Power system state estimation method and system based on edge aggregation graph attention network

Abstract

The invention provides a power system state estimation method and system based on an edge aggregation graph attention network, and high-precision and high-robustness power system state estimation is realized by combining a graph attention mechanism, edge feature aggregation and physical equation constraint. The core target of the invention is to enhance the contribution degree of edge features in state estimation; dynamically distributing attention weights of the nodes and the lines; and model output is ensured to strictly meet physical equation constraints of the power system.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent monitoring and control of power systems, and particularly relates to a power system state estimation method and system integrating cyber-physical constraints and graph attention network. Background Technique

[0002] Power system state estimation is one of the core technologies for the safe and stable operation of the power grid. Its goal is to infer the operating state of the system in real time through measurement data and power grid topology information. Traditional methods, such as weighted least squares method, Kalman filter, etc., rely on strict mathematical models but are insufficient in adapting to measurement noise, topology changes, and nonlinear problems.

[0003] In recent years, although the state estimation methods based on deep learning can capture data features, they have the following problems: they do not fully model the graph structure characteristics of the power grid, such as the physical laws of electrical connections between nodes; they ignore the inherent physical constraints of the power system, resulting in the estimation results may violate the actual physical laws; they are less sensitive to the dynamic changes at the edges of the power grid.

[0004] Therefore, there is an urgent need for a new power system state estimation method to solve the above problems. Summary of the Invention

[0005] The present invention provides a power system state estimation method and system based on an edge-aggregated graph attention network, which is used to improve the accuracy and robustness of state estimation in a complex power grid environment, and at the same time has the characteristics of high accuracy with small samples and fast convergence.

[0006] Technical Solution:

[0007] The present invention discloses a power system state estimation method based on an edge-aggregated graph attention network, including:

[0008] According to the topological structure and measurement data of the power system, a topological graph model of the power system is established, which represents nodes as vertices and transmission lines as edges;

[0009] Based on the topological graph model, an EGAT model is constructed, including a node feature encoding layer for accepting a set of node features and a set of edge features and generating a new set of node features; an edge feature aggregation module for accepting a set of node features and a set of edge features and generating a new set of edge features; a cyber-physical constraint module for training a neural network and fitting the solution of the power system state estimation problem;

[0010] Based on the real-time measurement data of the power system, the EGAT model is used for power system state estimation.

[0011] Further, the establishment of the topological graph model of the power system includes:

[0012] The power system is abstracted into a node-branch model and mathematically described in the form of a graph ; among them, the node set covers N nodes in the power grid, and each node is associated with a voltage magnitude V i , phase angle θ i , the edge set contains all transmission lines connecting nodes, and the transmission characteristics of each line are quantitatively characterized by the active power flow P ij and the reactive power flow Q ij .

[0013] Furthermore, the node features of the topological graph model include focused voltage and power injection, and the edge features include physical quantities that characterize line admittance and power transmission.

[0014] Furthermore, the power system state estimation problem is expressed as:

[0015]

[0016] At any time t, the system uses the noisy measurement data Z from N nodes t to solve for the state vector X of the nodes in the power grid i to achieve power system state estimation, there is:

[0017] Z t = h(X i ) + e t

[0018] where the function h(·) is defined based on the underlying topological relationship of the power grid and is used to characterize various combinations of power flows; e t represents the error vector introduced during the measurement process.

[0019] Furthermore, the attention coefficient a ij in the node feature encoding layer is expressed as:

[0020]

[0021] where h i and h j represent the hidden layer representations of nodes i and j, represents the edge feature connecting the i-th and j-th nodes, and N i represents the set of all nodes connected to node i, and a is a learnable attention weight vector;

[0022] The updated feature vector of the nodes in the node feature encoding layer is:

[0023]

[0024] Among them, σ represents the non-linear activation function, and N i represents the set of all nodes connected to the i-th node, is the feature vector of the neighbor node j.

[0025] Furthermore, the edge feature aggregation module accepts a set of node features and a set of edge features, and generates a new set of edge features;

[0026] The node feature set is transformed into an adjacency form by using the node mapping matrix. For each edge p, the normalized attention weight of edge q is expressed as:

[0027]

[0028] where N p is the first-order neighbor set of edge p, is a weight vector;

[0029] The new set of edge features in the edge feature aggregation module is expressed as:

[0030]

[0031] where β pq is the attention coefficient between node p and neighbor q, is the original feature vector of neighbor node q.

[0032] Furthermore, the physical information constraint module includes a data-driven machine learning model loss and a physics-driven physical loss:

[0033] The machine learning model loss is used to measure the difference between the observed data and the neural network prediction. The loss function under data driving is the difference between the state parameters output by the neural network and the true value:

[0034]

[0035] where y i is the predicted value of the data-driven model, is the true value;

[0036] The physical loss is the residual of the physical constraint equation, and the loss function is the imbalance of the node and line equations, expressed as:

[0037]

[0038] where P i is the active power injection of each node, Q i is the reactive power of each node, V i is the voltage amplitude of the node, θ i is the voltage phase angle of the node; P ijis the active power of the line, Q ij is the reactive power of the line, g ij is the conductance of the line, b ij is the susceptance of the line; y ic is the shunt susceptance to ground at node i;

[0039] The loss function expression for the fusion of physical drive and data drive is:

[0040]

[0041] where, ω i is the weight of each part of the imbalance, and the sum of all weights is 1.

[0042] Furthermore, using the EGAT model for power system state estimation includes: inputting the real-time measurement data P i , Q i , P ij and Q ij into the EGAT model, and outputting the node voltage magnitude V i and phase angle θ i that satisfy the physical constraints.

[0043] A computer system includes a memory, a processor, and a computer program stored on the memory, and the processor executes the computer program to implement the steps of the above method.

[0044] A computer-readable storage medium stores a computer program thereon, and when the computer program is executed by a processor, it implements the steps of the above method.

[0045] Beneficial effects: Compared with the prior art, the significant advantages of the present invention are:

[0046] (1) Deep mining of edge features: Traditional methods mostly focus on node features, while ignoring the key role of edge features such as the admittance and power flow of transmission lines in state estimation. The present invention constructs an EGAT model based on the topological graph model of the power system by designing a multi-granularity edge aggregation layer, explicitly fuses the features of the line itself and its adjacent edges, and constructs a high-dimensional edge feature representation.

[0047] (2) Dynamic attention allocation: In response to the challenges of dynamic changes in the power grid topology and measurement noise interference, the present invention introduces an adaptive graph attention mechanism to dynamically adjust the weights of nodes and edges through a node feature encoding layer and an edge feature aggregation module. Different from the traditional fixed adjacency matrix, this mechanism automatically adjusts the intensity of information propagation between nodes according to real-time measurement data and network status.

[0048] (3) Physical law guarantee: The pure data-driven model may deviate from the basic physical laws of the power system due to training bias or noise interference. The present invention innovatively encodes Kirchhoff's law and the power balance equation as hard constraint terms of the loss function, adds a physically driven loss function to the physical information constraint module, and forces the network output to strictly conform to the physical laws of the power grid. By jointly optimizing the data-driven loss and the physical constraint loss, the model synchronously learns the statistical characteristics of the measurement data and the physical essence of the power grid operation during the training process. Description of the Drawings

[0049] Figure 1 It is the EGAT network architecture diagram;

[0050] Figure 2 It is the line graph comparing the voltage amplitudes obtained from the EGAT prediction and the Matpower simulation of the IEEE 33-node system;

[0051] Figure 3 It is the comparison diagram of the model performance under different training sample scales;

[0052] Figure 4 It is the training Loss curve graph. Detailed Implementation Manner

[0053] The following further clarifies the present invention in conjunction with the drawings and the detailed implementation manner. It should be understood that the following detailed implementation manner is only used to illustrate the present invention and not to limit the scope of the present invention. After reading the present invention, various equivalent forms of modification by those skilled in the art fall within the scope defined by the appended claims of this application.

[0054] The present invention provides a power system state estimation method based on a physically informed constrained edge aggregation graph attention network. The process is as Figure 1 shown and includes the following steps:

[0055] Step (1): Establish a topological graph model.

[0056] According to the topological structure and measurement data of the power system, establish a topological graph model of the power system. This model represents nodes and transmission lines as vertices and edges in the graph and captures their characteristics.

[0057] Considering that the power system has a complex network architecture, highly digitized system components, diverse node attributes, and edge feature attributes, it is naturally suitable for graph structure modeling methods.

[0058] Specifically, the power system can be abstracted into a node-branch model and described mathematically in the form of a graph where the node set covers N nodes in the power grid, and each node is associated with core parameters such as voltage amplitude and phase angle, denoted as V iand θ i , the edge set contains all the transmission lines connecting the nodes, and the transmission characteristics of each line are quantified and characterized by the active power flow P ij and the reactive power flow Q ij ; Node characteristics: Focus on key attributes such as voltage and power injection, denoted as X i ; Edge characteristics: Characterize physical quantities such as line admittance and power transmission, denoted as E ij ; Through the above modeling, the multi-dimensional characteristics of nodes and edges are systematically integrated, providing a structured data basis for subsequent analysis.

[0059] The standard SE problem can be formulated as an optimization challenge to solve the following equations:

[0060]

[0061] At any time t, the core task of state estimation is to solve the state vector X of all buses (i.e., nodes in the power grid i ). To achieve this goal, the system utilizes noisy measurement data Z t from N nodes, and these data can be described by the equation Z t = h(X i ) + e t . Among them, the function h(·) is defined based on the underlying topology of the power grid and is used to characterize various combinations of power flows; e t represents the error vector introduced during the measurement process.

[0062] In this embodiment, the specific operation of this step is as follows: Based on the network architecture and measurement information of the IEEE 33-node standard test system, this study first constructed a power network topology structure model. To generate a large-scale time-series data set, the MATPOWER tool was used to simulate the system operating state. It is assumed that within the time interval of conventional SCADA state estimation, the system operating state remains relatively stable. On this basis, uniform (or normal) distribution perturbations are applied to the node load levels through random sampling, and a power flow sample set covering 50,000 different operating conditions is generated. In the model, the power grid topology is abstracted as a graph structure: the power generation nodes and load nodes are mapped to vertices, the transmission cables correspond to edges, and the electrical parameter characteristics of each element are fully recorded.

[0063] Step (2): Construct the EGAT model.

[0064] Construct an EGAT model containing a physical information constraint module, including a node feature encoding layer, an edge feature aggregation module, and a physical information constraint module. The network architecture of the EGAT model constructed in this embodiment is as Figure 2As shown in Figure 2, the constructed model extracts node features and edge features of the power grid through node aggregation and edge aggregation, and accelerates fitting in the training process that includes physical constraints.

[0065] Furthermore, the structure of the EGAT for state estimation in step (2) includes:

[0066] (2.1) Node feature encoding layer.

[0067] The core function of the node feature encoding layer is to process the initial node features H and edge feature data E, and output the updated node feature set H′ after internal calculations. Since the input edge features are usually arranged in a fixed order, it is difficult to directly establish the association relationship between the edge and its connected nodes. This module first restructures the original edge feature E.

[0068] Specifically, by introducing a dimensionally expanded mapping tensor, the original two-dimensional edge feature set is converted into a three-dimensional structure E containing node pair information. * In the converted edge features, each edge can clearly identify the node indexes connected to its two ends, for example, using represents the edge feature connecting the i-th and j-th nodes. This dimension expansion process is essentially achieved with the help of the three-dimensional edge mapping matrix M E The completed matrix space transformation enables the features of each edge to establish an accurate spatial correspondence with its corresponding node pair, thus overcoming the dimensional limitations of the traditional adjacency matrix in complex association modeling.

[0069] Before matrix multiplication, the edge mapping matrix needs to be reshaped so that its dimensions match the input tensor. After the operation is completed, the output result is converted into the format of an adjacency matrix, thereby mapping the original edge set to the connection relationship between nodes. Since the structure of the edge mapping matrix depends on the order of nodes and edges in the graph, its construction process can be completed once in the preprocessing stage before model training.

[0070] With the expression of the adjacency matrix, the model can efficiently locate the associated edges between any two nodes. On this basis, each node calculates the neighbor weight through the edge integrated attention mechanism, which combines the node characteristics and the attribute information of the connecting edge. For the target node i, the system will calculate the neighbor weight for itself and its directly connected neighbor nodes. Generate weight coefficient w ij These features are concatenated, linearly transformed using a learnable weight vector, and activated by the LeakyReLU function.

[0071] Finally, the softmax function is used to normalize all weights to ensure that the weight distribution of node j conforms to the probabilistic characteristics. The above process can be simplified into the following expression:

[0072]

[0073] When integrating features, the node not only fuses the information of adjacent nodes but also retains its own features. When the system does not contain edge features, the processing flow can be simplified by expanding the adjacency matrix (such as adding an identity matrix). However, after introducing edge features, the complexity of this process increases significantly.

[0074] To solve this problem, the present invention proposes to dynamically add virtual self-loop edges to the nodes lacking self-connections in the graph. Specifically, the eigenvalue of the virtual edge will be dynamically generated according to the average value of its adjacent edges in each dimension, so as to balance the information integrity. The above preprocessing operations need to be completed before the data is input into the model. Subsequently, the weighted fusion of adjacent node features is performed using the normalized attention weights, and the aggregation result is transformed through the non-linear activation function σ. Finally, the output of the node feature encoding layer can be expressed as:

[0075]

[0076] In particular, in the present invention, only the node features are aggregated to generate a new set of node features. The edge features only play a role in the weight calculation and are not part of the new node features. If the edge features are merged into the nodes in each iteration, all the features will be entangled, making the network more complex and chaotic. In fact, a set of node features H with edge fusion is also generated in the node feature encoding layer m , for each node i, its new edge integrated feature is generated as follows:

[0077]

[0078] These features will only be used in the final merging layer to achieve multi-scale cascading, and these features will not be passed as input to the next EGAT layer. Multi-scale cascading can enhance adaptability, and the final merging layer fuses features at different levels, enabling the model to capture both local measurement details (such as node voltage amplitude) and integrate global topological associations (such as regional power balance), and is applicable to the state estimation of power grids of different scales.

[0079] (2.2) Edge Feature Aggregation Module.

[0080] The node features are periodically updated in the node feature encoding layer to obtain high-level features, and it is unreasonable to repeatedly use the original low-level edge features during the weight calculation process. In addition, high-level edge features are required to balance the importance of nodes and edges. Therefore, an edge feature aggregation module is proposed. Each edge feature aggregation module receives a set of node features H and a set of edge features E and generates a new set of edge features E′.

[0081] A natural idea to achieve such chunking is to update the features of each edge by aggregating the features of adjacent edges. In an undirected graph, two edges are considered adjacent only when they have at least one common vertex.

[0082] To achieve aggregation, first switch the roles of nodes and edges in the graph.

[0083] The inputs of node and edge features are organized in the same sequence form. Thanks to the symmetric design, it is easy to perform the attention mechanism on the new graph, and the node feature set is converted to the adjacency form by using M H (node mapping matrix). For each edge p, the normalized attention weight of edge q can be expressed as:

[0084]

[0085] where N p is the set of first-order neighbors of edge p (including p), is a weight vector of size . When calculating the attention weight between any edge and itself, there is no intermediate node between the two edges. In this embodiment, an empty node is created between the two edges, and all features of this virtual node are filled with zeros. Similar to node features, the calculation of the new edge feature set can be expressed as:

[0086]

[0087] (2.3) Physical information constraint module.

[0088] In the general PINN formula, a neural network is trained to fit the solution of the state estimation by minimizing a loss function consisting of two terms. The first term is the machine learning model loss Loss data , which is used to measure the difference between the observed data and the neural network prediction. The second term is the physical loss Loss f , which is a residual of the physical constraint equation.

[0089] To incorporate the physical constraints, the neural network is trained by taking the equations of the neural network output with respect to the input variables, so that the neural network satisfies the control equations. Then these derivatives are combined with the equations to form the physical loss term. By minimizing the overall loss function, the neural network learns to produce solutions that not only effectively fit the provided data but also follow the underlying physics of the system. Mathematically, the basic form of PINN is expressed as equations and equations respectively, which include the general form of the equations and the function approximation provided by the neural network.

[0090] where the data-driven loss function is the difference between the state parameters output by the neural network and the true values

[0091]

[0092] The loss function driven by physics is the imbalance between the node and line equations:

[0093]

[0094] where P i is the active power injection at each node, Q i is the reactive power at each node, V i is the voltage magnitude of the node, θ i is the voltage phase angle of the node; P ij is the active power of the line, Q ij is the reactive power of the line, g ij is the conductance of the line, b ij is the susceptance of the line; y ic is the susceptance to ground at node i;

[0095] Therefore, the loss function under the fusion of physics and data is expressed as:

[0096]

[0097] Step (3): State estimation.

[0098] Based on the established EGAT model, power system state estimation is carried out. By inputting measurement data, the model can output a high-precision system state vector, including information such as voltage and phase angle.

[0099] Online state estimation is to input the real-time measurement data P i , Q i , P ij and Q ij into the EGAT model, and output the node voltage magnitude V i and phase angle θ i that satisfy the physical constraints. The model inference process is as follows:

[0100] Input preprocessing: Normalize the measurement data (voltage, power) and construct a real-time topology map;

[0101] Feature extraction: Based on the multi-granularity edge aggregation layer and the adaptive attention mechanism, extract spatio-temporal features through the node feature encoding layer and the edge feature aggregation module of the model;

[0102] Constraint optimization: Through the physical information constraint module of the model, adjust the network parameters in combination with the physical loss to ensure that the output conforms to power balance;

[0103] Result output: Obtain the final state estimation value after denormalization.

[0104] To verify the actual effect of the proposed method, in this embodiment, the weighted least squares method (WLS), graph neural network (GNN), and graph attention network (GAT) are selected as comparison methods, and their significant advantages in state estimation accuracy and anti-interference ability are verified through multi-dimensional performance tests. Under the condition that the measurement data contains Gaussian white noise, the estimation accuracy of the method and the generalization performance of the model are tested. To simultaneously reflect the estimation accuracy of the node voltage amplitude and the node voltage phase angle difference, the node voltage amplitude and the node voltage phase angle are taken as examples respectively. Table 1 shows the performance of different algorithms.

[0105] Table 1 Comparison of errors and efficiencies of various algorithms in the IEEE-33 node system

[0106]

[0107] To visually display the results of different estimation methods, the test set data is compared with the true value of the power flow to obtain the maximum absolute error and the average absolute error. Figure 3 Figure [X] shows the voltage phase angle error results obtained for the IEEE 33-node system when the measurement information contains Gaussian white noise. As can be seen from Figure 3 it, the results predicted by the model disclosed in this application have a good fitting effect with the true values, and this model can effectively perform high-precision state estimation.

[0108] In addition, the innovation of this study lies in explicitly embedding the physical constraints of the power system into the neural network training process, constructing a hybrid loss function guided by domain knowledge, and significantly improving the data utilization efficiency and physical consistency of the model.

[0109] First, different numbers of training samples are taken between 5000 and 50000 for training, and the prediction accuracies obtained under the same number of training epochs with and without physical constraints are recorded respectively, and a line chart is drawn. As can be seen from Figure 4 it, when setting the same number of training epochs, for the model with physical constraints to achieve a prediction accuracy of 0.01, the number of training samples required by the model with physical constraints is less than that of the model without physical constraints. The improvement effect of physical constraints on small sample scenarios is particularly significant: when the number of training samples is less than 15000 groups, the reduction amplitude of the mean absolute error (MAE) of the constrained model reaches 27.78%, but as the sample size increases to 50000 groups, the performance difference between the two types of models is reduced to less than 7%. This phenomenon verifies the application value of the physical constraint mechanism in the scenario of limited data in the power grid. This phenomenon can be explained by the "Inductive Bias" theory.

[0110] In addition, to test the training efficiency after adding physical constraints, the loss values during the training process without and with physical constraints are recorded. The training curve of the IEEE 33-node system is asFigure 4 As shown. The training curves of the three models gradually converge at 20 times. Among them, the loss value curve of the model with physical constraints in this application drops faster and the convergence speed is faster than that of other models. However, due to the different directions of decline of the model loss of machine learning and the model loss of physical constraints in the loss function, there will be large fluctuations at the beginning of training.

Claims

1. A power system state estimation method based on an edge aggregation graph attention network, characterized in that Including: Based on the topological structure and measurement data of the power system, a topological graph model of the power system is established, which represents nodes as vertices and transmission lines as edges. An EGAT model is constructed based on the topological graph model, including a node feature encoding layer for receiving a set of node features and a set of edge features and generating a new set of node features; an edge feature aggregation module for receiving a set of node features and a set of edge features and generating a new set of edge features. A physical information constraint module for training a neural network and fitting the solution to the power system state estimation problem. Based on the real-time measurement data of the power system, the EGAT model is used for power system state estimation.

2. The power system state estimation method according to claim 1, characterized in that The establishment of the topological graph model of the power system includes: The power system is abstracted into a node-branch model and mathematically described in the form of a graph ; among them, the node set covers N nodes in the power grid, and each node is associated with a voltage magnitude V i , phase angle θ i , the edge set contains all the transmission lines connecting the nodes, and the transmission characteristics of each line are quantitatively characterized by the active power flow P ij and reactive power flow Q ij .

3. The power system state estimation method according to claim 2, characterized in that, The node features of the topological graph model include focused voltage and power injection, and the edge features include physical quantities characterizing line admittance and power transmission.

4. The power system state estimation method according to claim 3, wherein The power system state estimation problem is expressed as: At any time t, the system uses the noisy measurement data Z from N nodes t to solve for the node state vector X i in the power grid to achieve power system state estimation, there is: Z t = h(X i ) + e t Among them, the function h(·) is defined based on the underlying topology of the power grid; e t represents the error vector introduced during the measurement process.

5. The power system state estimation method according to claim 4, wherein The attention coefficient a of the node feature encoding layer ij is expressed as: where h i and h j represent the hidden layer representations of nodes i and j, represents the edge feature connecting the i-th and j-th nodes, and N i represents the set of all nodes connected to node i, and a is a learnable attention weight vector; The new node features in the node feature encoding layer are expressed as: where σ represents the non-linear activation function, and N i represents the set of all nodes connected to node i, is the feature vector of neighbor node j.

6. The power system state estimation method according to claim 5, wherein The edge feature aggregation module receives a set of node features and a set of edge features and generates a new set of edge features. The node feature set is converted into an adjacency form by using a node mapping matrix. For each edge p, the normalized attention weight of edge q is expressed as: Among them, N p is the first-order neighbor set of edge p, is the weight vector; The new edge features in the edge feature aggregation module are expressed as: Among them, β pq is the attention coefficient between node p and neighbor q, and is the original feature vector of neighbor node q.

7. The power system state estimation method according to claim 6, characterized in that, The physical information constraint module includes a data-driven machine learning model loss and a physics-driven physical loss: The machine learning model loss is used to measure the difference between the observed data and the neural network prediction, and the loss function is: Among them, y i is the predicted value of the data-driven model, which is the true value; The physical loss is the residual of the physical constraint equation, and the loss function is the imbalance of the node and line equations, expressed as: Among them, P i is the active power injected into each node, Q i is the reactive power of each node, V i is the voltage amplitude of the node, θ i is the voltage phase angle of the node; P ij is the active power of the line, Q ij is the reactive power of the line, g ij is the conductance of the line, b ij is the susceptance of the line; y ic is the susceptance to ground of node i; The loss function expression of the fusion of physics-driven and data-driven is: where ω i is the weight of the unbalance of each part, and the sum of all weights is 1.

8. The power system state estimation method according to claim 7, characterized in that, Using the EGAT model for power system state estimation includes: Normalize the real-time measurement data, construct a real-time topology map, and input it into the pre-trained EGAT model. The real-time measurement data includes P i , Q i , P ij and Q ij ; The EGAT model outputs the node voltage amplitude V i and the phase angle θ i .

9. A computer system, comprising a memory, a processor, and a computer program stored on the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the method according to claims 1 to 8.

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