Typhoon disaster-oriented graph neural network-induced active power distribution network dynamic reconstruction system

Abstract

The application discloses a kind of typhoon disaster under graph neural network induced active power distribution network dynamic reconstruction system, including graph neural network module, pre-processing filtering module, post-processing selection module, optimization solving module and scene generation module.System is dynamically simulated topological reconstruction by switch gate message passing mechanism, adopts topology-independent local predictor to realize the expansion of cross-network configuration, in combination with pre-filtering non-critical switch and post-processing confidence selection, under the premise of guaranteeing physical feasibility, GNN prediction is combined with MIP optimization.In the actual measurement of IEEE 33 node system, 1.64 times of calculation speed is realized, only 0.67% average optimality gap is generated, effectively solve the problem of low computational efficiency of traditional method, significantly improve the resilience level of power distribution network in response to extreme weather.

Description

Technical Field

[0001] This invention belongs to the field of active distribution network dynamic reconfiguration technology, specifically an active distribution network dynamic reconfiguration system induced by a neural network under typhoon disaster. Background Technology

[0002] In recent years, extreme natural disasters such as typhoons have caused widespread and lasting damage to critical power system infrastructure, seriously threatening the reliable and economical operation of active distribution networks (ADNs). To enhance system resilience, ADNs need to possess dynamic reconfiguration capabilities, rapidly restoring loads through methods such as forming islanded microgrids. The dynamic network reconfiguration (NR) problem is typically modeled as a mixed-integer programming (MIP) problem, but its inherent NP-hard nature results in a heavy computational burden, making it difficult to meet the needs of real-time emergency response.

[0003] Existing research attempts to accelerate power system optimization using graph neural networks (GNNs), for example, in optimal power flow (OPF) and N-1 security constraint optimization. However, these methods typically treat network topology as a fixed parameter, failing to handle the inherent discrete switching decisions and dynamic topology changes in N-1. Although some studies have explored the theoretical feasibility of GNNs in solving combinatorial optimization problems, they generally lack integration with the physical operating constraints of the distribution network (such as radial structure and voltage limits), making it difficult to guarantee the physical feasibility and optimality of reconfiguration schemes.

[0004] Therefore, existing technologies face a significant contradiction in addressing the dynamic reconstruction problem of ADN under typhoon disasters: it is difficult to balance computational efficiency with solution quality. There is an urgent need for a new method that can both ensure physical feasibility and achieve rapid solution. Summary of the Invention

[0005] In view of this, the purpose of this invention is to solve the problems of low computational efficiency and difficulty in real-time response of traditional dynamic network reconfiguration methods under typhoon disasters. By proposing an active distribution network dynamic reconfiguration system induced by graph neural network under typhoon disasters, the invention achieves rapid and near-optimal reconfiguration of active distribution networks, significantly improving the resilience of the power grid in the face of extreme weather.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A dynamic reconfiguration system for active distribution networks induced by a neural network in response to typhoon disasters includes:

[0008] The graph neural network module is used to predict network reconfiguration strategies based on the topology and operating status of the active distribution network. The graph neural network module uses switches as a gating message passing mechanism, models switchable lines as learnable gates to dynamically control the information flow between nodes, and simulates the control of power flow by physical switches on the power grid.

[0009] The preprocessing filtering module is used to identify and filter non-critical switches based on the consistency index of switch states in the training dataset, thereby reducing model complexity and prediction error.

[0010] The post-processing selection module is used to perform confidence analysis based on the switch state probabilities output by the graph neural network, fix the high-confidence decisions and retain the uncertain variables as subsequent mixed integer programming optimization variables;

[0011] An optimization solution module is used to integrate the prediction results of the graph neural network into the mixed-integer programming solver to solve dynamic network reconstruction and optimal power flow problems. The optimization solution module uses the prediction of the graph neural network as a warm-start strategy to accelerate the solution process and ensure the feasibility and optimality of the solution.

[0012] The scenario generation module is used to simulate uncertain fault scenarios under typhoon disasters. It calculates the line fault probability based on the wind field model and component strength and wind load model, and generates time-varying fault scenarios to drive the dynamic reconfiguration process.

[0013] The system enables rapid dynamic reconfiguration of the active distribution network under typhoon disaster scenarios to minimize power outage costs and emergency power generation costs, thereby enhancing grid resilience. The objective function is expressed as:

[0014]

[0015]

[0016]

[0017] in: The objective function for resilient operation is determined by the cost of power outage losses. Distributed power generation costs and auxiliary power supply services constitute. It is the loss-of-load value coefficient, used to quantify the trade-off between cost and resilience, and to guide resource allocation to effectively shorten power outage duration and reduce loss of load. It is the load recovery ratio; For load power; This refers to the output power of the distributed power source. To fix the power generation cost parameters of the auxiliary generator; This is to assist in determining the primary parameters of generator power generation costs; For the set of distribution network nodes; This is a collection of all time periods.

[0018] Furthermore, the switch, as a gating message transmission mechanism, includes:

[0019] In the multi-layer message passing process of a graph neural network, for each switchable line, a gate function is used to control the information flow between nodes. The gate function is calculated based on the switch embedding vector and is defined as follows:

[0020]

[0021] in: For gated functions; Represents the sigmoid function; A set of switchable branches with switches; For a fixed set of branches; For the first The layer's switch embedding vector is updated using the following formula:

[0022]

[0023] in: and They are nodes and The embedding vector; and The weight matrix is ​​a learnable weight matrix;

[0024] When the switch is open, the threshold value approaches 0 to attenuate the information flow and simulate electrical isolation; when the switch is closed, the threshold value approaches 1 to allow complete information exchange.

[0025] Furthermore, the graph neural network module also includes a topology-independent local predictor, which includes:

[0026] A line predictor, used to predict power flow and node voltages of a stationary line based on local node embedding and global graph embedding, is represented as:

[0027]

[0028] in: branch road The predicted active power flow; and They are slave nodes and nodes Predicted local values ​​of node voltage; and They are nodes and nodes Embedded, Embedded in a global graph;

[0029] A switching predictor, used to predict the power flow, node voltage, and switching state probability of a switchable line based on local node embedding, switching embedding, and global graph embedding, is expressed as:

[0030]

[0031] in: branch road The probability of the on / off state; To indicate the branch road Switch-related feature vectors;

[0032] The aggregation of node voltages is calculated using the following formula:

[0033]

[0034] in: Let be the predicted voltage magnitude at node i; For nodes A set of connected branches; For node degree operator;

[0035] And scale to a feasible range to ensure that voltage constraints are automatically met:

[0036]

[0037] in: and These represent the lower and upper limits of the permissible node voltage amplitude, respectively.

[0038] Furthermore, the preprocessing filtering module identifies non-critical switches by analyzing the consistency index of switch states in the training dataset. The consistency index is defined as:

[0039]

[0040] when At that time, switches are classified as non-critical switches and excluded from the prediction task. The simplified set of switches is defined as follows:

[0041]

[0042] in: For training samples The optimal switching state; M is the number of training samples.

[0043] Furthermore, the post-processing selection module specifically includes:

[0044] Confidence analysis based on the probability output of the switch predictor Set confidence threshold and Switches are classified as follows:

[0045]

[0046]

[0047] For high-confidence switches, their state is fixed as follows:

[0048]

[0049] For indeterminate switches, they are retained as binary variables in mixed-integer programming;

[0050] Generate simplified mixed-integer programming problems:

[0051]

[0052]

[0053]

[0054] in: For a set of high-confidence switches; For a set of low-confidence switches; The "key switch set" to be retained; Branches predicted by GNN The probability of being in the "closed" state; The determined switch state; The low confidence threshold; The high confidence threshold; To simplify the set of decision variables.

[0055] Furthermore, the constraints of the simplified mixed-integer programming problem include:

[0056] Upper and lower limits constraints for the squares of voltage and current:

[0057]

[0058] Voltage relationship equation:

[0059]

[0060] Power balance equation:

[0061]

[0062]

[0063] Node power injection equations:

[0064]

[0065]

[0066] in: For the set of distribution network nodes; For branch set; and These represent nodes in the distribution network. The upstream node set and the child node set, where ; , and They are respectively Time Node Lower and upper limits of the square of voltage amplitude for Voltage amplitude at time node; , and They are respectively Time Node Lower and upper limits of the square of the current amplitude for Time Node Current amplitude; and They are respectively the branches through which the flow passes Active power and reactive power; and They are branch roads Resistance and reactance; and For nodes Injected active power and reactive power; for Time Node Active power of diesel generator; for Time Node Power purchased; for Time Node Photovoltaic power output; for Time Node Fan output; for Time Node Energy storage discharge power; for Time Node Energy storage charging power; for Time Node Active power of load; for Time Node Reactive power of diesel generator; for Time Node Purchased reactive power; for Time Node Reactive power of load.

[0067] Furthermore, the constraints of the simplified mixed-integer programming problem include radial constraints for network reconstruction:

[0068]

[0069]

[0070]

[0071]

[0072] in: It is a binary branch state. Indicates a branch in operation. Indicates a branch that is disconnected / isolated; Represents the binary virtual flow of electricity. This indicates that the actual power flow direction is from the bus. to ; For a collection of alternative islanded power buses that can be powered; This is a collection of distribution network branches.

[0073] Furthermore, the constraints of the simplified mixed-integer programming problem include switch-state related constraints:

[0074]

[0075]

[0076]

[0077]

[0078]

[0079] in: It is a very large positive number; This represents the residual of the voltage constraint.

[0080] The constraints of the simplified mixed-integer programming problem include second-order cone relaxation constraints:

[0081]

[0082] in: ,for Time Node voltage amplitude square; ,for Time Node Current amplitude square; and Branch roads The active and reactive power flow.

[0083] Furthermore, the graph neural network module is trained end-to-end using an unsupervised loss function, which combines the objective function and the constraint violation penalty term, and is defined as follows:

[0084]

[0085] in: This represents all learnable parameters; This represents the complete set of variables obtained from GNN prediction and recovery; Encoding inequality constraints; The `max` operator is used to assign penalty weights; it ensures that only constraint violations are included in the penalty calculation.

[0086] Training was performed using the AdamW optimizer and the OneCycleLR learning rate scheduler.

[0087]

[0088] in: Indicates the number of iterations Learning rate at that time; and These represent the minimum and maximum values ​​of the learning rate, respectively. Indicates the maximum number of iterations;

[0089] Gradient clipping with a threshold of 0.8 was used to stabilize training.

[0090]

[0091] If the verification loss continues If there is no improvement in the round, the early shutdown mechanism will be triggered.

[0092] Furthermore, the scene generation module calculates the line fault probability based on the wind field model and the component strength and wind load model, wherein the wind field model adopts the Batts model:

[0093]

[0094]

[0095]

[0096]

[0097] in: The radius of maximum wind speed; For pressure drop; The maximum gradient wind speed; K=6.72 is an empirical coefficient; This is the Earth's rotational angular velocity; Geographic latitude; and These are the average maximum wind speed and the wind field movement speed, respectively. Tangential wind speed; This is the radius distance from the center of the wind field; The intensity attenuation coefficient;

[0098] Component strength and wind load model calculation of wind load and failure probability:

[0099]

[0100]

[0101]

[0102]

[0103] in: Indicates the total wind load; , and These represent the outer diameter, size factor, and density of the power transmission line, respectively. and This refers to the wind pressure coefficient and the angle between the conductor and the wind direction; It is gravitational acceleration; For conductor height coefficient; The tangential wind speed is located at a radius of φ from the center of the wind field. and These represent the tension at the highest and lowest points of the transmission line, respectively. This refers to the cross-sectional area of ​​the steel-cored aluminum stranded wire; The equivalent force arm / distance between the highest and lowest points;

[0104] This represents the tower base bending moment caused by the conductor wind load; This represents the bending moment at the base of the tower caused by the wind load on the tower body. This represents the total bending moment at the base of the tower; Indicates the first Horizontal wind load on the suspended conductor; The average spacing between the conductors; It is the first The vertical distance between the conductor and the base of the tower; Indicates the number of conductors on the tower; , , and Representative tower dimensions; This represents the lever arm distance from the point of application of the resultant wind pressure force on the tower to the base of the tower.

[0105] The probability of a line fault is calculated using the following formula:

[0106]

[0107] in, and The fault probabilities for the line and the tower are respectively obtained by integrating the normal distribution function; Indicates a branch The number of wires on it; Indicates a branch The number of poles and towers.

[0108] The beneficial effects of this invention are as follows:

[0109] This invention addresses the active distribution network dynamic reconfiguration system induced by graph neural networks during typhoon disasters. By integrating graph neural networks with mathematical programming methods, it achieves groundbreaking technical results in active distribution network typhoon disaster response.

[0110] (1) Significantly improved computational efficiency: Traditional mixed-integer programming methods for solving dynamic network reconstruction problems are computationally time-consuming and cannot meet the real-time requirements of typhoon emergency response. This invention provides high-quality warm-start solutions through GNN prediction, which significantly reduces the dimensionality of key decision variables, thereby improving computational speed and effectively solving the computational bottleneck problem of traditional methods;

[0111] (2) Excellent solution quality: While improving computational efficiency, the present invention maintains excellent solution quality; through the confidence screening mechanism, only high reliability decisions are fixed and key uncertain variables are retained for optimization, which can reduce the average optimality gap and maintain the near-optimality of the scenario solution;

[0112] (3) Physical feasibility assurance: The innovative switching gating mechanism embeds physical topology changes into the neural network structure. The local predictor automatically satisfies the voltage constraint through constructive design. Combined with the accurate mathematical model of second-order cone relaxation, the physical feasibility and engineering practicality of the solution are fundamentally guaranteed.

[0113] (4) Enhanced system resilience: By integrating typhoon scenario generation and dynamic reconstruction decision-making, a full-chain solution from disaster prediction to prevention and control has been realized, effectively reducing power outage losses and power generation costs, and significantly improving the resilience of the distribution network in the face of extreme weather. Attached Figure Description

[0114] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:

[0115] Figure 1 This refers to the typhoon disturbance range in the active distribution network.

[0116] Figure 2 Flowchart of the GraNR model training algorithm;

[0117] Figure 3 System configuration for case studies;

[0118] Figure 4 MSE loss for GNN training and validation;

[0119] Figure 5 The prediction accuracy for GNN training and validation;

[0120] Figure 6 This is the cumulative speedup result;

[0121] Figure 7 This represents the loss of the optimal hot-start solution relative to the Gurobi optimal solution. Detailed Implementation

[0122] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0123] Typhoon-induced faults pose a significant threat to active distribution networks (ADNs), necessitating rapid dynamic network reconfiguration (NR) to enhance operational resilience. Traditional mixed-integer programming (MIP) methods are computationally burdensome and struggle to achieve real-time emergency response. This embodiment proposes a novel graph neural network (GNN) optimization framework (GraNR) to achieve rapid near-optimal dynamic reconfiguration during typhoons. This framework includes: a switch-gated message passing mechanism to model physical switching operations; a topology-independent local predictor to ensure configuration scalability; preprocessing filtering to identify non-critical switches; and post-processing confidence selection to strategically fix high-confidence decisions while retaining uncertain variables for subsequent MIP optimization. By fusing neural prediction and mathematical programming, GraNR combines machine learning speed with optimality guarantees from the optimization solver. Experiments on the IEEE 33-bus system demonstrate that GraNR achieves a 1.64x speedup and only... The average optimal gap verifies the practical value of improving the resilience of distribution networks in extreme weather.

[0124] Specifically, this embodiment addresses a graph neural network-induced active distribution network dynamic reconfiguration system under typhoon disaster conditions, comprising a graph neural network module, a preprocessing and filtering module, a post-processing and selection module, an optimization and solution module, and a scenario generation module. Specifically, the graph neural network module predicts network reconfiguration strategies based on the topology and operating status of the active distribution network; it uses switches as a gating message passing mechanism, modeling switchable lines as learnable gates to dynamically control information flow between nodes, simulating the control of power flow by physical switches. The preprocessing and filtering module identifies and filters non-critical switches based on consistency indices of switch states in the training dataset, reducing model complexity and prediction errors. The post-processing and selection module performs confidence analysis based on the switch state probabilities output by the graph neural network, fixing high-confidence decisions and retaining uncertain variables as subsequent mixed-integer programming optimization variables. The optimization and solution module integrates the graph neural network prediction results into the mixed-integer programming solver to solve dynamic network reconfiguration and optimal power flow problems; it uses the graph neural network prediction as a warm-start strategy to accelerate the solution process and ensure the feasibility and optimality of the solution. The scenario generation module is used to simulate uncertain fault scenarios under typhoon disasters. It calculates the line fault probability based on the wind field model and component strength and wind load model, and generates time-varying fault scenarios to drive the dynamic reconfiguration process.

[0125] I. Resilient Operation Model.

[0126] 1.1 Objective function.

[0127] The system enables rapid dynamic reconfiguration of the active distribution network under typhoon disaster scenarios, aiming to minimize power outage costs and emergency generation costs, thereby enhancing grid resilience. Specifically, the objective function is expressed as:

[0128]

[0129]

[0130]

[0131] in: The objective function for resilient operation is determined by the cost of power outage losses. Distributed power generation costs and auxiliary power supply services constitute. It is the loss-of-load value coefficient, used to quantify the trade-off between cost and resilience, and to guide resource allocation to effectively shorten power outage duration and reduce loss of load. It is the load recovery ratio; For load power; This refers to the output power of the distributed power source. To fix the power generation cost parameters of the auxiliary generator; This is to assist in determining the primary parameters of generator power generation costs; For the set of distribution network nodes; This is a collection of all time periods.

[0132] 1.2 Constraints.

[0133] (1) Power flow model: Let For the set of distribution network nodes; For branch set; and These represent nodes in the distribution network. The upstream node set and the child node set, where .

[0134] Upper and lower limits constraints for the squares of voltage and current:

[0135]

[0136] Voltage relationship equation:

[0137]

[0138] Power balance equation:

[0139]

[0140]

[0141] Node power injection equations:

[0142]

[0143]

[0144] in: For the set of distribution network nodes; For branch set; and These represent nodes in the distribution network. The upstream node set and the child node set, where ; , and They are respectively Time Node Lower and upper limits of the square of voltage amplitude for Voltage amplitude at time node; , and They are respectively Time Node Lower and upper limits of the square of the current amplitude for Time Node Current amplitude; and They are respectively the branches through which the flow passes Active power and reactive power; and They are branch roads Resistance and reactance; and For nodes Injected active power and reactive power; for Time Node Active power of diesel generator; for Time Node Power purchased; for Time Node Photovoltaic power output; for Time Node Fan output; for Time Node Energy storage discharge power; for Time Node Energy storage charging power; for Time Node Active power of load; for Time Node Reactive power of diesel generator; for Time Node Purchased reactive power; for Time Node Reactive power of load.

[0145] (2) Network reconfiguration: The reconfiguration of the distribution network needs to maintain a radial structure to facilitate the prevention of subsequent faults through relay protection settings, and at the same time simplify operation issues such as synchronization. The radial constraints during islanded operation are shown below.

[0146]

[0147]

[0148]

[0149]

[0150] in: It is a binary branch state. Indicates a branch in operation. Indicates a branch that is disconnected / isolated; Represents the binary virtual flow of electricity. This indicates that the actual power flow direction is from the bus. to ; It includes a collection of alternative islanded power buses that can be powered, including auxiliary power buses; This is a collection of distribution network branches.

[0151] (3) Switching state related constraints:

[0152]

[0153]

[0154]

[0155]

[0156]

[0157] in: It is a very large positive number; This represents the residual of the voltage constraint.

[0158] (4) Second-order cone relaxation: Given the non-convex constraints in the power flow model, second-order cone relaxation is used to simplify the distribution network model while maintaining a small difference from the original power flow equations. The voltage constraints in the power flow model can be converted to:

[0159]

[0160] in: ,for Time Node voltage amplitude square; ,for Time Node Current amplitude square; and Branch roads The active and reactive power flow.

[0161] II. Scene Generation Module.

[0162] This embodiment proposes a scenario generation method to describe uncertain damage in order to construct a typhoon disaster scenario, and simultaneously establishes an active distribution network resilience operation model. Specifically, the probability of line faults is affected by the severity of natural disasters and the vulnerability of components. By modeling the disaster disturbance process, time-varying fault probabilities are derived to capture the dynamic impact of extreme events. Figure 1 The diagram illustrates typhoon disturbances, with the blue dashed line representing the typhoon's path and the gray dashed line indicating the wind speed calculated by the wind field model. This allows for the calculation of time-varying wind loads on each branch line and the estimation of line fault probabilities, forming the basis for generating fault scenarios.

[0163] In this embodiment, the scene generation module calculates the line fault probability based on the wind field model and the component strength and wind load model, wherein the wind field model adopts the Batts model:

[0164]

[0165]

[0166]

[0167]

[0168] in: The radius of maximum wind speed; For pressure drop; The maximum gradient wind speed; K=6.72 is an empirical coefficient; This is the Earth's rotational angular velocity; Geographic latitude; and These are the average maximum wind speed and the wind field movement speed, respectively. Tangential wind speed; This is the radius distance from the center of the wind field; The intensity attenuation coefficient;

[0169] Component strength and wind load model calculation of wind load and failure probability:

[0170]

[0171]

[0172]

[0173]

[0174] in: Indicates the total wind load; , and These represent the outer diameter, size factor, and density of the power transmission line, respectively. and This refers to the wind pressure coefficient and the angle between the conductor and the wind direction; It is gravitational acceleration; For conductor height coefficient; The tangential wind speed is located at a radius of φ from the center of the wind field. and These represent the tension at the highest and lowest points of the transmission line, respectively. This refers to the cross-sectional area of ​​the steel-cored aluminum stranded wire; The equivalent force arm / distance between the highest and lowest points;

[0175] This represents the tower base bending moment caused by the conductor wind load; This represents the bending moment at the base of the tower caused by the wind load on the tower body. This represents the total bending moment at the base of the tower; Indicates the first Horizontal wind load on the suspended conductor; The average spacing between the conductors; It is the first The vertical distance between the conductor and the base of the tower; Indicates the number of conductors on the tower; , , and Representative tower dimensions; This represents the lever arm distance from the point of application of the resultant wind pressure force on the tower to the base of the tower.

[0176] The probability of a line fault is calculated using the following formula:

[0177]

[0178] in, and The fault probabilities for the line and the tower are respectively obtained by integrating the normal distribution function; Indicates a branch The number of wires on it; Indicates a branch The number of poles and towers.

[0179] III. Graph Neural Network Module.

[0180] 3.1 Graph Neural Network (GNN) Optimization Framework (GraNR).

[0181] The GraNR framework proposed in this embodiment solves the computational challenge of dynamic network reconstruction in typhoon scenarios through an innovative fusion of graph neural networks and mixed-integer programming. Unlike traditional methods that rely solely on cold-start MIP solvers, GraNR employs a learning-based warm-start strategy, significantly reducing computation time while maintaining near-optimal solution quality. This framework includes four major innovations: (i) topology-aware learning is achieved through switch-gated message passing; (ii) pre-machine learning filtering reduces complexity; (iii) confidence-based post-machine learning selection ensures solution quality; and (iv) a topology-independent architecture enhances generalization capabilities.

[0182] 3.2. Graphical representation of the reconstruction problem.

[0183] Let the busbar set of the distribution network be... The set of branches is Network topology is naturally modeled as an undirected graph. , where the vertex Corresponding busbar, edge Corresponding branch lines. Crucially, the branch line set is divided into fixed routes. and switchable lines And satisfy

[0184] Each vertex Through feature vectors Characterize its node attributes:

[0185]

[0186] in: Indicates node degree; Quantify the failure rate of associated branches; Represents load recovery capability; Aggregate the switching status of adjacent lines; This indicates the refactoring priority based on criticality analysis.

[0187] Edge features Capture operating status and fault characteristics:

[0188]

[0189] in: Indicates the fault status (0 = fault, 1 = normal); and Indicates the current switch and reconfiguration status; Measure the normalized fault duration; This indicates the priority of the repair process.

[0190] Unlike traditional methods that train independent models for each power grid topology, this framework integrates network topology. As direct input to the GNN, this topology-independent design enables: (i) simultaneous training with multiple grid configurations; (ii) adaptation to online topology changes due to maintenance or faults; and (iii) transfer learning across different distribution networks. Adjacency matrix Explicit encoding of fixed and switchable connections enables GNNs to learn topology-dependent network reconstruction representations within a unified framework.

[0191] 3.3. Opening and closing gate control message transmission mechanism.

[0192] (1) Physical explanation: Traditional GNNs treat the topology as static during inference, which is fundamentally contradictory to the dynamic reconstruction problem of the topology itself as the optimization target. The switch-gated message passing mechanism proposed in this embodiment solves this contradiction by modeling switchable lines as learnable gating. These gating continuously regulate the information flow in message passing, similar to physical switches controlling the power flow in the power grid.

[0193] (2) Message passing: GNN includes Each hidden layer dimension is The graph convolutional layer. The initial node and edge embeddings are obtained as follows:

[0194]

[0195]

[0196] in: Represents a node The initial embedding vector; Representing an edge The initial embedding vector; and These are the learnable weight matrices for node features and edge features, respectively; and Indicates the corresponding bias term; Indicates the dimension of the hidden layer; Dimensions representing node features The dimension representing the edge feature.

[0197] For each subsequent layer Node embeddings are updated via gated message aggregation:

[0198]

[0199] in: Represented as nodes The embedding vector; and Indicates the first The learnable weight matrix of the layer; Represents a node The set of neighboring nodes; This is a gated function.

[0200] Specifically, in the multi-layer message passing process of a graph neural network, for each switchable line, a gate function is used to control the information flow between nodes. This gate function is calculated based on the switch embedding vector and is defined as follows:

[0201]

[0202] in: For gated functions; Represents the sigmoid function; A set of switchable branches with switches; For a fixed set of branches; For the first The layer's switch embedding vector is updated using the following formula:

[0203]

[0204] in: and They are nodes and The embedding vector; and This is a learnable weight matrix.

[0205] Gating mechanisms embed physical knowledge directly into neural network architectures. When the switch... When disconnected, the gate value approaches 0, and the decay node... and The message flow between them is analogous to electrical isolation; closing the switch generates a gating value close to 1, enabling complete information exchange. This mechanism has three advantages: First, the gating value directly corresponds to the switch conduction level, providing physical interpretability; second, continuous gating values ​​ensure differentiability, supporting efficient gradient calculation; third, the architecture allows GNNs to control the physical switch by adjusting the gating value, thereby minimizing the objective function in adaptive topology learning.

[0206] (3) Multi-head graph attention: After the GCN layer, including The Graph Attention Network (GAT) of a certain size computes attention-weighted aggregation:

[0207]

[0208]

[0209] in: Aggregate features from all GCN layers using residual connections; Indicates the first Learnable attention vectors for each attention head; Indicates the first Linear transformation weight matrix for each attention head; Indicates the first Under the attention of each node, neighboring nodes For nodes Attention weights. The final node represents the concatenation of all attention heads: Global graph embedding Capture information from the entire network.

[0210] 3.4 Local predictors for scalable decision-making.

[0211] Traditional methods employ a global predictor (embedding all nodes and edges into decision variables), causing the input / output dimensions to grow with the network size. This approach has two major drawbacks: first, the model architecture is tied to a specific network and cannot be transferred to power grids of different sizes; second, the prediction results suffer from permutation variance, meaning that arbitrary changes in the node order will affect the output (even if the actual network configuration is the same).

[0212] The GraNR framework proposed in this embodiment introduces two local predictors. Its core idea is that the power flow relationship is locally determined by network reconstruction and power balance equations.

[0213] (1) Line Predictor (N-Predictor): Used to predict the power flow and node voltage of stationary lines based on local node embedding and global graph embedding. Specifically, for each stationary line... The L predictor estimates active power flow and node voltages:

[0214]

[0215] in: branch road The predicted active power flow; and They are slave nodes and nodes Predicted local values ​​of node voltage; and They are nodes and nodes Embedded, Embedded in the global graph.

[0216] (2) Switching Predictor (S-predictor): Used to predict the power flow, node voltage, and switching state probability of switchable lines based on local node embedding, switching embedding, and global graph embedding. For each switchable line... The S-predictor will also additionally estimate the probability of the switching state:

[0217]

[0218] in: branch road The probability of the on / off state; To indicate the branch road Switch-related feature vectors.

[0219] (3) Voltage aggregation and constraint satisfaction: Local prediction will generate multiple voltage estimates for each node (specifically, the degree is ). nodes It will generate (a total of several estimates) are aggregated by taking the average:

[0220] Specifically, the aggregation of node voltages is calculated using the following formula:

[0221]

[0222] in: Let be the predicted voltage magnitude at node i; For nodes A set of connected branches; This is the node degree operator.

[0223] To ensure that the voltage limit is met, the aggregated predictions will be scaled to a feasible range:

[0224]

[0225] in: and These represent the lower and upper limits of the permissible node voltage amplitude, respectively.

[0226] This design ensures that voltage constraints are met through its construction, eliminating a major source of infeasibility in learning-based optimization methods.

[0227] 3.5. Preprocessing and filtering module for reducing complexity.

[0228] Analysis of the optimal solutions in the training dataset shows that some switches remain in a constant state (normally open or normally closed) regardless of load conditions. Predicting these non-critical switches wastes model capacity and introduces unnecessary prediction errors.

[0229] In this embodiment, the preprocessing filtering module identifies non-critical switches by analyzing the consistency index of switch states in the training dataset. The consistency index is defined as:

[0230]

[0231] when At that time, switches are classified as non-critical switches and excluded from the prediction task. The simplified set of switches is defined as follows:

[0232]

[0233] in: For training samples The optimal switching state; M is the number of training samples.

[0234] 3.6 Post-processing selection module based on confidence level.

[0235] Existing technologies use physical information rounding to binarize all GNN predictions, transforming MILP into a fast-solvable but potentially suboptimal or infeasible LP. This embodiment proposes a post-processing selection module that introduces a confidence-based filtering mechanism to balance solution speed and quality.

[0236] (1) Confidence analysis based on the probability output of the switch predictor Set confidence threshold and Switches are classified as follows:

[0237]

[0238]

[0239] Switches with high confidence (close to 0 or 1) will be fixed to binary values. For high-confidence switches, their states will be fixed as follows:

[0240]

[0241] The switches in the equation remain binary variables in the subsequent MIP (Mixed Integer Programming) formula. For indeterminate switches, they are retained as binary variables in the mixed integer programming equation.

[0242] (2) Simplified NR-OPF formula: After fixing the selected switch, the complete NR-OPF problem generates a simplified mixed integer programming problem (MILP):

[0243]

[0244]

[0245]

[0246] in: For a set of high-confidence switches; For a set of low-confidence switches; The "key switch set" to be retained; Branches predicted by GNN The probability of being in the "closed" state; The determined switch state; The low confidence threshold; The high confidence threshold; To simplify the set of decision variables.

[0247] 3.7 Loss Function and Training Process.

[0248] In this embodiment, the graph neural network module is trained end-to-end using an unsupervised loss function. This loss function, which combines the objective function and a constraint violation penalty term, is defined as follows:

[0249]

[0250] in: This represents all learnable parameters; This represents the complete set of variables obtained from GNN prediction and recovery; Encoding inequality constraints; The `max` operator is used to assign penalty weights; it ensures that only constraint violations are included in the penalty calculation.

[0251] Training uses the AdamW optimizer with an initial learning rate of Weight decay Batch size 20, using OneCycleLR learning rate scheduler:

[0252]

[0253] in: Indicates the number of iterations Learning rate at that time; and These represent the minimum and maximum values ​​of the learning rate, respectively. In this embodiment, , ; This indicates the maximum number of iterations.

[0254] Gradient clipping with a threshold of 0.8 was used to stabilize training.

[0255]

[0256] If the verification loss continues If there is no improvement in the round, the early shutdown mechanism will be triggered.

[0257] The complete algorithm is as follows Figure 2As shown.

[0258] IV. Case Studies.

[0259] 4.1 Test system configuration.

[0260] This embodiment uses the IEEE 33-bus distribution system to numerically evaluate the proposed optimal load restoration method. The system configuration includes potentially faulty branches, such as... Figure 3 As shown, the disaster and failure model generates detailed uncertainty scenarios, with parameter settings based on actual typhoon characteristics and reported load curve data. Experiments were performed on a computer equipped with an R9 9950X CPU, an RTX 4090 GPU, and 192GB of RAM.

[0261] 4.2 Training performance analysis.

[0262] Figure 4 The convergence characteristics of the proposed GNN model over 300 training epochs are demonstrated. The MSE training loss rapidly decreases from 3.2 to around 0.6 within the first 80 epochs, then stabilizes and converges to a final value of 0.15. The validation loss exhibits a similar trend, reaching a minimum of 0.050 at the 150th epoch, at which point the model's generalization performance is optimal. The close fit between the training and validation curves indicates extremely low overfitting, and the final loss difference of 0.13 (validation loss minus training loss) is within an acceptable range.

[0263] Figure 5 The evolution of prediction accuracy between the training and validation sets is presented. The training accuracy eventually converged to 93%, while the validation accuracy stabilized at 81.6% after approximately 250 epochs. The 11.4% accuracy gap reflects the inherent complexity of network reconstruction decision prediction in multi-fault scenarios. Notably, the validation accuracy did not show a significant decrease in the later stages, confirming the model's robustness against overfitting. The 81.6% validation accuracy is significant for the network reconstruction task, indicating that GNN can accurately handle different typhoon scenarios in approximately 4 / 5 of the on / off state predictions.

[0264] 4.3 Computational efficiency.

[0265] Figure 6 The results demonstrate the cumulative speedup of the GraNR method compared to Gurobi's solution for traditional full NR-OPF across 40 test scenarios, showcasing its significant computational advantage. The speedup varies considerably across different scenarios: in scenarios 1-2, the initialization overhead of the GNN is only [amount missing]. The number of times, while the highest in scenario 5 is [number missing]. Times. Average The speedup ratio of several times indicates that, compared to cold-start MIP solutions, this method can reduce the average speedup by [number] times. Calculate the time.

[0266] 4.4 Improved computational efficiency.

[0267] The speedup distribution exhibits three distinct intervals: (i) the initialization phase (scenes 1-3), where the speedup is minimal due to GNN inference overhead; and (ii) the high-performance interval (scenes 4-12), where the speedup exceeds [a certain value]. The peak value of scenario 5 reached [number] times. (iii) In the stable range (scenarios 13-40), the speedup ratio remains at [number missing] times; It is worth noting that 6 out of 40 cases (15%) achieved more than [a certain number]. The speedup of several times demonstrates the effectiveness of this method for computationally intensive scenarios. The standard deviation of 2.74 reflects the dependence of the speedup on problem characteristics: complex failure mode scenarios benefit more from warm-start initialization, while the improvement is limited in simple scenarios.

[0268] The cumulative acceleration curve (blue filled area) shows that most test cases are consistently higher than [previous data]. Double the baseline (gray dashed line), only 2 cases were below the baseline. The high success rate verifies the robustness of the GNN method in typhoon-induced failure scenarios.

[0269] 4.5 Optimality assessment of the solution.

[0270] Figure 7 The objective function loss relative to the Gurobi optimal solution was quantified, revealing the key trade-offs in solution quality. The GraNR method achieves an average loss rate of 0.67%, meaning it retains an average of 99.33% of the optimal objective value. In 29 out of 40 test scenarios (72.5%), the optimality gap was less than [a certain value]. The results show that the solution quality for most cases is excellent. Three anomalous scenarios (numbered 19, 25, and 15) exist in the loss distribution, with the target value deteriorating by more than 1.5%, reaching a maximum of 1.837%. These anomalies correspond to extreme scenarios where multiple critical lines fail simultaneously, challenging the predictive capabilities of GNNs. However, even in the worst-case scenario, the target loss remains below 2%, fully meeting the tolerance threshold for computational speed priorities in emergency response applications.

[0271] Table 1 Performance Comparison of Benchmark Methods

[0272]

[0273] The horizontal reference line marks the key performance thresholds: green dashed line. The red dotted line represents the average performance, while the 1% threshold serves as the quality benchmark. Data points concentrated below the 1% threshold (orange shaded area) confirm that the proposed method consistently provides high-quality solutions. A standard deviation of 0.509% indicates reasonable consistency across different scenarios, suggesting that performance fluctuations stem from the inherent difficulty of failure modes rather than systemic method defects.

[0274] 4.6 Performance Comparison.

[0275] The performance benchmarks were set as follows: 1) solving the NR problem using Gurobi; 2) solving using GraPhyR; 3) solving using RGNN-MILP; and 4) the GraNR method proposed in this embodiment. Table 1 shows the overall performance comparison of all benchmark methods on the IEEE 33-node system.

[0276] As shown in Table 1, GraNR achieves the best balance between solution quality and computational efficiency: its average cost ratio of 100.67% is only 0.67% lower than the Gurobi benchmark, while also achieving... The acceleration reduces the average solution time by 39%. Notably, GraNR generates near-optimal solutions (within 1% of the optimal gap) in 72.5% of test cases, significantly outperforming all benchmark methods in terms of solution quality consistency.

[0277] Learning methods based on linear programming relaxation (GraPhyR and RGNN-MILP) achieve this by completely eliminating integer variables. While achieving a significant speedup, the aggressive relaxation strategy leads to a severe loss of optimality (average cost ratios of 101.78% and 102.34%, respectively). More importantly, these LP methods only generate near-optimal solutions in 12%-15% of test scenarios, indicating insufficient reliability in real-world grid resilience operations requiring quality assurance. Furthermore, because GraPhyR employs LP relaxation, its case studies even exhibit results that violate power flow constraints, which is unacceptable in disaster-resilient operations.

[0278] Performance comparisons validate the effectiveness of the GraNR hybrid framework: by strategically fixing high-confidence switch decisions while retaining uncertain switches as integer variables, this method maintains the accuracy of mathematical programming while leveraging neural network predictions to accelerate convergence. Near-optimal solution rate. The 72.5% improvement (compared to 15% of RGNN-MILP) demonstrates that the switch-gated message passing architecture and the confidence-based selection mechanism significantly improve the prediction accuracy of key reconstruction decisions. Although The speed-up method is slightly more conservative than the LP method, but The average optimal gap means minimal operating cost loss and maintains solution reliability in typhoon failure scenarios, which is extremely beneficial for emergency response applications.

[0279] V. Conclusion.

[0280] This embodiment proposes an active distribution network dynamic reconfiguration system induced by a neural network for typhoon disasters. It significantly shortens the computation time while ensuring the safe operation of the active distribution network. The main contributions are as follows.

[0281] 1) A message-passing architecture modeling the dynamic topology reconfiguration process is proposed, which treats the topology as a switch and gating mechanism. Unlike traditional GNNs that treat the topology as static, this mechanism embeds switchable lines as learnable gating mechanisms to continuously regulate the information flow in message passing—mimicking the principle of physical switches controlling power grid flow. This design, which incorporates physical cognition, allows the GNN to learn the optimal reconfiguration strategy while maintaining interpretability.

[0282] 2) Develop a topology-independent framework with local predictors to ensure scalability and portability across different network configurations. By predicting power flow and voltage based on local node embeddings (rather than global network representations), this architecture eliminates the dependence on fixed network size and can be seamlessly applied to different power distribution systems without modifying the structure or retraining.

[0283] 3) Introduce a two-stage filtering selection mechanism to balance computational efficiency and solution quality. The pre-processing machine learning filtering layer identifies non-critical switches with stable operating states, reducing model complexity and improving prediction accuracy; the post-processing confidence-based selection layer strategically fixes high-confidence predictions while retaining uncertain variables as binary decisions, enabling the subsequent mixed-integer programming solver to focus on key reconstruction decisions.

[0284] Theoretically, this embodiment proposes an active distribution network dynamic reconfiguration system induced by a graph neural network for typhoon disasters, which solves the computational challenge of real-time resilient operation and maintenance while maintaining solution optimality. Numerical experiments on the IEEE 33-bus system demonstrate that GraNR implementation... The method achieves an average speedup with only a 0.67% degradation in optimality, and maintains near-high-quality solutions in 72.5% of cases (within the 1% gap), significantly outperforming benchmark learning methods (12%-15%). Future research directions include: extending to integrated transmission and distribution systems, combining online learning with disaster pattern evolution, integrating uncertainty quantification with risk perception, and cross-regional transfer learning. This framework lays an important foundation for enhancing the smart resilience of modern distribution networks facing extreme weather.

[0285] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A dynamic reconfiguration system for active distribution networks induced by a neural network under typhoon disasters, characterized in that: include: The graph neural network module is used to predict network reconfiguration strategies based on the topology and operating status of the active distribution network. The graph neural network module uses switches as a gating message passing mechanism, models switchable lines as learnable gates to dynamically control the information flow between nodes, and simulates the control of power flow by physical switches on the power grid. The preprocessing filtering module is used to identify and filter non-critical switches based on the consistency index of switch states in the training dataset, thereby reducing model complexity and prediction error. The post-processing selection module is used to perform confidence analysis based on the switch state probabilities output by the graph neural network, fix the high-confidence decisions and retain the uncertain variables as subsequent mixed integer programming optimization variables; An optimization solution module is used to integrate the prediction results of the graph neural network into the mixed-integer programming solver to solve dynamic network reconstruction and optimal power flow problems. The optimization solution module uses the prediction of the graph neural network as a warm-start strategy to accelerate the solution process and ensure the feasibility and optimality of the solution. The scenario generation module is used to simulate uncertain fault scenarios under typhoon disasters. It calculates the line fault probability based on the wind field model and component strength and wind load model, and generates time-varying fault scenarios to drive the dynamic reconfiguration process. The system enables rapid dynamic reconfiguration of the active distribution network under typhoon disaster scenarios to minimize power outage costs and emergency power generation costs, thereby enhancing grid resilience. The objective function is expressed as: in: The objective function for resilient operation is determined by the cost of power outage losses. Distributed power generation costs and auxiliary power supply services constitute; It is the loss-of-load value coefficient, used to quantify the trade-off between cost and resilience, and to guide resource allocation to effectively shorten power outage duration and reduce loss of load. It is the load recovery ratio; For load power; This refers to the output power of a distributed power source. To fix the power generation cost parameters of the auxiliary generator; This is to assist in determining the primary parameters of generator power generation costs; For distribution network nodes; This is a collection of all time periods.

2. The active distribution network dynamic reconfiguration system induced by a neural network for typhoon disasters as described in claim 1, characterized in that: The switch serves as a gating message transmission mechanism, including: GNN includes Each hidden layer dimension is The graph convolutional layer; the initial node and edge embeddings are obtained in the following way: in: Represents a node The initial embedding vector; Representing an edge The initial embedding vector; and These are the learnable weight matrices for node features and edge features, respectively; and Indicates the corresponding bias term; Indicates the dimension of the hidden layer; Dimensions representing node features The dimension representing the edge features; For feature vectors; Edge features; For each subsequent layer Node embeddings are updated via gated message aggregation: in: Represented as nodes The embedding vector; and Indicates the first The learnable weight matrix of the layer; Represents a node The set of neighboring nodes; For gated functions; In the multi-layer message passing process of a graph neural network, for each switchable line, a gate function is used to control the information flow between nodes. The gate function is calculated based on the switch embedding vector and is defined as follows: in: For gated functions; Represents the sigmoid function; A set of switchable branches with switches; For a fixed set of branches; For the first The layer's switch embedding vector is updated using the following formula: in: and They are nodes and The embedding vector; and The weight matrix is ​​a learnable weight matrix; When the switch is open, the threshold value approaches 0 to attenuate the information flow and simulate electrical isolation; when the switch is closed, the threshold value approaches 1 to allow complete information exchange.

3. The active distribution network dynamic reconfiguration system induced by a neural network for typhoon disasters as described in claim 1, characterized in that: The graph neural network module further includes a topology-independent local predictor, which includes: A line predictor, used to predict power flow and node voltages of a stationary line based on local node embedding and global graph embedding, is represented as: in: branch road The predicted active power flow; and They are slave nodes and nodes Predicted local values ​​of node voltage; and They are nodes and nodes Embedded, Embedded in a global graph; A switching predictor, used to predict the power flow, node voltage, and switching state probability of a switchable line based on local node embedding, switching embedding, and global graph embedding, is expressed as: in: branch road The probability of the on / off state; To indicate the branch road Switch-related feature vectors; The aggregation of node voltages is calculated using the following formula: in: Let be the predicted voltage magnitude at node i; For nodes A set of connected branches; For node degree operator; And scale to a feasible range to ensure that voltage constraints are automatically met: in: and These represent the lower and upper limits of the permissible node voltage amplitude, respectively.

4. The active distribution network dynamic reconfiguration system induced by a neural network for typhoon disasters as described in claim 1, characterized in that: The preprocessing filtering module identifies non-critical switches by analyzing the consistency index of switch states in the training dataset. The consistency index is defined as follows: when At that time, switches were classified as non-critical switches and excluded from the prediction task. The simplified set of switches is defined as follows: in: For training samples The optimal switching state; M is the number of training samples.

5. The active distribution network dynamic reconfiguration system induced by a neural network for typhoon disasters as described in claim 1, characterized in that: The post-processing selection module specifically includes: Confidence analysis based on the probability output of the switch predictor Set confidence threshold and Switches are classified as follows: For high-confidence switches, their state is fixed as follows: For indeterminate switches, they are retained as binary variables in mixed-integer programming; Generate simplified mixed-integer programming problems: in: For a set of high-confidence switches; For a set of low-confidence switches; The "key switch set" to be retained; Branches predicted by GNN The probability of being in the "closed" state; The determined switch state; The low confidence threshold; The high confidence threshold; To simplify the set of decision variables.

6. The active distribution network dynamic reconfiguration system induced by a neural network for typhoon disasters as described in claim 5, characterized in that: The constraints of the simplified mixed-integer programming problem include: Upper and lower limits constraints for the squares of voltage and current: Voltage relationship equation: Power balance equation: Node power injection equations: in: For distribution network nodes; For branch set; and These represent nodes in the distribution network. The upstream node set and the child node set, where ; , and They are respectively Time Node Lower and upper limits of the square of voltage amplitude for Voltage amplitude at time node; , and They are respectively Time Node Lower and upper limits of the square of the current amplitude for Time Node Current amplitude; and They are respectively the branches through which the flow passes Active power and reactive power; and They are branch roads Resistance and reactance; and For nodes Injected active power and reactive power; for Time Node Active power of diesel generator; for Time Node Power purchased; for Time Node Photovoltaic power output; for Time Node Fan output; for Time Node Energy storage discharge power; for Time Node Energy storage charging power; for Time Node Active power of load; for Time Node Reactive power of diesel generator; for Time Node Purchased reactive power; for Time Node Reactive power of load.

7. The active distribution network dynamic reconfiguration system induced by a neural network for typhoon disasters as described in claim 5, characterized in that: The constraints of the simplified mixed-integer programming problem include radial constraints for network reconstruction: in: The binary branch state, Indicates a branch in operation. Indicates a branch that is disconnected / isolated; Represents the binary virtual flow of electricity. This indicates that the actual power flow direction is from the bus. to ; For a collection of alternative islanded power buses that can be powered; This is a collection of distribution network branches.

8. The active distribution network dynamic reconfiguration system induced by a neural network for typhoon disasters as described in claim 5, characterized in that: The constraints of the simplified mixed-integer programming problem include switch-state related constraints: in: It is a very large positive number; Represents the residual under voltage constraint; The constraints of the simplified mixed-integer programming problem include second-order cone relaxation constraints: in: ,for Time Node voltage amplitude square; ,for Time Node Current amplitude square; and Branch roads The active and reactive power flow.

9. The active distribution network dynamic reconfiguration system induced by a neural network for typhoon disasters as described in claim 1, characterized in that: The graph neural network module is trained end-to-end using an unsupervised loss function, which combines the objective function and a constraint violation penalty term, and is defined as follows: in: This represents all learnable parameters; This represents the complete set of variables obtained from GNN prediction and recovery; Encoding inequality constraints; The `max` operator is used to assign penalty weights; it ensures that only constraint violations are included in the penalty calculation. Training was performed using the AdamW optimizer and the OneCycleLR learning rate scheduler. in: Indicates the number of iterations Learning rate at that time; and These represent the minimum and maximum values ​​of the learning rate, respectively. Indicates the maximum number of iterations; Gradient clipping with a threshold of 0.8 was used to stabilize training. If the verification loss continues If there is no improvement in the round, the early shutdown mechanism will be triggered.

10. The active distribution network dynamic reconfiguration system induced by a neural network for typhoon disasters as described in claim 1, characterized in that: The scenario generation module calculates the line fault probability based on a wind field model and a component strength and wind load model, wherein the wind field model adopts the Batts model: in: The radius of maximum wind speed; For pressure drop; The maximum gradient wind speed; K=6.72 is an empirical coefficient; This is the Earth's rotational angular velocity; Geographic latitude; and These are the average maximum wind speed and the wind field movement speed, respectively. Tangential wind speed; This is the radius distance from the center of the wind field; The intensity attenuation coefficient; Component strength and wind load model calculation of wind load and failure probability: in: Indicates the total wind load; , and These represent the outer diameter, size factor, and density of the power transmission line, respectively. and This refers to the wind pressure coefficient and the angle between the conductor and the wind direction; It is gravitational acceleration; For conductor height coefficient; The tangential wind speed is located at a radius of φ from the center of the wind field. and These represent the tension at the highest and lowest points of the transmission line, respectively. This refers to the cross-sectional area of ​​the steel-cored aluminum stranded wire; The equivalent force arm / distance between the highest and lowest points; This represents the tower base bending moment caused by the conductor wind load; This represents the bending moment at the base of the tower caused by the wind load on the tower body. This represents the total bending moment at the base of the tower; Indicates the first Horizontal wind load on the suspended conductor; The average spacing between the conductors; It is the first The vertical distance between the conductor and the base of the tower; Indicates the number of conductors on the tower; , , and Representative tower dimensions; This represents the lever arm distance from the point of application of the resultant wind pressure force on the tower to the base of the tower. The probability of a line fault is calculated using the following formula: in, and The fault probabilities for the line and the tower are respectively obtained by integrating the normal distribution function; Indicates a branch The number of wires on it; Indicates a branch The number of poles and towers.

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