Low-dimensional visualization and security assessment method for static security domain of power system
By using the GraphSAGE framework and parametric manifold projection, low-dimensional visualization and security assessment of the static security domain of power systems are realized, solving the complexity and real-time problems of traditional assessment methods and providing a solution for global situational awareness and intuitive decision-making.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-14
- Publication Date
- 2026-03-27
AI Technical Summary
Traditional power system security assessment relies on repetitive power flow calculations, which makes it difficult to achieve real-time, accurate security assessment and intuitive decision-making due to the complexity and nonlinearity of the high-dimensional security domain. Existing research has only achieved visualization of some dimensions, leading to operation and scheduling errors.
Using the GraphSAGE framework, combined with the power system topology and operating parameters, we achieve low-dimensional visualization and security assessment of the static security domain of the power system through graph-structured data and parametric manifold projection. The dimensionality reduction effect is verified using the Pearson correlation coefficient.
It provides power system operation dispatchers with global situational awareness and intuitive decision-making, reduces computational burden, and improves the real-time performance and accuracy of safety assessments.
Smart Images
Figure CN121749529A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of power system technology, specifically to power system security analysis, and particularly to a low-dimensional visualization and security assessment method for the static security domain of a power system. Background Technology
[0002] With the continuous growth of electricity demand and the increasing penetration rate of new energy sources and flexible loads, the imbalance between electricity supply and demand has become more prominent, posing a severe challenge to the safe operation of the power system. Traditional power system safety assessment relies on power flow calculations at specific points, which limits real-time safety assessment. The safety domain provides a new paradigm from point-by-point analysis to regional analysis. By characterizing safety boundaries and quantifying safety margins, the static safety domain has become a key tool for assessing and ensuring the static safe operation of the power system. Visualizing the static safety domain of the power system provides operators with the relative positions of operating points and safety boundaries. However, the static safety domain of a real power grid inherently possesses complex characteristics of ultra-high dimensionality, non-convexity, and nonlinearity, which hinders power system dispatchers' situational awareness and intuitive decision-making regarding high-dimensional safety domains.
[0003] Solving the static security domain of a power system is essentially solving a constrained power flow problem that satisfies the power flow equations and system operation constraints. The injected power space, satisfying the equality constraints of the power flow equations and the inequality constraints of voltage magnitude at each node, line flow, and active and reactive power of generators, is defined as the static security domain of the power system. Regarding visualization, existing research only achieves visualization of the active or reactive power output of two or three units, while the output of other units remains fixed. This simplification can easily lead to erroneous decisions by operation and dispatch personnel. In terms of real-time security assessment, traditional security assessment relies on repetitive power flow calculations, resulting in a heavy computational burden; the injected power space in some dimensions of the static security domain cannot achieve a comprehensive assessment of the security margin, thus limiting its practical value.
[0004] Considering the above shortcomings, it is necessary to study a dimensionality reduction projection framework for the static security domain of power systems that combines intuitive visualization with real-time security assessment from the perspective of dimensionality reduction. This framework will allow for intuitive observation of the relative position of the operating point from the security boundary and rapid and accurate security assessment, making it more conducive to the situational awareness and intuitive decision-making of operation and dispatch personnel, and meeting the application conditions in actual engineering. Summary of the Invention
[0005] The purpose of this invention is to provide a low-dimensional visualization and security assessment method for the static security domain of a power system. Based on the mathematical expression of the static security domain of a power system, the local manifold characteristics of the static security domain are verified. Furthermore, based on the topology of the power system itself, and taking advantage of the characteristic that the security domain is located in a non-Euclidean space, a submanifold extraction framework based on GraphSAGE is constructed, providing a practical method for low-dimensional visualization and real-time security assessment of the static security domain of a power system.
[0006] To achieve the above objectives, the solution of the present invention is:
[0007] A low-dimensional visualization and security assessment method for the static security domain of a power system includes the following steps:
[0008] Step 1: Based on the mathematical expression of the static security domain of the power system, the local manifold characteristics of the static security domain are verified, and the manifold representation of the high-dimensional security domain is obtained.
[0009] Step 2: Based on the power system topology and operating parameters, randomly sample operating points and label them as safe / unsafe through power flow calculation and security verification, thereby generating graph structure data;
[0010] Step 3: Construct a low-dimensional visualization framework for the static security domain of the power system. Use GraphSAGE to fuse topological information and node net power injection to achieve feature reconstruction of the injected power space. Use the parametric manifold projection method to achieve dimensionality reduction visualization of graph-level feature vectors.
[0011] Step 4: Construct high- and low-dimensional security margin assessment indicators. Use the Pearson correlation coefficient to quantitatively verify the effectiveness of low-dimensional projection in preserving key security features in the high-dimensional security domain, thereby achieving efficient security assessment.
[0012] The specific process of step 1 above is as follows:
[0013] Step 11: Establish a mathematical model of the power system's security domain, including AC power flow equations and inequality equations for voltage magnitudes at system nodes, line power flow, and active and reactive power of generators. The power flow equations are as follows:
[0014] ,
[0015] The inequalities for voltage amplitude at each node of the system, line power flow, and active and reactive power of generators include:
[0016] ,
[0017] ,
[0018] In the formula, It is the set of nodes in a power system. and These are nodes Net injected active power and reactive power; and These are generator nodes The output active power and reactive power; and These are the load nodes. Active power and reactive power; For nodes The voltage amplitude; These are nodes and nodes Between lines Active power, reactive power, and apparent power, subscript Indicates the route; It is a node and nodes The phase angle difference between them; and These are nodes and nodes Between lines The conductivity and susceptance; the superscripts max and min indicate the upper and lower limits of the variable, respectively;
[0019] Set the number of power system nodes to The number of generator nodes is Control variables include Active power injection from generators excluding the slack node and Group voltage amplitude; state variables include Group voltage amplitude, active power of group slack node, The reactive power of the generator node. Group voltage amplitude; express Power flow equations; A vector representing the net active power injected into all nodes. This represents a vector of net reactive power injected into all nodes. Inject space for raw power;
[0020] Step 12, assuming 0 is the regularization value of the following mapping, then the feasible region of the power flow equation is of dimension . Local smooth manifolds,
[0021] ,
[0022] Dividing the original locally smooth manifold into multiple edge-bounded manifolds whose internal structures strictly satisfy inequality constraints, the safe region injection space is transformed into a combination of multiple feasible region manifolds.
[0023] ,
[0024] In the formula, For the feasible region manifold, It is a high-dimensional secure domain manifold.
[0025] The specific process of step 2 above is as follows:
[0026] Step 21: Abstract the power system topology as a graph. Each bus in the system is defined as a node on the graph, and the lines between buses are defined as edges. Construct an adjacency matrix based on the above definitions. To represent the interconnections of the entire power grid, a matrix is used. The element is defined as,
[0027] ,
[0028] Step 22, construct the feature matrix Each node eigenvectors Represented as,
[0029] ,
[0030] Step 23: Randomly sample load values at different levels within a certain percentage range near the standard load value to obtain the power injection sample space; for each load level, determine its safety status through power flow calculation and safety verification, and assign it a label. If the operating state satisfies all safe operating constraints, it is marked as safe. Otherwise remember Based on the power flow calculation results, a graph structure dataset is created for each load level group, the net injected power of each node is calculated, and a node feature matrix is formed. Transforming a fixed power grid topology into an adjacency matrix By combining the characteristic matrix and the adjacency matrix, we obtain... Group diagram structure data example .
[0031] The specific process of step 3 above is as follows:
[0032] Step 31: GraphSAGE, an inductive graph neural network, is used as the feature extraction layer. Each layer in the network... Middle node The eigenvectors are represented as follows:
[0033] ,
[0034] ,
[0035] In the formula, The depth of the neural network; Represents a node In the The feature vector of the layer, For nodes The set of neighboring nodes, The first term obtained by aggregation Layer nodes The feature vectors of the neighboring nodes; Represents a node In the The feature vector of the layer, where The weight matrix is a learnable matrix. The bias function is the hyperbolic tangent function, and the activation function is the hyperbolic tangent function.
[0036] Step 32, after After layer iterations, GraphSAGE generates high-dimensional features for each node that incorporate neighborhood topology information. The mean pooling layer is used to extract the final features of all nodes in the graph. Averaging is performed to obtain a vector of aggregated graph-level features.
[0037] ,
[0038] In the formula, Represents the number of datasets, Represents each graph-level aggregated feature The dimension;
[0039] Step 33: Use a classifier containing randomly deactivated neurons to classify graph-level feature vectors, and distinguish between safe and insecure graph-level feature vectors in high-dimensional space;
[0040] Step 34: Design a parameterized manifold projection network. The network architecture adopts a fully connected neural network to reduce the dimensionality of the graph-level feature vectors.
[0041] The specific process of step 34 above is as follows:
[0042] Step 341: Receive high-dimensional graph-level feature vectors And calculate the data point pairs in the high-dimensional space based on the feature vector. The directed similarity is as follows:
[0043] ,
[0044] in, Point The set of neighboring points, The set of data points in a high-dimensional graph-level eigenvector space. For point The shortest distance to its neighboring nodes, The scaling parameter is calculated using the following formula:
[0045] ,
[0046] Furthermore, design high-dimensional data pairs Symmetric similarity between The calculation formula is as follows:
[0047] (13)
[0048] Step 342: Obtain the corresponding parameterized manifold projection network through a fully connected parametric manifold projection network. eigenvectors of low-dimensional submanifolds for,
[0049] ,
[0050] In the formula, Let be the dimension of the low-dimensional feature vector, and satisfy . Low-dimensional similarity is calculated using the following formula:
[0051] ,
[0052] In the formula, The set of data points in a low-dimensional eigenvector space; variables and These are preset hyperparameters used to control the clustering properties of low-dimensional submanifolds;
[0053] Step 343: Based on the obtained high-dimensional symmetric similarity index and low-dimensional similarity index, the similarity between data distributions in the high-dimensional and low-dimensional spaces is measured using fuzzy cross-entropy loss. The calculation formula is as follows:
[0054] ,
[0055] The parameterized manifold projection network is trained using the loss function described above, thereby obtaining data points in the low-dimensional projection space, i.e., the extracted low-dimensional submanifold.
[0056] The specific process of step 4 above is as follows:
[0057] Step 41, based on the high-dimensional safe domain manifold obtained in Step 1 Based on the calculation results of node voltage and line power flow, the high-dimensional security margin in the high-dimensional security domain space is defined as follows.
[0058] ,
[0059] In the formula, vector This represents a vector composed of the net active and reactive power of all nodes, node voltage, and line apparent power. This indicates the upper limit of the values that each physical quantity can take. This represents the lower limit of the values of each physical quantity, obtained through calculation. This represents a high-dimensional security margin index in a high-dimensional security domain space.
[0060] Step 42: For the low-dimensional submanifold space obtained after dimensionality reduction, the low-dimensional security margin index in the low-dimensional security domain is quantified by the absolute functional distance from the data points to the decision boundary of the support vector machine.
[0061] Step 43: To further verify whether the security region in the low-dimensional submanifold space retains the key security features of the original high-dimensional security region, the Pearson correlation coefficient between the high-dimensional security margin index and the low-dimensional security margin index is calculated. The specific calculation formula is as follows:
[0062] ,
[0063] In the formula, Represents the number of data sets; Indicates the first Low-dimensional safety margin metrics for each dataset. This represents the average low-dimensional safety margin metric across all datasets. Indicates the first High-dimensional safety margin metrics for each dataset This represents the average high-dimensional safety margin metric across all datasets. This represents the Pearson correlation coefficient.
[0064] After adopting the above solution, the beneficial effects of the present invention are as follows:
[0065] This method directly establishes a low-dimensional visualization and security assessment framework for the static security domain of a power system. Compared to static security domains that only consider a portion of the generating units, it avoids erroneous decisions caused by fixing only a few units. Furthermore, the dimensionality-reduced static security domain provides operation and control personnel with global situational awareness and intuitive assessment and decision-making, demonstrating significant engineering application value. Attached Figure Description
[0066] Figure 1 This is a detailed flowchart of the present invention;
[0067] Figure 2 This is a low-dimensional visualization framework for the static security domain of the power system in this embodiment of the invention;
[0068] Figure 3 This is a low-dimensional visualization result of the standard power system calculation example in this invention. Detailed Implementation
[0069] 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, and 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.
[0070] by Figure 2 The low-dimensional visualization framework of the static security domain of the power system is illustrated, and the study is carried out on the IEEE 30-bus system.
[0071] like Figure 1 As shown, this embodiment of the invention provides a low-dimensional visualization and security assessment method for the static security domain of a power system, including the following steps:
[0072] Step 10) Based on the mathematical expression of the static security domain of the power system, the local manifold characteristics of the static security domain were verified;
[0073] Step 20) Based on the power system topology and operating parameters, randomly sample operating points and label them as safe / unsafe through power flow calculation and security verification, thereby generating graph structure data;
[0074] Step 30) Construct a low-dimensional visualization framework for the static security domain of the power system. Use GraphSAGE to fuse topological information and node net power injection to achieve feature reconstruction of the injected power space. Use the parametric manifold projection method to achieve dimensionality reduction visualization of graph-level feature vectors.
[0075] Step 40) Construct high- and low-dimensional security margin assessment indices and use the Pearson correlation coefficient to quantitatively verify the effectiveness of low-dimensional projection in preserving key security features in the high-dimensional security domain, thereby achieving efficient security assessment.
[0076] In the above embodiments, step 10) specifically includes:
[0077] Step 101) Establish a mathematical model of the power system's security domain, including AC power flow equations and inequality equations for voltage magnitudes at each node, line power flow, and active and reactive power of generators, as shown below:
[0078] (1)
[0079] (2)
[0080] (3)
[0081] In the formula, It is the set of nodes in a power system. and These are nodes The net injected active power (MW) and reactive power (MVar); and These are generator nodes The output active power (MW) and reactive power (MVar); and These are the load nodes. The active power (MW) and reactive power (MVar); For nodes The voltage amplitude, pu; These are nodes and nodes Between lines Active and reactive power, subscript Indicates the route; It is a node and nodes Between lines Apparent power, MVA; It is a node and nodes The phase angle difference between them, in rad; and These are nodes and nodes Between lines The conductance and susceptance; the superscripts max and min represent the upper and lower limits that the variables can take, respectively. The number of nodes in the power system is set to... The number of generator nodes is Control variables include Active power injection from generators excluding the slack node and Group voltage amplitude, state variables include Group voltage amplitude, active power of group slack node, The reactive power of the generator node. Group voltage amplitude. F(u, v(u))=0 indicates 2N. B Power flow equations (1); A vector representing the net active power injected into all nodes. This represents a vector of net reactive power injected into all nodes. To inject space for the original power.
[0082] Step 102): Assuming 0 is the regularization value of the following mapping, the feasible region of the power flow equation (1) is of dimension . Locally smooth manifolds:
[0083] (4)
[0084] Considering the inequality constraint equations in equation (3), the original locally smooth manifold is divided into multiple manifolds with edges. These manifolds strictly satisfy the inequality constraints internally. Therefore, the safe region injection space can be transformed into a combination of multiple feasible region manifolds:
[0085] (5)
[0086] In the formula, For the feasible region manifold, It is a high-dimensional secure domain manifold.
[0087] In the above embodiments, step 20) specifically includes:
[0088] Step 201) First, abstract the topology of the power system as a graph. Each bus in the system is defined as a node on the graph, and the lines between buses are defined as edges of the graph. Based on the above definitions, construct an adjacency matrix. This is used to represent the interconnections of the entire power grid. A matrix. The element is defined as:
[0089] (6)
[0090] This adjacency matrix It represents the topology of the system and remains unchanged during the sampling process.
[0091] Step 202) Next, the feature matrix needs to be constructed. This enables node characterization of operational status. For a given power injection space, the operational data of all buses are constructed into a node feature matrix. Specifically, each node eigenvectors It can be represented as:
[0092] (7)
[0093] Step 203) To train and evaluate the model, a labeled dataset needs to be generated, specifically including: (1) Data sampling: By randomly sampling different load values within a certain percentage range near the standard load value, a large number of power injection sample spaces covering different operating conditions are generated. (2) Safety labeling: For each load level, its safety status is determined through power flow calculation and safety verification, and a label is assigned to it. If the operating state satisfies all safe operating constraints, it is marked as safe. Otherwise remember (3) Graph structure data generation: Based on the power flow calculation results, a graph structure dataset is created for each load level group, the net injected power of each node is calculated, and a node feature matrix is formed. Transform a fixed power grid topology into an adjacency matrix. By combining the characteristic matrix with the adjacency matrix, we obtain... Group diagram structure data example .
[0094] In the above embodiments, step 30) specifically includes:
[0095] Step 301) First, considering that the graph dataset generated in step 20) is high-dimensional and distributed in a non-Euclidean space, traditional fully connected neural networks perform poorly in processing such data, failing to capture topological dependencies, resulting in insufficient feature extraction and poor classification performance. Therefore, an inductive graph neural network, GraphSAGE, is used as the feature extraction layer. Specifically, the depth of the neural network is set to... Layer, each layer in a network Middle node The feature vector can be represented as:
[0096] (8)
[0097] (9)
[0098] In the formula, Represents a node In the The feature vector of the layer, The first term obtained by aggregation Layer nodes The feature vectors of the neighboring nodes are aggregated using a differentiable aggregation function, mean aggregation. Equation (9) represents the node. In the eigenvectors of the layer ,in The weight matrix is a learnable matrix. The bias function is the hyperbolic tangent function, and the activation function is the hyperbolic tangent function.
[0099] Step 302) Then, after passing through After layer iterations, GraphSAGE generates high-dimensional features for each node that incorporate neighborhood topological information. However, the security assessment task is for the entire power grid state, thus requiring a graph-level feature vector. Specifically, an average pooling layer is added after the above steps to pool the final features of all nodes in the graph. The average is then performed to obtain the vector of aggregated graph-level features, as follows:
[0100] (10)
[0101] In the formula, Represents the number of datasets, Represents each graph-level aggregated feature Dimensions.
[0102] Step 303) After the pooling layer, a classifier containing randomly deactivated neurons is designed and activated using the Sigmoid function to output the security assessment result. This step uses the binary cross-entropy loss function for training to achieve secure classification. The training objective is to ensure that graph-level feature vectors in high-dimensional space have excellent separability, that is, secure and insecure graph-level feature vectors can be separated in high-dimensional space.
[0103] Step 304) The graph-level feature vectors obtained after training in step 303) have already encoded the topological information, node power injection information, and operational constraints of the power system, but are still in a high-dimensional space. To achieve dimensionality reduction, a parameterized manifold projection network is designed, and the network architecture adopts a fully connected neural network. This includes:
[0104] (1) Receive high-dimensional graph-level feature vectors And calculate the data point pairs in the high-dimensional space based on the feature vector. The directed similarity is as follows:
[0105] (11)
[0106] in, Point The set of neighboring points, The set of data points in a high-dimensional graph-level eigenvector space. For point The shortest distance to its neighboring nodes, The scaling parameter is calculated using the following formula:
[0107] (12)
[0108] Furthermore, design high-dimensional data pairs Symmetric similarity between The calculation formula is as follows:
[0109] (13)
[0110] (2) By using a fully connected parametric manifold projection network, the corresponding... eigenvectors of low-dimensional submanifolds for:
[0111] (14)
[0112] In the formula, Let be the dimension of the low-dimensional feature vector, and satisfy . Low-dimensional similarity can be calculated using the following formula:
[0113] (15)
[0114] In the formula, A set of data points in a low-dimensional eigenvector space. Variables and These are preset hyperparameters used to control the clustering properties of low-dimensional submanifolds.
[0115] (3) Based on the high-dimensional symmetric similarity index and low-dimensional similarity index obtained above, the similarity of data distributions in high-dimensional and low-dimensional spaces can be measured by fuzzy cross-entropy loss. The calculation formula is as follows:
[0116] (16)
[0117] The parameterized manifold projection network can be trained using the loss function described above, thereby obtaining data points in the low-dimensional projection space, i.e., the extracted low-dimensional submanifold.
[0118] In the above embodiments, step 40) specifically includes:
[0119] Step 401) Regarding the safety assessment issue, firstly, establish safety assessment indicators for the original space. Based on the original power injection space. The net active and reactive power at nodes, node voltage, and line power flow calculation results are defined as follows:
[0120] (17)
[0121] In the formula, vector This represents a vector composed of the node's net active power and reactive power, the node voltage, and the line apparent power vector; vector This indicates the upper limit of the values that each physical quantity can take. This represents the lower limit of the values of each physical quantity, obtained through calculation. This represents the high-dimensional safety margin index in the high-dimensional safety domain space. Theoretically, formula (17) captures the safety margin under the worst-case scenario by considering the minimum safety distance of each variable. However, a single variable cannot reflect the safety margin of all dimensions. Therefore, this invention uses the summation of the indices of all variables as the safety margin index of the original space.
[0122] (Step 402) Then, for the low-dimensional submanifold space obtained after dimensionality reduction, a support vector machine (SVM) is used in conjunction with radial basis function kernels to characterize the decision boundaries between different classes of running points in the low-dimensional safety domain. Therefore, the low-dimensional safety margin index in the low-dimensional safety domain can be quantified by the absolute functional distance from the data point to the decision boundary of the SVM.
[0123] Step 403) To further verify whether the security domain in the low-dimensional submanifold space retains the key security features of the original high-dimensional security domain, the Pearson correlation coefficient between the high-dimensional security margin index and the low-dimensional security margin index is calculated. The specific calculation formula is as follows:
[0124] (18)
[0125] In the formula, For the first Low-dimensional safety margin metrics for each dataset. This represents the average low-dimensional safety margin metric across all datasets. For the first High-dimensional safety margin metrics for each dataset The Pearson correlation coefficient represents the average of the high-dimensional safety margin indicators for all datasets. This is obtained by calculating the covariance of the two variables and dividing it by the product of their standard deviations. A significant positive correlation provides quantitative proof that the method of this invention not only achieves category differentiation in visualization but also partially preserves key safety margin information, confirming the dual effectiveness of the method in low-dimensional visualization and safety assessment in the security domain.
[0126] 2D visualization results of the IEEE 30-node system, such as Figure 3 As shown.
[0127] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0128] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0129] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0130] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.
[0131] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.
Claims
1. A low-dimensional visualization and security assessment method for the static security domain of a power system, characterized in that... Includes the following steps: Step 1: Based on the mathematical expression of the static security domain of the power system, the local manifold characteristics of the static security domain are verified, and the manifold representation of the high-dimensional security domain is obtained. Step 2: Based on the power system topology and operating parameters, randomly sample operating points and label them as safe / unsafe through power flow calculation and security verification, thereby generating graph structure data; Step 3: Construct a low-dimensional visualization framework for the static security domain of the power system. Use GraphSAGE to fuse topological information and node net power injection to achieve feature reconstruction of the injected power space. Use the parametric manifold projection method to achieve dimensionality reduction visualization of graph-level feature vectors. Step 4: Construct high- and low-dimensional security margin assessment indicators. Use the Pearson correlation coefficient to quantitatively verify the effectiveness of low-dimensional projection in preserving key security features in the high-dimensional security domain, thereby achieving efficient security assessment.
2. The method as described in claim 1, characterized in that: The specific process of step 1 is as follows: Step 11: Establish a mathematical model of the power system's security domain, including AC power flow equations and inequality equations for voltage magnitudes at system nodes, line power flow, and active and reactive power of generators. The power flow equations are as follows: ， The inequalities for voltage amplitude at each node of the system, line power flow, and active and reactive power of generators include: ， ， In the formula, It is the set of nodes in a power system. and These are nodes Net injected active power and reactive power; and These are generator nodes The output active power and reactive power; and These are the load nodes. Active power and reactive power; For nodes The voltage amplitude; These are nodes and nodes Between lines Active power, reactive power, and apparent power, subscript Indicates the route; It is a node and nodes The phase angle difference between them; and These are nodes and nodes Between lines The conductivity and susceptance; the superscripts max and min indicate the upper and lower limits of the variable, respectively; Set the number of power system nodes to The number of generator nodes is Control variables include Active power injection from generators excluding the slack node and Group voltage amplitude; state variables include Group voltage amplitude, active power of group slack node, The reactive power of the generator node. Group voltage amplitude; express Power flow equations; A vector representing the net active power injected into all nodes. This represents the vector of net reactive power injected into all nodes. Inject space for raw power; Step 12, assuming 0 is the regularization value of the following mapping, then the feasible region of the power flow equations is of dimension . Local smooth manifolds, ， Dividing the original locally smooth manifold into multiple edge-bounded manifolds whose internal structures strictly satisfy inequality constraints, the safe region injection space is transformed into a combination of multiple feasible region manifolds. ， In the formula, For the feasible region manifold, It is a high-dimensional secure domain manifold.
3. The method as described in claim 1, characterized in that: The specific process of step 2 is as follows: Step 21: Abstract the power system topology as a graph. Each bus in the system is defined as a node on the graph, and the lines between buses are defined as edges. Construct an adjacency matrix based on the above definitions. To represent the interconnections of the entire power grid, a matrix is used. The element is defined as, ， Step 22, construct the feature matrix Each node eigenvectors Represented as, ， Step 23: Randomly sample load values at different levels within a certain percentage range near the standard load value to obtain the power injection sample space; for each load level, determine its safety status through power flow calculation and safety verification, and assign it a label. If the operating state satisfies all safe operating constraints, it is marked as safe. Otherwise remember ; Based on the power flow calculation results, a graph structure dataset is created for each load level group, the net injected power of each node is calculated, and a node feature matrix is formed. Transforming a fixed power grid topology into an adjacency matrix ; Combining the feature matrix with the adjacency matrix yields Group diagram structure data example .
4. The method as described in claim 1, characterized in that: The specific process of step 3 is as follows: Step 31: GraphSAGE, an inductive graph neural network, is used as the feature extraction layer. Each layer in the network... Middle node The eigenvectors are represented as follows: ， ， In the formula, The depth of the neural network; Represents a node In the The feature vector of the layer, For nodes The set of neighboring nodes, The first term obtained by aggregation Layer nodes The feature vectors of the neighboring nodes; Represents a node In the The feature vector of the layer, where The weight matrix is a learnable matrix. The bias function is the hyperbolic tangent function, and the activation function is the hyperbolic tangent function. Step 32, after After layer iterations, GraphSAGE generates high-dimensional features for each node that incorporate neighborhood topology information. The mean pooling layer is used to extract the final features of all nodes in the graph. Averaging is performed to obtain a vector of aggregated graph-level features. ， In the formula, Represents the number of datasets, Represents each graph-level aggregated feature The dimension; Step 33: Use a classifier containing randomly deactivated neurons to classify graph-level feature vectors and distinguish between safe and insecure graph-level feature vectors in high-dimensional space; Step 34: Design a parameterized manifold projection network. The network architecture adopts a fully connected neural network to reduce the dimensionality of the graph-level feature vectors.
5. The method as described in claim 4, characterized in that: The specific process of step 34 is as follows: Step 341: Receive high-dimensional graph-level feature vectors And calculate the data point pairs in the high-dimensional space based on the feature vector. The directed similarity is as follows: ， in, Point The set of neighboring points, The set of data points in a high-dimensional graph-level eigenvector space. For point The shortest distance to its neighboring nodes, The scaling parameter is calculated using the following formula: ， Furthermore, design high-dimensional data pairs Symmetric similarity between The calculation formula is as follows: ，(13) Step 342: Obtain the corresponding parameterized manifold projection network through a fully connected parametric manifold projection network. eigenvectors of low-dimensional submanifolds for, ， In the formula, Let be the dimension of the low-dimensional feature vector, and satisfy . Low-dimensional similarity is calculated using the following formula: ， In the formula, The set of data points in a low-dimensional eigenvector space; variables and These are preset hyperparameters used to control the clustering properties of low-dimensional submanifolds; Step 343: Based on the obtained high-dimensional symmetric similarity index and low-dimensional similarity index, the similarity between data distributions in the high-dimensional and low-dimensional spaces is measured using fuzzy cross-entropy loss. The calculation formula is as follows: ， The parameterized manifold projection network is trained using the loss function described above, thereby obtaining data points in the low-dimensional projection space, i.e., the extracted low-dimensional submanifold.
6. The method as described in claim 1, characterized in that: The specific process of step 4 is as follows: Step 41, based on the high-dimensional safe domain manifold obtained in Step 1 Based on the calculation results of node voltage and line power flow, the high-dimensional security margin in the high-dimensional security domain space is defined as follows. ， In the formula, vector This represents a vector composed of the net active and reactive power of all nodes, node voltage, and line apparent power. This indicates the upper limit of the values that each physical quantity can take. This represents the lower limit of the values of each physical quantity, obtained through calculation. This represents a high-dimensional security margin index in a high-dimensional security domain space. Step 42: For the low-dimensional submanifold space obtained after dimensionality reduction, the low-dimensional safety margin index in the low-dimensional safety domain is quantified by the absolute functional distance from the data points to the decision boundary of the support vector machine. Step 43: To further verify whether the security region in the low-dimensional submanifold space retains the key security features of the original high-dimensional security region, the Pearson correlation coefficient between the high-dimensional security margin index and the low-dimensional security margin index is calculated. The specific calculation formula is as follows: ， In the formula, Represents the number of data sets; Indicates the first Low-dimensional safety margin metrics for each dataset. This represents the average low-dimensional safety margin metric across all datasets. Indicates the first High-dimensional safety margin metrics for each dataset This represents the average high-dimensional safety margin metric across all datasets. This represents the Pearson correlation coefficient.