Smart power grid state estimation method and system based on space-time diagram convolutional network, and medium

Abstract

The invention discloses a smart power grid state estimation method and system based on a space-time diagram convolutional network, and a medium, and the method comprises the steps: building a topological graph model of a power system according to the topological structure and measurement data of a smart power grid; an STGCN model containing a plurality of space-time convolution blocks is constructed, each space-time convolution block captures time dependence of time sequence data through a time gating convolution layer, and space features of the smart power grid are extracted through a space graph convolution layer; and establishing a power grid state estimation model based on the STGCN model to perform power system state estimation. According to the method, the accuracy and the reliability of an estimation result are ensured by fusing a space and time convolution technology. State estimation challenges under various topological structures can be effectively handled, stable estimation performance can be maintained, and a powerful guarantee is provided for safe operation of a smart power grid. And the operation efficiency and the response speed of the smart power grid are greatly improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of smart grids, and particularly relates to a smart grid state estimation method, system and medium based on a spatio-temporal graph convolutional network. Background Technique

[0002] Smart grids play an important supporting role in aspects such as energy transformation, grid stability, power transmission, and power interconnection. The state estimation of smart grids depends on accurate models and measurement data. Traditional methods have difficulties in terms of computational complexity and adaptability to topological changes. With the development of smart grids, nodes and transmission lines form a natural graph structure, making the application of graph networks (Graph Convolutional Networks, abbreviated as GCN) possible. In recent years, advancements in the field of artificial intelligence, such as recurrent neural networks (RNN), convolutional neural networks (CNN), and long short-term memory networks (LSTM), have improved the accuracy of state estimation by utilizing time series data. However, these methods still have deficiencies in simultaneously capturing the spatial and temporal characteristics of smart grids. Therefore, there is an urgent need to develop a smart grid state estimation method and system based on a spatio-temporal graph convolutional network, so as to provide a more accurate and practical solution for smart grid state estimation. Summary of the Invention

[0003] Object of the Invention: To solve the above technical problems, the present invention provides a smart grid state estimation method, system and medium based on a spatio-temporal graph convolutional network.

[0004] Technical Solution: A smart grid state estimation method based on a spatio-temporal graph convolutional network provided by the present invention includes the following steps:

[0005] According to the topological structure and measurement data of the smart grid, establish a topological graph model of the power system to quantify the connection relationship between nodes. This model represents nodes and transmission lines as vertices and edges in the topological graph, generates an adjacency matrix by quantifying the connection relationship between nodes, and captures the time series data of vertices and edges;

[0006] Construct a spatio-temporal graph convolutional network STGCN model including multiple spatio-temporal convolutional blocks. Each spatio-temporal convolutional block includes a time-gated convolutional layer and a spatial graph convolutional layer. The time-gated convolutional layer extracts the time dependence of the time series data and captures the evolution trend of the state quantity on the time axis. The spatial graph convolutional layer, based on the generated adjacency matrix, quantifies the connection strength between nodes and aggregates neighborhood information to extract the spatial characteristics of the smart grid;

[0007] A power grid state estimation model is established based on the spatio-temporal graph convolutional network (STGCN) model for power system state estimation. By inputting measurement data and utilizing the evolution trend of the captured state variables on the time axis, a high-precision system state vector, including information such as voltage and phase angle, is output through the fusion of jointly extracted spatial features of the smart grid, thereby estimating the state of the smart grid.

[0008] Among them, the topological graph model can abstractly represent the physical structure and electrical connection relationship of the power system, clearly describe the adjacency relationship, connection strength, and overall topological characteristics between nodes; provide structured data support for subsequent power system analysis, state assessment, and optimal dispatching; and can dynamically adapt to changes in the power grid topology. By updating the adjacency matrix to adjust the node connection relationship, it ensures that the neighborhood propagation range of the spatial graph convolutional layer is consistent with the actual power grid structure.

[0009] Through the time-gated convolutional layer, hierarchical extraction of the temporal characteristics of the measurement data is carried out, which can effectively extract time dependence, enhance the model's memory ability for historical information, capture the dynamic evolution trend of state variables on the time axis, reveal the change law of state variables, provide time context information and trend basis for predicting future states; smooth random noise using the continuity of historical data; identify dynamic patterns such as load fluctuations and new energy output, avoid estimation biases caused by ignoring historical information, comprehensively reflect the spatio-temporal evolution law of the power grid state, and provide a reliable guarantee for the stable operation of the smart grid. By extracting the spatial features of the smart grid, the physical connection and operation rules of the power grid are transformed into a computable graph structure representation. The spatio-temporal convolutional block jointly processes the time-gated convolutional layer and the spatial graph convolutional layer to fuse spatio-temporal features and achieve joint extraction of spatio-temporal features. This process not only provides a mathematical abstraction of the power grid topology for the model but also realizes efficient spatial dependence modeling, noise suppression, and dynamic adaptation through graph convolution technology. Combining time dependence analysis, spatial feature extraction enables STGCN to achieve high-precision and high-robustness state estimation in a complex and changing power grid environment, providing core technical support for the stable operation and real-time decision-making of the smart grid.

[0010] Furthermore, the establishment of the topological graph model includes the following steps:

[0011] Define the smart grid as a node / branch model and establish a topological graph model.

[0012] Conceptualize the smart grid from the perspective of graph theory, emphasizing structured time series data.

[0013] Among them, due to the complex network characteristics, highly informatized system characteristics, rich node attributes, and spatio-temporal characteristics of the smart grid, typical graph structure application scenarios can be formed in the smart grid. The connection relationships between nodes are quantified through graph theory tools (such as adjacency matrices and Laplacian matrices), providing a mathematical basis for subsequent graph convolution operations. The power grid state (such as voltage fluctuations) has strong spatial correlation, and the state changes of adjacent nodes will affect each other through transmission lines. The topological graph model directly captures the spatial propagation characteristics through graph convolutional layers (GCNs). At the same time, the topological graph model provides a unified input framework for time-gated convolutional layers (processing time series of measurement data) and spatial graph convolutional layers (processing topological spatial relationships), realizing the joint extraction of spatio-temporal features. Moreover, the topological graph model helps the model identify outliers (such as sensor failures) in measurement data through structured features (such as power balance constraints between nodes), improving the reliability of state estimation.

[0014] Furthermore, the smart grid is defined as a node / branch model, represented as a graph where the node set represents the set of N nodes in the smart grid, and the edge set represents all branches within the smart grid. For each node V i and θ i represent the voltage magnitude and phase angle associated with it, respectively. At the same time, P i and Q i represent the injected active power and reactive power. For the edge (i, j) ∈ ε, P ij and Q ij represent the active power flow and reactive power flow, respectively. For Z t := [V i，t , P i，t , Q i，t , P ij，t , Q ij，t T represents the measurement vector at time t. To extract node features and edge features separately, let Z tn := [V i，t , P i，t , Q i，t T be the node features, and Z te := [V i，t , P i，t , Q i，t T be the edge features.

[0015] The standard SE problem can be formulated as an optimization challenge aimed at solving the following equation:

[0016]

[0017] At each time point \(t\), the goal of state estimation is to determine the state vector for all buses (i.e., all nodes This is achieved by using the available noisy measurements \(Z\) from \(N\) nodes t These measurements are represented by the equation where are various combinations of power flow functions defined according to the underlying topological relationships, and \(\in\) represents the measurement error vector.

[0018] Conceptualize the smart grid from the perspective of graph theory, emphasizing structured time - series data.

[0019] Figure contains a set of vertices \(Z\) tn and \(X\) t which represent the observations of \(n\) monitoring stations within the smart grid. \(Z\) te defines the edges, representing the transmission lines connecting the nodes, and \(W\) represents the weighted adjacency relationship matrix corresponding to

[0020] Furthermore, the structure of the spatial graph convolutional layer is such that different types of main devices in the smart grid, such as power plants, substations, distribution substations, and end - users, are used as nodes, and the transmission lines between the nodes are used as edges, on which there is power flow. The nodes are interconnected through the transmission lines to form a complex and orderly network. Based on the network topology structure and the characteristics of each node and edge, the state quantity of the entire network is obtained, which has strong spatial dependence. Therefore, the spatial graph convolutional layer is directly used for graph - structured data to extract highly significant patterns and features in the spatial domain. Calculate the kernel \(\Theta\) in the graph convolution through formula (1). Since multiplications are performed using the graph Fourier law, the computational complexity is relatively large. Two approximation strategies, namely Chebyshev polynomial approximation and first - order approximation, can be used to overcome this problem.

[0021] (a) Chebyshev polynomial approximation

[0022] To localize the filter and reduce the number of parameters, the kernel \(\Theta\) can be restricted to a polynomial of \(\Lambda\), that is where is the polynomial coefficient vector. \(K\) is the kernel size of the graph convolution, which determines the maximum radius of convolution from the central node. Traditionally, the Chebyshev polynomial \(T\) k (x) is used to approximate the kernel as a truncated expansion of order \(K - 1\), that is Rescale (\(\lambda\) max represents the largest eigenvalue of \(L\)). Then the graph convolution can be rewritten as

[0023]

[0024] In the formula: is the Laplace operator The k-th order Chebyshev polynomial under. The K-local convolution is calculated recursively by polynomial approximation.

[0025] (b) First-order approximation

[0026] By stacking multiple localized graph convolutional layers and using the first-order approximation of the graph Laplacian, a layer-by-layer linear formula can be defined. Therefore, a deeper architecture can be constructed to deeply recover spatial information without being limited to the explicit parameterization given by the polynomial. Due to scaling and normalization in neural networks, we can further assume that λ max ≈ 2. Therefore, formula (3) can be simplified to

[0027]

[0028] In the formula: θ0 and θ1 are two shared parameters of the kernel. To constrain the parameters and stabilize the numerical performance, let θ = θ0 = -θ1, and replace θ0 and θ1 with a single parameter θ; W and D are respectively and Renormalized. Then, the graph convolution can be alternately represented as

[0029]

[0030] Using a stack of graph convolutions with first-order approximation in the vertical direction achieves a similar effect to the K-localized convolution in the horizontal direction, and all convolutions utilize the (K - 1)-th order neighborhood information of the central node. In this scenario, K is the number of consecutive filtering operations or convolutional layers in the model. In addition, the hierarchical linear structure is parameter-economical and efficient for large-scale graphs because the order of approximation is limited to 1.

[0031] Extension of graph convolution:

[0032] Defined on The graph convolution operator Can be extended to multi-dimensional tensors. For a signal with C i Channels The graph convolution can be generalized as

[0033]

[0034] Using the C i × C o Vector (C i , C o Are the input and output sizes of the feature map respectively). The graph convolution of two-dimensional variables is denoted as Among them Specifically, the input of the state estimation prediction consists of M frames of power grid diagrams. Each frame υ t can be regarded as a matrix, and its i-th column is the υ at the i-th node in the diagram t C i -dimensional value, (in this case, C i = 1). For each time step t of M, equal graph convolution operations with the same kernel Θ are applied in parallel. Therefore, graph convolution can be further generalized to three-dimensional variables, denoted as where Among them

[0035] Furthermore, the time-gated convolution layer structure uses a fully convolutional structure on the time axis to capture the time dynamic behavior of traffic flow.

[0036] Although RNN-based models have become widespread in time series analysis, recurrent networks for traffic flow prediction still have problems such as iterative time consumption, complex gate mechanisms, and slow response to dynamic changes. On the contrary, convolutional neural networks have the advantages of fast training speed, simple structure, and no dependence constraints on the previous few steps. Therefore, a fully convolutional structure is used on the time axis to capture the time dynamic behavior of traffic flow. This specific design allows for a parallel and controllable training process through a multi-layer convolutional structure formed as a hierarchical representation.

[0037] The temporal convolutional layer contains a one-dimensional causal convolution with a width kernel, followed by a gated linear unit (GLU) as the non-linearity. For each node in graph G, the temporal convolution explores the K t neighbors of the input elements without padding, resulting in a shortening of the sequence length by K t - 1 each time. Therefore, the temporal convolution input for each node can be regarded as a sequence of length M, where C i channels are Design the convolutional kernel to map the input Y to a single output element (divide P and Q into two equal parts with the same-sized channels). Therefore, the time-gated convolution can be defined as:

[0038]

[0039] Among them, P and Q are the inputs of the gates in GLU respectively; represents the element-wise Hadamard product. The sigmoid gate σ(Q) controls the input P of the current state, which is related to the compositional structure and dynamic variance in the discovery time series. The non-linear gate also helps to utilize the entire input field through the stacked time layers. In addition, residual connections are implemented between the stacked time convolutional layers. Similarly, the time convolution can also be extended to three-dimensional variables by using the same convolutional kernel Γ for each node in (such as sensor stations), denoted as and

[0040] Furthermore, the spatio-temporal convolution block jointly processes the graph-structured time series, and the spatio-temporal convolution blocks are stacked or extended according to the scale and complexity of the power grid.

[0041] The middle spatial layer bridges the two time layers, and the fast spatial state propagation of graph convolution can be achieved through time convolution. The "sandwich" structure also helps the network to fully apply the bottleneck strategy, downsizing and upsizing the channel C through the graph convolution layer to achieve scale compression and feature compression. In addition, layer normalization is used within each ST-Conv block to prevent overfitting.

[0042] Both the input and output of the ST-Conv block are three-dimensional tensors. For the input output of the l-th block, the calculation is as follows:

[0043]

[0044] where are the upper and lower time kernels within block l respectively; Θ l is the spectral kernel of graph convolution; ReLU(·) represents the rectified linear unit function. After stacking two ST-Conv blocks, we added an additional time convolutional layer with a fully connected layer at the end (see Figure 2 on the left) as the output layer. The time convolutional layer maps the output of the last ST-Conv block to a single-step prediction. Then, we can obtain a final output from the model and calculate the velocity prediction for n nodes by applying a linear transformation across the C-shaped column, where is a weight vector and b is a bias. The L2 loss is used to measure the performance of the model. Therefore, the loss function of STGCN for traffic prediction can be

[0045]

[0046] where W θare all trainable parameters in the model; υ t+1 is the true value, representing the prediction of the model.

[0047] Furthermore, the spatio-temporal graph convolutional network STGCN model consists of two spatio-temporal modules. Each spatio-temporal module contains a spatio-temporal attention module and a spatio-temporal convolutional module. Finally, a fully connected layer converts the spatio-temporal feature vector into the output of the smart grid state at each moment.

[0048] Furthermore, the power grid state estimation model is divided into two layers. The first layer is the bad data cleaning layer, and the second layer is the state estimation layer. Both layers of the model are trained with a large number of historical data sets and then put into online applications. In the online application stage, the original measurement data directly enters the STGCN model for state estimation after passing through the bad data cleaning layer. The STGCN model consists of two spatio-temporal modules. Each spatio-temporal module contains a spatio-temporal attention module and a spatio-temporal convolutional module. Finally, a fully connected layer converts the spatio-temporal feature vector into the output of the smart grid state at each moment. The input samples are the measurement data of the previous 3 time sections and the measurement data at the current moment. The STGCN automatically aggregates the relevant information in the time and space of the input samples for state estimation, and the output is the network state information at the current moment, that is, the estimated values of the node voltage amplitude V and the phase angle θ.

[0049] The present invention also discloses a smart grid state estimation system based on a spatio-temporal graph convolutional network, including:

[0050] A topological graph model, which establishes a topological graph of the power system according to the topological structure of the smart grid and the measurement data, represents the nodes and transmission lines as vertices and edges in the topological graph to generate an adjacency matrix, and captures the time series data of the vertices and edges;

[0051] An STGCN model containing multiple spatio-temporal convolutional blocks. Each spatio-temporal convolutional block includes a time-gated convolutional layer and a spatial graph convolutional layer. The time-gated convolutional layer extracts the time dependence of the time series data and captures the evolution trend of the state quantity on the time axis. The spatial graph convolutional layer quantifies the connection strength between nodes based on the generated adjacency matrix and aggregates the neighborhood information to extract the spatial features of the smart grid;

[0052] A smart grid state estimation module, which inputs the measurement data, uses the captured evolution trend of the state quantity on the time axis, fuses the extracted spatial features of the smart grid, outputs the system state vector, maps the smart grid state, and further estimates the smart grid state.

[0053] The spatio-temporal convolutional block captures the time dependence of the time series data through the time-gated convolutional layer and extracts the spatial features of the smart grid through the spatial graph convolutional layer.

[0054] Furthermore, the system further includes a data acquisition module for acquiring measurement data of the smart grid;

[0055] A dynamic topology update module for detecting grid topology changes in real time and adjusting the adjacency matrix to ensure that the neighborhood relationship of the spatial graph convolutional layer is consistent with the current grid structure.

[0056] The present invention also discloses a computer-readable storage medium storing a computer program for executing the smart grid state estimation method described above.

[0057] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following remarkable advantages:

[0058] (1) By integrating spatial and temporal convolution techniques, the present invention can deeply capture and analyze the complex spatio-temporal characteristics contained in the smart grid. This unique design enables the present invention to exhibit excellent high precision in the state estimation of the smart grid, ensuring the accuracy and reliability of the estimation results. Compared with the WLS, graph neural network (GNN), and graph attention network (GAT), the estimation accuracy and robustness of the method of the present invention are significantly improved under topologically time-varying conditions.

[0059] (2) In response to various topological structure changes that may occur during the actual operation of the smart grid, the method of the present invention demonstrates strong adaptability. It can not only effectively address the state estimation challenges under various topological structures but also maintain stable estimation performance, providing a strong guarantee for the safe operation of the smart grid.

[0060] (3) Compared with traditional methods, the present invention has achieved a significant improvement in computational efficiency. Thanks to its advanced data-driven algorithm and optimized calculation process, the present invention can achieve fast calculation while ensuring high-precision state estimation, making it particularly suitable for the state estimation task of large-scale smart grids and greatly improving the operation efficiency and response speed of the smart grid. Description of the Drawings

[0061] Figure 1 It is a schematic flowchart of the smart grid state estimation method based on the spatio-temporal graph convolutional network of the present invention;

[0062] Figure 2 It is a schematic diagram of the graph structure data of the smart grid;

[0063] Figure 3 It is a schematic diagram of the architecture of the spatio-temporal graph convolutional network in the present invention;

[0064] Figure 4Schematic diagram of the comparison between the voltage magnitude estimation value obtained by the intelligent power grid state estimation method based on the spatio-temporal graph convolutional network in different topologies of the IEEE 39-bus in the embodiment of the present invention and the true value of the power flow;

[0065] Figure 5 Schematic diagram of the comparison of voltage phase angle errors of different methods for the IEEE 39-bus under Topology 1 in the embodiment of the present invention. Detailed implementation manners

[0066] The following provides a further detailed description of the technical solution of the present invention through specific embodiments. However, it is necessary to point out that the following embodiments are only used for the description of the content of the invention and do not constitute a limitation on the protection scope of the present invention.

[0067] The present invention provides an intelligent power grid state estimation system based on a spatio-temporal graph convolutional network, including a data acquisition module for acquiring measurement data of the intelligent power grid;

[0068] A topology graph model, which establishes a topology graph of the power system according to the topology structure and measurement data of the intelligent power grid, represents nodes and transmission lines as vertices and edges in the topology graph to generate an adjacency matrix, and captures the time series data of the vertices and edges;

[0069] An STGCN model including multiple spatio-temporal convolutional blocks, each spatio-temporal convolutional block includes a time-gated convolutional layer and a spatial graph convolutional layer. The time-gated convolutional layer extracts the time dependence of the time series data and captures the evolution trend of the state quantity on the time axis. The spatial graph convolutional layer quantifies the connection strength between nodes based on the generated adjacency matrix and aggregates neighborhood information to extract the spatial features of the intelligent power grid;

[0070] An intelligent power grid state estimation module, which inputs measurement data, uses the captured evolution trend of the state quantity on the time axis, fuses the extracted spatial features of the intelligent power grid, outputs a system state vector to map the intelligent power grid state, and further estimates the intelligent power grid state.

[0071] The spatio-temporal convolutional block captures the time dependence of the time series data through the time-gated convolutional layer and extracts the spatial features of the intelligent power grid through the spatial graph convolutional layer.

[0072] Among them, the spatio-temporal convolutional block captures the time dependence of the time series data through the time-gated convolutional layer and extracts the spatial features of the intelligent power grid through the spatial graph convolutional layer.

[0073] As Figures 1-3 shown, an intelligent power grid state estimation method based on a spatio-temporal graph convolutional network provided by the present invention includes the following steps:

[0074] (1) Establish a topological graph model: Based on the topological structure and measurement data of the smart grid IEEE 39-bus system, establish a topological graph model of the power system. The MATPOWER simulation toolbox has been used to simulate large time series datasets. Assume that the system state is almost the same within a single interval of a typical scada-based SE. Sample the system load levels (each load) according to a uniform (normal) distribution to generate 50,000 samples of different power flows. This model represents nodes and transmission lines as vertices and edges in a graph and captures their characteristics. The specific steps are as follows:

[0075] (1.1) Establish a topological graph model: Due to its complex network characteristics, highly informatized system characteristics, rich node attributes, and spatio-temporal characteristics, the smart grid forms a typical graph structure application scenario.

[0076] The smart grid is defined as a node / branch model and can be represented as a graph where the node set represents the set of N nodes in the smart grid, and the edge set represents all the branches within the smart grid. For each node V i and θ i represent the voltage magnitude and phase angle associated with it, respectively. Meanwhile, P i and Q i represent the injected active power and reactive power. For the edge (i, j) ∈ ε, P ij and Q ij represent the active power flow and reactive power flow, respectively. For Z t : = [V i，t , P i，t , Q i，t , P ij，t , Q ij，t T represents the measurement vector at time t. To extract node features and edge features separately, let Z tn : = [V i，t , P i，t , Q i，t T be the node features, and Z te : = [V i，t , P i，t , Q i，t T be the edge features.

[0077] The standard SE problem can be formulated as an optimization challenge aiming to solve the following equations:

[0078] ​​​

[0079] At each time point t, the goal of state estimation is to determine the state vectors of all buses (i.e., all nodes ). This is achieved by using the available noisy measurements Z from N nodes t , and these measurements are represented by the equation . Where are various combinations of power flow functions defined according to the underlying topological relationships, and ∈ represents the measurement error vector.

[0080] (1.2) In this study, we conceptualize the smart grid from the perspective of graph theory, emphasizing structured time series data, such as Figure 1 shown. Figure contains the set of vertices Z tn and X t , which represent the observations of n monitoring stations within the smart grid. Z te defines the edges, illustrating the connections between nodes, and W represents the weighted adjacency relationship matrix corresponding to

[0081] (2) Constructing the STGCN model: Construct a spatio-temporal graph convolutional network (STGCN) model that contains multiple spatio-temporal convolutional blocks. Each spatio-temporal convolutional block captures the temporal dependencies of time series data through a temporal gated convolutional layer and extracts the spatial features of the smart grid through a spatial graph convolutional layer.

[0082] The structure of the spatio-temporal graph convolutional network is as follows:[[]]

[0083] (2.1) The graph convolutional structure for extracting spatial features is as follows: The power grid is a typical graph structure composed of multiple nodes such as power plants, substations, distribution substations, and end-users. These nodes are interconnected by transmission lines, forming a complex and orderly network. The transmission lines between nodes are the edges in the graph, and there is power flow on them. State estimation is based on the complex network topology and the characteristics of each node and edge to obtain the state quantities of the entire network, which has strong spatial dependence. Therefore, in our model, graph convolution is directly applied to graph-structured data to extract highly significant patterns and features in the spatial domain. The kernel Θ in graph convolution is calculated by formula (1). Since the graph Fourier law is used for multiplications, the computational cost is relatively large, and two approximation strategies are adopted to overcome this problem.

[0084] (a) Chebyshev polynomial approximation

[0085] To localize the filter and reduce the number of parameters, the kernel Θ can be restricted to a polynomial of Λ, that is Where is the polynomial coefficient vector. K is the kernel size of the graph convolution, which determines the maximum radius of convolution from the central node. Traditionally, the Chebyshev polynomial T k (x) is used to approximate the kernel as a truncated expansion of order K - 1, that is Rescaled (λ max (representing the largest eigenvalue of L)). Then the graph convolution can be rewritten as

[0086]

[0087] where: is the Laplacian operator is the k - th order Chebyshev polynomial under

[0088] (b) First - order approximation

[0089] By stacking multiple localized graph convolution layers and using the first - order approximation of the graph Laplacian, a layer - by - layer linear formula can be defined. Thus, a deeper architecture can be constructed to deeply recover spatial information without being limited to the explicit parameterization given by the polynomial. Due to the scaling and normalization in the neural network, we can further assume that λ max ≈ 2. Therefore, Equation (3) can be simplified to

[0090]

[0091] where: θ0, θ1 are the two shared parameters of the kernel. To constrain the parameters and stabilize the numerical performance, let θ = θ0 = - θ1, and replace θ0 and θ1 with a single parameter θ; W and D are respectively re - normalized by and Then, the graph convolution can be alternatively expressed as

[0092]

[0093] Using a stack of graph convolutions with first - order approximation in the vertical direction achieves a similar effect to the K - localized convolution in the horizontal direction, and all convolutions utilize the (K - 1) - order neighborhood information of the central node. In this scenario, K is the number of consecutive filtering operations or convolution layers in the model. Additionally, the hierarchical linear structure is parameter - economical and efficient for large - scale graphs because the order of approximation is limited to 1.

[0094] Expansion of graph convolution:

[0095] The graph convolution operator defined on can be extended to multi - dimensional tensors. For a signal with C i channels the graph convolution can be generalized as

[0096]

[0097] Using the C of Chebyshev coefficients i × C o vector (C i , C o are the input and output sizes of the feature map respectively). The graph convolution of two-dimensional variables is denoted as where Specifically, the input of the state estimation prediction consists of M frames of power grid graphs. Each frame υ t can be regarded as a matrix, and its i-th column is the υ at the i-th node in the graph t 's C i -dimensional value, (in this case, C i = 1). For each time step t of M, the same graph convolution operation with kernel Θ is applied in parallel to . Therefore, the graph convolution can be further extended to three-dimensional variables, denoted as where

[0098] (2.2) The graph convolution structure for extracting temporal features is as follows:

[0099] Although RNN-based models have become widespread in time series analysis, the recurrent networks for traffic flow prediction still have problems such as iterative time consumption, complex gate mechanisms, and slow response to dynamic changes. On the contrary, convolutional neural networks have the advantages of fast training speed, simple structure, and no dependence constraints on the previous few steps. Inspired by this, we use a fully convolutional structure on the time axis to capture the temporal dynamic behavior of traffic flow. This specific design allows for a parallel and controllable training process through a multi-layer convolutional structure formed as a hierarchical representation.

[0100] As Figure 2 (right) shows, the temporal convolutional layer contains a one-dimensional causal convolution with a width kernel, followed by a gated linear unit (GLU) as the non-linearity. For each node in the graph G, the temporal convolution explores the K t neighbors of the input elements without padding, resulting in a shortening of the sequence length by K t - 1 each time. Therefore, the input of the temporal convolution for each node can be regarded as a sequence of length M, where C i channels are Design the convolutional kernel to map the input Y to a single output element (divide P and Q into two equal parts with the same-sized channels). Therefore, the temporal gated convolution can be defined as:

[0101]

[0102] where P and Q are the inputs to the gates in GLU respectively; represents the element-wise Hadamard product. The sigmoid gate σ(Q) controls the input P to the current state and is related to the compositional structure and dynamic variance in the discovery time series. The non-linear gate also helps to utilize the entire input field through stacked temporal layers. In addition, residual connections are implemented between the stacked temporal convolutional layers. Similarly, temporal convolution can also be generalized to three-dimensional variables by using the same convolutional kernel Γ for each node in (e.g., sensor stations), denoted as and

[0103] (2.3) The structure of the spatio-temporal convolutional block is as follows:

[0104] To fuse the features from the spatial and temporal domains, a spatio-temporal convolutional block (ST-Conv block) is constructed to jointly process the graph-structured time series. The block itself can be stacked or extended according to the scale and complexity of a specific case.

[0105] As Figure 2 (in the middle) shows, the middle spatial layer bridges the two temporal layers, and fast spatial state propagation of graph convolution can be achieved through temporal convolution. The "sandwich" structure also helps the network to fully apply the bottleneck strategy, downscaling and upscaling the channels C through the graph convolutional layer to achieve scale compression and feature compression. In addition, layer normalization is used within each ST-Conv block to prevent overfitting.

[0106] Both the input and output of the ST-Conv block are three-dimensional tensors. For the input output of the l-th block, the calculation is as follows:

[0107]

[0108] where are the upper and lower temporal kernels within block l respectively; Θ l is the spectral kernel of graph convolution; ReLU(·) represents the rectified linear unit function. After stacking two ST-Conv blocks, we added an additional temporal convolutional layer with a fully connected layer at the end (see Figure 2 on the left) as the output layer. The temporal convolutional layer maps the output of the last ST-Conv block to a single-step prediction. Then, we can obtain a final output from the model and calculate the velocity prediction for n nodes by applying a linear transformation across the C-shaped column, where is a weight vector, and b is a bias. We use the L2 loss to measure the performance of our model. Therefore, the loss function of STGCN for traffic prediction can be

[0109]

[0110] where all Wθ are trainable parameters in the model; vt+1 is the true value, represents the prediction of the model.

[0111] (3) State estimation: Based on the established STGCN model, power system state estimation is carried out.

[0112] The model can be divided into two layers. The first layer is the bad data cleaning layer, and the second layer is the state estimation layer. Both layers of the model are trained with a large number of historical data sets and then put into online applications. In the online application stage, the original measurement data directly enters the STGCN model for state estimation after passing through the bad data cleaning layer. The STGCN model constructed in this embodiment consists of two spatio-temporal modules. Each spatio-temporal module contains a spatio-temporal attention module and a spatio-temporal convolution module, and finally outputs through a fully connected layer. The input samples are the measurement data of the first 3 time sections in history and the measurement data at the current moment. STGCN automatically aggregates the relevant information in time and space in the input samples for state estimation, and the output is the network state information at the current moment, that is, the estimated values of the node voltage amplitude V and the phase angle θ. By inputting the measurement data, the model can output a high-precision system state vector, including information such as voltage and phase angle.

[0113] First, in the case where the measurement data only contains Gaussian white noise, the estimation accuracy and model generalization performance of the intelligent grid state estimation method based on the spatio-temporal graph convolutional network of the present invention under topological changes are tested. In order 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.

[0114] In order to verify the estimation performance of the algorithm under the condition of frequent system topology changes, examples of the mean absolute error of voltage amplitude and voltage phase angle based on different topologies are given. Topology 1 is the complete topology of the IEEE39 bus system. Branches 4-14 are disconnected in Topology 2. In Topology 3, branches 16-19 are disconnected. In Topology 4, branches 28-29 are disconnected. As Figure 4 shown, the comparison between the estimated values of voltage amplitude and the true value of power flow of the intelligent grid state estimation method based on the spatio-temporal graph convolutional network of the present invention in 4 topologies. It shows that for various topological structure changes that may occur in the actual operation of the intelligent grid, the method of the present invention exhibits strong adaptability. It can not only effectively cope with the state estimation challenges under various topological structures, but also maintain stable estimation performance, providing a strong guarantee for the safe operation of the intelligent grid.

[0115] To intuitively demonstrate the advantages of the intelligent power grid state estimation method based on the spatio-temporal graph convolutional network in the power system, the intelligent power grid state estimation method based on the spatio-temporal graph convolutional network of the present invention is compared with three traditional algorithms, namely WLS, graph neural network (GNN), and graph attention network (GAT), to highlight the estimation accuracy and robustness of the algorithm of the present invention under topologically time-varying conditions.

[0116] Tables 1 and 2 show the performance of the intelligent power grid state estimation method based on the spatio-temporal graph convolutional network of the present invention and three traditional algorithms, namely WLS, graph neural network (GNN), and graph attention network (GAT), under different topologies.

[0117] Table 1 Mean absolute error of voltage magnitude

[0118]

[0119] Table 2 Mean absolute error of voltage phase angle

[0120]

[0121] As can be seen from Tables 1-2, when the measurement data only contains white Gaussian noise, the proposed algorithm is superior to traditional state estimation methods and simple graph neural networks by effectively learning the spatio-temporal correlation between measurement data and state variables. For example, in Topology 1, the voltage phase angle is 57.38% and 63.80% higher than that of WLS and GNN, respectively. In addition, the prediction results of the algorithm are consistent in different topologies, indicating its robustness to topological changes.

[0122] To further intuitively 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 mean absolute error. As Figure 5 shown, under Topology 1, when the measurement information of the IEEE 39-bus system only contains Gaussian white noise, the voltage phase angle error results obtained by using the intelligent power grid state estimation method based on the spatio-temporal graph convolutional network of the present invention and three traditional algorithms, namely WLS, graph neural network (GNN), and graph attention network (GAT). It can be seen from this that by skillfully integrating spatial and temporal convolution techniques, the present invention can deeply capture and analyze the complex spatio-temporal characteristics contained in the intelligent power grid. Compared with the three traditional algorithms, the present invention shows excellent high accuracy in the state estimation of the intelligent power grid, and can effectively ensure the accuracy and reliability of the estimation results.

[0123] The present invention also discloses a computer-readable storage medium, and the storage medium stores a computer program, and the computer program is used to execute the above method.

[0124] Although embodiments of the present invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the present invention, and such modifications and variations fall within the scope defined by the appended claims.

Claims

1. An intelligent power grid state estimation method based on a spatio-temporal graph convolutional network, characterized in that, Including the following steps: Based on the topological structure and measurement data of the smart grid, establish a topological graph model of the power system. This model represents nodes and transmission lines as vertices and edges in the topological graph to generate an adjacency matrix, and captures the time series data of vertices and edges; Construct a spatio-temporal graph convolutional network STGCN model containing multiple spatio-temporal convolutional blocks. Each spatio-temporal convolutional block includes a time-gated convolutional layer and a spatial graph convolutional layer. The time-gated convolutional layer extracts the time dependence of the time series data and captures the evolution trend of the state quantity on the time axis. The spatial graph convolutional layer, based on the generated adjacency matrix, quantifies the connection strength between nodes and aggregates neighborhood information to extract the spatial features of the smart grid; Based on the spatio-temporal graph convolutional network STGCN model, establish a smart grid state estimation model. By inputting measurement data, using the captured evolution trend of the state quantity on the time axis, and outputting the system state vector by fusing the extracted spatial features of the smart grid to map the smart grid state, and then estimate the smart grid state.

2. The intelligent power grid state estimation method based on a spatio-temporal graph convolutional network according to claim 1, wherein The establishment of the topological graph model of the power system includes the following steps: Define the smart grid as a node / branch model and establish a topological graph model; Conceptualize the smart grid from the perspective of graph theory, emphasizing structured time series data.

3. The intelligent power grid state estimation method based on a spatio-temporal graph convolutional network according to claim 1, characterized in that, The structure of the spatial graph convolutional layer is that different types of main equipment and end users in the smart grid are used as nodes, the transmission lines between nodes are used as edges, and the nodes are interconnected through transmission lines to form an ordered network; Based on the network topological structure and the characteristics of each node and edge, obtain the state quantity of the entire network. The spatial graph convolutional layer is directly used for graph structure data.

4. The intelligent power grid state estimation method based on a spatio-temporal graph convolutional network according to claim 3, wherein The smart grid is defined as a node / branch model, expressed as where the node set represents the set of N nodes in the smart grid, and the edge set represents all branches within the smart grid. The node V i and θ i represent the voltage magnitude and phase angle associated with the node, respectively. Meanwhile, P i and Q i represent the injected active power and reactive power, and the edge (i, j) ∈ ε; P ij and Q ij represent the active power flow and reactive power flow, respectively. For Z t : = [V i，t ,P i，t ,Q i，t ,P ij，t ,Q ij，t T represents the measurement vector at time t. To extract node features and edge features separately, let Z tn : = [V i，t ,P i，t ,Q i，t T be the node features, and Z te : = [V i，t ,P i，t ,Q i，t T be the edge features.​​​ 5. The intelligent power grid state estimation method based on a spatio-temporal graph convolutional network according to claim 1, wherein The structure of the time-gated convolutional layer uses a fully convolutional structure on the time axis to capture the time dynamic behavior of traffic flow.

6. The intelligent power grid state estimation method based on a spatio-temporal graph convolutional network according to claim 1, wherein The spatio-temporal convolutional block jointly processes the graph structure time series, and the spatio-temporal convolutional block is stacked or extended according to the scale and complexity of the power grid.

7. The intelligent power grid state estimation method based on a spatio-temporal graph convolutional network according to claim 1, wherein The spatio-temporal graph convolutional network STGCN model consists of two spatio-temporal modules. Each spatio-temporal module contains a spatio-temporal attention module and a spatio-temporal convolutional module. Finally, the fully connected layer converts the spatio-temporal feature vector into the smart grid state output at each moment.

8. The intelligent power grid state estimation method based on a spatio-temporal graph convolutional network according to claim 1, characterized in that The power grid state estimation model is divided into two layers. The first layer is the bad data cleaning layer, and the second layer is the state estimation layer.

9. The intelligent power grid state estimation method based on a spatio-temporal graph convolutional network according to claim 8, wherein Both layers of the power grid state estimation model are trained with a large number of historical data sets and then put into online applications.

10. An intelligent power grid state estimation system based on a spatio-temporal graph convolutional network, characterized in that, Including: A topological graph model. Based on the topological structure and measurement data of the smart grid, establish a topological graph of the power system, represent nodes and transmission lines as vertices and edges in the topological graph to generate an adjacency matrix, and capture the time series data of vertices and edges; A spatio-temporal graph convolutional network STGCN model containing multiple spatio-temporal convolutional blocks. Each spatio-temporal convolutional block includes a time-gated convolutional layer and a spatial graph convolutional layer. The time-gated convolutional layer extracts the time dependence of the time series data and captures the evolution trend of the state quantity on the time axis. The spatial graph convolutional layer, based on the generated adjacency matrix, quantifies the connection strength between nodes and aggregates neighborhood information to extract the spatial features of the smart grid; The smart grid state estimation module, by inputting measurement data, utilizes the evolution trend of the captured state variables on the time axis, fuses the extracted spatial features of the smart grid, outputs the system state vector to map the smart grid state, and further estimates the smart grid state.

11. The intelligent power grid state estimation system based on a spatio-temporal graph convolutional network according to claim 10, characterized in that, The system further includes a data acquisition module for acquiring the measurement data of the smart grid; A dynamic topology update module for detecting grid topology changes in real time and adjusting the adjacency matrix to ensure that the neighborhood relationship of the spatial graph convolutional layer is consistent with the current grid structure.

12. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, and the computer program is used to execute the method according to any one of claims 1-9.

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