Transform-adaptive graph fusion-based power distribution network state estimation method
The state estimation method based on Transformer-adaptive graph fusion solves the problems of high accuracy and robustness in distribution network state estimation under sparse measurement and topology changes, and realizes efficient state estimation under complex operating conditions, which is applicable to the field of power system operation and control.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-01-08
- Publication Date
- 2026-03-31
AI Technical Summary
Existing distribution network state estimation methods struggle to achieve high accuracy and robustness under complex operating conditions such as sparse measurements, high noise, frequent topology changes, and uneven data. In particular, the adaptability and robustness of traditional methods are insufficient after the integration of distributed generation and flexible loads.
A state estimation method based on Transformer-adaptive graph fusion is adopted. By constructing an adaptive graph adjacency matrix and multi-order diffusion convolution, combined with time coding and spatial aggregation, spatiotemporal feature extraction and global accumulation of multi-source measurement data of the distribution network are realized. The TAGF-Net model is then constructed to estimate the voltage amplitude and phase angle end-to-end.
It maintains high-precision estimation under topology changes and noisy environments, possesses good topology adaptation capability and spatiotemporal feature joint modeling capability, significantly improves the robustness and accuracy of distribution network state estimation, and meets real-time requirements.
Smart Images
Figure CN121765322A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of power system operation and control technology, and in particular to a distribution network state estimation method based on Transformer-adaptive graph fusion. Background Technology
[0002] With the rapid development of new power systems and active distribution networks, Distribution System State Estimation (DSSE) has become one of the key functions of Energy Management Systems (EMS). By estimating the voltage amplitude and phase angle of nodes in real time, dispatchers can obtain the internal operating status of the distribution network, providing reliable data support for power flow calculation, online security assessment, fault diagnosis, and operational decision-making.
[0003] Compared to transmission networks, distribution networks exhibit several significant characteristics: First, measurement points are more sparsely distributed and heterogeneous, including synchronous phasor measurement units (PMUs), traditional SCADA meters, and pseudo-measurements constructed based on typical load curves; second, distribution network communication infrastructure is relatively weak, with some terminals only able to upload data with low bandwidth and long sampling intervals; third, with the high proportion of distributed power sources and flexible loads integrated, the randomness and uncertainty of node power injection are significantly enhanced, resulting in highly time-varying operating states; fourth, distribution networks frequently achieve flexible operation across multiple scenarios through switching operations and feeder reconfiguration, leading to frequent changes in network topology over time. The combination of these factors presents distribution network state estimation with a series of engineering challenges, including weak observability, high noise levels, uneven data quality, and incomplete topological information.
[0004] Existing DSSE methods can be broadly categorized into model-driven and data-driven approaches. Model-driven methods are mostly based on Weighted Least Squares (WLS) estimation. Under ideal conditions where network parameters are accurate, measurements are dense, and noise follows a Gaussian distribution, WLS possesses statistically optimal properties such as minimum variance, and has therefore long been a standard algorithm in traditional scheduling automation systems. To improve the robustness of WLS in scenarios with outliers and bad data, researchers have proposed improved schemes such as L1 norm state estimation, adaptive linear neural networks (ADALINE–LMM), and enhanced estimators based on the maximum exponential square criterion. These methods have improved tolerance for outliers and convergence performance to some extent. However, these methods still heavily rely on accurate network models and high-quality measurements. When parameters are uncertain, spurious measurement biases are large, or communication limitations lead to sparse observations, the algorithm performance is prone to significant degradation.
[0005] With the advancement of power distribution network digitization and machine learning technologies, data-driven state estimation methods have gained increasing attention. These methods typically utilize historical operational data to directly learn the nonlinear mapping relationship between measured quantities and system states, thereby mitigating the reliance on precise physical models to some extent. Some studies have proposed combining shallow neural networks with iterative algorithms such as Gauss-Newton to accelerate convergence and improve adaptability to topology changes; others have explicitly embedded Kirchhoff's laws into graphical models or Bayesian frameworks, combining power system physical constraints with probabilistic graphical models to improve estimation accuracy and physical consistency. Although these methods have demonstrated good performance in specific scenarios, most schemes still assume a fixed network topology, considering only static or a few topologies, resulting in insufficient adaptability to frequently reconfigured active distribution networks. Furthermore, the mechanisms used to enhance robustness are relatively simple, and performance remains limited in environments with increased noise, amplified spurious measurement errors, and severe data gaps.
[0006] Graph Neural Networks (GNNs) naturally fit the node-edge structure of power systems by performing message passing and aggregation operations on graphs. GNNs offer advantages such as parameter sharing and permutation equivariance for node relabeling, enabling them to automatically learn spatial correlations from measurement data while maintaining locality and physical interpretability. Existing research has applied GNNs to tasks such as PMU-based linear state estimation, joint parameter-state estimation considering physical constraints, and injection prediction, demonstrating advantages in accuracy, computational efficiency, and robustness to bad data. However, most graph learning methods still target single topologies or a small number of predefined topologies. When the network structure changes, retraining or offline fine-tuning based on transfer learning is required. This consumes significant time and computational resources and necessitates the collection of additional training samples under the new topology, making it difficult to meet the real-time requirements of practical engineering.
[0007] On the other hand, distribution network operation suffers from numerous spurious measurement and prediction errors. Distributed power generation output and load power are strongly influenced by meteorological conditions and user behavior, exhibiting significant temporal correlation and multi-timescale coupling characteristics. Traditional models that only consider static measurements or employ fixed-time-window convolution struggle to simultaneously capture short-term fluctuations and long-term periodic changes, and are insufficiently sensitive to abnormal disturbances caused by sudden events and communication packet loss. Therefore, how to jointly mine the temporal dynamics and potential spatial correlations of multi-source measurement data in distribution networks without relying on precise fixed topology, and maintain high accuracy and robustness under complex operating conditions such as noise, missing data, and topology changes, is a critical problem that urgently needs to be solved in the current DSSE (Distributed Power Grid Security) field. Summary of the Invention
[0008] To address the aforementioned technical problems, this invention provides a simple and robust method for power distribution network state estimation based on Transformer-adaptive graph fusion.
[0009] The technical solution of this invention to solve the above-mentioned technical problems is: a distribution network state estimation method based on Transformer-adaptive graph fusion, comprising the following steps:
[0010] Step 1: Establish a measurement model for power distribution network state estimation;
[0011] Step 2: Reconstruct the multi-time measurement data of the distribution network into a measurement tensor;
[0012] Step 3: Perform linear lifting on the measurement tensor to obtain the hidden feature tensor;
[0013] Step 4: Construct from The Transformer-Adaptive Graph Fusion Model, also known as the TAGF-Net model, is a series of spatiotemporal fusion blocks. It extracts spatiotemporal features from the hidden feature tensor layer by layer to obtain the global accumulated features.
[0014] Step 5: Input the global accumulated features into the dual-branch regression head to obtain the node voltage magnitude estimate and phase angle estimate;
[0015] Step 6: Train the TAGF-Net model offline based on the simulated ground truth of the samples;
[0016] Step 7: After obtaining the hidden feature tensor from the real-time measurement data of the distribution network collected online according to Step 2 and Step 3, input it into the trained TAGF-Net model, and obtain the voltage amplitude and phase angle estimates of each node at the current time through one forward propagation, thereby realizing the state estimation of the distribution network.
[0017] The above-mentioned distribution network state estimation method based on Transformer-adaptive graph fusion, in step one, denotes the multi-source measurement data including active power, reactive power, branch power flow, and pseudo-measurements as the measurement vector z. Considering a distribution network with n nodes, the state vector formed by the voltage amplitude and phase angle of each node is denoted as x. The measurement relationship is expressed as:
[0018]
[0019] in, To embed the nonlinear measurement function of line parameters and switch states, where v is the measurement noise; based on this, the traditional weighted least squares state estimation problem is:
[0020]
[0021] in, This is the optimal solution. This represents minimizing the objective function, where the superscript T denotes the transpose of the matrix, and W is the diagonal weight matrix. , Let be the variance of the m-th measurement channel.
[0022] In the above-mentioned distribution network state estimation method based on Transformer-adaptive graph fusion, step two involves using a length of... Sliding time window The measurement vectors at each time step are collected and rearranged according to node and channel dimensions to obtain the measurement tensor M. , Let be the measurement vector obtained at time t. , Measure the number of channels for each node. For the number of nodes, It is the field of real numbers.
[0023] The above-mentioned distribution network state estimation method based on Transformer-adaptive graph fusion, in step three, utilizes a one-dimensional... Convolution expands the channels to obtain the hidden feature tensor. :
[0024]
[0025] in, For the input convolution weights, For bias terms, To hide the feature dimension;
[0026] This enables the mapping from the original measurement channel to a unified feature space.
[0027] In the above-mentioned distribution network state estimation method based on Transformer-adaptive graph fusion, each spatiotemporal fusion block in step four includes a time coding submodule, an adaptive spatial aggregation submodule, and a residual and cross-layer accumulation module.
[0028] The temporal encoding submodule feeds the output of the previous layer into the Transformer-based temporal encoder, and processes the feature matrix output by the i-th node. Perform multi-head self-attention calculation. , The query matrix is obtained by finding the i-th diagonal element of the degree matrix of the i-th node. Key matrix Sum matrix And calculate the time-dependent weight matrix by scaling dot product attention. :
[0029]
[0030] This involves normalizing the matrix row-wise so that the sum of the elements in each row is 1; then, the weighted output is calculated and superimposed with the residual and the feedforward network to obtain the time-coded result. Concatenate all nodes to obtain the time-coded tensor ;
[0031] Adaptive Spatial Aggregation Submodule: Based on Two Node Embedding Matrices , , The intermediate feature matrix is obtained by transforming the number of channels embedded in the node through two fully connected layers. Calculate the similarity matrix The adaptive adjacency matrix is obtained after symmetrization, rectification, and row-wise softmax normalization. ;
[0032]
[0033] Where ReLU is a non-linear activation function;
[0034] Will As a diffusion graph convolution kernel, it is used for the time-encoded tensor Perform K-order diffraction convolution to obtain the spatial aggregation result. ;
[0035]
[0036] in, For the first The first in the spacetime fusion block Trainable weights for order diffusion, , The dimension of the spatial aggregation input features;
[0037] Residuals and cross-layer accumulation: Perform residual concatenation between the spatial aggregation result and the input of the previous layer;
[0038]
[0039] in, For the first The feature matrix output by each spatiotemporal fusion block;
[0040] And for all The outputs of each spatiotemporal fusion block are summed to obtain the global accumulated feature. :
[0041] .
[0042] In the above-mentioned distribution network state estimation method based on Transformer-adaptive graph fusion, step five involves... Input two layers in sequence Convolution and nonlinear activation are used to refine features and obtain intermediate features. Then, through a gated structure composed of two independent gated linear units (GLUs), the voltage amplitude branching characteristics are obtained respectively. Phase angle branching characteristics Then through each branch Convolution achieves temporal compression, and through the final... Convolution output node voltage magnitude estimation Phase Angle Estimation .
[0043] In the aforementioned distribution network state estimation method based on Transformer-adaptive graph fusion, step five involves the gated linear unit reweighting the channel responses of both the voltage magnitude branch and the phase angle branch to obtain the voltage magnitude branch features. Phase angle branching characteristics for:
[0044]
[0045] in, Indicates element-wise product. , respectively through The gating coefficient matrix obtained from convolution and activation functions is used to suppress redundant features and achieve multi-task decoupling.
[0046] In the above-mentioned distribution network state estimation method based on Transformer-adaptive graph fusion, in step six, during the offline training phase, a multi-topology, multi-operating-condition, and multi-noise sample set is constructed using a simulation platform. Specifically, on multiple distribution network benchmark models, various radial topologies are generated by switching switch states, different operating scenarios are constructed by randomly sampling load ratios and distributed power outputs, and Gaussian white noise is superimposed on the measurements to simulate measurement errors. The measurements and actual node voltages at each moment under each scenario are recorded, and measurement tensors are generated in the manner of step two to construct training sets, validation sets, and test sets.
[0047] Using the actual voltage amplitude V and phase angle As a monitoring signal, the mean square error loss function is used. Optimize network parameters:
[0048]
[0049] in, For the voltage magnitude estimation of the i-th node, This represents the actual voltage amplitude at the i-th node. For the phase angle estimation of the i-th node, Let be the true phase angle of the i-th node.
[0050] In the aforementioned distribution network state estimation method based on Transformer-adaptive graph fusion, step six involves using the Adam optimization algorithm to iteratively update network parameters, monitoring validation set loss to achieve early shutdown, and determining the hidden feature dimension through hyperparameter search. diffusion order K, number of spatiotemporal fusion blocks Learning rate, batch size, and weight decay coefficient.
[0051] The beneficial effects of this invention are as follows:
[0052] 1. Strong Topology Adaptability. This invention replaces the traditional graph convolution kernel that relies on a fixed admittance matrix with an adaptive dynamic graph adjacency matrix constructed through trainable node embeddings and Softmax normalization. This adjacency matrix automatically learns the potential dependencies between nodes in the feature space, and can capture electrically influential node pairs even in the absence of precise line parameters and switch state information, through historical measurement data. In test scenarios containing unseen topologies, the method of this invention can maintain an estimation accuracy similar to that of the trained topology, demonstrating its good adaptability to topology changes.
[0053] 2. Spatiotemporal Feature Joint Modeling. By integrating Transformer temporal coding and diffusion graph convolution within a unified framework, this invention can simultaneously mine the long-term and short-term dynamic features and local / remote spatial correlations of distribution network measurement data. Multi-order diffusion convolution expands the receptive field while maintaining locality, capturing multi-hop electrical couplings, thus maintaining stable performance even in scenarios with increased noise, severe load fluctuations, and large spurious measurement errors.
[0054] 3. Excellent estimation accuracy and robustness. On the standard test set and topology generalization test set of the IEEE 33-bus system, the voltage magnitude and mean absolute error (MAE) of the method of this invention are maintained at a high level. Compared to representative baseline models such as GWNet, SCINet, fixed-topology GCN, and CNNs that only model temporal convolutions, this invention achieves the minimum MAE in both scenarios. Particularly in the topology generalization test set, this invention demonstrates orders of magnitude improvement in both magnitude and phase MAE metrics compared to methods like CNNs, indicating its strong robustness to noise, missing data, and topology changes.
[0055] 4. End-to-end, efficient, and easily scalable. This invention employs an end-to-end network structure comprised of linear lifting, spatiotemporal fusion, and gated regression to achieve a one-time mapping from multi-source measurements to state estimation, avoiding the Jacobian matrix construction and multiple linearization processes required by traditional iterative solutions. The parameter sharing and local filtering characteristics of the graph convolutional layers make the computational complexity approximately linear with the number of network edges, facilitating its expansion into larger-scale distribution networks. After training, online inference consists of a single forward propagation, and the computational overhead meets the real-time requirements of existing dispatch automation systems.
[0056] 5. Good physical consistency and interpretability. This invention can integrate power flow constraint terms into the loss function to impose physical constraints on the estimation results; at the same time, the diffusion convolution kernel and the adaptive adjacency matrix have clear meanings of "information propagation path", the attention weight reflects the contribution of different times to the current estimation, and the gating coefficient characterizes the importance of different feature channels, which helps operation and maintenance personnel understand the model decision-making process and improves the trust in engineering applications. Attached Figure Description
[0057] Figure 1 This is a flowchart of the present invention.
[0058] Figure 2 This is a schematic diagram of the IEEE 33-node distribution network topology and measurement configuration.
[0059] Figure 3 This is a training and validation loss curve of the present invention on the IEEE 33-node system.
[0060] Figure 4 This is a bar chart showing the distribution of the average absolute error of voltage amplitude in the standard test set for this invention.
[0061] Figure 5 This is a bar chart showing the distribution of the average absolute error of the phase angle in the standard test set for this invention.
[0062] Figure 6 This is a bar chart showing the distribution of the average absolute error of voltage amplitude on the topology generalization test set according to the present invention.
[0063] Figure 7 This is a bar chart showing the distribution of the average absolute error of the phase angle on the topology generalization test set of this invention. Detailed Implementation
[0064] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0065] like Figure 1 As shown, a distribution network state estimation method based on Transformer-adaptive graph fusion includes the following steps:
[0066] Step 1: Establish a measurement model for power distribution network state estimation.
[0067] In step one, the multi-source measurement data, including active power, reactive power, branch power flow, and pseudo-measurements, is denoted as measurement vector z. Considering a distribution network with n nodes, the state vector formed by the voltage amplitude and phase angle of each node is denoted as x. The measurement relationship is expressed as:
[0068]
[0069] in, To embed the nonlinear measurement function of line parameters and switch states, where v is the measurement noise; based on this, the traditional weighted least squares state estimation problem is:
[0070]
[0071] in, This is the optimal solution. This represents minimizing the objective function, where the superscript T denotes the transpose of the matrix, and W is the diagonal weight matrix. , Let be the variance of the m-th measurement channel.
[0072] However, the effectiveness of this model relies on the following assumptions: precise knowledge of network parameters and topology information, relatively dense measurement deployment, noise following an independent and identically distributed Gaussian distribution, and small spurious measurement errors. In actual distribution networks, line parameters often exhibit uncertainty, the real-time status of some switches cannot be obtained, spurious measurements suffer from systematic bias and heavy-tailed distribution, and the time-series correlation caused by distributed generation output and load fluctuations violates the assumption of measurement independence. These factors can lead to slow convergence or even divergence in the iterative process, and the estimation results are highly sensitive to bad data, making it difficult to meet the state awareness requirements of active distribution networks under complex operating conditions.
[0073] Step 2: Reconstruct the multi-time measurement data of the distribution network into a measurement tensor.
[0074] To overcome the limitations of traditional methods, this embodiment reconstructs the state estimation task into a spatiotemporal learning problem. To explicitly characterize the temporal dynamics of the distribution network's operating state, this invention uses a length of... Sliding time window The measurement vectors at each time step are collected and rearranged according to node and channel dimensions to obtain the measurement tensor M. , Let be the measurement vector obtained at time t. , Measure the number of channels for each node. For the number of nodes, It is in the real number field. This measurement tensor, as the input to the subsequent neural network, preserves the spatial and temporal distribution characteristics of the multi-source measurements.
[0075] Step 3: Perform linear boosting on the measurement tensor to obtain the hidden feature tensor.
[0076] To unify the feature dimensions of different types of measurements and improve their expressive power, this invention sets up a measurement lifting layer at the network input end to perform channel expansion on the measurement tensor M, specifically by utilizing one-dimensional... Convolution expands the channels to obtain the hidden feature tensor. :
[0077]
[0078] in, For the input convolution weights, For bias terms, To hide the feature dimension, the measurement lifting layer is essentially a node-by-node, time-step linear transformation used to map measurements with different dimensions and ranges to a unified high-dimensional feature space, providing a foundation for subsequent nonlinear feature extraction.
[0079] Step 4: Construct from The Transformer-Adaptive Graph Fusion Model, also known as the TAGF-Net model, is composed of a series of spatiotemporal fusion blocks. It extracts spatiotemporal features from the hidden feature tensor layer by layer to obtain the globally accumulated features.
[0080] In step four, each spatiotemporal fusion block includes a time coding submodule, an adaptive spatial aggregation submodule, and a residual and cross-layer accumulation module;
[0081] The temporal encoding submodule employs a multi-head self-attention mechanism, independently computing scaled dot-product attention on multiple attention heads. The outputs of each head are then concatenated along the channel dimension and subjected to linear transformation and a feedforward network to obtain temporal features fused from different temporal patterns. The temporal encoding submodule feeds the output of the previous layer into a Transformer-based temporal encoder, processing the feature matrix output by the i-th node. Perform multi-head self-attention calculation. , The query matrix is obtained by finding the i-th diagonal element of the degree matrix of the i-th node. Key matrix Sum matrix And calculate the time-dependent weight matrix by scaling dot product attention. :
[0082]
[0083] This involves normalizing the matrix row-wise so that the sum of the elements in each row is 1; then, the weighted output is calculated and superimposed with the residual and the feedforward network to obtain the time-coded result. Concatenate all nodes to obtain the time-coded tensor This enables the network to have an adaptive temporal receptive field;
[0084] Adaptive Spatial Aggregation Submodule: To reduce dependence on fixed electrical topology and address the issues of incomplete or dynamically changing topology information in practical applications, this invention constructs an adaptive adjacency matrix through trainable node embedding; based on two node embedding matrices... , , The intermediate feature matrix is obtained by transforming the number of channels embedded in the node through two fully connected layers. Calculate the similarity matrix The adaptive adjacency matrix is obtained after symmetrization, rectification, and row-wise softmax normalization. ;
[0085]
[0086] Where ReLU is a non-linear activation function;
[0087] Will As a diffusion graph convolution kernel, it is used for the time-encoded tensor Perform K-order diffraction convolution to obtain the spatial aggregation result. ;
[0088]
[0089] in, For the first The first in the spacetime fusion block Trainable weights for order diffusion, , The dimension of spatial aggregation input features; while maintaining locality, the aggregation of multi-hop neighborhood information is achieved to capture long-distance electrical coupling and cross-regional interactions caused by network reconstruction;
[0090] Residuals and cross-layer accumulation: Perform residual concatenation between the spatial aggregation result and the input of the previous layer;
[0091]
[0092] in, For the first The feature matrix output by each spatiotemporal fusion block;
[0093] And for all The outputs of each spatiotemporal fusion block are summed to obtain the global accumulated feature. This enhances the receptive field and alleviates the gradient vanishing problem;
[0094] .
[0095] Step 5: Input the global cumulative feature into the dual-branch regression head to obtain the node voltage magnitude estimate and phase angle estimate.
[0096] In step five, Input two layers in sequence Convolution and nonlinear activation are used to refine features and obtain intermediate features. Then, through a gated structure composed of two independent gated linear units (GLUs), the voltage amplitude branching characteristics are obtained respectively. Phase angle branching characteristics Then through each branch Convolution achieves temporal compression, and through the final... Convolution output node voltage magnitude estimation Phase Angle Estimation .
[0097] The gated linear unit reweights the channel responses for both the voltage amplitude branch and the phase angle branch to obtain the voltage amplitude branch characteristics. Phase angle branching characteristics for:
[0098]
[0099] in, Indicates element-wise product. , respectively through The gating coefficient matrix obtained from convolution and activation functions is used to suppress redundant features and achieve multi-task decoupling.
[0100] Step 6: Train the TAGF-Net model offline based on the simulated ground truth of the samples.
[0101] In step six, during the offline training phase, a multi-topology, multi-operating-condition, and multi-noise sample set is constructed using a simulation platform. Specifically, on multiple distribution network benchmark models, various radial topologies are generated by switching switch states. Different operating scenarios are constructed by randomly sampling load ratios and distributed power outputs. Gaussian white noise is superimposed on the measured quantities to simulate measurement errors. Measurements at each moment under each scenario and the actual node voltages are recorded. Measurement tensors are generated in the manner described in step two to construct training sets, validation sets, and test sets.
[0102] Using the actual voltage amplitude V and phase angle As a monitoring signal, the mean square error loss function is used. Optimize network parameters:
[0103]
[0104] in, For the voltage magnitude estimation of the i-th node, This represents the actual voltage amplitude at the i-th node. For the phase angle estimation of the i-th node, Let be the true phase angle of the i-th node.
[0105] The Adam optimization algorithm is used to iteratively update the network parameters, early stopping is achieved by monitoring the validation set loss, and the hidden feature dimension is determined through hyperparameter search. diffusion order K, number of spatiotemporal fusion blocks Learning rate, batch size, and weight decay coefficient.
[0106] Step 7: After obtaining the hidden feature tensor from the real-time measurement data of the distribution network collected online according to Step 2 and Step 3, input it into the trained TAGF-Net model, and obtain the voltage amplitude and phase angle estimates of each node at the current time through one forward propagation, thereby realizing the state estimation of the distribution network.
[0107] like Figure 2 As shown in the figure, this embodiment presents the overall process of distribution network state estimation based on TAGF-Net, including the following three stages:
[0108] (1) Data Synthesis and Partitioning: Using the PANDAPOWER simulation platform, power flow calculations were performed on multiple reference distribution feeders (including the IEEE 33-bus system). Various radial topologies were generated through random switching, and Monte Carlo sampling was used to change the load factor and distributed power output to cover a wide range of operating conditions. Independent and identically distributed Gaussian noise was superimposed on each measurement channel to construct a multi-source dataset containing real measurements, pseudo-measurements, and virtual measurements. The time series was divided according to window length. The stacks form a measurement tensor and are divided into training, validation, and test sets in chronological order.
[0109] (2) Offline training and model selection: The Adam optimizer was used to train TAGF-Net end-to-end on the training set. The performance on the validation set was monitored to achieve early stopping. Hyperparameters such as hidden dimension, diffusion order, number of spatiotemporal fusion blocks, and learning rate were determined by grid search or Bayesian optimization. The loss function was the sum of the mean square errors of voltage amplitude and phase angle.
[0110] (3) Online inference and generalization evaluation: During the online operation phase, the real-time measurements collected are constructed into a measurement tensor through a sliding time window and input into the trained TAGF-Net. The node-level voltage amplitude and phase angle are estimated through one forward inference. In order to evaluate the generalization ability, the model is tested in the test phase under topologies that have appeared in the training and topologies that have not appeared, and the performance of the model under topology extrapolation and load extrapolation conditions is examined.
[0111] This embodiment uses the IEEE 33-node power distribution network as the test system, such as... Figure 3 As shown, numerical verification of the method of the present invention is performed.
[0112] 1) Measurement Configuration and Dataset Construction: Three synchronous phasor measurement units (PMUs) are configured in this system. Their voltage amplitude measurement errors follow zero-mean Gaussian noise with a standard deviation of 0.1%, and their phase angle measurement errors have a standard deviation of [missing information]. Approximately half of the busbars are equipped with conventional SCADA meters to collect node voltage amplitudes and active and reactive power flow data for some branches. The measurement sampling interval is set to 15 minutes. Typical daily load curves are peak-normalized and superimposed with a 10% random disturbance. The resulting load trajectories are then distributed to each load node, and power flow calculations are performed using the PANDAPOWER toolbox to obtain the complete state vector. For nodes without physical meters, pseudo-measurements of active and reactive power injection are constructed using typical curves, and missing voltage or power flow components are filled with a constant 1× This results in a unified input tensor.
[0113] Under the above configuration, 42 radial topologies that satisfy voltage constraints are randomly generated. Each topology is simulated for 480 consecutive time steps, resulting in a total of 20,160 time series samples. These samples are then divided into training set, validation set, and standard test set in a 7:2:1 ratio. Additionally, 18 new topologies that do not share structural patterns with the training set are generated. Each topology is simulated for 480 time steps, resulting in 8,640 samples that constitute the topology generalization test set.
[0114] 2) Training Setup and Hyperparameters: Bayesian hyperparameter optimization was performed using the Optuna framework, and the final selected parameters were... =12、 =12、 , =2, learning rate 1× Batch size 32, Dropout rate 0.1, Weight decay coefficient 1× Configurations, etc. Training and validation loss curves are shown below. Figures 4-7 As shown, Figures 4-7 Medium, MAE v This represents the average absolute error of the voltage amplitude. This represents the mean absolute error of the phase angle. Figure 4 This indicates that when the measurement configuration and operating range do not deviate significantly, the model can stably extract the main variation patterns of voltage amplitude. Nodes with larger errors typically correspond to feeder front / branch connections or locations with more drastic voltage changes; their amplitudes are more sensitive to load disturbances and power flow redistribution, leading to some unevenness in the error distribution among nodes. Both converge smoothly and become close to each other after several iterations, indicating that the optimization process is stable and there is no significant overfitting. Figure 5 This indicates that the model relies more on network topology and measurement coverage in the phase angle dimension, and the error is more easily amplified when at nodes with weak observation or large power flow changes. Figure 6 This indicates that the generalization degradation in the amplitude dimension is relatively limited; Figure 7 This indicates that the inter-node differences and extreme values of phase angle error are more prominent in the generalization test.
[0115] 3) Test Results and Comparative Analysis: On the standard test set and the topology generalization test set, the node-level voltage magnitude and phase angle MAE of the method of this invention remain stable. The error trends of different nodes in the two test sets are highly consistent, with only a few nodes showing a slight increase in error under topology switching, indicating that the adaptive dynamic graph mechanism can effectively maintain the node-level estimation quality.
[0116] Meanwhile, GWNet, SCINet, Fixed Topology Graph Convolutional Network (GCN), and Temporal Convolutional Network (CNN) that does not explicitly model spatial dependencies were selected as baseline models for comparison, and their parameters were tuned using Bayesian optimization. The comparison results on the standard test set and the topology generalization test set are shown in Tables 1-6.
[0117]
[0118]
[0119]
[0120]
[0121]
[0122]
[0123] In both scenarios, the method of this invention achieves the best results in terms of voltage amplitude and phase angle MAE. It has significant advantages over SCINet, which only models temporal convolution, and GCN, which only uses fixed topology. Compared with GWNet, which uses an adaptive graph structure, the method of this invention also improves the accuracy of sample-level topology detection and the accuracy of state estimation.
[0124] As can be seen from the above embodiments, the power distribution network state estimation method based on Transformer-adaptive graph fusion proposed in this invention exhibits high estimation accuracy and robustness in multi-topology, multi-operating-condition, and multi-noise environments, verifying the effectiveness of the technical solution and its engineering application value.
Claims
1. A distribution network state estimation method based on Transformer-adaptive graph fusion, characterized in that, Includes the following steps: Step 1: Establish a measurement model for power distribution network state estimation; Step 2: Reconstruct the multi-time measurement data of the distribution network into a measurement tensor; Step 3: Perform linear lifting on the measurement tensor to obtain the hidden feature tensor; Step 4: Construct from The Transformer-Adaptive Graph Fusion Model, also known as the TAGF-Net model, is a series of spatiotemporal fusion blocks. It extracts spatiotemporal features from the hidden feature tensor layer by layer to obtain the global accumulated features. Step 5: Input the global accumulated features into the dual-branch regression head to obtain the node voltage magnitude estimate and phase angle estimate; Step 6: Train the TAGF-Net model offline based on the simulated ground truth of the samples; Step 7: After obtaining the hidden feature tensor from the real-time measurement data of the distribution network collected online according to Step 2 and Step 3, input it into the trained TAGF-Net model, and obtain the voltage amplitude and phase angle estimates of each node at the current time through one forward propagation, thereby realizing the state estimation of the distribution network.
2. The distribution network state estimation method based on Transformer-adaptive graph fusion according to claim 1, characterized in that, In step one, the multi-source measurement data, including active power, reactive power, branch power flow, and pseudo-measurements, is denoted as measurement vector z. Considering a distribution network with n nodes, the state vector formed by the voltage amplitude and phase angle of each node is denoted as x. The measurement relationship is expressed as: ； in, To embed the nonlinear measurement function of line parameters and switch states, where v is the measurement noise; based on this, the traditional weighted least squares state estimation problem is: ； in, This is the optimal solution. This represents minimizing the objective function, where the superscript T denotes the transpose of the matrix, and W is the diagonal weight matrix. , Let be the variance of the m-th measurement channel.
3. The distribution network state estimation method based on Transformer-adaptive graph fusion according to claim 2, characterized in that, In step two, the length is Sliding time window The measurement vectors at each time step are collected and rearranged according to node and channel dimensions to obtain the measurement tensor M. , Let be the measurement vector obtained at time t. , Measure the number of channels for each node. For the number of nodes, It is the field of real numbers.
4. The distribution network state estimation method based on Transformer-adaptive graph fusion according to claim 3, characterized in that, In step three, one-dimensional... Convolution expands the channels to obtain the hidden feature tensor. : ； in, For the input convolution weights, For bias terms, To hide the feature dimension; This enables the mapping from the original measurement channel to a unified feature space.
5. The distribution network state estimation method based on Transformer-adaptive graph fusion according to claim 4, characterized in that, In step four, each spatiotemporal fusion block includes a time coding submodule, an adaptive spatial aggregation submodule, and a residual and cross-layer accumulation module; The temporal encoding submodule feeds the output of the previous layer into the Transformer-based temporal encoder, and processes the feature matrix output by the i-th node. Perform multi-head self-attention calculation. , The query matrix is obtained by finding the i-th diagonal element of the degree matrix of the i-th node. Key matrix Sum matrix And calculate the time-dependent weight matrix by scaling dot product attention. : ； This involves normalizing the matrix row-wise so that the sum of the elements in each row is 1; then, the weighted output is calculated and superimposed with the residual and the feedforward network to obtain the time-coded result. Concatenate all nodes to obtain the time-coded tensor ; Adaptive Spatial Aggregation Submodule: Based on Two Node Embedding Matrices , , The intermediate feature matrix is obtained by transforming the number of channels embedded in the node through two fully connected layers. Calculate the similarity matrix The adaptive adjacency matrix is obtained after symmetrization, rectification, and row-wise softmax normalization. ; ； Where ReLU is a non-linear activation function; Will As a diffusion graph convolution kernel, it is used for the time-encoded tensor Perform K-order diffraction convolution to obtain the spatial aggregation result. ; ； in, For the first The first in the spacetime fusion block Trainable weights for order diffusion, , The dimension of the spatial aggregation input features; Residuals and cross-layer accumulation: Perform residual concatenation between the spatial aggregation result and the input of the previous layer; ； in, For the first The feature matrix output by each spatiotemporal fusion block; And for all The outputs of each spatiotemporal fusion block are summed to obtain the global accumulated feature. : 。 6. The distribution network state estimation method based on Transformer-adaptive graph fusion according to claim 5, characterized in that, In step five, Input two layers in sequence Convolution and nonlinear activation are used to refine features and obtain intermediate features. Then, through a gated structure composed of two independent gated linear units (GLUs), the voltage amplitude branching characteristics are obtained respectively. Phase angle branching characteristics Then through each branch Convolution achieves temporal compression, and through the final... Convolution output node voltage magnitude estimation Phase Angle Estimation .
7. The distribution network state estimation method based on Transformer-adaptive graph fusion according to claim 6, characterized in that, In step five, the gated linear unit reweights the channel response for both the voltage amplitude branch and the phase angle branch to obtain the voltage amplitude branch characteristics. Phase angle branching characteristics for: ； in, Indicates element-wise product. , respectively through The gating coefficient matrix obtained from convolution and activation functions is used to suppress redundant features and achieve multi-task decoupling.
8. The distribution network state estimation method based on Transformer-adaptive graph fusion according to claim 7, characterized in that, In step six, during the offline training phase, a multi-topology, multi-operating-condition, and multi-noise sample set is constructed using a simulation platform. Specifically, on multiple distribution network benchmark models, various radial topologies are generated by switching switch states. Different operating scenarios are constructed by randomly sampling load ratios and distributed power outputs. Gaussian white noise is superimposed on the measured quantities to simulate measurement errors. Measurements at each moment under each scenario and the actual node voltages are recorded. Measurement tensors are generated in the manner described in step two to construct training sets, validation sets, and test sets. Using the actual voltage amplitude and phase angle as monitoring signals, the mean square error loss function is employed. Optimize network parameters: ； in, For the voltage magnitude estimation of the i-th node, This represents the actual voltage amplitude at the i-th node. For the phase angle estimation of the i-th node, Let be the true phase angle of the i-th node.
9. The distribution network state estimation method based on Transformer-adaptive graph fusion according to claim 8, characterized in that, In step six, the Adam optimization algorithm is used to iteratively update the network parameters, early stopping is achieved by monitoring the validation set loss, and the hidden feature dimension is determined through hyperparameter search. diffusion order K, number of spatiotemporal fusion blocks Learning rate, batch size, and weight decay coefficient.