Fault-Chain-Based Prevention and Control Method for Typhoon Disaster

Summary

A fault-chain-based prevention and control method for typhoon disasters is proposed. By modeling typhoon wind fields, the calculation of the failure probability of transmission branches can be performed. Screening of high-risk branches for fault chain analysis and implementing prevention and control measures for power grids under typhoon conditions can then be done.

Abstract

Extreme disasters such as typhoons pose a great threat to the operational integrity and stability of power grids, making pre-disaster preventive and control measures increasingly important. Motivated by the limitations of conventional N-1 and N-2 security criteria in addressing spatially correlated and probability-driven failures, this paper proposes a fault-chain-based prevention and control method for typhoon disasters. A typhoon wind field model is combined with a transmission branch vulnerability model to quantify the spatiotemporal failure probabilities of transmission branches, based on which high-risk branches under forecast typhoon scenarios are identified. Taking these branches as initial contingencies, a systematic fault chain search is performed to enumerate critical cascading outage paths, and a risk index is established by integrating the failure probabilities at each stage with the corresponding load shedding. On this basis, a risk-oriented preventive control optimization model is formulated, in which generator outputs and load shedding are coordinated to minimize the expected consequences of high-risk fault chains while satisfying operational constraints. Case studies on the IEEE 39-bus test system and the Hainan power grid under Typhoon Yagi verify that the proposed method can effectively capture typhoon-induced failure characteristics, significantly reduce expected load curtailment, and alleviate excessive control costs compared with traditional deterministic criteria. The results demonstrate that the proposed method provides a practical and economical decision-support tool for online operation of power grids under extreme typhoon conditions.

Introduction

Strong winds, heavy rainfall, thunderstorms, and other factors associated with typhoons can cause equipment failures in urban power systems, posing a serious threat to regional energy security and causing great damage to urban economies¹. Extreme weather, such as typhoons, may also trigger chain failures in the power system, resulting in large-scale power outages². Super Typhoon Lekima 2019 landed in China's Zhejiang Province with heavy rainfall, causing 72 substations and more than 4,000 lines on the local power grid to be out of service and 7.72 million users to be without power³. In February 2021, the state of Texas in the United States experienced a prolonged and widespread power outage in the region due to a winter storm that resulted in the icing of transmission grid lines and interlocking failures of transmission equipment⁴. According to statistics, more than 80% of global power grid outages are triggered by extreme weather disasters such as typhoons and rainstorms, causing direct economic losses to the power grid of more than $30 billion per year, and showing a rising trend year after year⁵. It is necessary to strengthen the abilities of the power grid to cope with extreme accidents. Among them, preventive control is an important means to mitigate the likelihood of cascading failures within power systems⁶. Preventive measures can effectively block interlocking faults, reduce the scope of outages and restoration time, and the investment in prevention is much lower than the cost of repair and compensation after a fault.

Typhoons are divided into three main parts: the eye of the typhoon, the wall of the eye, and the spiral rain band, whose radius usually varies in tens of kilometers⁷. The radial distribution of typhoon wind speed exhibits a sharp increase near the eye, reaching a peak at a certain distance, and then declines rapidly further outward. Accurate representation of the key features of a typhoon wind field requires constructing a wind field model grounded in the structural parameters of the typhoon⁸. Typhoon wind field modeling plays a critical role in analyzing the impact of typhoon-induced hazards on transmission networks, and the selected typhoon wind field model should satisfy the demand for simulation accuracy as well as computational efficiency. In engineering applications, the computation of the model must account for the strong coupling between the pressure and velocity fields⁹, and obtaining an accurate nonlinear solution of this model is often computationally challenging, so in practical calculations, it is often necessary to obtain only its approximate solution. In the 1970s, Russell was the first to introduce a stochastic approach for simulating the developmental process of typhoons¹⁰, and extensive efforts have been made by researchers worldwide to develop and refine typhoon wind field models, along with associated computational methodologies, and a lot of modeling methods have emerged. The Batts typhoon model assumes that the typhoon moves in a straight line after landfall, which is inconsistent with reality. Holland and other typhoon models simulate the typhoon with high accuracy, but it remains challenging to fully satisfy practical engineering requirements^11,12. In this paper, Jelesnianski wind field model is used to simulate the movement and decay process of typhoon disaster and to find the magnitude of wind speeds at various locations within the impact area of typhoon disaster¹³.

In the current research on chained faults, in terms of fault chain search, the branch with the largest risk index is usually selected as the lower open branch of the fault chain, but it is possible to miss some of the fault chain paths with more serious consequences¹⁴. In the preventive control of fault chain, the preventive control scheme is mostly given from the perspective of relay protection, with the goal of maximizing the safety margin of the grid, but it cannot reflect the risk consequences of fault chain on the grid¹⁵. Some studies combine the preventive control of the fault chain and blocking control for coordinated optimization, and at the same time give the pre-fault preventive control scheme and the blocking control scheme for the specified fault chain^16,17. But the optimization process only considers the fault probability of the lines within the chain fault path, and neglects the fault probability associated with transmission lines outside the cascading failure path, which may lead to the problem of the control scheme to change the propagation path of the fault chain, makes the proposed control scheme invalid, and the coordinated optimization model established is usually difficult to solve^18,19.

This paper tests the hypothesis that a fault-chain-based preventive control framework, which explicitly integrates typhoon wind-field characteristics, transmission branch vulnerability, and cascading outage mechanisms into a unified risk-oriented optimization model, can provide more effective and economical decision support for power system operation under extreme typhoon conditions than traditional deterministic N-1/N-2 criteria. Specifically, it is hypothesized that by 1) quantifying branch failure probabilities driven by spatially correlated typhoon loads, 2) identifying critical fault chains and evaluating their associated risk in terms of expected load loss, and 3) optimizing pre-contingency generator outputs and load shedding with respect to these fault-chain risks, the proposed method can more accurately capture disaster-induced failure behavior, significantly reduce expected load curtailment and blackout risk, and avoid excessive or unnecessary preventive actions compared with conventional security standards.

In this paper, the branches with high failure probability under extreme weather are screened out by using the typhoon wind field model and the transmission branch vulnerability model. The high-risk branch under extreme weather is used as the initial open branch to search all possible fault chains. By adjusting the output of power system units and shedding loads, the expected consequences of each fault chain can be mitigated.

The proposed method requires input including typhoon wind field data, grid topology, and operating parameters. Typical assumptions include constant maximum wind radius and simplified series-structure reliability modeling for transmission branches. However, computational efficiency may be challenged when applied to very large-scale systems due to the combinatorial nature of fault chain enumeration.

Protocol

Calculation of line failure probability under typhoon disaster

Overhead transmission lines and towers supported circuits are highly vulnerable to the spatially varying wind loads imposed by a translating typhoon²⁰. When the wind speed of a typhoon is too high, it is very easy to cause transmission equipment to fail^21,22. Empirical wind field formulations, such as the Jelesnianski wind field model, enable the reconstruction of time-varying wind speed fields over the storm's footprint. When these wind field outputs are coupled with the vulnerability models for individual line sections or towers, it becomes possible to translate spatiotemporal wind loads into cumulative fault probabilities²³.

Typhoon wind field model

The simulation in Jelesnianski's model was divided into two steps: firstly, the axisymmetric wind field of the typhoon was derived based on a predefined analytical formulation, and the translational wind field associated with the typhoon's movement was superimposed to obtain the resultant wind field. This typhoon model utilized parameters such as the typhoon's highest wind speed and the radius of highest wind speed to estimate the tangential wind component of the cyclonic circulation, which was given in the following formula:

     (1)

Where V_s is the tangential wind speed of the typhoon circulation at a distance r  from the typhoon center; V_max is the highest wind speed; R₀ is the radius of the highest wind speed.

The moving wind field of the typhoon model was then calculated using the following equation:

     (2)

Where V_d is the speed of the typhoon at a distance r from its center; V_c is the speed of movement of the typhoon center.

When 7th-level wind circle data were available, the radius of maximum wind was typically estimated as 1/10th of the radius of the Beaufort scale level-seven wind field. For typhoons lacking observational data on the radius of the level seven gale wind field, the highest wind radius was calculated by an empirical relationship equation²¹:

     (3)

Where R_k is an empirical constant, usually between 30 and 60; P₀ is the pressure at the center of the typhoon.

The wind field velocity formula for the typhoon model was obtained by superimposing the typhoon circulation tangential wind speed V_s and the moving speed V_d as follows:

When 0 ≤ r ≤ R₀

     (4)

     (5)

When R₀ ≤ r ≤ ∞

     (6)

     (7)

Where V_x is the velocity component of the typhoon on the x-axis at a distance r from the center of the typhoon; V_y is the velocity component of the typhoon on the y-axis at a distance r from the center of the typhoon; V_dx and V_dy are the two components of the speed of the center of the typhoon on the x-axis and y-axis; x₀ and y₀ are the two coordinate values of the typhoon center on the x-axis and y-axis; x and y are the two coordinate values on the x-axis and y-axis at a distance r from the center of the typhoon; θ is the typhoon inflow angle.

Figure 1 shows a schematic of the movement process of the typhoon after landfall. From the typhoon wind field model, it can be seen that the horizontal wind speed of the typhoon increases and then decreases from the center outward. Taking a position O on the transmission branch as an example, at the moment of t₁, the maximum wind radius of the typhoon is r_max(t₁), and the distance between the center of the typhoon and O is d(t₁). This time, d(t₁) is greater than r_max(t₁), and as the typhoon moves, the distance between O and the typhoon center decreases, so the wind speed at O increases. At the moment of t₂, d(t₂) is less than r_max(t₂) and d(t₂) is decreasing, so the wind speed at O decreases. At moment t₃, d(t₃) continues to increase but is less than r_max(t₃), so the wind speed at O will increase. Similarly, at t₄, d(t₄) continues to increase and is larger than r_max(t₄), so the wind speed at O decreases as the typhoon center moves away. It can be seen that the wind speed at any location on the transmission branch changes with time, and even on the same transmission branch, the wind speed changes at different locations are not the same.

Transmission branch vulnerability model

The strong impact of typhoon disasters on the transmission network may cause transmission branch outages and potentially trigger regional or widespread power outages²⁴. The probability of failure in different segments of the same transmission branch is not the same. Due to the large size and complex structure of the transmission grid, modeling the vulnerability of transmission branches can lead to huge computations if every transmission device in it is modeled and analyzed²⁵. Therefore, this section only focuses on transmission line segments and towers to establish a transmission branch vulnerability model that reflects the mapping relationship between transmission branch failure probability and typhoon wind speed. Both temporal and spatial dimensions will be used to model the probabilistic vulnerability of transmission branch failures, reflecting the impact of typhoon disasters. It takes the wind speed information that changes in space and time within the typhoon wind field as the input quantity, and the cumulative failure risk of overhead components (including line segments and support structures under typhoon impact) is evaluated based on local wind speed fluctuations. Subsequently, the fault probability of each transmission path is determined through the application of a series-structure model under established reliability assessment frameworks.

When solving for the failure probability of a certain transmission equipment, it was possible to solve for its failure rate first, and then select an appropriate stochastic process model based on its failure characteristics to determine its failure probability during the period affected by the typhoon disaster. Failure rate was defined as the number of failures of transmission equipment per unit of time²⁶, which reflected the average intensity of its failures during the typhoon impact time. For ease of calculation, it was assumed that the transmission line sections connected between every two transmission towers were subjected to the same wind speed, and the total duration T_w of the typhoon disaster was divided into T time intervals of length Δt, with the wind speed remaining constant during each time interval. The schematic diagram of the m transmission branch was shown in Figure 2, where the failure rate of the l transmission line section t at the time interval could be calculated using the following equation:

     (8)

Where v_m,l(t) is the typhoon wind speed sustained by the I transmission line section of the m transmission branch at the t time interval; v_d,line is the design wind speed of this transmission line section, which was taken as 30 m/s in this paper; Δl is the length of this transmission line section in kilometers. Since the typhoon wind speed remained constant over the range of lengths of each transmission line section and over the range of time intervals selected for typhoon impacts, the failure rate of individual transmission line sections remained constant. Accordingly, the accumulated risk of failure for the segment l within the transmission path m during the typhoon exposure period T_w could be evaluated using the following expression:

     (9)

Similarly, the failure rate of the k transmission tower of the m transmission branch at the t time interval of the typhoon impact time T_w could be calculated by the following equation:

     (10)

Where v_m,k(t) is the typhoon wind speed that the k transmission tower of the m transmission branch is subjected to in the t time interval; γ is a model parameter, the value range was 0-0.4, in this paper, γ was set to 0.2; v_d,tower is the structural wind load threshold of the transmission tower, which can be determined according to the destructive test; this paper took 35 m/s.

Correspondingly, the cumulative failure probability of the k transmission tower of the m transmission branch during the typhoon impact time T_w was denoted as:

     (11)

Transmission branches were viewed as a series model consisting of multiple transmission line sections in series with multiple transmission towers. According to the method of calculating the probability of failure of the series model in the reliability assessment theory, assuming that the failures of each transmission line section and pole tower are independent of each other, the failure of any transmission line section or pole tower might lead to the interruption of the transmission of electric energy of the entire transmission branch circuit²⁷. Therefore, the probability of failure of the m transmission branch was calculated using the following equation:

     (12)

Where L is the number of transmission line segments included in the m transmission branch line; K is the number of transmission towers included in the m transmission branch.

Prevention and control measures based on fault chains

To mitigate the risk of cascading failures and large-scale blackouts triggered by faults on high-risk transmission lines during extreme disasters, the power system requires preventive control. Based on the previous section, each line with a high failure probability under extreme disasters was obtained. Each high-risk branch was sequentially used as the initial open branch for the fault chain search. Based on all fault chains, the prevention and control method was carried out, aiming at minimizing the impacts of cascading failures and providing decision support for grid dispatch operators²⁸.

Proposed method

Figure 3 outlined the step-by-step framework of the proposed prevention and control method, which addressed fault chains under extreme weather scenarios.

Data loading and initial fault chain identification

First, load all basic input data, such as the power grid model, normal operating mode, and meteorological information under extreme disaster. The power grid model was in MATPOWER (.m) format, containing bus parameters, generator specifications, branch parameters, and network topology.The meteorological forecast data for the extreme disaster was in JSON format, providing the typhoon center coordinates,translation speed, radius of maximum wind, and central pressure.

Next, screen high-risk transmission lines by calculating the failure probability for all branches. This process involved two core computational models.The Jelesnianski typhoon wind field model was first executed to compute the time-varying wind speed. Subsequently, the transmission branch vulnerability model was applied to calculate the failure rate for each line segment and tower based on the local wind speed.

Finally, select one or more high-risk branches from the initial contingency set as the initial outage branches to initiate fault chain searching. Disconnect the selected branch, modify grid topology parameters, perform DC power flow calculation on the target power grid, identify overloaded branches as subsequent outage branches, and repeat this process. The fault chain search terminated when the system collapse occurred, the preset maximum search depth was reached, or no additional overloaded branches were found.

Fault chain evaluation and optimization model solving

This phase established the optimization framework, solved the model, and validated the final solution through the following procedure.

First, establish a piecewise linear function representing the influence of transmission line outages on branch power flows. Compute the risk value of each fault chain based on DC power flow calculations. Specifically, risk values were determined by multiplying the probability of each fault chain and the minimal load shedding value required to ensure branch power flow safety. Select fault chains with higher risk values and incorporate them into the candidate fault chain set.

Next, execute the two previous steps for each line in the initial contingency set until all branches have been processed. This systematic iteration ensured comprehensive coverage of all potential fault initiation points, resulting in a complete candidate fault chain set that represents the union of all identified high-risk fault paths.

Finally, solve the optimization model using commercial solvers such as GUROBI and evaluate whether new severe fault chains occur after optimization. This validation was performed by re-executing the fault chain search process with the optimized generation dispatch. If new fault chains emerge, incorporate them into the candidate fault chain set and repeat the optimization process. If no severe fault chains were generated, output the optimized generator power output and load shedding plan to reduce the risk of cascading failures.

Final output and archival

Output the optimized generator power output and load shedding plan. Systematically archive all relevant input data, configuration files, intermediate results, and the final output scheme for documentation and reproducibility.This comprehensive archival practice ensured full reproducibility, facilitated post-event analysis, and provided reference cases for future grid resilience enhancement projects.

Fault chain search

One or more branches with high fault probability were selected for fault chain search. Take the selected high-risk branches as the initial open branches of the fault chain, disconnect them, modify the network parameters, carry out DC power flow calculation for the target grid, take all the overloaded branches as the next stage open branches of the fault chain in turn, and repeat the process. The fault chain search terminated when the stopping condition was satisfied. Then, all the fault chains starting with this high-risk branch were obtained.

Disregarding the influence of the external environment, when the line power flow did not exceed its power flow limit, the probability of transmission line fault tripping was the hidden fault probability of relay protection, whose value was close to 0. In the process of the development and propagation of the fault chain, the grid dispatchers tended to take the corresponding blocking measures, so that the depth of search of the fault chain would not exceed the set maximum depth (usually 4). The grid islanding triggered by a fault chain usually leads to the occurrence of a major blackout. Therefore, in this paper, the stopping condition of the fault chain search was set as: 1) the grid islanding occurred; 2) the fault chain search reached the maximum search depth; and 3) a certain stage of the fault chain search did not lead to overloading of any branches. The fault chain search stopped when any of the conditions were satisfied.

Utilize a piecewise linear function to describe the relationship between the transmission line's fault probability and line power flow, given by:

     (13)

Where p_l is the probability of fault occurrence on l; p_l is the real power flow on l; P_l,max is the transmission capacity limit of l; P_H is the probability of hidden protection failure; b is the overload threshold multiplier, typically set to 1.4, which implies that if the power flow transmitted by a line exceeds 1.4 times its rated transmission capacity, protection devices will operate and trip the line, resulting in a fault probability of 1.

Calculation of the risk value for the fault chain

Suppose a certain fault chain involves faults on k transmission lines. Upon the removal of these k lines, the minimum level of load curtailment ensuring secure DC power transfer within the network was calculated. The objective function was then defined as follows:

     (14)

Where n_B represents the total count of buses in the power system; D_{i_cut} is the amount of load shedding at the node i. The constraints to be satisfied include:

Node load shedding constraints

     (15)

Where S_N is the set of buses in the power system; D_i is the original load at the node i.

Generator output constraints

     (16)

Where S_G is the set of generator nodes in the power system; PG_i denotes the power output from the generator at node i; PG_{i_min} and PG_{i_max} represent the minimum and maximum technical generation limits at the node i, respectively.

Line power flow security constraints

     (17)

Where S_L is the set of transmission lines in the power system; P_ij is the power flow on line ij; P_{ij_max} is the transmission capacity limit for the line ij.

Node power balance constraints

     (18)

DC power flow constraints

     (19)

Where θ_i and θ_j denote the voltage angles at buses i and j, x_ij is the reactance of the line ij.

For a given fault chain L with v stages, the probability of its occurrence P_L is:

     (20)

Where p_l0 is the probability of the initial failure event of the event chain; P_l1 ~ P_lv are the probabilities of occurrence of each stage in the fault chain. The risk value R_L for the fault chain L  is defined as:

     (21)

Where D_L is the amount of load shedding caused after the occurrence of the fault chain L.

The fault chain search allowed multiple high-risk branches to be simultaneously selected as initial outages. Assuming independence among initial branch failures, the joint probability of the initial event was the product of the independent failure probabilities of each high-risk branch.

Prevention and control optimization model

Based on the obtained set of fault chains, construct a prevention and control optimization model. The objective function was formulated as:

     (22)

Where n_G represents the total number of generator nodes; a_i and ΔPG_i  represent the cost coefficient and the power adjustment amount of the generator node i, respectively; ΔL_j represents the amount of load shedding at the node j. n_R refers to the number of fault chains; R_k denotes the risk value of the fault chain k; and b is the cost coefficient of load shedding.

The constraints are as follows:

Power balance constraint

     (23)

Generator output adjustment constraints

     (24)

Line power flow security constraints

     (25)

Where PTDF is the power flow transfer distribution factor matrix of the grid; P is the power injection vector; ΔPG is the generation adjustment vector; and F_max is the vector of line transmission capacity limits.

Considering the propagation stage t in a fault chain (1 ≤ t ≤ v), assume the preceding outage branch is km. The impact of the km branch outage on the flow redistribution in the remaining network was assessed using the DC power flow model. The grid operation satisfied the following conditions before the outage of the branch km

     (26)

After the outage of the branch km

     (27)

Neglecting the small second-order terms, it becomes:

     (28)

Combining equations (26) and (28), the following is obtained:

     (29)

Further simplification leads to:

     (30)

Where P_km denotes the active power flow on branch km; is a row vector in which the k-th entry is 1, the m-th entry is -1, and all remaining components are zero.

According to equation (30), at propagation stage t of the event chain L, when branch km was disconnected, the incremental active power flow in subsequent branches was represented as a linear function related to the active power flow of branch km. Further, based on equation (13), this increment was directly mapped to the fault probabilities of subsequent branches.

In the power flow optimization model established in this section, the objective function involved the product of fault probabilities of each stage of the event chain. Considering the probability of failure at each stage of the fault chain as variables, the model was difficult to solve if the order of multiplication of the variables is too large. Employing heuristic algorithms such as particle swarm optimization or genetic algorithms typically makes it difficult to obtain global optimal solutions. Therefore, this paper treated the multiplication product of the failure probabilities of different stages in the fault chain as a single new variable, thereby effectively reducing the multiplication order of variables in the objective function. Afterwards, commercial optimization solvers such as CPLEX and GUROBI were used to obtain solutions.

Results

Case analysis of the typhoon wind field model

This section presents a case study based on Typhoon Yagi, which made landfall in Hainan Province, China, in 2024. The wind field data used for modeling are extracted from weather station forecasts issued 24 h prior to the event. Using the Jelesnianski model, the spatial distribution of wind speed can be computed at any given moment. Combined with the transmission branch vulnerability model, this enables the assessment of failure probabilities for individual branches within the Hainan Grid.The duration T_w is set to 1 h. The wind speed is assumed to remain constant during this period T_w, hence Δt = T_w = 1 h.

Hourly wind speed data in Haikou City were analyzed alongside the corresponding number of damaged lines, with results presented in Figure 4. A clear positive correlation is observed: as wind intensity increases, the number of line failures rises accordingly. By integrating the predicted meteorological conditions with the wind field modeling framework proposed here, the method more effectively captures the actual grid failure risk.

Typical routes were selected from four cities-Haikou, Danzhou, Sanya, and Qionghai, each measuring 10 km in length with 500 m intervals. Using the method proposed in this paper, the probability of line failure under maximum wind speeds was calculated and compared with the ratio of failed lines to total lines during actual typhoon events, as shown in Figure 5. The results demonstrate good consistency between the calculated failure probability and the observed failure ratio: The failure probability increases as the maximum wind speed in the relevant cities rises, further validating the practicality of the model developed in this paper when combined with typhoon forecast information.

Prevention and control optimization based on the fault chains

The effectiveness of the proposed approach is demonstrated through a simulation conducted on the IEEE 39 bus test system. Branches 1-2, 2-3, and 4-5 are assumed to be high-risk under extreme disaster conditions, as shown in Figure 6. The active power flow limit of each branch is set to 0.9 times its thermal flow capacity, and the fault chain forecast depth d_max is set to 3. Generator dispatch cost coefficients, output bounds, and other information are listed in Table 1. The risk-cost coefficient b is 100/MW, and the failure probability of the initially tripped branch is assumed to be 1. The probability of a hidden protection failure P_H is set to 0.01. After formulating the model, the editor used MATLAB R2022b to call the GUROBI solver. Solution time: 0.14 s, gap: 0.0000%.

By performing the event-chain search, it was found that opening lines 2-3 or 4-5 does not overload any remaining lines, and hence no event chains originate from these outages. However, when lines 1-2 are disconnected, four possible event chains may occur: [1-2, 2-3, 26-27], [1-2, 2-3, 25-26], [1-2, 2-3, 17-18,26-27], [1-2, 2-3, 17-18, 25-26].

The search result of the fault chain starting with branch 1-2 is shown in Figure 7. Among these, the fault chain [1-2, 2-3, 25-26] causes no load shedding, and the risk of the fault chain [1-2, 2-3, 17-18, 25-26] is much lower than that of the other two fault chains. Therefore, only the fault chains [1-2, 2-3, 26-27] and [1-2, 2-3, 17-18, 26-27] are retained for subsequent prevention and control optimization.

Table 2 presents the outcomes of the prevention and control optimization, while Figure 8 depicts the corresponding optimized fault chains initiated from branch 1-2. After adjusting generator outputs, the expected load shedding resulting from the related fault chains is reduced from 11.835 MW to 0.670 MW, which reveals that the risk of the IEEE 39-bus system decreases substantially. The validation after optimization confirms that no additional fault chains arise, indicating that the prevention and control solution can be implemented directly to support system dispatchers.

Case study on a real-world power grid: Hainan system under typhoon Yagi

To further validate the practical applicability of the proposed method, a case study was conducted based on the Hainan Power Grid in China during Typhoon Yagi in 2024. This case focuses on the effectiveness of the method in large-scale systems and its advantages over the conventional N-1 and N-2 security criteria.

Prevention and control methods compared with N-2 safety criteria

Under the impact of Typhoon Capricorn, multiple lines in the Hainan power grid experienced outages. The power flow distribution of the regional grid at 19:50 on September 6 is shown in Figure 9. In the figure, red indicates the 500 kV voltage level, black indicates the 220 kV voltage level, blue indicates the 110 kV voltage level, solid lines represent operational lines, and dashed lines represent outage lines.

At this moment, lines LQ-JD and YZU-WQ were high-risk lines. Considering the cascading failure process triggered by the outage of these two lines, the power flow distribution of the regional grid after the outages of lines LQ-JD and YZU-WQ is shown in Figure 9. The power flow on line DL-WC increases to 173.9 MW, far exceeding its long-term current-carrying capacity of 82 MW. With a load factor reaching 214%, chain tripping of the line becomes unavoidable. This will result in the isolated operation of WQ, JD, DL, and their associated 110 kV substations. Since the load is below the minimum technical output of WQ Plant's units, maintaining frequency stability during isolated operation becomes difficult, ultimately leading to a blackout.

Preventive control optimization of the regional grid is performed. The optimized power flow distribution is shown in Figure 10. One unit at the WQ plant is shut down, and the output of the remaining unit is adjusted to 221.3 MW. After the LQ-JD and YZU-WQ lines are tripped, the power flow on the DL-WC line is only 58.8 MW, thereby avoiding cascading faults. Considering the N-2 security criterion, if only N-2 faults on WQ substation feeders are considered, adjusting WQ plant output to 133.5 MW would be required to ensure safe power flow on DL-WC. This control approach incurs excessively high costs.

Prevention and control methods compared with the N-2 safety criteria

The power flow distribution of the regional grid at 19:58 on September 6 is shown in Figure 11. At this moment, both lines LQ-JD and YZU-WQ are open due to typhoon damage. Lines YZG-DY (failure probability P₁=0.1) and DY-YZU (failure probability P₂=0.7) are included in the high-risk line set. The current-carrying capacity of the transmission line TP-PT is 82 MW.

Considering the cascading failure process triggered by a single branch disconnection, the disconnection of either the YZG-DY or DY-YZU line would cause severe overloading on the TP-PT line. This would inevitably lead to the cascading tripping of the TP-PT line, ultimately resulting in system disconnection. The fault chain search results are shown in Figure 11. Under the N-1 security criteria, ensuring power flow stability after tripping line YZG-DY alone requires shedding 213 MW of load. Under the N-2 security criteria, ensuring power flow stability after tripping both lines YZG-DY and DY-YZU requires shedding 213 MW of load. The load shedding quantities for the three methods are compared in Table 3.

The results demonstrate that the proposed method, by considering the failure probabilities of each high-risk branch and the failure probabilities at each stage of the fault chain propagation, can significantly reduce the high control costs associated with the N-1 and N-2 security criteria. Compared to the N-1 and N-2 security criteria, the proposed method better meets the requirements for online control during disasters.

Data availability:

The IEEE 39-bus test system used in Case Study I is based on the publicly available benchmark network distributed with MATPOWER and related repositories and can be obtained from the MATPOWER project website. The input data and simulation results generated by the proposed method for this benchmark system (including identified fault chains and corresponding risk indices) are available from the corresponding author upon reasonable request.

The real-system data used in Case Study II are derived from the Hainan power grid and include detailed network topology, equipment parameters, and operation records. These data are owned by the local power utility and are subject to contractual confidentiality obligations and critical infrastructure protection regulations. Consequently, the raw Hainan grid dataset and the full model output directly linked to this dataset cannot be made publicly available. Only aggregated and anonymized results necessary to support the findings of this study are provided in the article. Researchers who wish to access the underlying Hainan system data for legitimate academic purposes may contact the corresponding author; any potential data sharing will require prior written approval from the data owner and, where necessary, the signing of an appropriate non-disclosure agreement.

The general modelling framework, algorithms, and parameter settings are described in sufficient detail in the main text and Supporting Information to allow other researchers to implement and validate the proposed method on publicly accessible test systems or on their own datasets.

Figure 1: Schematic of the typhoon's movement after landfall. Based on the typhoon wind field model, the horizontal wind speed increases from the eye and subsequently decreases with radial distance. Taking position O on the transmission branch as an example, at the moment of t₁, the maximum wind radius of the typhoon is r_max(t₁), and the distance between the center of the typhoon and O is d(t₁). This time, d(t₁) is greater than r_max(t₁), and as the typhoon moves, the distance between O and the typhoon center decreases, so the wind speed at O increases. At the moment of t₂, d(t₂) is less than r_max(t₂) and d(t₂) is decreasing, so the wind speed at O decreases. At moment t₃, d(t₃) continues to increase but is less than r_max(t₃), so the wind speed at O will increase. Similarly, at t₄, d(t₄) continues to increase and is larger than r_max(t₄), so the wind speed at O decreases as the typhoon center moves away. It can be seen that the wind speed at any location on the transmission branch changes with time, and even on the same transmission branch, the wind speed changes at different locations are not the same. Please click here to view a larger version of this figure.

Figure 2: Schematic diagram of transmission branch m. This figure shows a single transmission branch composed of sequential towers (labeled as Tower m to Tower k) and lines (labeled as Line m to Line k. Each adjacent pair of towers forms one conductor span. A tower is a discrete evaluation point for meteorological load and component state, and a line denotes the conductor span between two neighboring towers on the same branch. The state of branch m is obtained by aggregating the states of its towers and lines under a series-structure assumption. Please click here to view a larger version of this figure.

Figure 3: Procedure for prevention and control measures based on fault chains. This flowchart presents the workflow used. Branches identified as high-risk under extreme disasters are first included in the initial fault set. For each candidate, one branch is chosen as the initial tripping branch, the branch is tripped, and the network parameters are updated. If system islanding occurs or the preset maximum depth is reached, the search for this fault chain stops. If overloaded branches appear, each overloaded branch is taken in turn as the next-level tripping branch and the trip-update-check loop continues. If no overload occurs, the risk index of the fault chain is calculated. After all initial faults are processed, the fault-chain paths with relatively high risk values are identified, and then preventive measures are applied to the target network. Please click here to view a larger version of this figure.

Figure 4: Relationship between typhoon wind speed and the number of faulty lines in Haikou City. This figure shows the hourly typhoon wind speed in Haikou City (left y-axis) and the number of faulty lines recorded in the corresponding hour (right y-axis). As wind speed increases from 10 m/s to above 50 m/s, the number of faulty lines rises accordingly, reaching its maximum around 19:00-20:00 and then decreasing as the wind weakens. The synchronous variation indicates a clear positive association between local wind intensity and line faults, consistent with the assumption made here that the failure risk of transmission components grows with increasing wind speed. Please click here to view a larger version of this figure.

Figure 5: Comparison of line failure probability and actual failure ratio. This figure compares the ratio of actual faulty lines to total lines (left y-axis) with the probability of line failure (right y-axis) across four cities. Both indicators follow the same spatial pattern: Haikou is the highest, Danzhou is next, Sanya is the lowest, and Qionghai shows a modest rebound. The two curves track closely, indicating a strong positive association between the modeled failure probability and the observed fault incidence, which supports the interpretation that cities with higher estimated risk also experience higher actual failure ratios. Please click here to view a larger version of this figure.

Figure 6: IEEE 39-bus system. This figure shows the IEEE 39-bus test system used in the case study. Buses are numbered, generator buses are marked G, and transmission branches interconnect the buses. Branch segments highlighted in red denote high-risk branches identified for the extreme-disaster scenario by the risk-assessment procedure described here; these branches constitute the initial fault set for constructing fault chains in the subsequent analysis. The diagram is schematic and is used to clarify the test-system topology and the locations of the identified high-risk branches. Please click here to view a larger version of this figure.

Figure 7: Fault chain search results. This figure lists the fault chains obtained in the IEEE 39-bus case. Starting from the initial tripping branch 1-2, the chain proceeds to 2-3 and then branches to candidate next-level tripping branches (26-27, 25-26, 17-18). Numbers on the arrows indicate the stage probability for the next tripped branch. Text at the terminal nodes reports the resulting minimum load shedding for that chain (e.g., 73.73 MW, 39.36 MW) or indicates that no load shedding occurs. The diagram provides a compact record of candidate fault-chain paths and their outcomes. Please click here to view a larger version of this figure.

Figure 8: Optimized fault chains. This figure lists the optimized fault chains in the IEEE 39-bus case. Starting from the initial tripping branch 1-2, the chain proceeds to 2-3 and then follows one of two next-level tripping branches: directly to 26-27, or through 17-18 and then to 26-27. Numbers on the arrows (e.g., 0.01, 0.9) indicate the stage probability for the next tripped branch along each path. The diagram provides a compact record of the optimized fault-chain paths and their stage probabilities. Please click here to view a larger version of this figure.

Figure 9: Power flow simulation results for a regional grid on 19:50 September 6 and power flow distribution in the regional grid after disconnection of lines LQ-JD and YZU-WQ. The figure above is the power flow simulation results for a regional grid on 19:50 September 6. Baseline power-flow of the regional grid under typhoon influence. Colors denote voltage levels (500/220/110 kV). At this moment, the lines LQ-JD and YZU-WQ are identified as high-risk elements. The figure below is the power flow distribution in the regional grid after the disconnection of lines LQ-JD and YZU-WQ. When the two high-risk lines are tripped, power redistributes, and the line DL-WC becomes heavily overloaded, driving the WQ-JD-DL corridor toward potential islanding of the connected 110 kV substations and possible outages. Please click here to view a larger version of this figure.

Figure 10: Power flow distribution in the regional grid after prevention and control measures. With the proposed preventive control in place, one unit at WQ is shut down, and the remaining generation is rescheduled. The overloads are relieved and the cascading risk is significantly reduced, achieving security with much lower curtailment than the conventional N-2 criterion. Please click here to view a larger version of this figure.

Figure 11: Power flow simulation results for a regional grid on 19:58 September 6 and fault chain search results for the Hainan power grid. The figure above is the power flow simulation results for a regional grid on 19:58 September 6. The system operates with LQ-JD and YZU-WQ open. The screening indicates YZG-DY and DY-YZU as the next most critical lines, while the 110 kV TP-PT corridor becomes the binding thermal constraint in this area. The figure below is the fault chain search results for the Hainan power grid. The search identifies two dominant one-step chains initiated by high-risk lines: LQ-JD (initial failure probability 0.1) and DY-YZU (initial failure probability 0.7). In both cases, the overload forces TP-PT to trip (stage probability ≈ 1), leading to system splitting with estimated load shedding of 295 MW and 144 MW, respectively. Please click here to view a larger version of this figure.

Generator Bus	Initial Active Power Output (MW)	Active Power Output Lower Limit (MW)	Active Power Output Upper Limit (MW)	Adjustment Cost (1/MW)
30	250	0	1040	1
31	677.87	0	976	1.1
32	650	0	725	1.1
33	632	0	652	1.2
34	508	0	508	1.2
35	650	0	687	1.3
36	560	0	580	1.3
37	540	0	564	1.1
38	830	0	865	1.1
39	1000	0	1200	1.5

Table 1: IEEE 39-bus system related information. This table reports generator-side parameters for the IEEE 39-bus case. For each generator bus, it lists the initial active power output, the admissible range given by the active-power lower/upper limits, and the adjustment cost. These entries specify the initial dispatch, allowable adjustment bounds, and the per-MW adjustment coefficient for each generator used in the case study.

No.	Generator Bus	Output Adjustment (MW)
1	30	32.64
2	31	-32.64

Table 2: Power flow optimization results. This table lists the generator-side adjustments produced by power flow optimization. For each generator bus, the output adjustment column gives the change relative to the initial active-power output; positive values indicate an increase, and negative values indicate a decrease. In this instance, Bus 30 is adjusted by +32.64 MW, and Bus 31 by -32.64 MW.

Method	Load Shedding (MW)
Preventive Control Method	62
N-1 Security Criterion	>213
N-2 Security Criterion	>>213

Table 3: Comparison of load shedding amounts for the three methods. This table compares the load shedding amounts required by the three methods. The proposed preventive control method requires only 62 MW of load shedding, whereas both the N-1 and N-2 security criteria necessitate more than 213 MW, demonstrating a significant reduction in control cost achieved by the proposed approach.

Discussion

In this paper, a fault-chain-based prevention and control method for typhoon disasters is proposed, which firstly screens the high-risk branches under typhoon disasters, and subsequently adjusts grid power unit output and shed load according to the fault chains, with the objective of mitigating failure propagation risk. Compared to online control methods based on N-1 and N-2 security criteria during disasters, the proposed method in this paper significantly reduces control costs under N-1 and N-2 security criteria by considering the fault probability of each line during typhoon disasters and the cascading fault probability of line overloads^29,30.

The proposed research contributes to the advancement of power system resilience analysis in several aspects. First, it captures the spatially correlated and time-varying impacts of typhoon loads on transmission infrastructure, which are often simplified or neglected in traditional contingency analysis. Second, by screening high-risk branches and constructing corresponding fault chains, the method focuses preventive resources on a limited set of critical cascading paths, effectively reducing expected load shedding and avoiding overly conservative preventive schedules compared with classical N-1/N-2-based controls. Third, the unified risk index, defined by combining fault probabilities and load-loss consequences, offers a practical metric for operators to balance security and cost control in real-time decision support.

Nevertheless, several limitations should be acknowledged. The vulnerability model concentrates on line segments and towers and adopts a series-structure assumption, which may not fully represent complex component interactions and correlated failures in practice. The fault chain analysis is based on DC power flow and simplified cascading mechanisms, and parameter uncertainties in typhoon forecasts and fragility curves may affect risk quantification accuracy. In addition, the optimization framework mainly addresses preventive control; coordinated blocking or remedial actions during fault chain propagation are not explicitly modeled in this work.

Alternative approaches to investigate the same hypothesis include robust or chance-constrained optimal power flow formulations considering typhoon scenarios, comprehensive N-k or Monte Carlo-based cascading failure simulations and coordinated preventive-blocking control models that jointly optimize pre-contingency dispatch and post-contingency corrective or islanding measures along specified fault chains³¹. These methods provide complementary perspectives and could be combined with the proposed framework to enhance modeling fidelity.

The proposed method has important potential applications in disaster-resilient operation and planning of power systems in typhoon-prone and coastal regions. It can be embedded into online decision-support platforms to generate risk-informed preventive control strategies prior to typhoon landfall, assist operators in prioritizing monitoring and reinforcement of high-risk corridors, and support medium to long-term planning for hardening critical transmission branches. With appropriate adaptation of the vulnerability and hazard models, the framework can also be extended to other weather-related and natural hazards such as severe windstorms, icing events, and wildfires, thereby offering a general tool for enhancing the resilience of modern power grids³².

Modifications and troubleshooting

Although the proposed method has been validated in both the IEEE 39-bus and Hainan power grid cases, practitioners may need to adapt it or might encounter challenges during implementation. This section provides guidance on potential modifications and troubleshooting for common problems.

Modifications for specific scenarios:

The method proposed in this paper is not limited to typhoon disasters. It can be adapted to other disasters, such as ice storms and wildfires, by modifying the corresponding hazard and vulnerability models. In practical implementation, the Jelesnianski typhoon wind field model should be replaced with appropriate hazard-specific models, and the transmission line vulnerability model should be recalibrated based on the distinct failure mechanisms of components under the new disaster conditions.

In systems with high penetration of renewables, the pre-disaster operating point becomes more variable. The method can be modified to a stochastic or robust optimization framework. The fault chain risk assessment would then need to consider multiple scenarios of renewable generation, increasing the number of candidate fault chains and the overall computational burden.

Troubleshooting common implementation problems:

The proposed method may encounter prohibitively long computation times when applied to large-scale systems. This is attributed to the combinatorial complexity inherent in the fault chain search process. In extra-large systems containing numerous high-risk initial lines, the number of potential fault chains increases dramatically, particularly when a large search depth is configured, consequently leading to excessive computational duration. To address this issue, the following mitigation strategies can be considered: First, the initial contingency set can be appropriately reduced by raising the failure probability threshold for inclusion, thereby screening high-risk lines more stringently. Priority should be given to lines located within the forecasted core disaster area. Second, the search depth can be limited. Based on engineering judgment and the typical propagation length of historical cascading failures in the target grid, the maximum search depth can be reduced from 4 to 3 or even 2. Furthermore, the proposed method may encounter infeasibility of the optimization model. Given the severe contingency scenarios being addressed, the constraints-such as N-1 security criteria and generator output limits-may be overly restrictive, resulting in no feasible generation dispatch solution that can simultaneously mitigate all high-risk fault chains. To resolve such issues, the following approaches can be considered: First, the security constraints can be relaxed by converting strict N-1 security constraints into soft constraints within the objective function, allowing for minor and temporary violations to achieve an overall reduction in system risk. Second, re-examine the set of candidate fault chains. It is possible that some very low-probability, but high-consequence chains are driving infeasibility. A risk-based trimming of the candidate set might be necessary.

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
GUROBI	Gurobi Optimization, LLC	10.0.1	Commercial solver used for the optimization model
MATLAB	MathWorks	2020b	Core environment for all simulations
Notebook PC	Lenovo	X1 Carbon Gen 9	CPU: Intel Core i7-1165G7;RAM: 16 GB;SSD: 512 GB;OS: Windows 11
Self-developed MATLAB Scripts	Self-developed	v1.0	Implements the fault-chain search and optimization routines