Generator power angle trajectory prediction method based on graph embedding physical information neural network

Abstract

The present application relates to the technical field of power system transient stability analysis, and discloses a generator power angle trajectory prediction method based on a graph embedding physical information neural network, which classifies and divides operation scenarios containing renewable energy uncertainty and fault disturbance through a clustering algorithm, effectively reducing the learning difficulty of complex scenarios; with the strong feature extraction capability of a graph neural network, general node and line features under different power grid topologies are mined, and the model cross-topology generalization performance is improved; and the generator rotor motion equation is embedded as a physical constraint in the training process of the neural network, realizing double-driven optimization of data driving and physical law in the training process. The method can realize fast and accurate prediction of the generator power angle trajectory of a high-proportion renewable energy power system under different topologies and fault scenarios on the premise of ensuring the physical consistency of the prediction results, and provides efficient and reliable technical support for power grid transient stability analysis.

Description

Technical Field

[0001] This invention relates to the field of transient stability analysis technology for power systems, and specifically to a generator power angle trajectory prediction method based on a graph-embedded physical information neural network. Background Technology

[0002] Traditional electromechanical transient analysis and parameter prediction of power systems are mainly based on physical models and often employ time-domain simulation methods. This approach constructs a system of differential-algebraic equations containing generator rotor motion equations and network algebraic constraints, and then uses numerical algorithms such as the improved Euler method for step-by-step integration to solve the problem. These methods can accurately reproduce the dynamic response of the system under disturbances such as short-circuit faults and load surges, and are fundamental methods for system dynamic analysis. However, for complex power grids with a high proportion of renewable energy integration, the establishment of physical models becomes more complex, and there are problems such as difficulty in handling the randomness and volatility of source and load outputs, and extremely time-consuming computation.

[0003] With the advancement of artificial intelligence technology, data-driven methods, represented by deep neural networks, have shown broad application prospects in power system analysis. Researchers have utilized convolutional neural networks, long short-term memory networks, or graph neural networks to mine statistical patterns in massive historical operating data, achieving rapid end-to-end prediction of system transient parameters. These methods have alleviated the bottleneck of computational efficiency in traditional time-domain simulation to some extent, but under complex power grid conditions with indeterminate topology and strong physical constraints, they still face limitations such as insufficient generalization ability and lack of physical consistency. Summary of the Invention

[0004] This invention provides a generator power angle trajectory prediction method based on graph-embedded physical information neural network to solve the limitations of existing power system power angle prediction technology when facing indeterminate topology, high proportion of renewable energy randomness and strong coupling characteristics of physical constraints.

[0005] In a first aspect, the present invention provides a generator power angle trajectory prediction method based on a graph-embedded physical information neural network, the method comprising: A multi-topology operation scenario dataset for power systems containing renewable energy was constructed. By setting different network topologies, renewable energy configurations, and fault locations, transient operation data of the power system under different operating conditions were obtained using time-domain simulation. Extract feature indicators that reflect the complexity of the scene, cluster the running scenes based on the K-means algorithm, divide scenes with similar features into the same cluster and assign cluster labels to each scene; A physical information neural network model with fused graph structure perception capability is constructed. The graph neural network module captures cross-topological graph structure features, combines scene cluster labels to construct a fused feature vector, and inputs it into the feedforward neural network module to generate system parameter prediction values ​​that meet the preconditions of physical constraints. A physical-data dual-drive loss function is constructed to train the physical information neural network model. Based on the data fitting error, the generator rotor motion equation is introduced as a regularization constraint to optimize the model parameters. Using the trained model, generator power angle trajectory prediction is performed on a power system with any given topology.

[0006] This invention provides a generator power angle trajectory prediction method based on a graph-embedded physical information neural network. It classifies operating scenarios involving renewable energy uncertainties and fault disturbances using a clustering algorithm, effectively reducing the learning difficulty of complex scenarios. Leveraging the strong feature extraction capabilities of graph neural networks, it mines common node and line features across different power grid topologies, improving the model's cross-topology generalization performance. Furthermore, it embeds the generator rotor motion equations as constraints into the physical information neural network, achieving dual-driven optimization based on data and physical laws during training. This method can achieve rapid and accurate prediction of generator power angle trajectories in high-proportion renewable energy power systems under different topologies and fault scenarios, while ensuring the physical consistency of the prediction results, providing efficient and reliable technical support for power grid transient stability analysis.

[0007] In one alternative implementation, before constructing the multi-topology running scenario dataset, the method further includes: A dynamic model of a power generation unit in a power system is constructed, wherein the power generation unit includes a synchronous generator and a renewable energy power generation device; Kron simplification technique is used to reduce the dimensionality of the power system network. By eliminating passive nodes through matrix transformation, the original sparse network is mapped into an equivalent network containing only nodes inside the generators.

[0008] In one optional implementation, a multi-topology operation scenario dataset of a power system containing renewable energy is constructed. By setting different network topologies, renewable energy configurations, and fault locations, transient operation data of the power system under different operating conditions is obtained using time-domain simulation, including: A single operational scenario is defined as a triple containing network topology, renewable energy configuration, and fault information. Based on the aforementioned dynamic model and the equivalent network, diverse operating scenarios are generated by changing the power grid topology, renewable energy access nodes and output coefficients, faulty lines, fault locations, and fault timing. Transient operating data under various scenarios are obtained based on time-domain simulation, and a node feature matrix is ​​constructed that includes node active / reactive power, node type, renewable energy access identifier, and inertia constant.

[0009] In one optional implementation, feature indicators reflecting scene complexity are extracted, and the running scenes are clustered based on the K-means algorithm. Scenes with similar features are grouped into the same cluster, and cluster labels are assigned to each scene, including: Extract renewable energy uncertainty indicators and fault location severity indicators to construct a two-dimensional scenario risk feature vector; The optimal number of clusters is determined using the silhouette coefficient method, and K-means clustering iteration is performed based on the optimal number of clusters. Scenarios with similar operational characteristics are grouped into the same cluster, and each scenario is assigned a corresponding cluster label.

[0010] In one optional implementation, a physical information neural network model with fused graph structure perception capabilities is constructed. This model captures cross-topological graph structure features through a graph neural network module, constructs a fused feature vector by combining scene cluster labels, and inputs it into a feedforward neural network module to generate predicted system parameters that satisfy the preconditions of physical constraints. This includes: The power system is modeled as an equivalent undirected graph structure, with buses and generators as nodes and transmission lines as edges, to construct graph structure data that adapts to the physical information neural network model. A message-passing neural network is used as the graph neural network module, and neural network convolution is used as the graph convolution operator. Convolution weights are dynamically generated through the edge network to adapt to the impedance parameters of the transmission line. Cross-topological graph structural features are extracted through multi-layer graph convolution. Scene cluster labels are converted into trainable embedding vectors and concatenated with the cross-topological graph structural features to obtain a fused feature vector. The fused feature vector is input into the feedforward neural network module, which outputs the equivalent parameters after Kron simplification, and uses them as the predicted values ​​of system parameters that meet the preconditions of physical constraints.

[0011] In one optional implementation, a physical-data dual-drive loss function is constructed to train the physical information neural network model. Based on the data fitting error, the generator rotor motion equation is introduced as a regularization constraint to optimize the model parameters, including: Construct a physical-data dual-driven loss function composed of a weighted average of data loss and physical loss; Data loss is calculated using mean square error; Based on the generator rotor oscillation equation in the dynamic model, physical loss is calculated by dense collocation in the spatiotemporal domain, and the generator rotor motion equation is embedded in the loss function in the form of residual penalty as a regularization constraint. The physical information neural network model is trained based on the physical-data dual-driven loss function, and the model parameters are iteratively updated and optimized.

[0012] In one optional implementation, the trained model is used to predict the generator power angle trajectory of a power system with any given topology, including: Obtain the grid topology parameters, renewable energy operation parameters, and fault characteristic parameters of the scenario to be predicted; The power grid topology parameters, the renewable energy operating parameters, and the fault characteristic parameters are input into the trained physical information neural network model; The physical information neural network model outputs the generator power angle trajectory that satisfies physical constraints.

[0013] Secondly, the present invention provides a generator power angle trajectory prediction device based on a graph-embedded physical information neural network, the device comprising: The dataset construction module is used to build a multi-topology operation scenario dataset for power systems containing renewable energy. By setting different network topologies, renewable energy configurations, and fault locations, it uses time-domain simulation to obtain transient operation data of the power system under different operating conditions. The scene clustering module is used to extract feature indicators that reflect the complexity of the scene. It clusters the running scenes based on the K-means algorithm, divides scenes with similar features into the same cluster, and assigns cluster labels to each scene. The graph embedding feature extraction module is used to build a physical information neural network model that integrates graph structure perception capabilities. It captures cross-topological graph structure features through the graph neural network module, constructs a fused feature vector by combining scene cluster labels, and inputs it into the feedforward neural network module to generate predicted system parameters that meet the preconditions of physical constraints. The physical constraint training module is used to construct a physical-data dual-drive loss function to train the physical information neural network model. Based on the data fitting error, the generator rotor motion equation is introduced as a regularization constraint to optimize the model parameters. The online prediction module is used to predict the generator power angle trajectory of a power system with any given topology using a trained model.

[0014] This invention provides a generator power angle trajectory prediction device based on a graph-embedded physical information neural network. It classifies operating scenarios involving renewable energy uncertainties and fault disturbances using a clustering algorithm, effectively reducing the learning difficulty of complex scenarios. Leveraging the strong feature extraction capabilities of graph neural networks, it mines common node and line features across different power grid topologies, improving the model's cross-topology generalization performance. Furthermore, it embeds the generator rotor motion equations as constraints into the physical information neural network, achieving dual-driven optimization based on data and physical laws during training. This method can achieve rapid and accurate prediction of generator power angle trajectories in high-proportion renewable energy power systems under different topologies and fault scenarios, while ensuring the physical consistency of the prediction results, providing efficient and reliable technical support for power grid transient stability analysis.

[0015] Thirdly, the present invention provides an electronic device, comprising: a memory and a processor, wherein the memory and the processor are communicatively connected to each other, the memory stores computer instructions, and the processor executes the computer instructions to perform the generator power angle trajectory prediction method based on graph embedded physical information neural network described in the first aspect or any corresponding embodiment.

[0016] Fourthly, the present invention provides a computer-readable storage medium storing computer instructions for causing a computer to execute the generator power angle trajectory prediction method based on a graph-embedded physical information neural network as described in the first aspect or any corresponding embodiment thereof. Attached Figure Description

[0017] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0018] Figure 1 This is a schematic diagram of the first process of a generator power angle trajectory prediction method based on a graph-embedded physical information neural network according to an embodiment of the present invention. Figure 2 This is the equivalent circuit diagram of a synchronous generator; Figure 3 This is the equivalent circuit diagram of the converter; Figure 4 This is a schematic diagram of the second process of the generator power angle trajectory prediction method based on graph-embedded physical information neural network according to an embodiment of the present invention; Figure 5 This is a schematic diagram of a graph-embedded physical information neural network model according to an embodiment of the present invention; Figure 6 This is a structural block diagram of a generator power angle trajectory prediction device based on a graph-embedded physical information neural network according to an embodiment of the present invention; Figure 7 This is a schematic diagram of the hardware structure of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] It is understood that before using the technical solutions disclosed in the various embodiments of the present invention, users should be informed of the types, scope of use, and usage scenarios of the personal information involved in the present invention and their authorization should be obtained in accordance with relevant laws and regulations through appropriate means.

[0021] This invention provides a generator power angle trajectory prediction method based on a graph-embedded physical information neural network, such as... Figure 1 As shown, the process includes the following: Step S1: Construct a multi-topology operation scenario dataset for a power system containing renewable energy. By setting different network topologies, renewable energy configurations, and fault locations, use time-domain simulation to obtain transient operation data of the power system under different operating conditions.

[0022] Specifically, the first step is to construct a sample library of multi-topology power system scenarios covering different operating conditions. By changing the grid topology, the location of renewable energy units, the active power output level, and fault conditions, diverse operating scenarios are created. Using time-domain simulation based on dynamic models of synchronous generators and renewable energy converters, the responses under each scenario are obtained, including generator power angle, speed, node voltage, and line power. Through batch simulations of scenarios with different topologies, different fault times, and different renewable energy penetration rates, a sufficiently large and comprehensive training and testing dataset is formed, providing data support for subsequent model learning.

[0023] Step S2: Extract feature indicators that reflect the complexity of the scene, cluster the running scenes based on the K-means algorithm, divide similar feature scenes into the same cluster, and assign cluster labels to each scene.

[0024] Specifically, to improve the model's adaptability to diverse scenarios, feature extraction and classification are performed on multi-topology operating scenarios. Key features reflecting the complexity of a scenario are selected, including the degree of fluctuation in renewable energy output and the severity of the impact of fault locations on the system, to construct scenario feature vectors. The K-means clustering algorithm is used for unsupervised classification of all scenarios, grouping scenarios with similar electrical characteristics and disturbance intensities into the same cluster, and assigning a unique label to each cluster. Scenario clustering reduces the learning difficulty of complex scenarios, enabling the model to more efficiently capture the dynamic patterns of the power grid under different types of scenarios.

[0025] Step S3: Build a physical information neural network model that integrates graph structure perception capabilities. Capture cross-topological graph structure features through the graph neural network module, construct a fused feature vector by combining scene cluster labels, and input it into the feedforward neural network module to generate system parameter prediction values ​​that meet the preconditions of physical constraints.

[0026] Specifically, the power system is abstracted as a graph structure, with generators and buses as nodes and transmission lines as edges, to construct graph data that represents the topological connections of the power grid. A message-passing neural network is used as the graph feature extraction module to learn the topological features of the power grid and automatically capture the dynamic characteristics between different topologies.

[0027] The scene cluster labels obtained in step S2 are converted into learnable embedding vectors and concatenated with the topological features output by the graph neural network to form a high-level feature vector that integrates scene and topological information. This feature vector is then input into a feedforward neural network, which outputs equivalent parameters simplified by Kron, providing prerequisites for subsequent physical constraint prediction.

[0028] Step S4: Construct a physical-data dual-drive loss function, train the physical information neural network model, and introduce the generator rotor motion equation as a regularization constraint based on the data fitting error to optimize the model parameters.

[0029] Specifically, a dual-drive loss function, weighted by data loss and physical loss, is constructed to train the physical information neural network model. The data loss uses mean squared error to measure the deviation between the model's predicted power angle trajectory and the actual trajectory, ensuring accurate model fitting of measured / simulated data. The physical loss, based on the generator rotor motion equations, performs dense collocation calculations of the equation residuals in the spatiotemporal domain, embedding physical laws into the training process in a regularized manner to force the model output to meet physical consistency. Through joint optimization of the dual-drive loss, the model simultaneously possesses high-precision fitting capability and strong physical constraint capability, maintaining stable and reliable prediction performance under different topologies.

[0030] Step S5: Using the trained model, predict the generator power angle trajectory for a power system with any given topology.

[0031] Specifically, the power grid topology parameters, renewable energy operating parameters, and fault information of the scenario to be predicted are input into the trained model. Based on the learned cross-topology features and physical laws, the model quickly outputs the generator power angle trajectory that satisfies electromechanical transient characteristics. This method does not require remodeling or retraining for new topologies, and can directly achieve generalized rapid prediction. It is suitable for online stability analysis and safety early warning of complex power grids with a high proportion of renewable energy.

[0032] This invention provides a generator power angle trajectory prediction method based on a graph-embedded physical information neural network. It classifies operating scenarios involving renewable energy uncertainties and fault disturbances using a clustering algorithm, effectively reducing the learning difficulty of complex scenarios. Leveraging the strong feature extraction capabilities of graph neural networks, it mines common node and line features across different power grid topologies, improving the model's cross-topology generalization performance. Furthermore, it embeds the generator rotor motion equations as constraints into the physical information neural network, achieving dual-driven optimization based on data and physical laws during training. This method can achieve rapid and accurate prediction of generator power angle trajectories in high-proportion renewable energy power systems under different topologies and fault scenarios, while ensuring the physical consistency of the prediction results, providing efficient and reliable technical support for power grid transient stability analysis.

[0033] In one alternative implementation, the method further includes, before constructing the multi-topology running scenario dataset: Step S01: Construct a dynamic model of the power generation unit of the power system. The power generation unit includes synchronous generators and renewable energy power generation devices.

[0034] Specifically, before conducting power grid simulation and scenario construction, a dynamic model of the power generation unit of the power system is first established to provide an accurate physical basis for subsequent transient analysis, time-domain simulation and physical constraint training.

[0035] In power systems with a high proportion of renewable energy integration, the main power generation units include synchronous generators and renewable energy generation devices connected to the grid via converters. Their equivalent circuit diagrams are as follows: Figure 2 and Figure 3 As shown. Figure 2 As shown, for a synchronous generator, a classic second-order model is used to describe its rotor motion characteristics during transient processes, where, R s,i The resistance of the synchronous generator, For the first i The internal potential of the generator unit. Ignoring the rapid dynamics of the speed governor and excitation system, the generator is equivalent to a constant potential source after transient reactance. i The rotor oscillation equation of the synchronous generator is described as follows: (1) in, Represents the rotor angle. Represents the rotor angular velocity. Represents the rotor angular acceleration. M i The inertial time constant, D i The damping coefficient is... P m,i For mechanical input power, P e,i To output electromagnetic power, the equation reflects the energy conservation relationship between the change in the generator rotor's kinetic energy and the power imbalance.

[0036] For renewable energy units such as wind power and photovoltaic power, their dynamic characteristics mainly depend on the control strategy of the grid-connected converter. If we consider a power electronic converter equipped with a conventional frequency droop controller, its equivalent circuit is as follows: Figure 3 As shown, droop control simulates the static frequency characteristics of a synchronous generator, enabling the converter components to respond to system frequency changes. If a Virtual Synchronous Generator (VSG) control strategy is used to simulate the mechanical characteristics of a traditional synchronous generator, allowing the converter to achieve operating characteristics similar to a synchronous generator, then its model is identical to that of a synchronous generator. jx f,i The inductive reactance of the filter inductor. R f,i This is the equivalent resistance of the filter. V dc This is the DC bus voltage. C f,i This is a filter capacitor.

[0037] use Pf The droop characteristic curve, the relationship between converter component frequency and active power, can be expressed as: (2) in, k i Indicates the first i The droop factor of each converter component f i The instantaneous output frequency at the converter port. f N The system's rated frequency, P ref,i This is a reference value for active power. P e,i The electromagnetic power actually injected into the power grid by the converter. This refers to the maximum allowable frequency deviation range of the converter. This refers to the rated active power adjustment range of the converter.

[0038] Simplifying the above equations, the dynamic equations based on the droop-controlled converter unit can be uniformly described as a Kuramoto-like oscillator model: (3) in, d i Corresponding to the reciprocal of the droop coefficient, This indicates the deviation between the actual frequency and the rated frequency of the converter.

[0039] If the converter uses VSG control and virtual inertia is introduced, its dynamic equations are mathematically consistent with the second-order equations of a synchronous generator. Therefore, the dynamic model of the power generation unit can be uniformly expressed as a system of nonlinear second-order differential equations.

[0040] Step S02: The power system network is reduced to an equivalent dimension using Kron simplification technology. Passive nodes are eliminated through matrix transformation, and the original sparse network is mapped to an equivalent network containing only nodes inside generators.

[0041] Specifically, the Kron simplification technique is used to perform equivalent dimensionality reduction on the network. This process is based on the constant impedance load assumption and eliminates passive nodes through matrix transformation, mapping the original sparse network into a compact fully connected network containing only nodes inside the generator.

[0042] At the steady-state operating point, assuming the system load has constant impedance characteristics, for any load node... k It is possible to calculate its corresponding equivalent parallel admittance to ground. y L,k The equivalent admittance is then superimposed onto the original nodal admittance matrix. Y bus The corresponding diagonal elements eliminate explicit load injection current in the network. y L,k It can be represented as: (4) in, P L,k and Q L,k The active and reactive power consumed by the load. This is the load node voltage. It is the imaginary unit.

[0043] To accurately describe the electrical connection between the generator and the power grid, the set of network nodes is expanded from the original... N The node is expanded to include virtual nodes inside the generator. N+N g There are nodes, among which NIndicates the number of nodes in the system. N g This represents the number of generating units. The transient reactance of the generator is defined as... Then its corresponding admittance y d,i And the admittance used to represent all generators is constructed N g Diagonal matrix of order Y tr It can be represented as: (5) (6) Based on network nodes and virtual generator nodes, a dimension of ( ) is constructed. N g +N )×( N g +N The system admittance matrix Y sys The system nodes are divided into a set of reserved nodes. S G and the set of eliminated nodes S N Only reserved nodes N g For each virtual node of a generator, according to Kirchhoff's current law, the current-voltage relationship of the system can be represented in blocks as follows: (7) in, I G The current vector injected into the virtual generator node. E G Let be the electric potential vector inside the generator. V N Let be the voltage vector of the network node to be eliminated. In the block matrix... This represents the self-admittance matrix of the virtual generator node. This represents the connection matrix between virtual nodes and network endpoints, where the non-zero elements are represented by - y d,i constitute; This represents the connection matrix between network nodes and virtual generator nodes; ,in The modified network matrix includes the equivalent admittance of the load. Is it extended to N×N dimensional matrix Y tr .

[0044] (8) The simplified effective admittance matrix is ​​defined by equation (8). Y Kron for: (9) Based on this simplified network model, the system contains only generator nodes and all nodes are connected. Assuming the system's lines are lossless and inductive, for the generator node... i Equation (1) can be described as: (10) in, , For the first i , j The power angle value of the generator. , Let be the values ​​of the first and second derivatives of the work angle. , For nodes i , j bus voltage, B ij For the effective admittance matrix Y Kron The Middle i Line number j The imaginary part of the column, i.e., the susceptance value.

[0045] In one optional implementation, step S1 includes the following process: Step S11: Define a single operating scenario as a triple containing network topology, renewable energy configuration, and fault information.

[0046] Step S12: Based on the dynamic model and equivalent network, diverse operating scenarios are generated by changing the grid topology, renewable energy access nodes and output coefficients, fault lines, fault locations and fault timing.

[0047] Step S13: Obtain transient operation data for each scenario based on time-domain simulation, and construct a node feature matrix that includes node active / reactive power, node type, renewable energy access identifier, and inertia constant.

[0048] Specifically, a single scene in the dataset S A triple containing network topology, renewable energy configuration, and fault information can be represented as: (11) in, G TP This represents the network topology of the power system. C RE For the configuration of renewable energy sets, This is a collection of fault information.

[0049] For the configuration of renewable energy in the system, it is necessary to describe the nodes in the system that are replaced with renewable energy power generation and their output status, defined as: (12) in, U RE For a set of nodes connected to renewable energy, For nodes The installed capacity, For nodes in this scenario u The output coefficient.

[0050] The fault information in the system needs to describe the characteristics of the short-circuit fault, defined as a quadruple: (13) in, l fault The line number where the fault occurred. This represents the ratio of the relative position of the fault point to the beginning of the line. t start The time when the fault occurred. t clear This is the time when the fault is cleared.

[0051] Based on the operating scenario, an input node feature matrix is ​​constructed, where the first... i The feature vector v of each node i This includes the node's initial steady-state operating parameters and physical model parameters before the failure, expressed as: (14) in, and These represent the active and reactive power injected into the nodes, respectively. Encode the node type. For renewable energy access identification, is the inertia constant.

[0052] In one optional implementation, step S2 includes the following process: Step S21: Extract the uncertainty index of renewable energy and the severity index of fault location to construct a two-dimensional scenario risk feature vector.

[0053] Step S22: Determine the optimal number of clusters using the silhouette coefficient method, and perform K-means clustering iteration based on the optimal number of clusters.

[0054] Step S23: Scenarios with similar operational characteristics are divided into the same cluster, and each scenario is assigned a corresponding cluster label.

[0055] Specifically, for each operational scenario in the dataset, scalar indicators reflecting the uncertainty of renewable energy output and the severity of fault locations are extracted to construct a scenario risk feature vector with fixed dimensions. Based on this, a search range for the number of clusters is defined, and the silhouette coefficient method is used to optimize the number of clusters in the K-means clustering algorithm to determine the optimal number of clusters. Based on the obtained optimal number of clusters, the K-means algorithm is used to iteratively partition the risk feature vectors of all scenarios, grouping scenarios with similar risk characteristics into one cluster and assigning a cluster label to each scenario.

[0056] The scenario risk feature vector z is defined as including renewable energy uncertainty indicators. and fault location severity index Two-dimensional vector: (15) Among them, renewable energy uncertainty indicators The comprehensive characterization of the penetration breadth and output dispersion of renewable energy is shown in the calculation formula (16); fault location severity index The importance of the faulty line in the system power transmission is represented by the formula shown in Equation (17).

[0057] (16) in, N total This represents the total number of nodes in the system. N RE The number of nodes connected to renewable energy sources, This represents the average output factor of all renewable energy nodes in this scenario.

[0058] (17) in, This represents the active power transmitted on the faulty line before the fault occurred. This represents the total load power of the system at that time.

[0059] The number of clusters was determined using the profile coefficient method. K To perform optimization, it is necessary to optimize each element within the search range. K For each value, perform K-means clustering and calculate the average silhouette coefficient of the current partition result: (18) in, M total This represents the total number of scene samples. For the first k The average distance between a sample and other samples in the same cluster For the firstk The average distance between each sample and its nearest neighbor cluster. Select the average silhouette coefficient. The largest k The value is used as the final optimal number of clusters.

[0060] The K-means algorithm first randomly selects from the set of risk feature vectors of all scenarios. K The vector is used as the initial cluster centroid. Then calculate the risk feature vector z for each scenario. (i) Calculate the Euclidean distance between the scene and the centroid of each cluster, and assign the scene to the nearest cluster. After all scenes are assigned, recalculate the centroid of each cluster based on the current assignment results. The new centroid is the mean of all feature vectors in the cluster.

[0061] Repeat the assignment and update steps until the cluster centroids no longer change or the maximum number of iterations is reached. Output the converged cluster labels and encode them as embedding vectors, which will serve as conditional inputs for the corresponding scenarios in subsequent neural network models.

[0062] In one optional implementation, step S3 includes the following process: Step S31: The power system is modeled as an equivalent undirected graph structure, with buses and generators as nodes and transmission lines as edges, to construct graph structure data that adapts to the physical information neural network model.

[0063] Step S32: A message-passing neural network is used as the graph neural network module, and neural network convolution is used as the graph convolution operator. Convolution weights are dynamically generated through the edge network to adapt to the transmission line impedance parameters.

[0064] Step S33: Extract cross-topological graph structure features through multi-layer graph convolution, convert scene cluster labels into trainable embedding vectors, and concatenate them with cross-topological graph structure features to obtain fused feature vectors.

[0065] Step S34: Input the fused feature vector into the feedforward neural network module, output the equivalent parameters after Kron simplification, and use them as the predicted values ​​of system parameters that meet the preconditions of physical constraints.

[0066] Specifically, the network structure of a power system is essentially a non-Euclidean graph, and the coupling relationship between nodes is determined by the network topology and line parameters. In this embodiment, a message-passing neural network (MPNN) is used to construct a graph embedding module. The topology of the power network is used as the graph carrier, and the bus is abstracted as a node and the transmission line is abstracted as an edge to realize the modeling of network structure information.

[0067] The MPNN framework proposed in this embodiment integrates a feature extraction module based on edge conditional convolution and a multi-layer perceptron head (MLP head) to achieve end-to-end mapping from the original power grid topology to Kron-simplified equivalent parameters. The power system is modeled as an undirected graph. ,in For a set of nodes, Let be the set of edges, for node eigenvector v i It can be represented by equation (14), the edge eigenvector e ij Defined as: (19) in, R ij and X ij For the line To maintain the symmetry of the graph and support bidirectional information transmission, a bidirectional index is constructed for undirected edges, considering the resistance and reactance. And copy the corresponding edge features, so that e ij = e ji This ensures that messages can be fully exchanged between adjacent nodes.

[0068] This implementation uses Neural Network Convolution (NNConv) as the basic graph convolution operator. It dynamically generates convolution kernels through an edge network, enabling the model to adaptively adjust the information aggregation method based on the parameters of different transmission lines. Traditional graph convolution typically uses a fixed weight matrix to process all edges, while NNConv generates unique convolution weights for each edge, thus more accurately modeling the impact of transmission line impedance on information transmission.

[0069] For the l Layered graph convolution, nodes i The feature update process involves weighted aggregation and averaging of the features of neighboring nodes, followed by batch normalization (BN), and finally, the introduction of non-linearity through the GELU activation function. The update rule is expressed as follows: (20) in, For nodes i The set of neighboring nodes, For the first l Layer nodes i Hidden features, For the edge The corresponding convolution weight matrix, This represents the GELU activation function. For the first l+ Level 1 node i Hidden features, For the first l Layer nodes j Hidden features.

[0070] Convolution weight matrix Dynamically generated from the edge network, edge network Designed as a two-layer fully connected neural network, using edge features e ij As input, the output, after being flattened, is reshaped into a weight matrix: (twenty one) The multi-layer architecture of the MPNN designed in this embodiment is given by the hidden layer dimension sequence as [ d 1 , d 2 ,…, d L During the forward propagation process, the node features are used as the hidden state at layer 0 during the initialization phase. Each convolutional layer is performed according to equations (20)-(21). L The next operation updates the node features. Through multiple layers of propagation, the node features gradually incorporate information from multi-hop neighbors. The first layer aggregates directly connected neighbors, the second layer aggregates nodes within a two-hop range, and so on.

[0071] After L layers of graph convolution, the vectors are concatenated and fused with the continuous vectors transformed from discrete scene clusters obtained by clustering. The discrete scene category labels are first transformed into continuous embedding vectors through a trainable lookup table operation. These embedding vectors are then copied and expanded, and concatenated with the topological features of nodes and edges to obtain a fused feature vector for use by the network model, which can be represented as: (twenty two) in, The final fused feature vector is obtained. For discrete scene category labels r The continuous embedding vector obtained after transformation through lookup table operation Represents a node i go through L The final hidden feature vector obtained after the convolutional propagation is This is a feature splicing operation.

[0072] In the above content, the trainable lookup table is a trainable matrix with the following structure: , The dimension of the embedded vector represents the complexity of the current feature. The lookup table acts as a dictionary, transforming discrete IDs without actual numerical meaning into continuous vectors with semantic information that the neural network can understand.

[0073] The input to the lookup table is a discrete integer label. r and this integer r As an index, find the first [value] in the embedding matrix. r The vector corresponding to the row e r ,vector e r The final continuous embedding vector can be represented as follows: (twenty three) in, This represents the embedding matrix.

[0074] Finally, the fused feature vectors are passed through the MLP Head layer to obtain the simplified equivalent network parameters.

[0075] In one optional implementation, step S4 includes the following process: Step S41: Construct a physical-data dual-drive loss function composed of a weighted average of data loss and physical loss.

[0076] Step S42: Calculate the data loss using mean square error.

[0077] Step S43: Based on the generator rotor oscillation equation in the dynamic model, perform dense collocation calculation of physical loss in the spatiotemporal domain, and embed the generator rotor motion equation into the loss function in the form of residual penalty as a regularization constraint.

[0078] Step S44: Train the physical information neural network model based on the physical-data dual-driven loss function, and iteratively update and optimize the model parameters.

[0079] Specifically, the power angle trajectory of a power system follows the generator rotor oscillation equation. Purely data-driven models struggle to guarantee the physical consistency of prediction results when training samples are limited. This embodiment designs a physical information neural network architecture, embedding the generator rotor oscillation equation into the loss function as a residual penalty term. Based on data fitting, physical equations are introduced as regularization constraints, making the model's predicted trajectory closer to the true physical reality.

[0080] In this embodiment, the input vector x of PINN is defined as a time series describing the output of renewable energy units, and the output is the power angle trajectory of each synchronous generator. For multiple outputs, a network architecture of shared encoder and independent decoder is adopted. The shared encoder extracts global features from the input variables to capture the temporal evolution, while the independent decoders map the shared features to the power angle output of each generator, achieving refined modeling of the dynamic characteristics of different generators. This architecture will transform the input x into the output... The mapping is represented as: (twenty four) in, To share encoder parameters, , For the first 1 , N g Decoder parameters.

[0081] The total loss function consists of two parts: data loss and physical loss. (25) in, L data This is the data loss function, which measures the deviation between the network's predicted values ​​and the true labels. L phy This is the physical loss function, used to penalize the degree of violation of the physical equations. These are the weighting coefficients.

[0082] The mean squared error is used as the metric for data loss. For multi-output problems, the data loss is the weighted sum of the errors of each output component, which can be expressed as: (26) in, k For generator index, For the first k The data loss weighting coefficients of each generator must satisfy the normalization condition. N g The total data loss weight for each generator is 1. N u The number of sample data points. The predicted work angle value, This is the label for the angle of attack, i.e., the true value.

[0083] Unlike data loss, to fully leverage the regularization effect of physical laws, the calculation of physical loss typically requires dense sampling of collocation points in the spatiotemporal domain. This results in a collocation point count far exceeding the number of data points in the training samples. This allows the model to not only fit the true trajectory at a limited number of observed data points but also satisfy the constraints of the physical equations throughout the entire spatiotemporal domain, thereby achieving accurate predictions even with a small dataset. Various strategies, such as hypercubic Latin sampling, can be used to select collocation points.

[0084] The physical equation (10) is chosen to calculate the residual of the physical loss function. Ideally, if the predicted work angle trajectory strictly satisfies the physical law, the physical residual should be always equal to zero. However, actual simulation and network simplification processes introduce errors, making the physical residual non-zero. Therefore, the physical law, as a soft constraint, aims to minimize the residual. The physical loss function is defined as the weighted mean square value of the physical residuals at all collocation points: (27) in, k For generator index, For the first k The physical loss weighting coefficients for each generator satisfy the normalization condition. The residuals of the physical equations, N f The number of points to be assigned.

[0085] In one optional implementation, step S5 includes the following process: Step S51: Obtain the grid topology parameters, renewable energy operation parameters, and fault characteristic parameters of the scenario to be predicted.

[0086] Step S52: Input the power grid topology parameters, renewable energy operation parameters, and fault characteristic parameters into the trained physical information neural network model.

[0087] Step S53: The physical information neural network model outputs the generator power angle trajectory that satisfies the physical constraints.

[0088] Specifically, based on the actual operating state of the power system to be analyzed, corresponding grid topology parameters, line electrical parameters, and generator and renewable energy unit operating parameters are collected. Simultaneously, the existence of faults and their corresponding locations, types, and timing information are determined, forming complete scenario input information. These parameters are then organized according to a unified data format used in the model training phase and input into the trained physical information neural network model. The model extracts features from the grid topology using its internal graph neural network module, combines this with scenario information to form fused features, and completes forward inference calculations. During the output of prediction results, the model is constrained by built-in physical equations, ensuring that the generator power angle trajectory numerically conforms to data patterns while physically satisfying the system dynamics constraint of the rotor motion equations. Ultimately, it outputs a continuous, reasonable, and physically consistent generator power angle time trajectory, providing a basis for system transient stability assessment.

[0089] To address the limitations of existing power system power angle prediction technologies when dealing with indeterminate topologies, the randomness of high-proportion renewable energy sources, and the strong coupling characteristics of physical constraints, particularly the low computational efficiency of traditional time-domain simulation, the poor generalization ability of purely data-driven models, and the inability of existing physical information neural networks to effectively handle non-Euclidean graph structure data, this invention aims to construct a power system power angle prediction method based on the fusion of a graph neural network assisted by scene clustering and a physical information neural network. This method achieves accurate prediction of the system power angle under any given topology, ensures that the prediction results satisfy physical laws, and improves the training efficiency and adaptability of the model in complex operating scenarios. For details, please refer to [link to specific procedures]. Figure 4 .

[0090] like Figure 5 The diagram shown illustrates the model proposed in this embodiment. The process of predicting relevant parameters of a power system using the proposed model requires acquiring the topological information of the scenario to be predicted, renewable energy input parameters, and fault parameters. Preprocessing the initial data before inputting it into the trained fusion prediction model allows the model to rapidly output the complete transient trajectory of the system within a very short time, leveraging its cross-topological feature extraction capabilities and physical constraint mapping relationships learned during training. Furthermore, in online prediction processes, if the prediction is verified to be effective, the input and output of that prediction can be used as a sample in the model's training process to enhance its performance.

[0091] This embodiment also provides a generator power angle trajectory prediction device based on a graph-embedded physical information neural network. This device is used to implement the above embodiments and preferred embodiments, and details already described will not be repeated. As used below, the term "module" can be a combination of software and / or hardware that implements a predetermined function. Although the device described in the following embodiments is preferably implemented in software, hardware implementation, or a combination of software and hardware, is also possible and contemplated.

[0092] This embodiment provides a generator power angle trajectory prediction device based on a graph-embedded physical information neural network, such as... Figure 6 As shown, it includes: The dataset construction module 501 is used to construct a multi-topology operation scenario dataset for power systems containing renewable energy. By setting different network topologies, renewable energy configurations, and fault locations, transient operation data of the power system under different operating conditions are obtained using time-domain simulation.

[0093] The scene clustering module 502 is used to extract feature indicators that reflect the complexity of the scene, cluster the running scenes based on the K-means algorithm, divide scenes with similar features into the same cluster, and assign cluster labels to each scene.

[0094] The graph embedding feature extraction module 503 is used to build a physical information neural network model that integrates graph structure perception capabilities. It captures cross-topological graph structure features through the graph neural network module, constructs a fused feature vector by combining scene cluster labels, and inputs it into the feedforward neural network module to generate predicted system parameter values ​​that meet the preconditions of physical constraints.

[0095] The physical constraint training module 504 is used to construct a physical-data dual-drive loss function to train the physical information neural network model. Based on the data fitting error, the generator rotor motion equation is introduced as a regularization constraint to optimize the model parameters.

[0096] The online prediction module 505 is used to predict the generator power angle trajectory of a power system with any given topology using a trained model.

[0097] The generator power angle trajectory prediction device based on graph-embedded physical information neural network provided in this embodiment of the invention can execute the generator power angle trajectory prediction method based on graph-embedded physical information neural network provided in any embodiment of the invention, and has the corresponding functional modules and beneficial effects of the method. Further functional descriptions of the above modules and units are the same as those in the corresponding embodiments described above, and will not be repeated here.

[0098] This invention provides a generator power angle trajectory prediction device based on a graph-embedded physical information neural network. It classifies operating scenarios involving renewable energy uncertainties and fault disturbances using a clustering algorithm, effectively reducing the learning difficulty of complex scenarios. Leveraging the strong feature extraction capabilities of graph neural networks, it mines common node and line features across different power grid topologies, improving the model's cross-topology generalization performance. Furthermore, it embeds the generator rotor motion equations as constraints into the physical information neural network, achieving dual-driven optimization based on data and physical laws during training. This method can achieve rapid and accurate prediction of generator power angle trajectories in high-proportion renewable energy power systems under different topologies and fault scenarios, while ensuring the physical consistency of the prediction results, providing efficient and reliable technical support for power grid transient stability analysis.

[0099] Figure 7 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention.

[0100] The following is a detailed reference. Figure 7This diagram illustrates a suitable structural design for implementing an electronic device according to embodiments of the present invention. The electronic device may include a processor (e.g., a central processing unit, graphics processor, etc.) 601, which can perform various appropriate actions and processes based on a program stored in read-only memory (ROM) 602 or a program loaded from memory 608 into random access memory (RAM) 603. RAM 603 also stores various programs and data required for the operation of the electronic device. The processor 601, ROM 602, and RAM 603 are interconnected via a bus 604. An input / output (I / O) interface 605 is also connected to the bus 604.

[0101] Typically, the following devices can be connected to I / O interface 605: input devices 606 including, for example, touchscreens, touchpads, keyboards, mice, cameras, microphones, accelerometers, gyroscopes, etc.; output devices 607 including, for example, liquid crystal displays (LCDs), speakers, vibrators, etc.; memory devices 608 including, for example, magnetic tapes, hard disks, etc.; and communication devices 609. Communication device 609 allows electronic devices to communicate wirelessly or wiredly with other devices to exchange data. Although Figure 7 Electronic devices with various devices are shown, but it should be understood that it is not required to implement or have all of the devices shown, and more or fewer devices may be implemented or have instead.

[0102] In particular, according to embodiments of the present invention, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of the present invention include a computer program product comprising a computer program carried on a non-transitory computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication device 609, or installed from a memory 608, or installed from a ROM 602. When the computer program is executed by the processor 601, it performs the functions defined in the generator power angle trajectory prediction method based on a graph-embedded physical information neural network according to embodiments of the present invention.

[0103] Figure 7 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of use of the embodiments of the present invention.

[0104] This invention also provides a computer-readable storage medium. The methods described above according to embodiments of the invention can be implemented in hardware or firmware, or implemented as computer code that can be recorded on a storage medium, or implemented as computer code downloaded via a network and originally stored on a remote storage medium or a non-transitory machine-readable storage medium and then stored on a local storage medium. Thus, the methods described herein can be processed by software stored on a storage medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware. The storage medium can be a magnetic disk, optical disk, read-only memory, random access memory, flash memory, hard disk, or solid-state drive, etc.; further, the storage medium can also include combinations of the above types of memory. It is understood that computers, processors, microprocessor controllers, or programmable hardware include storage components capable of storing or receiving software or computer code. When the software or computer code is accessed and executed by the computer, processor, or hardware, the generator power angle trajectory prediction method based on a graph-embedded physical information neural network shown in the above embodiments is implemented.

[0105] Although embodiments of the 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 invention, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. A generator power angle trajectory prediction method based on graph-embedded physical information neural network, characterized in that, The method includes: A multi-topology operation scenario dataset for power systems containing renewable energy was constructed. By setting different network topologies, renewable energy configurations, and fault locations, transient operation data of the power system under different operating conditions were obtained using time-domain simulation. Extract feature indicators that reflect the complexity of the scene, cluster the running scenes based on the K-means algorithm, divide scenes with similar features into the same cluster and assign cluster labels to each scene; A physical information neural network model with fused graph structure perception capability is constructed. The graph neural network module captures cross-topological graph structure features, combines scene cluster labels to construct a fused feature vector, and inputs it into the feedforward neural network module to generate system parameter prediction values ​​that meet the preconditions of physical constraints. A physical-data dual-drive loss function is constructed to train the physical information neural network model. Based on the data fitting error, the generator rotor motion equation is introduced as a regularization constraint to optimize the model parameters. Using the trained model, generator power angle trajectory prediction is performed on a power system with any given topology.

2. The generator power angle trajectory prediction method based on graph-embedded physical information neural network according to claim 1, characterized in that, Before constructing the multi-topology runtime scenario dataset, the method further includes: A dynamic model of a power generation unit in a power system is constructed, wherein the power generation unit includes a synchronous generator and a renewable energy power generation device; Kron simplification technique is used to reduce the dimensionality of the power system network. By eliminating passive nodes through matrix transformation, the original sparse network is mapped into an equivalent network containing only nodes inside the generators.

3. The generator power angle trajectory prediction method based on graph-embedded physical information neural network according to claim 2, characterized in that, A multi-topology operation scenario dataset for power systems containing renewable energy was constructed. By setting different network topologies, renewable energy configurations, and fault locations, transient operation data of the power system under different operating conditions were obtained using time-domain simulation, including: A single operational scenario is defined as a triple containing network topology, renewable energy configuration, and fault information. Based on the aforementioned dynamic model and the equivalent network, diverse operating scenarios are generated by changing the power grid topology, renewable energy access nodes and output coefficients, faulty lines, fault locations, and fault timing. Transient operating data under various scenarios are obtained based on time-domain simulation, and a node feature matrix is ​​constructed that includes node active / reactive power, node type, renewable energy access identifier, and inertia constant.

4. The generator power angle trajectory prediction method based on graph-embedded physical information neural network according to claim 1, characterized in that, Extract feature metrics reflecting scene complexity, cluster the running scenes based on the K-means algorithm, group scenes with similar features into the same cluster, and assign cluster labels to each scene, including: Extract renewable energy uncertainty indicators and fault location severity indicators to construct a two-dimensional scenario risk feature vector; The optimal number of clusters is determined using the silhouette coefficient method, and K-means clustering iteration is performed based on the optimal number of clusters. Scenarios with similar operational characteristics are grouped into the same cluster, and each scenario is assigned a corresponding cluster label.

5. The generator power angle trajectory prediction method based on graph-embedded physical information neural network according to claim 1, characterized in that, A physical information neural network model with fused graph structure perception capabilities is constructed. This model captures cross-topological graph structure features through a graph neural network module, constructs a fused feature vector by combining scene cluster labels, and inputs it into a feedforward neural network module to generate predicted system parameters that satisfy preconditions of physical constraints, including: The power system is modeled as an equivalent undirected graph structure, with buses and generators as nodes and transmission lines as edges, to construct graph structure data that adapts to the physical information neural network model. A message-passing neural network is used as the graph neural network module, and neural network convolution is used as the graph convolution operator. Convolution weights are dynamically generated through the edge network to adapt to the impedance parameters of the transmission line. Cross-topological graph structural features are extracted through multi-layer graph convolution. Scene cluster labels are converted into trainable embedding vectors and concatenated with the cross-topological graph structural features to obtain a fused feature vector. The fused feature vector is input into the feedforward neural network module, which outputs the equivalent parameters after Kron simplification, and uses them as the predicted values ​​of system parameters that meet the preconditions of physical constraints.

6. The generator power angle trajectory prediction method based on graph-embedded physical information neural network according to claim 2, characterized in that, A physical-data dual-driven loss function is constructed to train the physical information neural network model. Based on the data fitting error, the generator rotor motion equation is introduced as a regularization constraint to optimize the model parameters, including: Construct a physical-data dual-driven loss function composed of a weighted average of data loss and physical loss; Data loss is calculated using mean square error; Based on the generator rotor oscillation equation in the dynamic model, physical loss is calculated by dense collocation in the spatiotemporal domain, and the generator rotor motion equation is embedded in the loss function in the form of residual penalty as a regularization constraint. The physical information neural network model is trained based on the physical-data dual-driven loss function, and the model parameters are iteratively updated and optimized.

7. The generator power angle trajectory prediction method based on graph-embedded physical information neural network according to claim 1, characterized in that, Using the trained model, generator power angle trajectory prediction is performed on a power system with any given topology, including: Obtain the power grid topology parameters, renewable energy operating parameters, and fault characteristic parameters of the scenario to be predicted; The power grid topology parameters, the renewable energy operating parameters, and the fault characteristic parameters are input into the trained physical information neural network model; The physical information neural network model outputs the generator power angle trajectory that satisfies physical constraints.

8. A generator power angle trajectory prediction device based on graph-embedded physical information neural network, characterized in that, The device includes: The dataset construction module is used to build a multi-topology operation scenario dataset for power systems containing renewable energy. By setting different network topologies, renewable energy configurations, and fault locations, it uses time-domain simulation to obtain transient operation data of the power system under different operating conditions. The scene clustering module is used to extract feature indicators that reflect the complexity of the scene. It clusters the running scenes based on the K-means algorithm, divides scenes with similar features into the same cluster, and assigns cluster labels to each scene. The graph embedding feature extraction module is used to build a physical information neural network model that integrates graph structure perception capabilities. It captures cross-topological graph structure features through the graph neural network module, constructs a fused feature vector by combining scene cluster labels, and inputs it into the feedforward neural network module to generate predicted system parameters that meet the preconditions of physical constraints. The physical constraint training module is used to construct a physical-data dual-drive loss function to train the physical information neural network model. Based on the data fitting error, the generator rotor motion equation is introduced as a regularization constraint to optimize the model parameters. The online prediction module is used to predict the generator power angle trajectory of a power system with any given topology using a trained model.

9. An electronic device, characterized in that, include: The system includes a memory and a processor, which are interconnected. The memory stores computer instructions, and the processor executes the computer instructions to perform the generator power angle trajectory prediction method based on a graph-embedded physical information neural network as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions for causing the computer to execute the generator power angle trajectory prediction method based on a graph-embedded physical information neural network as described in any one of claims 1 to 7.

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