, The unsupervised training of the spatiotemporal graph convolutional network model using measurement time-series data from each node of the distribution network includes: Step A: Preprocess the measurement time series data of each node in the distribution network, and construct an initial feature vector for each node in each time slice; Step B: Input the preprocessed measurement time series data into the spatiotemporal graph convolutional network model, and pass it through the spatiotemporal graph encoder and dual-branch decoder for forward propagation to obtain the predicted voltage and the probability adjacency matrix representing the probability of nodes entering edges. Step C: Calculate the voltage rebuilding loss and physical consistency loss, and calculate the total loss based on the voltage rebuilding loss and physical consistency loss; Step D: With the goal of minimizing the total loss, update the parameters of the spatiotemporal graph convolutional network model using the backpropagation algorithm; Step E: Repeat steps B through D until the rate of change of the total loss is less than the preset threshold.

9. An unsupervised inference system for distribution network topology, characterized in that, include: Spatiotemporal graph convolutional network model; The spatiotemporal graph convolutional network model is obtained through unsupervised training based on unlabeled measurement time-series data of each node in the distribution network. The spatiotemporal graph convolutional network model is used to infer the topology of the distribution network based on the input measurement time series data of the distribution network nodes to be inferred, and output the distribution network topology map. The spatiotemporal graph convolutional network model includes: a spatiotemporal graph encoder and a dual-branch decoder; The spatiotemporal graph encoder includes a temporal convolutional layer and a spatial graph convolutional layer, which are used to extract spatiotemporal correlation features from the measurement time series data and output node spatiotemporal embedding feature vectors. The dual-branch decoder includes a voltage reconstruction decoder and an edge prediction decoder. The voltage reconstruction decoder includes a differentiable push-back simulation layer. The differentiable push-back simulation layer simulates the voltage drop calculation based on linearized power flow to obtain the predicted voltage according to the node spatiotemporal embedding feature vector and the known node injection power data. The edge prediction decoder predicts the node edge entry probability according to the node spatiotemporal embedding feature vector. The loss function of the spatiotemporal graph convolutional network model includes voltage reconstruction loss and physical consistency loss. The voltage reconstruction loss is the error between the predicted voltage and the actual voltage measurement value. The physical consistency loss is determined based on the node edge probability under the constraint of the node current law.

10. The unsupervised inference system for distribution network topology according to claim 9, characterized in that, Also includes: Feature building module; The feature construction module is used to construct a feature vector for each node in each time slice based on the preprocessed measurement time-series data of each node; for a length of The time window will be used to determine the time window for each node. The feature vectors of each time slice are stacked into a feature matrix; The measurement timing data includes: voltage amplitude, voltage phase angle, active power, and reactive power; Each node's feature vector contains the original measurement values ​​from the measurement time series data, as well as multiple derived features, including: voltage change, sine and cosine values ​​of voltage phase angle, current amplitude calculated by active and reactive power approximation, and load factor calculated based on node capacity or historical maximum value.

11. The unsupervised inference system for distribution network topology according to claim 9, characterized in that, The spatial graph convolutional layer in the spatiotemporal graph encoder contains a learnable adjacency matrix; The initial value of the learnable adjacency matrix is ​​set as a matrix based on the correlation coefficient of node measurement data, and is updated during training through gradient descent.

12. The unsupervised inference system for distribution network topology according to claim 11, characterized in that, The spatial graph convolutional layer measures the potential connection strength between nodes through a learnable adjacency matrix. After linear transformation, the current features of the nodes are weighted and summed according to the normalized weights of the learnable adjacency matrix, and then the updated features are obtained through an activation function.

13. The unsupervised inference system for distribution network topology according to claim 9, characterized in that, The physical consistency loss includes Kirchhoff's current law-based KCL constraint loss and radial constraint loss, which avoids loops by penalizing non-zero elements in the powers of the predicted adjacency matrix.

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