A power system cascading failure prediction method

Abstract

The application discloses a power system cascading failure prediction method, comprising the following steps: S1, constructing a hypergraph model of the power system; the hyperedge in the hypergraph model represents an initial fault event and a high-order physical constraint; S2, constructing a graph convolution network of node and edge attributes, mapping the physical characteristics of the bus to the node attributes, and mapping the physical characteristics of the branch to the edge attributes; the odd layers in the graph convolution network reduce the fault stress of the edge and the hyperedge and converge on the node, and the even layers increase the voltage support response of the node and diffuse to the edge and the hyperedge; the initial static spatial feature matrix of the node, the edge and the hyperedge is obtained by inputting the hypergraph model into the graph convolution network; S3, constructing a liquid neural network model and inputting the output of the graph convolution network; S4, constructing a parallel hybrid prediction head model to obtain the fault probability of the bus and the branch in the power system. The application realizes efficient and accurate end-to-end prediction and risk assessment of the cascading failure of the power system.

Description

Technical Field

[0001] This invention relates to the field of power system security analysis and operation control technology, specifically to a method for predicting cascading faults in power systems. Background Technology

[0002] As modern power systems evolve towards a "dual-high" trend of high proportions of renewable energy and high proportions of power electronic equipment, the power grid operating environment is becoming increasingly complex, significantly increasing the risk of large-scale blackouts caused by cascading faults. Cascading faults are typically triggered by initial disturbances in local components. Due to the high coupling of power grid physical parameters and drastic fluctuations in power flow, they can easily trigger chain reactions, leading to large-scale power system collapses in a short period. Therefore, real-time and accurate prediction of the final evolution of cascading faults is crucial for dispatchers to implement preventative control and emergency auxiliary decision-making.

[0003] Currently, the analysis of cascading faults in power systems faces two major bottlenecks: incomplete spatial topology representation and distortion in temporal dynamic simulation. In the spatial dimension, while traditional physical simulation models have clear mechanisms, they require hundreds or even thousands of iterations of high-dimensional nonlinear equations to solve complex, multi-disturbance scenarios in large-scale power grids, resulting in extremely high computational costs and failing to meet the timeliness requirements of online real-time early warning. While graph neural networks, which have emerged in recent years, have improved prediction efficiency, most are based on ordinary graph models consisting of bus-branch structures. This point-to-point binary connection structure struggles to accurately depict the high-order spatial topological relationships in a power system where a single initial fault simultaneously affects multiple specific components, leading to insufficient model perception of the global stress distribution caused by local faults.

[0004] In the time dimension, the evolution of cascading failures exhibits significant nonlinearity and continuity, with its propagation rate dynamically fluctuating with changes in system transient and steady-state pressures. However, existing prediction methods based on recurrent neural networks often employ fixed discrete time steps. This static time evolution mechanism lacks simulation of the underlying continuous dynamic characteristics of the power system, leading to a significant decrease in prediction accuracy and robustness when faced with intertwined fault sequences at different time scales. This lack of spatial correlation and the fragmentation of temporal evolution often prevents existing technologies from accurately identifying weak components and assessing risk paths in extreme and rare cascading failure scenarios. Therefore, there is an urgent need to construct a novel prediction framework that integrates high-order spatial modeling and continuous temporal dynamics deduction. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting cascading faults in power systems, enabling efficient and accurate end-to-end prediction and risk assessment of cascading faults in power systems.

[0006] To achieve the above objectives, this invention provides a method for predicting cascaded faults in power systems, comprising the following steps: S1, obtaining the topology parameters of the power system and constructing a power system hypergraph model; the hyperedges in the hypergraph model represent initial fault events and higher-order physical constraints; S2, constructing a graph convolutional network of node and edge attributes, mapping the physical characteristics of the bus to the node attributes of the graph convolutional network, and mapping the physical characteristics of the branch to its edge attributes; the odd-numbered layers in the graph convolutional network reduce the dimensionality of the fault stresses of the edges and hyperedges and converge them to the nodes; the even-numbered layers in the graph convolutional network increase the dimensionality of the voltage support response of the nodes and diffuse it to the edges and hyperedges; obtaining the initial static spatial feature matrix of nodes, edges, and hyperedges by inputting the hypergraph model into the graph convolutional network; S3, constructing a liquid neural network model, using the output of the graph convolutional network as the input of the liquid neural network model; S4, constructing a parallel hybrid prediction head model as the output layer of the liquid neural network model to obtain the fault probabilities of the bus and branches in the power system.

[0007] Optionally, the method for constructing the graph convolutional network of node and edge attributes in step S2 includes: At odd-numbered layers, the features of the edges and hyperedges themselves are updated by a linear transformation, as follows: In the formula, Indicates the first Edges after layer linear transformation The intermediate feature vector; Indicates the first The layer is a learnable weight matrix used for linear transformation of edge features; Indicates the edge at the 1st Feature vectors output by the layer; Indicates the first Hyperedge after layer linear transformation The intermediate feature vector; Indicates the first The layer is a learnable weight matrix used for linear transformation of hyperedge features; Indicates the superedge In the Feature vectors output by the layer; Then, the node aggregates messages from its directly connected edge, represented as: In the formula, Represents a node The received aggregated message vector from all directly connected edges; Aggregate functions representing edge features; This represents the set of edges that have a direct physical connection to the node. At the same time, nodes aggregate messages from their subordinate superedges, represented as: In the formula: This represents the aggregated message vector received by the node from all faulty hyperedges; This represents the total number of hyperedges defined by the system. Represents the elements of the hyperedge incidence matrix; For nodes The degree; For super-edge The degree; These are the normalization coefficients; For super-edge The weights; Finally, merge all messages to update the node. In the The spatial hidden state of a layer is represented as: In the formula, Indicates the updated node In the The feature vector of the layer; Represents a nonlinear activation function; , , These represent the learnable weight matrices resulting from the concatenation and transformation of the corresponding feature dimensions, and are the parameters that need to be optimized. Represents a node The feature vector in the previous layer; Represents a node The electrical neighbor nodes are in the feature set of the upper layer. Represented as the total number of nodes; This represents the fusion operation of features between itself and its neighboring nodes; This represents the concatenation operation between multiple feature vectors.

[0008] Optionally, the method for constructing the graph convolutional network of node and edge attributes in step S2 further includes: At even-numbered layers, the features of the nodes themselves are updated by a linear transformation, as follows: In the formula, Represents the nodes after linear transformation in even-numbered layers. The intermediate feature vector; This represents the learnable weight matrix used for node feature transformation in even-numbered layers; Then, the edge performs reverse aggregation of messages from its two connected nodes, represented as: In the formula, Indicates edge The received aggregate message vector; Aggregate functions representing node features; Indicates connection to the edge The set of nodes at both ends; Finally, update the edges separately. and super edge In the The spatial hidden state of a layer is represented as: In the formula, Indicates the first Edges after layer update eigenvectors; , These represent the learnable weight matrices used for dimensionality reduction fusion of edge features and convergence features, respectively. These are the edge features of the previous layer; Update super edge The method is expressed as: In the formula, Indicates the first Faulty superedge after layer update eigenvectors; This represents the learnable weight matrix used for hyperedge state updates; For super-edge The feature vector in the previous layer; This represents the total number of busbars. The total number of branch roads; These are elements of the hyperedge incidence matrix; The intermediate feature vector of the node after linear transformation of even-numbered layers; For the first The updated edge feature vector after layer; and These are the degree of the associated vertex and the degree of the hyperedge, respectively. This indicates a splicing operation.

[0009] Optionally, in step S2, the method for obtaining the initial static spatial feature matrix includes: Step S2.1: Extract physical quantities that are strongly correlated with the steady state and fault triggering of the busbar itself, and construct a node attribute matrix. Extract physical quantities that are strongly correlated with the electrical transmission capacity of transmission lines or transformer branches, and construct an edge attribute matrix. Extract state variables that are strongly correlated with the comprehensive properties of hyperedges, and construct the hyperedge attribute matrix. ; Step S2.2 involves constructing a learnable mapping matrix to project the node attribute matrix, edge attribute matrix, and hyperedge attribute matrix onto a hidden feature space of the same dimension, forming aligned initial embeddings and obtaining the node embedding matrices. Edge embedding matrix and hyperedge embedding matrix , represented as: In the formula, , , These represent the learnable weight mapping matrices used for feature projection of nodes, edges, and hyperedges, respectively. , , These represent the learnable bias vectors of the projection layer corresponding to the node, edge, and hyperedge, respectively. Unify the column dimensions of the node embedding matrix, edge embedding matrix, and hyperedge embedding matrix; Step S2.3: Input the node embedding matrix, edge embedding matrix, and hyperedge embedding matrix of the initial layer into the graph convolutional network; Step S2.4: Obtain the final output of the graph convolutional network; Extract the output matrix of the last layer K of the graph convolutional network. The output matrix of the graph convolutional network includes: the initial static spatial feature matrix of the nodes, the initial static spatial feature matrix of the edges, and the initial static spatial feature matrix of the hyperedges. Extract the spatial features of the nodes to obtain the initial static spatial feature matrix of the nodes. , represented as: In the formula, This represents the hidden state matrix of the nodes output by the last layer of the graph convolutional network; This represents the total number of graph convolutional layers in a graph convolutional network. Extract edge spatial features to obtain the initial static spatial feature matrix of the edge. , represented as: In the formula, This represents the graph convolutional network. The edge hidden state matrix output by the layer; Extract hyperedge space features to obtain the initial static space feature matrix of the hyperedge. , represented as: In the formula, This represents the graph convolutional network. The hyperedge hidden state matrix output by the layer.

[0010] Optionally, in step S3, the method of using the output of the graph convolutional network as the input to the liquid neural network model includes: Step S3.1: Use the output matrix of the graph convolutional network as the initial hidden state of the ordinary differential equation; construct the input sequence of the liquid neural network based on the output matrix of the graph convolutional network; The output of the graph convolutional network is used as the initial hidden state vector of the liquid neuron at the start of the evolution. , represented as: In the formula, This represents the initialization layer perceptron used for dimension alignment and feature mapping; and These represent the initial static spatial feature matrices of the nodes and the initial static spatial feature matrices of the edges extracted in the graph convolutional network, respectively. At any evolution time t of the cascading fault propagation, the comprehensive input feature vector of the liquid neuron is represented as: In the formula, This indicates the liquid neural network model at the current propagation time. The comprehensive input feature vector; This represents the concatenation operation of vectors or matrices along the feature dimensions. Indicates at time The dynamic fault mask vector; Indicates time The protection action status characteristics reflect the current action command and time limit margin of the relay protection device; Indicates time The system active / reactive power flow residual reflects the degree of system power imbalance caused by fault tripping. Indicates time Branch overload margin distribution characteristics; This represents the one-hot encoded information in the cascading propagation stage.

[0011] Optionally, S3's method for capturing the temporal dynamic evolution of cascaded faults using liquid neurons includes: Step S3.2: Based on the comprehensive input feature vector at propagation time t, construct the evolution equation of the hidden state of the liquid neuron; In the formula, This indicates that the liquid neuron is at time 10:00. The hidden state feature vector reflects the liquid neural network model's assessment of the current deep state of the cascaded fault; It represents the first derivative of the hidden state with respect to time, i.e., the instantaneous acceleration of fault evolution or state drift; This represents the preset learnable time constant baseline parameter; Indicates that it has learnable parameters The head function of a nonlinear neural network; Indicates the moment of transmission The comprehensive input feature vector; The bias vector represents the liquid neuron and serves as the steady-state baseline controlling the hidden state; The Hadamard product represents the element-wise multiplication of a matrix or vector.

[0012] Optionally, step S3 further includes: Step S3.3: Update the hidden state of the liquid neuron using gated approximation and residual state; A closed-loop continuous-time model of the hidden states of the liquid neuron is constructed, represented as follows: In the formula, This represents the hidden state feature vector of the liquid neuron at the previous time step; Indicates the time evolution step size; This represents the Sigmoid nonlinear gate function; and Indicates that each is composed of parameters and A controllable, trainable nonlinear neural network head; Introducing a residual learning mechanism for state fusion can be represented as: In the formula, This represents the fused state feature matrix after introducing residual connections and undergoing normalization. Indicates the layer normalization operation function; Step 3.4: The liquid neural network model outputs the final hidden state matrix of the fault dynamic evolution; According to the evolutionary stages of cascading fault propagation Performing iterative updates in a loop is represented as: In the formula, The final hidden state matrix representing the fault dynamic evolution output by the liquid neural network; This represents the total number of time steps required for a cascading fault to converge. Indicates the last time step The calculated fusion state feature matrix; This indicates a feature extraction operation that extracts and outputs the final hidden state after undergoing a complete temporal evolution.

[0013] Optionally, step S4 involves constructing a parallel hybrid prediction head model as the output layer of the liquid neural network model, including: Step S4.1: Construct the bus fault prediction head; In the formula, This represents the predicted failure probability value of the i-th bus after the cascaded fault terminates, and its value range is [0,1]. This represents the logistic regression activation function, and the formula is: ; and These represent the learnable weight matrices of the first and second fully connected layers in the bus prediction header, respectively. and These represent the learnable bias vectors of the corresponding feature mapping layers; Represents the final hidden state matrix In the middle, the slice corresponding to the specific bus index dimension is extracted. i The final dynamic evolution hidden state row vector of each busbar; Step S4.2: Construct the branch fault prediction head; In the formula: Indicates the predicted first The failure probability value of a branch after the cascaded fault terminates; This indicates the first [unit / section] that incorporates information from the terminal bus. The combined feature vector of each branch; This represents a multilayer perceptron operation used for deep feature fusion; Represents the final hidden state matrix The first segment extracted based on the branch index slice k The hidden state row vector of the final dynamic evolution of each branch; and These represent the hidden state matrices from the final dynamic evolution. Branches extracted based on the corresponding node index slice k The final hidden state row vectors of the busbars at the beginning and end; This represents the horizontal concatenation operation of feature vectors; and represents the learnable weight matrix and bias vector of the branch prediction classification layer, respectively.

[0014] Optionally, step S4 further includes: Step S4.3: Physically verify the failure probability of the busbar and branches, establish a set of high-risk components, and prioritize the components based on their importance in the power system. Bus failure probability and branch failure probability Each component is logically compared with a preset safety threshold to obtain a set of high-risk components, represented as follows: In the formula: Indicates a set of high-risk components; and These represent the preset failure thresholds for the busbar and branch, respectively. For the busbar, the comprehensive risk score Represented as: In the formula: Indicates busbar Voltage safety margin; Indicates the busbar Importance level weight of the load under load; This indicates the centrality index of the bus in the power system topology; For the corresponding bus evaluation index, the weighting coefficient is , and ; For branch roads, comprehensive risk score Represented as: In the formula, This represents the probability value of branch failure. This represents the reciprocal of the overload margin of that branch. This indicates the centrality index of the branch in the power system topology; These are the weighting coefficients for the corresponding branch road evaluation indicators; Step S4.4: Output a complete fault warning report; and construct a joint loss function by integrating spatial distribution and temporal constraints to optimize the fault warning report; The fault warning report includes: probability of busbar failure. Mapped to the corresponding node to generate a bus fault probability map; via branch failure probability Mapped to the branch failure probability distribution generated by the corresponding edge; directly output the set of high-risk components. Based on high-risk components A geospatial map of weak areas in the power grid is generated by density clustering of the spatial distribution of components in the actual power system; and a liquid neural network is used to generate a geospatial map of weak areas in the power grid at different time steps.t The dynamic evolution hidden state matrix output is used to track high-probability topological connected branches of fault propagation in a time series, generating a potential cascading propagation risk path evolution graph. The joint training loss function is constructed as follows: In the formula, Represents the total loss function. and These represent the standard cross-entropy loss between the predicted results for the bus and the branch and the actual labels, respectively. Indicates physical constraint loss; This represents the loss due to topology consistency constraints; This represents the time-series smoothing constraint loss; This represents the penalty factor for each physical and logical constraint.

[0015] Optionally, the method for constructing the hypergraph model of the power system in step S1 includes: Step S1.1, the topology parameters include the topology of the power system, which is represented by bus b, branch... The original graphical model consisting of electrical connections. ; It is the set of busbars in a power system, represented as , Indicates the busbar. The total number of busbars; is the set of branches in the power system, represented as... , As a side road, The total number of branches; the electrical connection relationships in the original graphical model are represented by an electrical connection relationship matrix indicating whether there are branch connections between two buses; Step S1.2: Define the bus in the power system as the bus vertex and the branch as the branch vertex, and jointly construct a heterogeneous component vertex set containing the bus vertex and the branch vertex; wherein, the heterogeneous component vertex set is the union of the bus set and the branch set.

[0016] Step S1.3: Define the initial fault event and higher-order physical constraints as hyperedges connecting the vertices of the bus or branches, and construct a set of hyperedges; construct the weights of arbitrary hyperedges based on the dimensions of fault electrical impact, topology association coverage, steady-state power flow congestion, and secondary system reliability. ; Step S1.4: Construct the hyperedge association matrix based on the membership relationship between the set of heterogeneous component vertices and each hyperedge. H Each element in the hyperedge incidence matrix Represented as: .

[0017] Compared with the prior art, the technical solution of the present invention has at least the following beneficial effects: In this invention, the bus is defined as a node, branches as edges, and initial fault events and higher-order physical constraints as hyperedges connecting multiple components. By defining a multi-dimensional graph of nodes, edges, and hyperedges, the limitations of traditional single graph theory are avoided. This allows the liquid neural network model to construct independent feature spaces for nodes, edges, and hyperedges respectively and perform alternating feature updates, thereby achieving synchronous deduction and prediction of the state of all components. Furthermore, by constructing a hyperedge model, this invention accurately maps the higher-order spatial spillover range of cascading faults with multiple causes, overcoming the limitations of traditional ordinary graph models in topological representation and providing accurate data support for subsequent extraction of high-dimensional spatial features.

[0018] When constructing the node and edge attribute graph convolutional network, this invention implements an alternating node-edge-hyperedge information transmission mechanism on the hypergraph model. By alternating the operations of "reducing the dimension of the fault stress of the edge and hyperedge to the node" and "increasing the dimension of the voltage support response of the node to the edge and hyperedge", the feature oversmoothing phenomenon under sparse power grid topology is effectively avoided, and the initial static spatial features of the multi-source heterogeneous components of the power grid are deeply mined and integrated.

[0019] In constructing a liquid neural network model based on ordinary differential equations, this invention utilizes the "liquid" characteristic of the time constant of liquid neurons dynamically changing with the hidden state to accurately capture the continuous nonlinear time evolution trajectory of cascaded faults from triggering to termination, significantly improving the model's robustness in time-series prediction under highly dynamic environments.

[0020] This invention constructs a parallel hybrid prediction head, based on the final evolutionary hidden state output by the liquid neural network model, to simultaneously achieve high-precision prediction of bus and branch fault probabilities in power systems. It replaces the traditional power flow iteration simulation that relies on a large amount of computing power, and realizes efficient, end-to-end risk assessment and early warning of complex power grid cascade failures. Attached Figure Description

[0021] Figure 1 This is an architecture diagram of the power system cascading fault prediction method described in this invention.

[0022] Figure 2 This is a flowchart illustrating the power system cascading fault prediction method described in this invention. Detailed Implementation

[0023] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. 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.

[0024] In the description of this invention, it should be noted that the terms "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0025] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0026] like Figure 1 and Figure 2 As shown, this invention provides a method for predicting cascading faults in power systems, used to achieve efficient and accurate prediction and risk assessment of cascading faults in complex power grids. The specific method is as follows: Step 1: Obtain the initial operating state data and topology parameters of the power system, and construct a power system hypergraph model. The hyperedges in the hypergraph model represent initial fault events and higher-order physical constraints.

[0027] Step 1.1: Acquire initial operating status data and topology parameters of the power system through the synchronous phasor measurement device, data acquisition and monitoring control system, or energy management system in the wide area measurement system.

[0028] In a power system, the common node for collecting and distributing electrical energy is called a bus (e.g., generator, load), and the power channel connecting two different bus is called a branch (e.g., transmission line, transformer).

[0029] The topology parameters include the topology of the power system. The initial operating state data represents the real-time operating state of the power system at a specific analysis start time (usually the moment of fault triggering or in steady state), including initial characteristics of the bus and initial characteristics of the branches.

[0030] Specifically, the topology of the power system is represented as consisting of bus v, branches The original graphical model consisting of electrical connections. .

[0031] in, It is the set of busbars in a power system, represented as , Indicates the busbar. This represents the total number of busbars. It is the set of branches in a power system, represented as , For branch nodes, Let A be the total number of branches; the electrical connections in the original graphical model are represented by an electrical connection matrix A, which indicates whether there are branch connections between two buses. The elements in this matrix are shown in Equation 1.

[0032] (Equation 1) In the formula, The matrix is ​​the mother line. With busbar The electrical connection between them.

[0033] The initial characteristics of the busbar include: busbar voltage amplitude, voltage phase angle, and generator active / reactive power output; the initial characteristics of the branch include: line power flow, apparent power, and line reactance.

[0034] By extracting feature quantities at steady state or fault-triggered instants, the initial state matrix of the bus is constructed, represented as follows: ,in Define the feature dimension of the busbar (i.e., the number of initial features of the busbar); construct the initial state matrix of the branches, represented as... ,in The feature dimension for each branch (i.e., the number of initial features of the branch).

[0035] Step 1.2: Construct the set of heterogeneous component vertices and the mapping of feature attributes.

[0036] Within the hypergraph framework, to ensure that buses and branches reside in an equal graph representation space, buses in the power network are defined as bus vertices, and branches are directly mapped to branch vertices, jointly constructing a heterogeneous component vertex set containing both bus vertices and branch vertices. This heterogeneous component vertex set is the union of the bus set and the branch set.

[0037] Step 1.3: Construct the hyperedge and calculate the hyperedge weight.

[0038] The initial fault event and higher-order physical constraints are defined as hyperedges connecting the vertices (i.e., bus vertices or branch vertices). Based on hypergraph theory (i.e., a hyperedge can contain any number of vertices), a single fault and its resulting complex ripple effects are wrapped within a hyperedge to construct a set of hyperedges. .

[0039] Specifically, the hyperedge set Includes: Initial fault event superedge subset Electrical and physical related hyperedge subset Super-edge subsets of power flow coupling relationship Protecting the linkage relationship of super-edge subsets .Right now , where e represents a superedge and M represents the total number of superedges.

[0040] Among them, the initial fault event super-edge subset In this context, a hyperedge represents an independent initial fault event. That is, each hyperedge is enclosed by a physical element that experiences an initial fault (i.e., the fault source) and all first-order physical spillover components (e.g., direct-connect branches and opposite buses) that have direct topological connections to it.

[0041] Electrophysical correlation super-edge subset The hyperedge in the diagram is formed by wrapping each bus in the power system with all its directly connected branches, thus reflecting the inherent Kirchhoff node energy conservation topological constraint.

[0042] Super-edge subset of power flow coupling relationship Each coupling hyperedge is formed by branches and buses that are strongly correlated with the power flow transfer distribution factor.

[0043] Protecting the super-edge subset of the linkage relationship The linkage super-edge in the system consists of components belonging to the same main protection and backup protection configuration zone.

[0044] Based on the dimensions of fault electrical impact, topology correlation coverage, steady-state power flow congestion, and secondary system reliability, an arbitrary hyperedge is constructed. weight , can be represented as: (Equation 2) In the formula, The severity of the fault (e.g., a three-phase short circuit is more severe than a single-phase ground fault). This represents the number of vertices contained in the hyperedge (i.e., the number of affected components). It is the reciprocal of the branch load factor or power flow margin; To protect the action status (i.e., the risk value of no action / false action; if there is a risk of no action, take the higher value); All are normalized adjustment coefficients.

[0045] The hyperedge weight This is used to ensure that in the subsequent steps (step S2.3) during the graph convolution message passing process, the feature information inside the high-risk superedge can be multiplied by the above weight coefficients to obtain a greater gradient passing basis and feature aggregation ratio.

[0046] Construct a weight matrix W for the weights of the hyperedges. The weight matrix of the hyperedges is a diagonal matrix, which can be represented as follows: (M represents the total number of hyperedges). In subsequent steps (step S2.3), the graph convolutional network can look up the weight of the corresponding hyperedge from the weight matrix W of the hyperedge using an index.

[0047] Step 1.4, based on the set of busbars and the set of superedges Determine the membership relationships between them and construct the hyperedge incidence matrix H.

[0048] Based on the vertices in the heterogeneous component vertex set and each hyperedge (i.e., the subset of initial fault event hyperedges) Electrical and physical related hyperedge subset Super-edge subsets of power flow coupling relationship Protecting the linkage relationship of super-edge subsets Construct a hyperedge incidence matrix to determine the membership relationships between hyperedges in the graph. H Each element in the hyperedge incidence matrix Represented as: (Equation 3) By establishing the hyperedge correlation matrix H, the originally unstructured power system fault impact range, topological constraints, and operational logic are completely and accurately mapped into a binary algebraic structure composed of 0s and 1s, thus completing the construction of the hypergraph model in the power system.

[0049] It should be noted that in the hypergraph topology construction stage (step S1) of this invention, both buses and branches are treated as equal 'topological vertices' to ensure the algebraic completeness of the hyperedge association matrix H. In the subsequent graph convolutional feature extraction stage (step S2), to conform to the standardized naming conventions for feature channels in deep learning networks, the physical features of the 'bus vertices' in the power system are mapped to 'node attributes' of the graph convolutional network, and the physical features of the 'branch vertices' are mapped to 'edge attributes' of the graph convolutional network. Through this mapping, equal topology processing of the topological space and independent evolution and update of the feature space are achieved.

[0050] Step 2: Construct a node and edge attribute graph convolutional network, convert the hypergraph model into a numerical tensor and input it into the graph convolutional network.

[0051] The data input to the graph convolutional network includes: the hyperedge incidence matrix, which serves as the topological structure operator. and the node attribute matrix as the input source of multi-source heterogeneous features. Edge attribute matrix and hyperedge attribute matrix The graph convolutional network is based on the hyperedge correlation matrix. The topological membership relationship drives the node-edge-hyperedge alternating message passing of each attribute matrix to extract initial static spatial features, providing static initial samples for subsequent time dynamic evolution models.

[0052] Step 2.1, based on the set of buses in the hypergraph model The set of branches E and the set of superedges Each node's physical state variable is extracted to construct an independent node attribute matrix. Edge attribute matrix Hyperedge attribute matrix This serves as the underlying data input source for the node and edge attribute graph convolutional network.

[0053] Constructing the node attribute matrix The node attribute matrix is ​​the initial feature matrix of node attributes for all buses in the power system, expressed as: (Equation 4) In the formula, This represents the initial feature column vector of the i-th node v, whose internal elements specifically include the per-unit value of the voltage magnitude of the bus, the voltage phase angle, the active power injected by the generator, the reactive power injected by the generator, and the active / reactive power consumed by the load. This represents the total number of nodes in the power system. This indicates the physical dimension of the node feature vector (i.e., how many types of bus physical quantities were extracted). This represents the transpose operation of a matrix or vector. This indicates that the matrix belongs to OK The real space of the column.

[0054] Constructing the edge attribute matrix The edge attribute matrix is ​​the initial feature matrix of edge attributes for all branches of the power system, expressed as: (Equation 5) In the formula: The initial feature matrix represents the edge attributes of the power system. This represents the initial feature column vector of the j-th physical branch. Its internal elements specifically include the branch's longitudinal resistance, longitudinal reactance, ground susceptance, current active / reactive power flow distribution, and branch load factor (the ratio of real-time current to thermal stability limiting current). This represents the total number of physical branches in a power system. This represents the physical dimension of the edge feature vector.

[0055] Extract and each hyperedge (which belongs to the subset of the initial fault event hyperedges) Electrical and physical related hyperedge subset Super-edge subsets of power flow coupling relationship Protecting the linkage relationship of super-edge subsets Construct a hyperedge attribute matrix by integrating strongly correlated state variables. The hyperedge attribute matrix is ​​the initial feature matrix of hyperedge attributes for all fault events in the power system, which can be expressed as: (Equation 6) In the formula, This represents the initial feature matrix of the hyperedge attributes in the power system. Indicates the first The initial feature column vectors of the hyperedges, where belong to the initial fault event subset. The superedges in the array have their own unique fault characteristic bits. Specifically, for the subset of initial fault events... The hyperedge in the equation contains internal elements (i.e., the initial characteristics of the hyperedge) including one-hot codes for fault types (such as three-phase short circuit, two-phase ground fault, etc.), fault severity coefficients, and associated protection action commands; for hyperedges belonging to the electrical-physical associated subset... Super-edge subsets of power flow coupling relationship Protecting the linkage relationship of super-edge subsets In the superedges, the positions of the internal elements (i.e., the initial features of the superedges) corresponding to the fault feature bits are zero-paddinged. M represents the total number of superedges. This represents the physical dimension of the hyperedge feature vector, and its specific value is determined by the maximum value of the initial features of the hyperedge (i.e., the initial subset of fault events). The number of initial features of the hyperedges in the region is uniquely determined.

[0056] Step 2.2: By constructing a learnable mapping matrix, the node attribute matrix, edge attribute matrix, and hyperedge attribute matrix are uniformly projected onto the hidden layer feature space of the same dimension to form an aligned initial embedding.

[0057] Because the physical dimensions (such as voltage kilovolts, power megawatts) and feature dimensions (i.e., ...) of the node attribute matrix, edge attribute matrix, and hyperedge attribute matrix in step 2.1 are different. The node attribute matrix, edge attribute matrix, and hyperedge attribute matrix are all different, and directly performing graph convolution will cause numerical computation conflicts. Therefore, a learnable mapping matrix (i.e., a multilayer perceptron mapping layer) is constructed to uniformly project the node attribute matrix, edge attribute matrix, and hyperedge attribute matrix onto a hidden layer feature space of the same dimension. The initial embedding formulas for the node attribute matrix, edge attribute matrix, and hyperedge attribute matrix are as follows: (Equation 7) (Equation 8) (Equation 9) In the formula, , , These represent the node embedding matrix, edge embedding matrix, and hyperedge embedding matrix of the 0th layer (i.e., the initial layer) of the graph convolutional network after dimensionality reduction / upgrading alignment, respectively, and the column dimension of the three is uniformly d; and the superscript (0) of the three represents the number of the initial layer of the forward propagation of the graph convolutional network. , , represents the learnable weight mapping matrix used for the projection of node, edge, and hyperedge features, respectively. , , These represent the learnable bias vectors of the projection layers corresponding to nodes, edges, and hyperedges, respectively. This represents a nonlinear activation function; in a preferred embodiment, The LeakyReLU function is used to preserve small gradients in the negative range, preventing neuron death.

[0058] Step 2.3: Construct an alternating message passing mechanism between nodes, edges, and hyperedges.

[0059] To address the issue of feature oversmoothing in sparse power grid topologies, this invention designs an alternating information transmission mechanism between nodes, edges, and hyperedges. Odd and even layers of the graph convolutional network are designed separately. In the multi-layered deep structure of the node-edge attribute graph convolutional network (NEA-GNN), odd layers are responsible for "dimensionality reduction and aggregation" of fault stresses at edges and hyperedges onto the nodes; even layers are responsible for dimensionality up-diffusion of the voltage support response of the nodes onto the edges and hyperedges.

[0060] On the odd-numbered layers, dimensionality reduction propagation from edge to node and from hyperedge to node is implemented.

[0061] Specifically, the features of the edges and hyperedges themselves are first updated by linear transformation, which can be expressed as: (Equation 10) (Equation 11) In the formula, Indicates the first Edges after layer linear transformation The intermediate feature vector; Indicates the first The learnable weight matrix of the layer used for linear transformation of edge features requires parameters to be optimized; Indicates edge In the The feature vector output by the layer (i.e., the even-numbered layer or the 0th initial embedding layer). Indicates the first Hyperedge after layer linear transformation The intermediate feature vector; Indicates the first The layer is a learnable weight matrix used for linear transformation of hyperedge features; Indicates the superedge In the The feature vector output by the layer (i.e., the even-numbered layers).

[0062] After that, the node The aggregation of messages from its directly connected edges (i.e., tributaries) can be represented as: (Equation 12) In the formula, Represents a node The received aggregated message vector from all directly connected edges; Aggregate functions representing edge features; Represents nodes There is a set of edges that are directly physically connected.

[0063] Meanwhile, nodes The aggregation of messages from its subordinate superedges can be represented as: (Equation 13) In the formula: Represents a node The received aggregate message vector from all faulty hyperedges; M represents the total number of hyperedges defined by the system; Represents the elements of the hyperedge incidence matrix; For nodes The degree; For super-edge The degree; This is a normalization coefficient used to prevent the characteristic value explosion of central nodes with excessively high degree during propagation; The corresponding hyperedge calculated in step S1.3 The weights are used to amplify the characteristic impact intensity of high-risk failure events.

[0064] Finally, merge all messages to update the node. In the The spatial hidden state of the layer is shown in Equation 14. The spatial hidden state is used to characterize the static spatial topology and features at the moment of the initial fault.

[0065] (Equation 14) In the formula: Indicates the updated node In the The feature vectors of the layer (i.e., the spatial hidden states); This represents a non-linear activation function (such as LeakyReLU). , , These represent the learnable weight matrices resulting from the concatenation and transformation of the corresponding feature dimensions, and are the parameters that need to be optimized. Represents a node The feature vector of the previous layer (i.e., the even-numbered layer or the 0th initial embedding layer); Represents a node The electrical neighbor nodes are in the feature set of the previous layer; This represents the fusion operation of features between itself and its neighboring nodes; This represents the concatenation operation between multiple feature vectors.

[0066] On the even-numbered layers, dimensionality-upward transmission from nodes to edges and from nodes to hyperedges is achieved.

[0067] Specifically, the node's own features are first updated using a linear transformation, which can be represented as: (Equation 15) In the formula: Represents the nodes after linear transformation in even-numbered layers. The intermediate feature vector; This represents the learnable weight matrix used for node feature transformation in even-numbered layers, which is a parameter that needs to be optimized. Represents a node The feature vectors of the previous layer (i.e., the odd-numbered layers); The set of features of electrical neighbor nodes in the previous layer; This indicates a feature fusion operation.

[0068] Subsequently, the edge back-converges messages from its two connected nodes, which can be represented as: (Equation 16) In the formula: Indicates edge The received aggregate message vector; Aggregate functions representing node features; Indicates connection to the edge The set of nodes at both ends.

[0069] Finally, update the edges separately. and super edge In the Hidden state of layer space, update edges The method can be expressed as: (Equation 17) In the formula: Indicates the first Edges after layer update ; feature vectors (i.e., spatial hidden states); It is a non-linear activation function; , , respectively, represent the learnable weight matrices used for dimensionality reduction fusion of edge features and convergence features, which are parameters that need to be optimized; These are the edge features of the previous layer; This indicates a splicing operation.

[0070] Update super edge The method can be expressed as: (Equation 18) In the formula, Indicates the first Faulty superedge after layer update eigenvectors; This represents the learnable weight matrix used for hyperedge state updates; For super-edge The feature vector in the previous layer; This represents the total number of busbars. H represents the total number of branches; H represents the elements of the hyperedge incidence matrix. The intermediate feature vector of the node after linear transformation of even-numbered layers; For the first The updated edge feature vector after layer; and These are the degree of the associated vertex and the degree of the hyperedge, respectively. This indicates a splicing operation.

[0071] It should be noted that in the above formulas... to The learnable weight matrices represent the model parameters that need to be optimized in the subsequent (step 3) liquid neural network model. In the initial stage of building the liquid neural network model, these learnable weight matrices are typically initialized randomly using a specific distribution. In the subsequent joint training stage (such as step 4), these learnable weight matrices will serve as variables to be optimized, based on the subsequently constructed joint training loss function. The algorithm uses gradient-based backpropagation to continuously iterate and optimize gradients until convergence, thereby automatically extracting the optimal high-order feature mapping relationship.

[0072] Step 2.4: Based on the node-edge-hyperedge alternating message passing mechanism, obtain the initial static spatial features of the final output of the graph convolutional network.

[0073] After multiple layers of alternating node-edge-hyperedge attribute graph convolutions, the graph convolutional network completes the deep spatial topology decoding of the initial fault propagation mechanism. The feature vector of each power grid component has fully absorbed the state change information of its physical neighborhood and higher-order fault association domain.

[0074] Extract the output matrix of the last layer (Kth layer) of the graph convolutional network. The output matrix of the graph convolutional network includes: the initial static spatial feature matrix of the nodes, the initial static spatial feature matrix of the edges, and the initial static spatial feature matrix of the faulty hyperedges.

[0075] Extracting node spatial features to obtain the initial static spatial feature matrix of the nodes can be represented as: (Equation 19) In the formula, This represents the initial static spatial feature matrix of all nodes in the power system that is finally extracted; This represents the graph convolutional network. The hidden state matrix of the nodes output by the last layer; This indicates the total number of graph convolutional layers configured in the network.

[0076] Extracting edge spatial features to obtain the initial static spatial feature matrix of the edge can be represented as: (Equation 20) In the formula, This represents the initial static spatial feature matrix of the edges in the final extracted power system; This represents the graph convolutional network. The edge hidden state matrix output by the layer.

[0077] Extracting the hyperedge space features to obtain the initial static space feature matrix of the faulty hyperedge can be represented as: (Equation 21) In the formula: This represents the initial static spatial feature matrix of all fault hyperedges in the power system that are finally extracted; This represents the graph convolutional network. The hyperedge hidden state matrix output by the layer.

[0078] The output matrices of the aforementioned graph convolutional networks will be integrated into a comprehensive spatial feature. This feature not only carries the physical state of the components at the time of failure but also encodes the propagation trend of cascaded faults in the spatial topology. Subsequently, these initial static spatial features will be fully fed into the subsequent (i.e., step S3) liquid neural network (LNN) model, serving as the initial parameters of the ordinary differential equation system. The key incentive input.

[0079] Step 3: Construct a liquid neural network model, taking the output matrix of the graph convolutional network (initial static spatial feature matrix of nodes, initial static spatial feature matrix of edges, and initial static spatial feature matrix of fault hyperedges) as input, and using liquid neurons to capture the temporal dynamic evolution process of cascaded faults.

[0080] The liquid neural network model is built on ordinary differential equations. Its core advantage lies in the fact that the time constant can establish a "liquid" dependency relationship with the hidden state of the power system, thereby giving the neurons extremely high efficiency and adaptability in extracting time features.

[0081] Step 3.1: Construct the input sequence of the liquid neural network based on the output matrix of the graph convolutional network.

[0082] In order to enable the liquid neural network model to fully perceive the degree of system state deterioration over time, the output matrix of the convolutional network in S2.4 is concatenated with dynamic physical indicators that reflect the real-time safety margin of the power grid at the feature level to construct a high-dimensional input sequence that can fully perceive the spatiotemporal state changes.

[0083] At any moment of the evolution of cascading fault propagation The comprehensive input feature vector of the liquid neuron (i.e., at the propagation time) The comprehensive input feature vector can be represented as: (Equation 22) In the formula, This indicates the liquid neural network model at the current propagation time. The comprehensive input feature vector; and These represent the initial static spatial feature matrix of the node and the initial static spatial feature matrix of the edge extracted in step S2.4, respectively. This represents the concatenation operation of vectors or matrices along the feature dimensions. Indicates at time The dynamic fault mask vector is used to mark the index position of the component that has been taken out of operation due to cascading trip in real time; Indicates time The protection action status characteristics reflect the current action command and time limit margin of the relay protection device; Indicates time The system active / reactive power flow residual reflects the degree of system power imbalance caused by fault tripping. Indicates time Branch overload margin distribution characteristics; This represents the one-hot encoded information of the cascading propagation stage, used to assist the model in identifying the propagation cycle in which the fault occurs.

[0084] It should be noted that the aforementioned fault mask vector, protection action status characteristics, power flow residuals, and branch overload margin distribution characteristics that dynamically change over time are determined by the wide-area measurement system, energy management system, and relay protection information subsystem in the context of power system online monitoring and early warning. t Real-time data acquisition and computation; in offline model training and simulation scenarios, the power system time-domain dynamic simulation program performs evolution calculations up to the time step. t The output is provided in real time. Furthermore, the formatted data, such as the unique heat encoding information, is obtained by preprocessing and transforming the corresponding basic physical state quantities.

[0085] Step 3.2: Use the output matrix of the graph convolutional network as the initial hidden state of the ordinary differential equation. Based on the propagation time... The comprehensive input feature vector is used to construct a liquid neuron based on ordinary differential equations.

[0086] The core of the liquid neuron lies in constructing a liquid neural network using a first-order linear dynamic system and controlling it through a nonlinear gating mechanism. To depict the continuous impact of cascading faults on a power system, an initial value problem is established using ordinary differential equations to continuously define the evolution rate of the hidden states. Specifically, in response to the initial excitation of the power system, the output matrix of the convolutional network in step S2.4 is used as the initial hidden state of the ordinary differential equation system. Its initialization formula is as follows: (Equation 23) In the formula, This represents the initial hidden state vector of the liquid neuron at the start of evolution (i.e., the instant the initial fault occurs at t=0); This represents the initialization layer perceptron used for dimension alignment and feature mapping; and These represent the initial static spatial feature matrix of the nodes and the initial static spatial feature matrix of the edges extracted in step S2, respectively.

[0087] Based on the comprehensive input feature vector at propagation time t, the ordinary differential equation for the evolution of the hidden state of the liquid neuron can be constructed as follows: (Equation 24) In the formula: This indicates that the liquid neuron is at time 10:00. The hidden state feature vector reflects the liquid neural network model's assessment of the current deep state of the cascaded fault; It represents the first derivative of the hidden state with respect to time, i.e., the instantaneous acceleration of fault evolution or state drift; This represents a preset learnable time constant baseline parameter used to control the natural decay of the state when there is no external input; Indicates that it has learnable parameters The nonlinear neural network head function is used to calculate the combined effect of the input signal and the historical state; I(t) represents the combined input feature vector constructed in step 3.1 at propagation time t; The bias vector represents the liquid neuron and serves as the steady-state baseline controlling the hidden state; The Hadamard product represents the element-wise multiplication of a matrix or vector.

[0088] The evolution equation of the hidden state of a liquid neuron (as shown in Equation 24) endows the neuron with dynamic "liquid" characteristics, in which the time constant term... This is the current hidden state of the liquid neuron. and external input The function. This allows the liquid neural network model to rapidly shorten the time constant to capture high-frequency shocks when cascading faults occur suddenly, while automatically extending it to retain long-term memory when the fault spreads slowly.

[0089] Step 3.3: Update the hidden state of the liquid neuron using gated approximation and residual state.

[0090] Solving the ordinary differential equations of the aforementioned continuous system directly using numerical solvers is extremely time-consuming. Therefore, it is necessary to derive an approximate closed-form solution. This is because the exponentially decaying term in the fully closed-form solution causes the evolution of the hidden states of neurons to converge rapidly to the bias parameter. Furthermore, by eliminating temporal dependencies, this invention replaces the exponential term with a smooth, nonlinear Sigmoid gate and replaces the static parameters with a learnable neural network prediction head, thereby achieving highly efficient discrete updates.

[0091] A closed-loop continuous-time model (approximate update equation) of the hidden state of the liquid neuron is constructed as follows: (Equation 25) In the formula, This represents the hidden state feature vector of the liquid neuron at the current time step t; This represents the hidden state feature vector of the liquid neuron at the previous time step; Indicates the time evolution step size; This represents the Sigmoid nonlinear gate function, which maps the evolution weights to... The interval smoothly simulates the continuous decay process of the state; and Indicates that each is composed of parameters and A controlled, trainable nonlinear neural network head replaces the fixed bias term in the original equation (Equation 24). The addition of initial state constants enhances the model's ability to express nonlinearity.

[0092] To alleviate the training burden of deep models over long periods of evolution, a residual learning mechanism is introduced for state fusion, which can be represented as: (Equation 26) In the formula, This represents the fused state feature matrix after introducing residual connections and undergoing normalization. The representation layer normalization operation function is used to stabilize the numerical distribution gradient within the hidden feature layer; This represents the hidden state feature vector (i.e., the dynamic evolution state) of the liquid neuron at the current time t. This represents the initial static spatial characteristics of the nodes in step S2.4. The addition operation ensures that the original topological background information of the power system is not lost while capturing the dynamic characteristics of time.

[0093] Step 3.4: The liquid neural network model outputs the final hidden state matrix of the dynamic evolution of the fault.

[0094] By performing time-series cyclic calculations, the hidden states of the liquid neural network model are extrapolated along the time axis of fault propagation. Finally, a high-order latent variable vector containing the evolutionary laws of the entire process is extracted for the final probability classification.

[0095] According to the evolutionary stages of cascading fault propagation Performing iterative updates can be represented as: (Equation 27) In the formula, The final hidden state matrix (i.e., the final hidden state) represents the dynamic evolution of the fault output by the liquid neural network. This represents the total number of time steps required for a cascaded fault to converge (either the cascade terminates or the power system reaches a new steady state). Indicates the last time step The calculated fusion state feature matrix; This indicates a feature extraction operation that extracts and outputs the final hidden state after undergoing a complete temporal evolution.

[0096] The final hidden state matrix The deep learning captures the complete nonlinear continuous evolution trajectory of a fault, from its initial triggering, causing a large-scale redistribution of power flow, inducing successive actions of protection devices, until the power system collapses or stabilizes. This final hidden state (i.e....) This will be directly used as input data for the parallel hybrid prediction head in the subsequent step (i.e., step S4).

[0097] Step 4: Construct a parallel hybrid prediction head model, and obtain the fault probabilities of buses and branches in the power system based on the final hidden state matrix output by the liquid neural network model.

[0098] After the deep dynamic deduction of the liquid neural network model in step S3, the liquid neural network model has output the final hidden state matrix (i.e., the final hidden state) containing the evolution law of the whole process. To transform these high-dimensional abstract features into physical probabilities that power system dispatchers can intuitively understand, this step constructs a parallel hybrid prediction head model as the output layer of the liquid neural network model. This parallel hybrid prediction head simultaneously determines the failure risk of buses and branches through two structurally independent but logically related branch outputs, and introduces a multi-constraint joint loss function to ensure that the prediction results conform to the basic physical logic of the power system.

[0099] Step 4.1: Construct the bus fault prediction head.

[0100] Nonlinear logistic regression and multilayer fully connected network techniques are employed. By establishing a mapping from the hidden layer feature space to the Bernoulli probability space, the survival state of the bus components at the cascade termination time is accurately quantified.

[0101] The hidden layer feature vector corresponding to the bus is extracted from the final hidden state matrix output by the liquid neural network and input into the bus classifier.

[0102] The formula for calculating the busbar failure probability is as follows: (Equation 28) In the formula: Indicates the predicted first The failure probability value of each bus (i.e. node) after the cascading fault terminates is in the range of [0,1]. This represents the logistic regression activation function, and the formula is: ; and These represent the learnable weight matrices of the first and second fully connected layers in the bus prediction header, respectively. and These represent the learnable bias vectors of the corresponding feature mapping layers; Represents the final hidden state matrix In the middle, the slice corresponding to the specific bus index dimension is extracted. i The final dynamic evolution of the hidden state row vector of each bus line.

[0103] Step 4.2: Construct the branch fault prediction head.

[0104] Considering that branch disconnection is usually caused by the power angle difference or voltage fluctuation of the two busbars, this step constructs a composite branch discriminator by integrating the characteristics of the branch itself and the characteristics of its associated terminal nodes to obtain the failure probability of the branch.

[0105] (Equation 29) (Formula 30) In the formula: Indicates the predicted first The failure probability value of a branch after the cascaded fault is terminated. This indicates the first [unit / section] that incorporates information from the terminal bus. The combined feature vector of each branch; This represents a multilayer perceptron operation used for deep feature fusion; Represents the final hidden state matrix The first segment extracted based on the branch index slice k The hidden state row vector of the final dynamic evolution of each branch; and These represent the results from the final hidden state matrix. Branches extracted based on the corresponding node index slice k The final dynamic evolution hidden state row vectors of the busbars at the beginning and end; This represents the horizontal concatenation operation of feature vectors; and represents the learnable weight matrix and bias vector of the branch prediction classification layer, respectively.

[0106] Step 4.3: By physically verifying the failure probability of the busbar and branches, a set of high-risk components is established, and the components are prioritized based on their importance in the power system.

[0107] We introduce threshold discrimination and multi-index comprehensive evaluation model from decision theory to construct a joint discrimination and risk ranking mechanism.

[0108] Bus failure probability and branch failure probability Each component is logically compared with a preset safety threshold to obtain a set of high-risk components, which can be represented as: (Equation 31) In the formula: This represents a set of high-risk components. and These represent the preset failure thresholds for the busbar and branch, respectively.

[0109] For the set of high-risk components Each component (i.e., the selected high-risk bus or high-risk branch) is ranked by comprehensive risk score.

[0110] For the set of high-risk components The high-risk busbar components are assessed, and a comprehensive risk score is given. It can be represented as: (Equation 32) In the formula: This represents the overall risk score of the i-th busbar. Indicates busbar Voltage safety margin. This indicates the importance level weight (load importance) of the loads connected to this bus. This indicates the centrality index (topological importance) of the bus in the power system topology. For the corresponding bus evaluation index, the weighting coefficient is , and .

[0111] It should be noted that in Equation 32, the voltage safety margin of the bus is... The load importance level weights are calculated from real-time state estimation cross-sectional data of the energy management system. Static values ​​are assigned based on the pre-configured load protection levels in the power system basic management database; bus centerness index (e.g., betweenness centrality or degree centrality) is obtained offline using a graph theory network analysis algorithm based on the electrical connection matrix A constructed in step S1.1; weighting coefficients. The weighting is determined by power grid dispatchers using subjective weighting algorithms such as the analytic hierarchy process (AHP) or objective weighting algorithms such as the entropy weighting method, based on the emphasis of the actual operating scenario.

[0112] Similarly, for the entire set of high-risk power grid components... Comprehensive risk scoring is performed on high-risk branch components. The sorting formula is as follows: (Equation 33) In the formula, Indicates the first The overall risk score of each branch road. This represents the branch failure probability value predicted in step 4.2. It represents the reciprocal of the overload margin of this branch (the larger the value, the higher the risk of thermal stability). This indicates the centrality index of the branch in the power system topology. These are the weighting coefficients for the corresponding branch road evaluation indicators.

[0113] Step 4.4: Output a complete fault warning report; and construct a joint loss function by integrating spatial distribution and temporal constraints to optimize the fault warning report.

[0114] Output a fault warning report.

[0115] Specifically, the probability of bus failure Mapping to the corresponding nodes generates a bus fault probability map; branch failure probabilities are then mapped. The fault probability distribution of the branch is generated by mapping to the corresponding edge; the power system directly outputs the set of high-risk components obtained from the above discrimination according to step 4.2. Based on high-risk components Density clustering of the spatial distribution of components in the actual power system is performed to generate a geographic location map of weak areas in the power grid; and combined with the liquid neural network in step 3.4 at different time steps t The dynamically evolving hidden state matrix output is used to track high-probability topological connectivity branches of fault propagation in a time series, generating a potential cascading propagation risk path evolution graph.

[0116] Constructing a joint training loss function This is to optimize fault warning reports. It can be represented as: (Equation 34) In the formula: Represents the total loss function. and These represent the standard cross-entropy loss between the predicted results for the bus and the branch and the actual labels, respectively. This represents the physical constraint loss, and Kirchhoff's current law is used to check whether the prediction results violate power flow balance. This represents the topology consistency constraint loss, used to ensure that components within isolated islands have a consistent failure trend. This represents the temporal smoothing constraint loss, which utilizes the differential properties of the liquid neural network model to constrain the rationality of state transitions between adjacent time steps. The penalty factor (hyperparameter) represents the penalty factor for each physical and logical constraint.

[0117] Among them, the total loss function During the model training phase, gradient descent is used to perform global end-to-end joint optimization of all the learnable parameters mentioned above. Specifically, the optimized parameters include: the graph convolutional network weight matrix used for feature alignment and alternating message passing in step S2 (e.g., ...). to , ); Time constant reference of the liquid neuron in step S3.2 and nonlinear gated network head parameters ; and step S4, the classification mapping weights and bias parameters of the hybrid prediction head in this step (e.g. , ).

[0118] Through parallel processing and joint optimization in this step, the present invention can not only produce highly accurate discrete failure probabilities, but also output multi-dimensional comprehensive early warning analysis results that conform to the physical evolution logic of the power system (i.e., the aforementioned high-risk component set, the geographical location of weak areas in the power grid, and the evolution diagram of potential cascading propagation risk paths).

[0119] In summary, the power system cascading fault prediction method described in this invention overcomes the limitation of traditional graph models, which can only express univariate relationships, by constructing a power system hypergraph model. It accurately depicts the high-order spatial impact range of cascading faults with "one cause, multiple effects." Through alternating message passing and feature updates of nodes, edges, and hyperedges, it deeply explores the propagation patterns of faults in complex spaces. By using a liquid neural network model for temporal evolution deduction and outputting the fault probabilities of all components through a parallel prediction head, it ultimately achieves efficient and accurate end-to-end prediction and risk assessment of power system cascading faults.

[0120] Although the present invention has been described in detail through the preferred embodiments above, it should be understood that the above description should not be considered as a limitation of the present invention. Various modifications and substitutions to the present invention will be apparent to those skilled in the art after reading the above description. Therefore, the scope of protection of the present invention should be defined by the appended claims.

Claims

1. A method for predicting cascading failures in a power system, the method comprising: Includes the following steps: S1. Obtain the topology parameters of the power system and construct a hypergraph model of the power system; the hyperedges in the hypergraph model represent initial fault events and higher-order physical constraints. S2. Construct a graph convolutional network (GCNN) of node and edge attributes, mapping the physical characteristics of the bus to the node attributes of the GCNN, and mapping the physical characteristics of the branch to its edge attributes; the odd-numbered layers in the GCNN reduce the dimensionality of the fault stresses of the edges and hyperedges and converge them onto the nodes; the even-numbered layers in the GCNN increase the dimensionality of the voltage support response of the nodes and diffuse it onto the edges and hyperedges; obtain the initial static spatial feature matrices of the nodes, edges, and hyperedges by inputting the hypergraph model into the GCNN. S3. Construct a liquid neural network model, using the output of the GCNN as the input of the liquid neural network model. S4. Construct a parallel hybrid prediction head model as the output layer of the liquid neural network model to obtain the fault probabilities of the bus and branches in the power system.

2. The power system cascading failure prediction method of claim 1, wherein, The method for constructing the graph convolutional network of node and edge attributes in step S2 includes: At odd-numbered layers, the features of the edges and hyperedges themselves are updated by a linear transformation, as follows: In the formula, Indicates the first Edges after layer linear transformation The intermediate feature vector; Indicates the first The layer is a learnable weight matrix used for linear transformation of edge features; Indicates the edge at the 1st Feature vectors output by the layer; Indicates the first Hyperedge after layer linear transformation The intermediate feature vector; Indicates the first The layer is a learnable weight matrix used for the linear transformation of hyperedge features; Indicates the superedge In the Feature vectors output by the layer; Then, the node aggregates messages from its directly connected edge, represented as: In the formula, Represents a node The received aggregated message vector from all directly connected edges; Aggregation functions representing edge features; This represents the set of edges that have a direct physical connection to the node. At the same time, nodes aggregate messages from their subordinate superedges, represented as: In the formula: This represents the aggregated message vector received by the node from all faulty hyperedges; This represents the total number of hyperedges defined by the system. Represents the elements of the hyperedge incidence matrix; For nodes The degree; For super-edge The degree; These are the normalization coefficients; For super-edge The weights; Finally, merge all messages to update the node. In the The spatial hidden state of a layer is represented as: In the formula, Indicates the updated node In the The feature vector of the layer; Represents a non-linear activation function; , , These represent the learnable weight matrices resulting from the concatenation and transformation of the corresponding feature dimensions, and are the parameters that need to be optimized. Represents a node The feature vector in the previous layer; Represents a node The electrical neighbor nodes are in the feature set of the upper layer. Represented as the total number of nodes; This represents the fusion operation of features between itself and its neighboring nodes; This represents the concatenation operation between multiple feature vectors.

3. The power system cascading fault prediction method according to claim 2, characterized in that, The method for constructing the graph convolutional network of node and edge attributes in step S2 also includes: At even-numbered layers, the features of the nodes themselves are updated by a linear transformation, as follows: In the formula, Represents the nodes after linear transformation in even-numbered layers. The intermediate feature vector; This represents the learnable weight matrix used for node feature transformation in even-numbered layers; Then, the edge performs reverse aggregation of messages from its two connected nodes, represented as: In the formula, Indicates edge The received aggregate message vector; Aggregate functions representing node features; Indicates connection to the edge The set of nodes at both ends; Finally, update the edges separately. and super edge In the The spatial hidden state of a layer is represented as: In the formula, Indicates the first Edges after layer update eigenvectors; , These represent the learnable weight matrices used for dimensionality reduction fusion of edge features and convergence features, respectively. These are the edge features of the previous layer; Update super edge The method is expressed as: In the formula, Indicates the first Faulty superedge after layer update eigenvectors; This represents the learnable weight matrix used for hyperedge state updates; For super-edge The feature vector in the previous layer; This represents the total number of busbars. The total number of branch roads; These are elements of the hyperedge incidence matrix; The intermediate feature vector of the node after linear transformation of an even number of layers; For the first The updated edge feature vector after layer; and These are the degree of the associated vertex and the degree of the hyperedge, respectively. This indicates a splicing operation.

4. The power system cascading fault prediction method according to claim 3, characterized in that, In step S2, the method for obtaining the initial static spatial feature matrix includes: Step S2.1: Extract physical quantities that are strongly correlated with the steady state and fault triggering of the busbar itself, and construct a node attribute matrix. Extract physical quantities that are strongly correlated with the electrical transmission capacity of transmission lines or transformer branches, and construct an edge attribute matrix. Extract state variables that are strongly correlated with the comprehensive properties of hyperedges, and construct the hyperedge attribute matrix. ; Step S2.2 involves constructing a learnable mapping matrix to project the node attribute matrix, edge attribute matrix, and hyperedge attribute matrix onto a hidden feature space of the same dimension, forming aligned initial embeddings, and obtaining the node embedding matrices respectively. Edge embedding matrix and hyperedge embedding matrix , represented as: In the formula, , , These represent the learnable weight mapping matrices used for feature projection of nodes, edges, and hyperedges, respectively. , , These represent the learnable bias vectors of the projection layer corresponding to the node, edge, and hyperedge, respectively. Unify the column dimensions of the node embedding matrix, edge embedding matrix, and hyperedge embedding matrix; Step S2.3: Input the node embedding matrix, edge embedding matrix, and hyperedge embedding matrix of the initial layer into the graph convolutional network; Step S2.4: Obtain the final output of the graph convolutional network; Extract the output matrix of the last layer K of the graph convolutional network. The output matrix of the graph convolutional network includes: the initial static spatial feature matrix of the nodes, the initial static spatial feature matrix of the edges, and the initial static spatial feature matrix of the hyperedges. Extract the spatial features of the nodes to obtain the initial static spatial feature matrix of the nodes. , represented as: In the formula, This represents the hidden state matrix of the nodes output by the last layer of the graph convolutional network; This represents the total number of graph convolutional layers in a graph convolutional network. Extract edge spatial features to obtain the initial static spatial feature matrix of the edge. , represented as: In the formula, This represents the graph convolutional network. The edge hidden state matrix output by the layer; Extract hyperedge space features to obtain the initial static space feature matrix of the hyperedge. , represented as: In the formula, This represents the graph convolutional network. The hyperedge hidden state matrix output by the layer.

5. The power system cascading fault prediction method according to claim 1, characterized in that, In step S3, the method of using the output of the graph convolutional network as the input of the liquid neural network model includes: Step S3.1: Use the output matrix of the graph convolutional network as the initial hidden state of the ordinary differential equation; construct the input sequence of the liquid neural network based on the output matrix of the graph convolutional network; The output of the graph convolutional network is used as the initial hidden state vector of the liquid neuron at the start of the evolution. , represented as: In the formula, This represents the initialization layer perceptron used for dimension alignment and feature mapping; and These represent the initial static spatial feature matrices of the nodes and the initial static spatial feature matrices of the edges extracted in the graph convolutional network, respectively. At any evolution time t of the cascading fault propagation, the comprehensive input feature vector of the liquid neuron is represented as: In the formula, This indicates the liquid neural network model at the current propagation time. The comprehensive input feature vector; This represents the concatenation operation of vectors or matrices along the feature dimensions. Indicates at time The dynamic fault mask vector; Indicates time The protection action status characteristics reflect the current action command and time limit margin of the relay protection device; Indicates time The system active / reactive power flow residual reflects the degree of system power imbalance caused by fault tripping. Indicates time Branch overload margin distribution characteristics; This represents the one-hot encoded information in the cascading propagation stage.

6. The power system cascading fault prediction method according to claim 5, characterized in that, Step S3, which utilizes liquid neurons to capture the time-dynamic evolution of cascaded faults, includes: Step S3.2: Based on the comprehensive input feature vector at propagation time t, construct the evolution equation of the hidden state of the liquid neuron; In the formula, This indicates that the liquid neuron is at time 10:

00. The hidden state feature vector reflects the liquid neural network model's assessment of the current deep state of the cascaded fault; It represents the first derivative of the hidden state with respect to time, i.e., the instantaneous acceleration of fault evolution or state drift; This represents the preset learnable time constant baseline parameter; Indicates that it has learnable parameters The head function of a nonlinear neural network; Indicates the moment of transmission The comprehensive input feature vector; The bias vector represents the liquid neuron and serves as the steady-state baseline controlling the hidden state; The Hadamard product represents the element-wise multiplication of a matrix or vector.

7. The power system cascading fault prediction method according to claim 6, characterized in that, Step S3 also includes: Step S3.3: Update the hidden state of the liquid neuron using gated approximation and residual state; A closed-loop continuous-time model of the hidden states of the liquid neuron is constructed, represented as follows: In the formula, This represents the hidden state feature vector of the liquid neuron at the previous time step; Indicates the time evolution step size; This represents the Sigmoid nonlinear gate function; and Indicates that each is composed of parameters and A controllable, trainable nonlinear neural network head; Introducing a residual learning mechanism for state fusion can be represented as: In the formula, This represents the fused state feature matrix after introducing residual connections and undergoing normalization. Indicates the layer normalization operation function; Step 3.4: The liquid neural network model outputs the final hidden state matrix of the fault dynamic evolution; According to the evolutionary stages of cascading fault propagation Performing iterative updates in a loop is represented as: In the formula, The final hidden state matrix representing the fault dynamic evolution output by the liquid neural network; This represents the total number of time steps required for a cascading fault to converge. Indicates the last time step The calculated fusion state feature matrix; This indicates a feature extraction operation that extracts and outputs the final hidden state after undergoing a complete temporal evolution.

8. The power system cascading fault prediction method according to claim 7, characterized in that, Step S4 involves constructing a parallel hybrid prediction head model as the output layer of the liquid neural network model, including: Step S4.1: Construct the bus fault prediction head; In the formula, This represents the predicted failure probability value of the i-th bus after the cascaded fault terminates, and its value range is [0,1]. This represents the logistic regression activation function, and the formula is: ; and These represent the learnable weight matrices of the first and second fully connected layers in the bus prediction header, respectively. and These represent the learnable bias vectors of the corresponding feature mapping layers; Represents the final hidden state matrix In the middle, the slice corresponding to the specific bus index dimension is extracted. i The final dynamic evolution hidden state row vector of each busbar; Step S4.2: Construct the branch fault prediction head; In the formula: Indicates the predicted first The failure probability value of a branch after the cascaded fault terminates; This indicates the first [unit / section] that incorporates information from the terminal bus. The combined feature vector of each branch; This represents a multilayer perceptron operation used for deep feature fusion; Represents the final hidden state matrix The first segment extracted based on the branch index slice k The hidden state row vector of the final dynamic evolution of each branch; and These represent the hidden state matrices from the final dynamic evolution. Branches extracted based on the corresponding node index slice k The final hidden state row vectors of the busbars at the beginning and end; This represents the horizontal concatenation operation of feature vectors; and represents the learnable weight matrix and bias vector of the branch prediction classification layer, respectively.

9. The power system cascading fault prediction method according to claim 8, characterized in that, Step S4 also includes: Step S4.3: Physically verify the failure probability of the bus and branches, establish a set of high-risk components, and prioritize the components based on their importance in the power system. Bus failure probability and branch failure probability Each component is logically compared with a preset safety threshold to obtain a set of high-risk components, represented as follows: In the formula: Indicates a set of high-risk components; and These represent the preset failure thresholds for the busbar and branch, respectively. For the busbar, the comprehensive risk score Represented as: In the formula: Indicates busbar Voltage safety margin; Indicates the busbar Importance level weight of the load under load; This indicates the centrality index of the bus in the power system topology; For the corresponding bus evaluation index, the weighting coefficient is , and ; For branch roads, comprehensive risk score Represented as: In the formula, This represents the probability value of branch failure. This represents the reciprocal of the overload margin of that branch. This indicates the centrality index of the branch in the power system topology; These are the weighting coefficients for the corresponding branch road evaluation indicators; Step S4.4: Output a complete fault warning report; and construct a joint loss function by integrating spatial distribution and temporal constraints to optimize the fault warning report; The fault warning report includes: probability of busbar failure. Mapped to the corresponding node to generate a bus fault probability map; via branch failure probability Mapped to the branch failure probability distribution generated by the corresponding edge; directly output the set of high-risk components. Based on high-risk components A geospatial map of weak areas in the power grid is generated by density clustering of the spatial distribution of components in the actual power system; and a liquid neural network is used to generate a geospatial map of weak areas in the power grid at different time steps. t The dynamic evolution hidden state matrix output is used to track high-probability topological connected branches of fault propagation in a time series, generating a potential cascading propagation risk path evolution graph. The joint training loss function is constructed as follows: In the formula, Represents the total loss function. and These represent the standard cross-entropy loss between the predicted results for the bus and the actual labels, respectively. Indicates physical constraint loss; This represents the loss due to topology consistency constraints; This represents the time-series smoothing constraint loss; This represents the penalty factor for each physical and logical constraint.

10. The power system cascading fault prediction method according to claim 1, characterized in that, The method for constructing the hypergraph model of the power system in step S1 includes: Step S1.1, the topology parameters include the topology of the power system, which is represented by bus b, branch... The original graphical model consisting of electrical connections. ; It is the set of busbars in a power system, represented as , Indicates the busbar. The total number of busbars; is the set of branches in the power system, represented as... , As a side road, The total number of branches; the electrical connection relationships in the original graphical model are represented by an electrical connection relationship matrix indicating whether there are branch connections between two buses; Step S1.2: Define the bus in the power system as the bus vertex and the branch as the branch vertex, and construct a heterogeneous component vertex set containing the bus vertex and the branch vertex; wherein, the heterogeneous component vertex set is the union of the bus set and the branch set; Step S1.3: Define the initial fault event and higher-order physical constraints as hyperedges connecting the vertices of the bus or branches, and construct a set of hyperedges; construct the weights of arbitrary hyperedges based on the dimensions of fault electrical impact, topology association coverage, steady-state power flow congestion, and secondary system reliability. ; Step S1.4: Construct the hyperedge association matrix based on the membership relationship between the set of heterogeneous component vertices and each hyperedge. H Each element in the hyperedge incidence matrix Represented as: 。

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