Modeling method for resilience assessment of power system considering cascading overload fault under typhoon disaster

Abstract

The application discloses a kind of typhoon disaster under the consideration of cascading overload fault occurrence power system resilience evaluation modeling method, it is related to electric power system analysis field.This method establishes two kinds of fault models of physical fault and overload fault caused by extreme typhoon scene, analyzes the inherent relationship between transmission line fault probability space-time variation and overload outage probability and its operating limit;Double-dimensional time sequence fault model under typhoon sustained disturbance is constructed, the entire fault evolution process is with fault occurrence time as only search standard, improves the accuracy of fault path search;Established transmission system resilience evaluation model, respectively quantifies system overall resilience and identifies weak line of system resilience clamp, it is favorable to grid operating personnel accurately perceive the ability of power system to respond to typhoon disaster, and formulate targeted resilience improvement strategy.The research results of the application can effectively provide ideas for resilience expansion and upgrading of transmission system and formulation of operation control strategy in future typhoon disaster.

Description

Technical Field

[0001] This invention relates to the field of power system analysis, specifically to a modeling method for assessing the resilience of power systems under typhoon disasters, taking into account cascading overload faults. Background Technology

[0002] Rising global temperatures will lead to an increased frequency of typhoon disasters, significantly increasing the risk of large-scale power outages and severely impacting the healthy development of the social economy and the normal production and lives of the people. Resilience assessment for such events is attracting widespread attention from academia and industry. However, existing resilience assessment methods only consider the impact of severe weather on the power grid, rarely taking into account the cascading overload outages within the grid itself. To address this, we propose a transmission network resilience assessment modeling method that considers cascading overload faults caused by persistent typhoon disturbances. This is of great significance for accurately assessing the power system's ability to cope with typhoon disasters.

[0003] Patents such as 202110295576.5 "A Rapid Method for Evaluating Economic Losses of RC Frame Structures for Multi-Disaster Resilience Assessment", 202110659995.2 "A Method and System for Elastoscopy Assessment of Power Systems under Extreme Disaster Conditions", and 202011599832.1 "A High-Resolution Power Grid Elastoscopy Assessment Method" mainly study the impact of extreme disasters on the physical disconnection of power systems and the subsequent load shedding operations of the power grid. They do not consider the cascading overload fault process caused by power flow transfer due to topology changes, resulting in optimistic model evaluation results. Patents such as 202210156343.1 "A Method for Elastoscopy Assessment of Power Systems Considering Time-Delayed Chaining Faults" and 202210397176.X "A Method for Elastoscopy Assessment of Power Systems Considering Chaining Fault Evolution under Typhoon Disasters" study the relationship between existing chaining fault models and extreme disasters. They do not consider the time difference between the occurrence time of chaining faults and the time difference between the retrieval of physical faults and chaining faults caused by typhoons, resulting in poor model applicability.

[0004] Therefore, in order to solve the above problems, a more comprehensive power system assessment and modeling method under disaster conditions is needed. Summary of the Invention

[0005] To address the problem that existing power system assessments under typhoon disaster conditions are not comprehensive enough, this invention provides a power system resilience assessment modeling method that considers cascading overload faults under typhoon disaster conditions.

[0006] This invention is achieved through the following technical solution: a power system resilience assessment modeling method considering cascading overload faults under typhoon disasters, comprising the following steps:

[0007] S1: Estimation model for transmission line operating capacity under high wind speeds:

[0008] (1) Estimation model for dynamic limit carrying capacity of the line:

[0009] Based on the principle of thermal balance, the ultimate current carrying capacity of the transmission line is calculated, that is, the heat loss on the surface of the transmission line is equal to the heat absorbed at that moment, as shown in equation (1):

[0010]

[0011] In the formula: T s,max For the line's extreme temperature; I max K is the ultimate carrying capacity; k1 and k2 are constant terms, and the specific calculation formulas are shown in equations (2) and (3):

[0012]

[0013]

[0014] In the formula: k f R is the thermal conductivity of air. e T is the Reynolds number; s T a Indicates the surface temperature of the line and the ambient temperature; v represents the ambient wind speed; d represents the outer diameter of the conductor; μ f α is the aerodynamic viscosity; α is the solar heat absorption coefficient; q se R(T) represents solar radiation intensity. s,max ) indicates the line temperature at T s,max The AC resistance value at that time;

[0015] Considering the maximum permissible power flow limit of the transmission line The equation for the change of the power flow limit value of the line with wind speed is:

[0016]

[0017] In the formula: F max (v) represents the tidal current limit value of wind speed v; F max (v0) represents the tidal current limit value under normal wind speed;

[0018] (2) Transmission line operation capacity estimation model

[0019] τ is taken from each weather region within a certain time period. L The minimum value is taken as the actual τ of the line. L The value is shown in equation (5); in order to ensure computational efficiency without losing versatility, the transmission line is divided into an appropriate number of equal segments according to its location, and the wind speed of each segment is equal to the wind speed at the center of the segment. It is assumed that the line L is composed of d segments connected in series:

[0020] τ L,t=min{τ L,t,q |q∈D l} (5)

[0021] In the formula: τ L,t τ represents the dynamic capacity expansion rate of line L at time t; L,t,q D represents the dynamic capacity expansion rate of the transmission line calculated based on the weather conditions of the q-th segment at time t; l Represents the set of segments of line L;

[0022] S2: Power system fault model under the influence of typhoon:

[0023] (1) Wind-induced physical line breakage model

[0024] The Batts model, which uses typhoon parameterization, simulates the typhoon's wind field. The wind speed in the model is related to the geographical distance from the typhoon's center. The probability of failure of the q-th segment of the L-th transmission line at time t is:

[0025]

[0026] In the formula: v L,t,q Let be the center wind speed of line segment q of line L at time t; V be the design wind speed of the transmission line. The transmission line is segmented according to formula (5). Assuming that the design wind speeds of all segments of line L are the same, the line failure rate is:

[0027]

[0028] (2) Wind-induced overload shutdown model

[0029] Based on reliability theory, the overload failure rate of a transmission line can be expressed as a piecewise function as the power flow increases. This allows for the analysis of the spatiotemporal variation of the transmission line failure probability and the intrinsic relationship between the overload outage probability and its operating limits. The failure probability of a line under the influence of a typhoon can be expressed as follows:

[0030]

[0031] In the formula: F L,t This represents the real-time power flow of line L at time t; This represents the upper limit of power flow for line L at time t; This represents the power flow limit value of line L at time t; where, ξ is the limiting multiple, with a value of 1.3;

[0032] S3: Power system fault evolution model under the influence of typhoons:

[0033] The typhoon system simulation spans from landfall to offshore, while the power system simulation spans from the first unexpected line fault caused by the typhoon to the point where the system is no longer affected and there are no more overloaded lines. Furthermore, typhoon-induced transmission line physical faults exhibit clear temporal characteristics within the overall disaster timeframe, but the order in which these faults occur is independent, termed independent successive faults. The distribution of these faults along the disaster evolution timeline often shows a certain degree of concentration, exhibiting a concentrated-dispersed pattern throughout the typhoon period, with a cumulative impact on the power grid. Typhoon-induced overload faults are the result of power flow redistribution, with a clear causal relationship between successive faults. The duration of overload faults depends on the degree of line overload and its ability to adapt to overload, generally ranging from a few seconds to tens of minutes, making it difficult to standardize simulation steps and step sizes. Considering the differences in simulation timeframes and line disconnection timing calculation methods, this fault process can be modeled as a two-dimensional time-sequential dynamic process considering both typhoon-induced physical faults and cascading faults, including a typhoon physical fault retrieval model and a typhoon-induced cascading fault retrieval model.

[0034] (1) Typhoon physical fault retrieval model:

[0035] A sequential Monte Carlo simulation with equal time intervals is used to preserve the temporal characteristics of component states during a disaster. The component operating time and failure time are sampled according to the failure probability to obtain the system state sequence and the ambient wind speed of each line at that moment. The specific steps are as follows:

[0036] Step 1: Initialize power grid data and disaster information, set the initial simulation time t, input the sampling interval Δt, and the disaster duration T;

[0037] Step 2: Update the typhoon forecast information at time t;

[0038] Step 3: Calculate the instantaneous failure rate of the components based on the typhoon wind speed at that moment and sample the component status;

[0039] Step 4: Determine if the component state at this moment is the same as the previous moment. If they are the same, merge them with the previous state and modify the state duration. If they are different, update the component state.

[0040] Step 5: Proceed to the next simulation moment, repeating steps 2-4 until the typhoon moves away;

[0041] (2) Model for retrieving chain failures caused by typhoons:

[0042] A cascading failure retrieval model that considers the occurrence time of overload shutdown failures is adopted. The specific steps are as follows:

[0043] Step 1: Input the fault time series set H caused by the typhoon in terms of time dimension;

[0044] Step 2: Input the fault information at time h=1, and the system simulation will begin;

[0045] Step 3: Update the network topology, determine if the system has been unblocked, if it has been unblocked, reselect the load balancer and perform islanding processing based on the optimal load shedding model, if it has not been unblocked, proceed to Step 4;

[0046] Step 4: Update system performance and calculate the load loss caused by the failure at that moment;

[0047] Step 5: Based on the system's operating status at this moment, filter all overloaded lines and predict their interruption time;

[0048] Overload line interruption time prediction takes into account the dynamic limit value of accumulated overload line load:

[0049]

[0050] In the formula: O L (t,Δt) represents the cumulative overload of line L during the time interval Δt starting from time t; F represents the power flow limit value of line L at time t; L,t This represents the power flow value of line L at time t; it should be noted that... It changes dynamically over time and is updated during the calculation as the simulation progresses;

[0051] Step 6: Determine if the overloaded line set is empty. If it is not empty, find the overloaded line in the overloaded set that takes the shortest time to stop and proceed to Step 7. If it is empty, proceed to Step 8.

[0052] Step 7: Determine if there is a physically faulty line within the selected overload line disconnection time. If not, disconnect the overload line and update the simulation time; otherwise, proceed to Step 8.

[0053] Step 8: Disconnect the (h = h + 1)th physically faulty line;

[0054] Step 9: Proceed to the next simulation and repeat steps 3 through 8;

[0055] Step 10: Output the timing fault chain;

[0056] S4: Power System Resilience Assessment Model under Typhoon Impact

[0057] Multiple rounds of typhoon simulations were conducted for S2 and S3, and the overall resilience value was calculated based on resilience assessment indicators:

[0058]

[0059] In the formula: γ resilience (λ) represents the system resilience value; λ count(K) represents the total number of simulated typhoon rounds; S0 represents the system performance under normal operating conditions; S k (t) represents the system's performance curve in the k-th simulation round; T0 is the moment when the typhoon begins to hit the system; T5 is the moment when the system's performance returns to normal.

[0060] S5: Identification indicators for vulnerable power lines under the influence of typhoons:

[0061] A fault evolution graph is constructed based on an offline fault evolution dataset from multiple rounds of single typhoon simulations. After performing M simulations, M fault chains can be obtained for construction. The node L of the m-th fault chain is then constructed. i and node L j Weights considering timing, consequences, and cumulative failure effects Consider three scenarios:

[0062] (1) Only overload faults occurred during this stage:

[0063]

[0064]

[0065] Where: ΔP ij m This represents the load loss caused by the overload fault of line j following the fault of line i in the m-th fault chain, and describes the consequences of the loss of line j. Let represent the order of line j in the m-th fault chain, describing the importance and timing of line j in the fault chain; considering that faulty lines closer to the end of the fault chain have lower importance, we take . P is a coefficient in the denominator of the fault weighting; j The probability of overload failure occurring during this stage is represented by equation (12); This indicates that the load loss of the j-th order fault is affected by the preceding fault disconnection and load loss;

[0066] (2) Only physical faults occur during this stage:

[0067]

[0068]

[0069] In the formula, h represents the representation of typhoon topology interference in the graph using virtual nodes to illustrate the timing of physical fault occurrence; j represents the faulty line caused by the typhoon; ΔP hj mThis indicates the consequence of a physical fault causing line j to disconnect; the physical meanings expressed by each formula in equation (13) are similar to those described in equation (11), the only difference being that the cause of the physical fault is represented by a virtual node not included in the fault evolution diagram, and the virtual node represents the topological disturbance of the typhoon; P j The probability of a physical line break during a typhoon is represented by equation (14);

[0070] (3) Both overload faults and physical faults occur simultaneously during this stage:

[0071]

[0072]

[0073] In the formula: η ω With η ρ These represent the proportions of load losses caused by overload faults and physical faults, respectively, within the total load loss of that phase.

[0074] Finally, the key nodes in the merged fault evolution diagram reflect the vulnerability of the power system under typhoon. By calculating the in-degree and out-degree of the weighted node j in the fault evolution diagram, the line susceptibility and propagation can be classified and identified, namely the degree of influence of node j on other faulted lines and the degree of influence of node i's fault on other line faults.

[0075]

[0076]

[0077] In the formula: D in With D out These are the weighted in-degree and out-degree of node j, respectively, and D in This indicates that line j is more susceptible to damage from other faulty lines; D out This indicates that line j has higher propagation potential and is more likely to affect other lines, causing them to malfunction; among which:

[0078]

[0079] To avoid excessive differences in vulnerability indices among different power lines, the methods described in the literatures Guo J, Feng T, Cai Z, et al. (Vulnerability Assessment for Power Transmission Lines under Typhoon Weather Based on a Cascading Failure State Transition Diagram [J]. Energies, 2020, 13) and Lian X, Qian T, Li Z, et al. (A Resilience Assessment Framework for Power System Against Continuous Disturbance Caused by Extreme Weather [J]. International Journal of Electrical Power and Energy Systems, 2023, 145) are adopted to eliminate such effects. In the formula: D j ∈{D in D out};D' j ∈{D′ in ,D' out}:

[0080]

[0081] Compared with existing technologies, this invention has the following advantages: The power system resilience assessment modeling method considering cascading overload faults under typhoon disasters provided by this invention can significantly improve system resilience through the deployed DLR technology, providing insights for the operation of systems severely affected by disasters and experiencing power shortages. Therefore, the resilience assessment model proposed in this invention can not only accurately assess the system's ability to cope with extreme weather events, but also evaluate its potential to cope with such events. Furthermore, this invention, based on the concept of graphs, assesses two types of weak lines that constrain system resilience: propagation-related and susceptible lines. It analyzes the causes of these weaknesses and proposes pre-disaster reinforcement strategies such as strengthening or expanding transmission lines with propagation-related weaknesses, as well as in-disaster control measures for susceptible lines. This can provide insights for effectively extending and upgrading the resilience of transmission systems and formulating operational control strategies for future typhoon disasters. Moreover, the method proposed in this invention can be easily extended to the handling of other extreme events. Attached Figure Description

[0082] Figure 1 This is a diagram illustrating the system evolution process under typhoon interference according to the present invention.

[0083] Figure 2 This invention describes the sampling process for single-cycle typhoon fault sequences based on the equal time interval sampling method.

[0084] Figure 3 This is the dual-time-dimensional system performance simulation model of the present invention.

[0085] Figure 4 This invention provides a resilience assessment model that takes into account the dynamic changes in transmission line capacity.

[0086] Figure 5 The geographical location of the IEEE 39-node system involved in the specific embodiments of the present invention.

[0087] Figure 6 This refers to the dynamic capacity expansion rate of each line during the typhoon impact period involved in the specific embodiments of the present invention.

[0088] Figure 7 This refers to the average power supply of transmission systems with different capacities under different load shedding strategies in specific embodiments of the present invention.

[0089] Figure 8 The diagram shows the toughness assessment results of each reinforcement group involved in a specific embodiment of the present invention.

[0090] Figure 9 The percentage represents the load loss ratio under different line capacity factors in the specific embodiments of the present invention.

[0091] Figure 10 The specific embodiments of the present invention involve line losses under different line capacity coefficients. Detailed Implementation

[0092] The present invention will be further described below with reference to specific embodiments.

[0093] This implementation adopts Figure 5 The IEEE 39-bus system example demonstrates and verifies the proposed system performance simulation, resilience assessment, and vulnerability identification under typhoon disturbance. It assumes the typhoon is located in the coastal region of South my country, and the typhoon's trajectory, origin and destination, and affected area are as follows: Figure 5 As shown, the dashed line represents the proposed typhoon path. The method provided in this invention is used for power system resilience assessment modeling. Geographical location parameters of each node are shown in Table 1. The proposed typhoon movement speed is 45 km / h, the line design wind speed is taken as 30 km / h using a unified standard, the ambient temperature is 40℃, the solar radiation intensity is 1000 W / m², the normal wind speed is 3 m / s, and the simulation time interval is 5 min.

[0094] Table 1. Node Latitude and Longitude Table

[0095]

[0096]

[0097] from Figure 5 As can be seen, the simulation begins with the system interfering with the typhoon, and the dynamic line capacity expansion rate is calculated over the entire time period. Figure 6 As shown, the line's dynamic capacity expansion rate exceeds 99.6% for a period of time, with the capacity increasing from 5% to 50%, and some lines even exceeding 80% at specific times. Therefore, the line's operating capacity is greatly affected by wind speed.

[0098] Load shedding statistics are performed using optimal power flow that considers both line dynamic capacity and non-dynamic capacity. Figure 6 As shown, as the system transmission capacity increases from 80% to 120%, the load power supply increases under both load shedding strategies, but the rate of increase slows down. When the transmission capacity is insufficient, the application of DLR significantly improves the load power supply, while when the transmission capacity of the transmission line is sufficient, the improvement in load power supply is not significant. Therefore, the application of DLR technology can improve system resilience, but there is an upper limit.

[0099] Simulations were conducted using over 1000 single-typhoon power system disruption events. System resilience values ​​were calculated by comparing resilience assessments that considered and did not account for cascading failures. Since component recovery was not considered during the fault evolution process, the resilience performance of the power grid during the fault process was first evaluated, including the average load loss P. loss With line loss L loss Secondly, the components are repaired, and finally the overall system toughness is assessed. resilience (λ) is used for evaluation. Table 2 shows the resilience evaluation results. The results indicate that ignoring cascading failures leads to a more optimistic evaluation result. Ignoring the impact of wind speed on system operation and ignoring the timing of failures also lead to a more optimistic evaluation result.

[0100] Table 2 Toughness Assessment Results

[0101]

[0102] The 1000 simulation results generated above were compressed into a fault evolution diagram, and the vulnerability of power grid components in typhoons was assessed based on the system's weak line evaluation index. The distribution of lines that experienced faults in all simulation scenarios is as follows: Figure 7 As shown, based on the above analysis, the impact of cascading failures can be analyzed from a spatiotemporal perspective. Temporally, within the same typhoon interference period, cascading failures accelerate the typhoon's impact on the power system. Spatially, in addition to physical faults along the typhoon's path, cascading failures expand the area affected by the typhoon.

[0103] The system's weak lines are divided into two categories: 1. Weak lines that are prone to causing fault propagation; 2. Weak lines that are easily affected by faults.

[0104] 1. Transmission characteristics and routes

[0105] Lines with propagation characteristics include two categories: physical faults and overload faults. These lines typically cause significant load losses in the system. Considering the poor effectiveness of reinforcing a single line, this embodiment uses a grouping resilience enhancement method to verify the effect. The grouping of lines with weak propagation characteristics and their vulnerability values ​​are shown in Table 3. The larger lines are mainly of two types: important channels for generators to transmit power externally and important channels for power supply to the region, such as L27, L46, and L33. Once these lines are disconnected, the system will experience disconnection, causing a large power deficit within the subgrid and a large-scale power flow shift.

[0106] Table 3 lists the first 24 weak propagation paths.

[0107]

[0108] The following method was used to reinforce a certain component: ensuring that the component did not fail in any simulation round, i.e., adaptively increasing its wind resistance or maximum static transmission capacity, and evaluating its resilience using two types of indicators: load loss and line loss. Group 0 is the control group, which did not receive any reinforcement measures; Groups 1-6 reinforced the lines grouped in Table 3; and Group 7 reinforced only the transmission lines with the highest weakness ranking that had experienced physical faults. The reinforcement effect was... Figure 8 As shown in Table 4, the results indicate that the load loss of the faulty line in the first reinforced group was reduced by 15.62%, the line loss was reduced by 6.11%, and the toughness was improved by 27.39%. From Group 1 to Group 6, the toughness improvement effect gradually weakened, and even the results were lower than those of the control group.

[0109] Table 4. Toughness assessment results for each reinforcement group

[0110]

[0111] 2. Identification of susceptible circuits

[0112] Vulnerable lines are always overloaded lines, and these lines are easily affected during fault propagation. This embodiment uses overload control during system operation to mitigate the impact of faults on these lines. It also considers the control exerted by grid operators over transmission line overloads, calculating resilience values ​​under different transmission line operating capacity coefficients η. The physical meaning of η is consistent with ξ in equation (8). The first 20 vulnerable lines and their groupings are shown in Table 5.

[0113] The toughness assessment results of each group after overload control are as follows: Figure 9 , Figure 10 As shown in Table 5, the results indicate that the system resilience varies significantly depending on the control methods used for different groups. For the first group of lines, strict overload control was applied throughout the simulations, resulting in a 13.54% reduction in load loss, a 7.22% reduction in line loss, and an 18.98% improvement in resilience. However, the resilience improvement gradually weakens from Group 1 to Group 4. This is because overload control on less vulnerable overloaded lines may cause overload on more vulnerable lines, leading to a poorer resilience improvement. Therefore, during extreme weather conditions, power grid operators can implement strict transmission line overload control measures to eliminate line overloads with minimal load reduction, preventing fault propagation and avoiding larger accidents, thereby improving power system resilience. This embodiment also provides different resilience assessment results for different η values, which can guide operators to adopt different line capacity coefficients for overload control of critical overloaded lines under fault conditions, based on acceptable control costs and consequences.

[0114] Table 5 lists the top 20 vulnerable lines.

[0115]

[0116] Table 6. Resilience assessment values ​​for different line capacity coefficients in each group.

[0117]

[0118] Comparing the two ranking methods of vulnerable lines in Tables 3 and 5, there is a high degree of overlap between the lines ranked high in susceptibility and those ranked high in transmissibility. This indicates that these lines have a relatively weak overall capacity to cope with typhoons and require focused monitoring and protection by operational staff during critical stages of system operation.

[0119] The scope of protection claimed by this invention is not limited to the specific embodiments described above. Moreover, for those skilled in the art, this invention can have various modifications and alterations. Any modifications, improvements, and equivalent substitutions made within the concept and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A power system resilience assessment modeling method considering cascading overload faults under typhoon disasters, characterized in that: Includes the following steps: S1: Estimation model for transmission line operating capacity under high wind speeds: (1) Estimation model for dynamic limit carrying capacity of the line: Based on the principle of thermal balance, the ultimate current carrying capacity of the transmission line is calculated, that is, the heat loss on the surface of the transmission line is equal to the heat absorbed at that moment, as shown in equation (1): In the formula: T s,max For the line's extreme temperature; I max K is the ultimate carrying capacity; k1 and k2 are constant terms, and the specific calculation formulas are shown in equations (2) and (3): In the formula: k f R is the thermal conductivity of air. e T is the Reynolds number; s T a Indicates the surface temperature of the line and the ambient temperature; v represents the ambient wind speed; d represents the outer diameter of the conductor; μ f α is the aerodynamic viscosity; α is the solar heat absorption coefficient; q se R(T) represents solar radiation intensity. s,max ) indicates the line temperature at T s,max The AC resistance value at that time; Considering the maximum permissible power flow limit of the transmission line The equation for the change of the power flow limit value of the line with wind speed is: In the formula: F max (v) represents the tidal current limit value of wind speed v; F max (v0) represents the tidal current limit value under normal wind speed; (2) Transmission line operation capacity estimation model τ is taken from each weather region within a certain time period. L The minimum value is taken as the actual τ of the line. L The value is shown in equation (5); in order to ensure computational efficiency without losing versatility, the transmission line is divided into an appropriate number of equal segments according to its location, and the wind speed of each segment is equal to the wind speed at the center of the segment. It is assumed that the line L is composed of d segments connected in series: t L,t =min{τ L,t,q ∣q∈D l } (5) In the formula: τ L,t τ represents the dynamic capacity expansion rate of line L at time t; L,t,q D represents the dynamic capacity expansion rate of the transmission line calculated based on the weather conditions of the q-th segment at time t; l Represents the set of segments of line L; S2: Power system fault model under the influence of typhoon: (1) Wind-induced physical line breakage model Batts, a parameterized model of typhoons, is used to simulate the wind field of typhoons. The wind speed in the model is related to the geographical distance from the typhoon center. The probability of a fault in the qth segment of the Lth transmission line at time t is: In the formula: v L,t,q Let q be the center wind speed of line segment q of line L at time t; V is the design wind speed of the transmission line. The transmission line is divided into segments according to formula (5). Assuming that the design wind speeds of all segments of line L are the same, the line failure rate is: (2) Wind-induced overload shutdown model Based on reliability theory, the overload failure rate of a transmission line can be expressed as a piecewise function as the power flow increases. This allows for the analysis of the spatiotemporal variation of the transmission line failure probability and the intrinsic relationship between the overload outage probability and its operating limits. The failure probability of a line under the influence of a typhoon can be expressed as follows: In the formula: F L,t This represents the real-time power flow of line L at time t; This represents the upper limit of power flow for line L at time t; This represents the power flow limit value of line L at time t; where, ξ is the limiting multiple, with a value of 1.3; S3: Power system fault evolution model under the influence of typhoons: Considering the differences in simulation periods for independent successive faults and overload faults, as well as the differences in the calculation methods for disconnection timing, this fault process is modeled as a two-dimensional time-series dynamic fault process that considers both physical faults and cascading faults caused by typhoons. This includes a typhoon physical fault retrieval model and a typhoon-induced cascading fault retrieval model. (1) Typhoon physical fault retrieval model: A sequential Monte Carlo simulation with equal time intervals is used to preserve the temporal characteristics of component states during a disaster. The component operating time and failure time are sampled according to the failure probability to obtain the system state sequence and the ambient wind speed of each line at that moment. The specific steps are as follows: Step 1: Initialize power grid data and disaster information, set the initial simulation time t, input the sampling interval Δt, and the disaster duration T; Step 2: Update the typhoon forecast information at time t; Step 3: Calculate the instantaneous failure rate of the components based on the typhoon wind speed at that moment and sample the component status; Step 4: Determine if the component state at this moment is the same as the previous moment. If they are the same, merge them with the previous state and modify the state duration. If they are different, update the component state. Step 5: Proceed to the next simulation moment, repeating steps 2-4 until the typhoon moves away; (2) Model for retrieving chain failures caused by typhoons: A cascading failure retrieval model that considers the occurrence time of overload shutdown failures is adopted. The specific steps are as follows: Step 1: Input the fault time series set H caused by the typhoon in terms of time dimension; Step 2: Input the fault information at time h=1, and the system simulation will begin; Step 3: Update the network topology, determine if the system has been unblocked, if it has been unblocked, reselect the load balancer and perform islanding processing based on the optimal load shedding model, if it has not been unblocked, proceed to Step 4; Step 4: Update system performance and calculate the load loss caused by the failure at that moment; Step 5: Based on the system's operating status at this moment, filter all overloaded lines and predict their interruption time; Overload line interruption time prediction takes into account the dynamic limit value of accumulated overload line load: In the formula: O L (t,Δt) represents the cumulative overload of line L during the time interval Δt starting from time t; This represents the power flow limit value of line L at time t; F L,t This represents the power flow value of line L at time t; it should be noted that... It changes dynamically over time and is updated during the calculation as the simulation progresses; Step 6: Determine if the overloaded line set is empty. If it is not empty, find the overloaded line in the overloaded set that takes the shortest time to stop and proceed to Step 7. If it is empty, proceed to Step 8. Step 7: Determine if there is a physically faulty line within the selected overload line disconnection time. If not, disconnect the overload line and update the simulation time; otherwise, proceed to Step 8. Step 8: Disconnect the (h = h + 1)th physically faulty line; Step 9: Proceed to the next simulation and repeat steps 3 through 8; Step 10: Output the timing fault chain; S4: Power System Resilience Assessment Model under Typhoon Impact Multiple rounds of typhoon simulations were conducted for S2 and S3, and the overall resilience value was calculated based on resilience assessment indicators: In the formula: γ resilience (λ) represents the system resilience value; λ count (K) represents the total number of simulated typhoon rounds; S0 represents the system performance under normal operating conditions; S k (t) represents the system's performance curve in the k-th simulation round; T0 is the moment when the typhoon begins to hit the system; T5 is the moment when the system's performance returns to normal. S5: Identification indicators for vulnerable power lines under the influence of typhoons: A fault evolution graph is constructed based on an offline fault evolution dataset from multiple rounds of single typhoon simulations; after performing M simulations, M fault chains can be obtained for construction. Construct the m-th fault chain node L i and node L j Weights considering timing, consequences, and cumulative failure effects Consider three scenarios: (1) Only overload faults occurred during this stage: Where: ΔP ij m This represents the load loss caused by the overload fault of line j following the fault of line i in the m-th fault chain, and describes the consequences of the loss of line j. This represents the order of line j in the m-th fault chain, describing the importance and timing of line j in the fault chain; Considering that the importance of a faulty line decreases as it approaches the end of the fault chain, we take... P is a coefficient in the denominator of the fault weighting; j The probability of overload failure occurring during this stage is represented by equation (12); This indicates that the load loss of the j-th order fault is affected by the preceding fault disconnection and load loss; (2) Only physical faults occur during this stage: In the formula, h represents the representation of typhoon topology interference in the graph using virtual nodes to illustrate the timing of physical fault occurrence; j represents the faulty line caused by the typhoon; ΔP hj m This indicates the consequence of a physical fault causing line j to disconnect; the physical meanings expressed by each formula in equation (13) are similar to those described in equation (11), the only difference being that the cause of the physical fault is represented by a virtual node not included in the fault evolution diagram, and the virtual node represents the topological disturbance of the typhoon; P j The probability of a physical line break during a typhoon is represented by equation (14); (3) Both overload faults and physical faults occur simultaneously during this stage: In the formula: η ω With η ρ These represent the proportions of load losses caused by overload faults and physical faults, respectively, within the total load loss of that phase. Finally, the key nodes in the merged fault evolution diagram reflect the vulnerability of the power system under typhoon. By calculating the in-degree and out-degree of the weighted node j in the fault evolution diagram, the line susceptibility and propagation can be classified and identified, namely the degree of influence of node j on other faulted lines and the degree of influence of node i's fault on other line faults. In the formula: D in With D out These are the weighted in-degree and out-degree of node j, respectively, and D in This indicates that line j is more susceptible to damage from other faulty lines; D out This indicates that line j has higher propagation potential and is more likely to affect other lines, causing them to malfunction; among which: To avoid excessive differences in vulnerability indices across different lines, a unified method is adopted to eliminate such influences, where: D j ∈{D in ,D out };D' j ∈{D′ in ,D' out }:

Images