A robust pre-disaster enhancement method for distribution networks considering the timing of disasters and the fault tolerance of specific sections.

Abstract

A robust pre-disaster reinforcement method for distribution networks considering the temporal nature of disasters and the fault tolerance of fault location includes: establishing a time-varying vulnerability model for distribution network components and generating an uncertain disaster scenario set containing fault states of lines and feeder terminal units across multiple time periods based on the Monte Carlo method; constructing a distribution network segment location model and quantifying the location error under each disaster scenario by comparing the difference between the actual and expected states of nodes; establishing a robust pre-disaster reinforcement model with the goal of minimizing the overall system cost; constructing constraints for the robust pre-disaster reinforcement model and iteratively solving the robust pre-disaster reinforcement model using a column and constraint generation algorithm to output the optimal pre-disaster reinforcement scheme. This method, by meticulously characterizing the time-varying evolution of disasters, incorporates the fault tolerance performance of fault segment location into the pre-disaster reinforcement decision-making framework, seeking the optimal resource allocation scheme under the worst-case disaster scenario, thereby achieving a balance between economy and robustness and improving the resilience of the distribution network to extreme disasters.

Description

Technical Field

[0001] This invention relates to a robust pre-disaster reinforcement method for distribution networks that considers the timing of disasters and the fault tolerance of segment locations, belonging to the field of power system disaster prevention and resilience enhancement technology. Background Technology

[0002] Against the backdrop of global climate change, extreme natural disasters such as typhoons and torrential rains are occurring more frequently and with increasing intensity, posing a serious threat to the safe and stable operation of power distribution networks. As the final link in the power system facing users, failures in the power distribution network can lead to widespread power outages and cause significant socio-economic losses.

[0003] Traditional pre-disaster reinforcement studies primarily focus on enhancing the disaster resilience of physical equipment to reduce failure probability or load loss, often employing static or scenario-based methods to describe disaster impacts. However, disasters such as typhoons and rainstorms exhibit significant spatiotemporal evolution characteristics, and their impact on distribution networks is dynamic and time-series. Existing methods fail to fully characterize the time-varying impact of the entire disaster process on equipment failure probability and rarely consider the influence of pre-disaster reinforcement measures on the critical post-fault handling stage of distribution network failure—fault section location.

[0004] With the increasing automation of power distribution networks, monitoring equipment such as fault detection units (FTUs) are widely deployed, and their operational reliability directly affects the accuracy of fault location. Under extreme disasters, FTUs themselves may be damaged by strong winds and heavy rains, resulting in missed or false alarms. This leads to distorted information obtained by the control center, causing misjudgments of faulty sections and delaying repairs and recovery. Therefore, how to rationally select and strengthen FTUs within a limited pre-disaster strengthening budget to improve their reliability under disasters, thereby ensuring the fault-tolerant performance of fault location and systematically balancing economic costs and disaster resilience is a critical issue that urgently needs to be addressed. Summary of the Invention

[0005] This invention proposes a robust pre-disaster reinforcement method for distribution networks that considers the temporal nature of disasters and the fault tolerance of fault location. This method incorporates the fault tolerance performance of fault location into the pre-disaster reinforcement decision-making framework by finely characterizing the time-varying evolution process of disasters, and uses a robust optimization method to seek the optimal resource allocation scheme under the worst disaster scenario, thereby achieving a balance between economy and robustness and comprehensively improving the resilience of distribution networks in the face of extreme disasters.

[0006] The technical solution adopted in this invention is as follows:

[0007] A robust pre-disaster enhancement method for distribution networks that considers the timing of disasters and the fault tolerance of specific sections includes the following steps: Step 1: Establish a time-varying vulnerability model for distribution network components, and generate an uncertain disaster scenario set containing fault states of lines and feeder terminal units across multiple time periods based on the Monte Carlo method; Step 2: Construct a distribution network segment location model, and quantify the location error under various disaster scenarios by comparing the difference between the actual state and the expected state of the nodes; Step 3: Establish a robust pre-disaster reinforcement model with the goal of minimizing the overall system cost, whereby the overall cost includes FTU reinforcement cost and positioning error penalty cost; Step 4: Construct the constraints of the robust pre-disaster reinforcement model, including μPMU observation constraints, circuit breaker protection constraints, fault multiple number constraints, reinforcement budget constraints, FTU immunity constraints, and fault state continuation constraints. Step 5: Combining the constraints in Step 4, the column and constraint generation algorithm is used to iteratively solve the robust pre-disaster reinforcement model and output the optimal pre-disaster reinforcement scheme.

[0008] In step 1, during a typhoon disaster, high wind speeds generate lateral wind loads on the power distribution lines and towers, causing additional stress and bending moments in the line and tower structures. Based on fundamental aerodynamic principles, these stresses act on the power lines... ij The instantaneous wind load on the surface can be expressed as: (1); In formula (1): Indicates the action on the line ij Instantaneous wind load on the surface; The density of air is typically taken as 1.225. For the line ij The drag coefficient; for t Constantly acting on the line ij Instantaneous wind speed; For the line ij diameter; For adjacent towers m With towers n Between lines ij length; As a supporting structure, the tower is also subject to wind pressure, and its stress can be calculated from the wind-receiving area of ​​the tower: (2); In formula (2): Indicates pole tower i The force exerted by wind pressure; for t Constantly acting on the tower i Instantaneous wind speed; For towers i The windward coefficient; For towers i The equivalent windward area; Based on the principles of statics, towers i The root bending moment is: (3); In formula (3): For towers k Equivalent arm; wire ij The lateral stress caused by wind load is: (4); In equation (4): Indicates wire ij Lateral stress is generated due to wind load; For wires ij The windward cross-sectional area.

[0009] When wind speed varies with time, both wind load and the resulting stress fluctuate over time. A normalized stress ratio is then introduced: (5); In formula (5): Reflecting the route during the typhoon ij The percentage of wind intensity received; For wires ij The design limit stress.

[0010] The impact of heavy rain on power line structures is mainly manifested in insulation degradation and foundation bearing capacity reduction. The former increases the probability of insulator flashover faults, while the latter reduces the stability of tower structures. ij The probability of flashover of the upper insulator has an S-shaped relationship with rainfall intensity, which can be represented by a logic function: (6); In formula (6): for t Timetable ij Probability of flashover of upper insulator; for t Always on the line ij Instantaneous rainfall intensity at the top insulator; For the line ij Critical flashover rainfall intensity for upper insulators; The steepness coefficient reflects the sensitivity of insulation performance to changes in rainfall; This represents the core operation of a logical function, used to map any real number to the interval (0,1).

[0011] Continuous rainfall will increase the moisture content of the foundation soil, leading to a decrease in bearing capacity. The ultimate bending moment of the tower can be described as a linear decay function with increasing foundation wetting: (7); In equation (7): for tThe ultimate bending moment of the tower at any given moment; Design the ultimate bending moment for the tower under dry conditions; This is the humidification sensitivity coefficient; This is the soil wetting coefficient.

[0012] (8); In equation (8): for t Cumulative rainfall at all times; This represents the soil saturation rainfall threshold. Wetting of the foundation weakens the towers' ability to resist wind-induced bending moments, thus amplifying the structural effects of typhoon loads.

[0013] To systematically characterize the combined effects of typhoons and rainstorms, this invention introduces a time-varying damage index based on the principle of multi-source damage superposition. This index comprehensively considers the effects of wind-induced stress, foundation wetting, and insulation degradation. (9); In equation (9): For the line ij exist t Comprehensive damage indicators at any given time; Indicates pole tower i Root bending moment; These are the weighting coefficients; Indicates pole tower i The probability of insulator flashover between adjacent lines.

[0014] At this time, the line ij exist t The failure probability at time t can be expressed as: (10); In formula (10): Indicates the line ij exist t The probability of failure at any given moment; Baseline risk parameters reflect the risk level of the line. ij The probability of natural failure under disaster-free conditions; The damage sensitivity coefficient describes the intensity of the impact of changes in damage indicators on the failure probability. FTUs are critical monitoring and control nodes in distribution network automation systems, and their operating status directly affects the accuracy of fault location and the system's resilience. Under extreme weather conditions, although FTUs do not directly transmit power, their casings, supports, and internal electrical components are still susceptible to physical damage from typhoons and rainstorms, which can lead to abnormal sampling data, including missed and false alarms.

[0015] Typhoons exert mechanical impact and electronic drift on the FTU through strong wind loads and wind-induced vibration effects, causing deviations or jitter in its sampling signal. The vulnerability of the FTU itself can be quantified by the accumulation of structural strain energy caused by wind pressure. At time... t , No. j The local wind pressure of an FTU can be expressed as: (11); In equation (11): Indicates the first j Local wind pressure of each FTU; Indicates the first j The drag coefficient of each FTU; for t The moment of action at the j Instantaneous wind speed of each FTU; Indicates the first j The equivalent windward area of ​​each FTU.

[0016] When the wind pressure exceeds the load-bearing threshold of the FTU structure This will lead to misalignment of internal components of the FTU or drift of sensor signals. Based on the logistic vulnerability function in reliability engineering, the probability of structural damage can be defined as: (12); In equation (12): Indicates the first j The probability of structural damage to an FTU; The wind-induced damage coefficient; Indicates the first j Structural load-bearing threshold for each FTU.

[0017] Heavy rain affects the dielectric properties of the FTU electronic module through moisture penetration and water ingress short circuits, leading to decreased sampling accuracy or shifts in detection thresholds. Based on environmental reliability standards, the probability of damage caused by heavy rain can be expressed as: (13); In equation (13): Indicates the first j Probability of damage caused by heavy rain to each FTU; The rain-induced damage coefficient; For the first j Instantaneous rainfall intensity per FTU; For the first j Critical rainfall intensity corresponding to each FTU protection level; Typhoons and torrential rains often occur simultaneously and are positively correlated: strong winds can damage the sealing structure of equipment, increasing rainwater penetration; while humidification reduces rigidity, amplifying wind-induced vibration. To characterize this interactive amplification effect, we define the first... jThe probability of each FTU failure is: (14); In equation (14): Indicates the first j The failure probability of an FTU; The basic component reflects the level of latent damage under normal conditions; , These are the edge effect coefficients for a single disaster cause; This is the disaster coupling coefficient, used to quantify the synergistic amplification effect of typhoons and rainstorms; Under extreme weather events, the intensity, spatial distribution, and trajectory of typhoons and rainstorms exhibit significant uncertainties. Different disaster processes will have differentiated impacts on the power distribution network at different times and spatial locations. To fully consider the uncertainty of disaster disturbances in pre-disaster reinforcement decision-making, this invention uses the Monte Carlo method to randomly generate various typical typhoon-rainstorm disaster samples and constructs an uncertain scenario set based on their time-varying action processes. The uncertain scenario set can be directly used in subsequent robust optimization models as an uncertainty set describing disaster disturbances. The disaster characteristic parameter set is defined as follows: (15); In equation (15): Represents a single set of disaster characteristic parameters; The wind speed at the center of the typhoon; The intensity of rainfall at the center; Indicates the direction of the typhoon's movement; This refers to the typhoon's movement speed; The Monte Carlo method was used to randomly select N groups of disaster samples within their statistical distribution range. , These represent different disaster samples, which include the disaster intensity distribution and spatiotemporal evolution trajectory; This represents the total number of disaster samples drawn in Monte Carlo; each sample Corresponding to a disaster intensity distribution and spatiotemporal evolution trajectory, .

[0018] Typhoons can be simulated as a circular model, with wind speeds at the radius of maximum wind speed, decreasing towards the eye and outside the typhoon's range. The radius of maximum wind speed often coincides with the area of ​​maximum rainfall intensity, decreasing towards the eye and outside the range. (In the sample...) Below, for distribution network lines ij With the j The local disaster intensity of an FTU can be modeled as follows: (16); In equation (16): Indicates the first nUnder a disaster sample t Constantly acting on the line ij or the j Local wind speed intensity of each FTU; Indicates the first n Under a disaster sample t Constantly acting on the line ij or the j The localized rainfall intensity of each FTU; Indicates the first n Under a disaster sample t Timeline or distance from FTU to the disaster center; The distance from the line or FTU to the disaster center; , These are the spatial attenuation coefficients for wind speed and rainfall intensity, respectively.

[0019] Based on the previously established time-varying vulnerability models of the line and FTU: the time-varying vulnerability model of the line includes equations (1) to (10), and the time-varying vulnerability model of the FTU is equations (11) to (14). The failure probability of each component can be calculated: the line failure probability is calculated by equation (10), and the FTU failure probability is calculated by equation (14).

[0020] Since disaster scenario analysis requires a clear fault state as a basis, probability quantities need to be considered. and It is transformed into a discrete fault form, as shown in equations (17) and (18).

[0021] (17); In equation (17): For the first i There are several section fault status variables, where 1 indicates a section fault and 0 indicates a section normal. This is the threshold for the probability of line faults.

[0022] (18); In equation (18): For the first j Each section has a fault status variable, where 1 indicates an FTU fault and 0 indicates a normal FTU. This is the FTU failure probability threshold.

[0023] This invention establishes that the enhanced FTU can stably and accurately report status information in all disaster samples. This means that the uncertainty dimension corresponding to the enhanced FTU is removed from the scenario set, and its status always equals the theoretically expected state. This assumption aligns with engineering practice; after adding protective shields, backup communication links, and independent power supplies, the reliability of the FTU is far higher than that of ordinary nodes, and can almost be considered an ideal state.

[0024] Finally, by overlaying state combinations from multiple disaster samples, multiple time periods, and multiple components, a set of decision-related uncertain scenarios was formed. Specifically, for each disaster sample... and each time period t Record the discrete fault states of all lines and all FTUs, and combine them into a complete scenario in chronological order. n The scenario corresponding to each disaster sample can be represented as: (19); In equation (19): For the first n The scenario corresponding to each disaster sample; For the first n Each sample in the time period t Discrete fault state vectors for each section; For the first n Each sample in the time period t Discrete state vectors of each FTU; To set the number of time periods.

[0025] Therefore, the overall set of uncertain scenarios can be written as: (20); In equation (20): This represents a set of uncertain scenarios as a whole.

[0026] This set includes both physical layer uncertainties caused by natural disturbances such as typhoons and rainstorms, and reflects the randomness of FTU distortion and information loss. Different enhancement schemes s will change the distribution characteristics of information uncertainty in the scene set, thus affecting the worst-case response of the subsequent robust optimization model.

[0027] In step 2, the fault-tolerant principle of segment location is as follows: the expected state of the node is calculated by switching function, the actual state of the node is collected by FTU, and the approximation model between the expected state of the node and the actual state of the node is constructed by using minimum set theory, so as to realize the fault-tolerant location of the fault segment. The switching function is a logic function that calculates the desired state of the distribution network FTU based on the segment status and distribution network topology. Its construction mechanism is as follows: (twenty one); In equation (21): FTU j Upstream power supply reachability discrimination quantity, i.e., used to determine FTU. j Are there any faulty sections along the path to the upstream power source? FTU jDownstream fault presence discriminant, i.e., used to determine the presence of FTU. j Are there faulty sections in the downstream network? FTU j The theoretical expected state; For FTU j Number of power sources in the upstream network; For FTU j Number of power sources in the downstream network; For FTU j Upstream power The set of segments along the path; For FTU j The set of all segments in the downstream network; For FTU j to downstream power supply The set of segments along the path; For FTU j The set of all segments in the upstream network; This is a section fault status variable, where 1 indicates a section fault and 0 indicates a normal section. Indicates the logical AND. Indicates the logical "NOT"; Indicates the first k The first path i Fault status variables for each section; Indicates the first l Fault state variables of each section This indicates the power supply number, which is the serial number of the upstream or downstream power supply. express Path or The segment number in the path; express Path or The segment number in the path.

[0028] Under normal operating conditions, FTU j The following situations may occur: (twenty two); Based on the fault-tolerant principle of segment positioning, the positioning function is as follows: (twenty three); In equation (23): This represents the set of FTU nodes in the distribution network; This indicates the actual status of the FTU received by the distribution network operation center; This indicates the expected status of the FTU received by the distribution network operation center; Meanwhile, when the FTU malfunctions, the signal it transmits to the control center will be distorted, resulting in either missed alarms or false alarms. Therefore, the first... j FTU underreporting indicator variable False alarm indicator variable The formula is as follows: (twenty four); (25).

[0029] In step 3, based on the established segment positioning model and the set of uncertain scenarios, this invention further constructs a robust pre-disaster reinforcement model. This model aims to minimize the risk of segment positioning misjudgment under all possible disaster disturbance scenarios by selecting a limited number of key FTU nodes for reinforcement, while balancing reinforcement cost and positioning fault tolerance. The objective function of the robust pre-disaster reinforcement model can be expressed as: (26); In equation (26): n This represents the number of FTU nodes in the system. For the first i Unit reinforcement cost of an FTU; The penalty coefficient for misjudging segment positioning; s This is a pre-disaster reinforcement plan; For the first i The enhancement variable for each FTU is set to 1 if it is enhanced and 0 if it is not enhanced. For the scene u Next i The actual status of each segment; The first output of the segment positioning model i The expected state of each segment.

[0030] Step 4 includes: 1) μPMU observation branch constraints: To improve the ability to identify feeder conditions under extreme weather conditions, this invention introduces a small number of deployed μPMUs as high-precision condition observation points, and each μPMU can provide real-time voltage and current phasor information of its branch. Because the μPMUs have consistent time scales and high accuracy, once they detect fault characteristics, it indicates that the fault must occur within the observed branch. Based on this, the following constraints can be established: (27); In equation (27): For the first j A set of segments on a μPMU installation branch.

[0031] 2) Circuit breaker constraints: According to the principle of three-stage current protection, if the circuit breaker operates, the section fault must be within the protection range of the operating protection device. Therefore, the circuit breaker constraint can be expressed as: (28); In equation (28): For the first j A set consisting of sections within the protection range of a circuit breaker.

[0032] 3) Fault multiplicity constraint: Based on historical statistics and the patterns of wind disasters, while the number of multiple faults on power lines is higher in extreme scenarios than in normal weather, its overall scale still has an upper limit. To avoid meaningless high-dimensional combinations in the model, the maximum number of faults is limited to a given threshold: (29); In equation (29): m The number of segments in the system; The maximum number of faults in a given section.

[0033] 4) Strengthen budget constraints: To characterize the resource constraints of pre-disaster reinforcement decision-making, it is necessary to limit the reinforcement costs: (30); In equation (30): To strengthen the available total budget cap.

[0034] 5) Enhanced immune restraint: If a certain FTU is reinforced before a disaster, it will not fail in any time period across all planned scenarios, subject to the following constraints: (31); In equation (31): Indicates the first i FTU during the period t The underreporting indicator variable; Indicates the first i FTU during the period t False alarm indicator variables; For the first i The enhancement variable for each FTU is 1, indicating that the FTU has been enhanced, and 0 indicates that the FTU has not been enhanced.

[0035] 6) Section fault continuation constraints: If a segment is already in a faulty state in a previous time period, it will remain in a faulty state in subsequent time periods, subject to the following constraints: (32); In equation (32): Indicates the first i The fault status variables of each segment in time period t; Indicates the first i The fault status variables of each segment in time period t+1.

[0036] In addition, it also includes section positioning switch function constraints and FTU state variable constraints, as shown in equation (21) and equation (22) respectively.

[0037] In step 5, since the robust pre-disaster reinforcement model has a typical min-max-min three-layer structure, where the reinforcement decision s and the uncertain scenario set are... There are coupling relationships between them, and direct solution will lead to the curse of dimensionality and exponential computational cost. To address this, this invention introduces the Column and Constraint Generation (CCG) algorithm to efficiently solve the robust pre-disaster reinforcement model; The core idea of ​​the Column and Constraint Generation (CCG) algorithm is to decompose the three-level structure into two parts: the Master Problem (MP) and the Subproblems (SP). 1) Main Problem MP: Given a finite set of scenarios, find reinforcement decisions s such that the reinforcement cost and the worst-case penalty cost in these scenarios are minimized; specifically as follows: In the current iteration, not all disaster scenarios are considered directly; instead, optimization is performed only on a limited number of representative scenarios that have been identified. Under these known scenarios, the model is enhanced using the FTU (Free-Touch) scheme. s As the decision variable, under the conditions of satisfying budget constraints, post-enhancement immunity constraints, and fault location constraints, we seek an optimal reinforcement configuration that can balance economy and disaster resistance. Its optimization objective consists of two parts: one is the direct investment cost required to enhance FTU, and the other is the maximum location misjudgment penalty cost that may occur in the current limited set of scenarios. The role of the main problem is to provide a phased optimal reinforcement scheme based on the currently known "most unfavorable scenario information", providing a basis for subsequent sub-problems to continue searching for worse scenarios. As the iteration progresses, the scenarios included in the main problem gradually increase, and the reinforcement scheme obtained will continuously approach the true optimal solution of the original robust optimization problem. The relevant mathematical expressions are shown in Equations (33) and (34) below.

[0038] 2) Sub-problem SP: Under a fixed reinforcement scheme, find the worst-case scenario for the current reinforcement scheme among all disaster scenarios, and add the penalty cost of the worst-case scenario to the main problem MP for further iteration. Details are as follows: After the main problem has given a current reinforcement scheme, the scheme is fixed, and then the search is performed in the complete disaster scenario space to find the worst scenario that would lead to the maximum location misjudgment penalty cost under the reinforcement scheme. If the penalty cost corresponding to the worst scenario found by the subproblem is higher than the worst cost currently estimated by the main problem, it means that the current scenario set in the main problem is not sufficient, and the new scenario needs to be added to the main problem and the reinforcement scheme is re-optimized in the next iteration. Through this alternating process of "main problem determining the scheme, subproblem finding the worst scenario", the algorithm can gradually filter out the key scenarios that truly constrain the decision from all uncertain disaster scenarios, thereby avoiding the dimensionality disaster and exponential computational complexity caused by directly solving in the entire scenario space. When the subproblem can no longer find a scenario worse than the current one, it means that the main problem and the subproblem have reached a consensus, the algorithm converges, and the reinforcement scheme obtained at this time is the robust optimal scheme. The relevant mathematical expressions are shown in the following equation (35).

[0039] The Column and Constraint Generation (CCG) algorithm continuously generates new worst-case scenarios, gradually approximating the actual worst-case perturbation scenario, thereby completing the search of the uncertainty space; Ultimately, when the subproblem SP cannot find a worse scenario penalty cost than the current one, the solution to the main problem MP is the globally optimal solution.

[0040] Assume the current main problem MP contains K Given a given set of generated scenarios, the main problem MP can be written as: (33); (34); In the above formula: This is the upper bound of the worst-case localization misjudgment penalty cost for the currently known scenario; Indicates the fault status variable of the section; Indicates the penalty coefficient for misjudging segment location; Indicates the number of FTU nodes in the system; Representing a scene u Next i The actual status of each segment; The output of the segment positioning model represents the first... i The expected state of each segment.

[0041] Based on the objective function in step 3, the subproblem SP can be written as: (35); In equation (35): Represents a set of uncertain scenarios One of the scenes.

[0042] To facilitate solver processing, this invention performs standard linearization on the absolute value term and transforms the inner minimization problem of the model into an equivalent maximization form: First, introduce an integer misjudgment indicator variable for each segment: (36); In equation (36): Indicates the first i The misjudgment indicator variable for each segment is used to measure the true fault status of that segment. With location results The degree of deviation between them.

[0043] And constraints are added for linearization: (37); The inner target then becomes: (38); In equation (38): Indicates the fault state in a given real section. x The minimum total penalty cost corresponding to the segment location model can also be understood as the inner optimal objective function value under this fault scenario.

[0044] Then, set a maximum number. M Its value is the penalty cost of locating no faults when all sections are faulty, i.e. (39); In the formula: This represents the total number of segments in the system.

[0045] Finally, minimizing the inner layer can be equivalently written as: (40); The subproblem SP can be transformed into: (41); After each round of alternating solutions to the main problem (MP) and the subproblem (SP), it is necessary to compare the upper and lower bounds of the maximum loss of the current reinforcement scheme to determine whether to continue iterating.

[0046] The worst-case penalty cost obtained by the main problem MP under a finite set of scenarios can be considered as the upper bound (UB), while the minimum penalty cost corresponding to the true worst-case scenario identified by the subproblem SP in the complete scenario library constitutes the lower bound (LB). The difference between the two is considered a lower bound. (42); In equation (42): The convergence tolerance of the column and constraint generation algorithm is represented by the maximum allowable error range between the upper bound UB obtained from the main problem MP and the lower bound LB obtained from the subproblem SP.

[0047] Or it satisfies the relative error criterion: (43); We can then consider that the main problem MP has accurately approximated the worst-case scenario, and the iterative process has converged. At this point, the current enhancement scheme is the robust optimal solution; if not, we continue to add the worst-case scenario to the scenario set and proceed to the next round of iteration.

[0048] This invention provides a robust pre-disaster reinforcement method for distribution networks that considers the timing of disasters and the fault tolerance of specific sections. The beneficial effects are as follows: 1) This invention constructs a time-varying vulnerability model and generates a multi-period disaster scenario set to finely depict the temporal and spatial differences in the impact of the dynamic evolution of disasters such as typhoons and rainstorms on the power distribution network, making risk assessment and decision-making more realistic and credible.

[0049] 2) This invention is the first to explicitly incorporate the fault tolerance performance of fault segment location into the pre-disaster reinforcement decision-making objectives, and comprehensively considers the impact of physical layer reinforcement and information layer reliability on the emergency response capability after the fault, thereby improving the systematicness and practicality of the reinforcement strategy.

[0050] 3) This invention adopts a robust optimization framework and CCG algorithm to directly optimize for the worst disaster scenario. The resulting reinforcement scheme can still maintain good fault location performance and economy under extreme uncertainty, and achieves an effective balance between resilience improvement and cost control.

[0051] 4) The framework and model of this invention can be easily integrated with other disaster types, resilience enhancement measures or location algorithms, and have good universality and scalability. Attached Figure Description

[0052] The present invention will be further described below with reference to the accompanying drawings and examples; Figure 1 This is a topology diagram of a 14-node distribution network.

[0053] Figure 2 Disaster trajectories for 8 typical disaster scenarios.

[0054] Figure 3 The results show the probability distribution of instantaneous line faults for eight typical disaster scenarios.

[0055] Figure 4 The results show the instantaneous failure probability distribution of FTUs in eight typical disaster scenarios.

[0056] Figure 5 This is a comparison chart of the positioning accuracy of the two methods.

[0057] Figure 6 Example diagram of line fault and location results.

[0058] Figure 7 This is a comparison chart of the total costs of the three options. Detailed Implementation

[0059] A robust pre-disaster enhancement method for distribution networks considering the timing of disasters and the fault tolerance of specific sections. The method includes the following steps: 1) Establish a time-varying vulnerability model for distribution network components, and generate a set of uncertain disaster scenarios containing fault states of lines and feeder terminal units in multiple time periods based on the Monte Carlo method; 2) Construct a distribution network segment location model, and quantify the location error under various disaster scenarios by comparing the difference between the actual state and the expected state of the nodes; 3) Establish a robust optimization objective function with the goal of minimizing the overall system cost, whereby the overall cost includes the reinforcement cost of the feeder terminal unit (FTU) and the positioning error penalty cost; 4) Construct the constraints of the robust optimization model, including observation constraints of the micro-synchronous phasor measurement unit (μPMU), circuit breaker protection constraints, fault multiple number constraints, enhanced budget constraints, FTU immunity constraints, and fault state continuation constraints. 5) Combining the constraints of step S4, the objective function of step S4 is iteratively solved using the Column-and-Constraint Generation (CCG) algorithm to output the optimal pre-disaster reinforcement scheme. This invention analyzes the section location accuracy, overall system cost, and reinforcement configuration results of the distribution network before and after the implementation of the proposed robust pre-disaster reinforcement method under multi-disaster scenarios. The results show that the proposed method can effectively reduce costs in the worst-case disaster scenario and significantly improve the overall disaster resilience and operational reliability of the distribution network.

[0060] Example: This invention uses a 14-node distribution network system as a case study, and its topology is as follows: Figure 1 As shown. The system comprises 14 nodes and 14 lines, using a radial power supply structure. To implement fault location, an FTU is configured at each node, for a total of 14 FTUs.

[0061] From a large number of random disaster trajectories generated based on Monte Carlo simulations, this invention further filters out eight disaster paths that have the most significant impact on the power distribution network, using them as typical disaster scenarios for subsequent analysis, such as... Figure 2As shown, since the disaster intensity and vulnerability parameters are fixed, these trajectories actually represent the most unfavorable combination of extreme disasters in terms of spatial action, reflecting the maximum potential damage to the system under different impact directions and sequences. It should be noted that each disaster scenario is not static, but rather a complete disaster process evolved from typhoons and rainstorms over multiple consecutive periods. Therefore, these eight scenarios constitute the key uncertainty set in robust optimization, enabling its reinforcement strategies to remain effective and adaptable even under the most threatening disaster conditions.

[0062] Figure 3 The instantaneous fault probability distribution of power distribution network lines under eight typical typhoon-rainstorm combined disaster scenarios is presented. It can be seen that the impact of different disaster trajectories on the lines varies significantly spatially. In some scenarios, lines closer to the typhoon center path exhibit a higher fault probability within the same time period, while lines farther from the disaster area are relatively less affected. This indicates that the line fault probability is mainly influenced by the spatial distribution of disaster intensity and its relationship with the geographical location of the lines. Different typhoon intrusion directions and ranges can lead to significant changes in the location of high-risk lines in the system. These results verify that the line fault probability model can effectively reflect the differentiated effects of extreme disasters on the power distribution network.

[0063] Figure 4 The distribution of instantaneous failure probability of FTUs under the same typical disaster scenarios is presented. Compared with the lines, the overall failure probability of FTUs is relatively low, but it still increases significantly in local areas and specific scenarios. This is mainly because FTUs are more sensitive to changes in local wind speed and rainfall intensity. When they are located in areas affected by high-intensity disasters, they are more prone to sampling anomalies or communication distortions, thus exhibiting a higher instantaneous failure probability. The distribution locations of high-risk FTUs vary greatly in different scenarios, reflecting the high dependence of information layer equipment on the spatial effects of disasters.

[0064] In extreme disaster scenarios, the segment location results are highly dependent on the accuracy of FTU observation information. To evaluate the impact of FTU reliability on segment location performance under disaster conditions, this invention sets up two comparative schemes to analyze the segment location performance under the same disaster scenario and line fault conditions: Option 1: The baseline option without pre-disaster reinforcement of the FTU; Option 2: An improvement plan to enhance the FTU in preparation for disaster.

[0065] By comparing the segment location results of the two schemes under the same typical disaster scenario, we can intuitively analyze the effect of FTU enhancement measures on improving the location accuracy, where the location accuracy is the ratio of the located faulty line to the actual faulty line.

[0066] Figure 5The segment positioning accuracy of two schemes was compared under eight typical disaster scenarios. Scheme 1 is the baseline scheme without enhanced FTU, and Scheme 2 is the scheme with enhanced FTU. It can be seen that the positioning accuracy of Scheme 2 is higher than that of Scheme 1 in all scenarios, and the improvement is more significant in most scenarios. This indicates that under extreme disaster conditions, the reliability of FTU information has a significant impact on segment positioning results. Without enhancement, FTU false alarms and missed alarms easily interfere with positioning judgment, resulting in a generally low positioning accuracy and significant differences between scenarios. Enhancing the FTU effectively improves the quality of observation information, thereby significantly improving segment positioning accuracy and enhancing the stability of positioning results under different disaster scenarios.

[0067] However, it should be noted that in some typical disaster scenarios, the improvement in positioning accuracy after enhancement is still limited, which is closely related to the fault topology. Taking the worst-case fault scenario in scenario 3 as an example, its segmental fault distribution and positioning observability are as follows: Figure 6 As shown. By Figure 6 It is known that lines 4, 8, 9, and 13 have faults, but the location results only show faults in lines 4, 8, and 13. This is because the segment location model needs to locate the faulty lines based on the FTU signals. When multiple faults occur, some FTUs cannot receive fault current signals, resulting in the inability to accurately locate all faulty lines. Regarding the location of faulty lines 4 and 5, FTU1, FTU2, FTU3, and FTU4 all received positive fault current signals. However, when only line 4 has a fault, the signals received by the FTUs are identical, leading to inaccurate location. These results indicate that segment location fault tolerance is affected not only by the reliability of the information layer but also by the physical constraints of the electrical topology, thus limiting the overall improvement in location accuracy even with pre-disaster FTU reinforcement.

[0068] To further evaluate the economics of different strategies under extreme disaster conditions, this invention compares and analyzes the total cost performance of various operational strategies based on the aforementioned disaster scenarios and segment location results. The specific settings for each comparative scheme are given in Table 1, covering different decision-making levels from taking no proactive measures to simultaneously introducing segment location and FTU pre-disaster reinforcement. By uniformly evaluating the total cost of each scheme under typical disaster scenarios while maintaining consistency in disaster scenarios, line fault states, and cost parameters, the impact of segment location and FTU reinforcement measures on the system's total cost and risk exposure level can be systematically characterized.

[0069]

[0070]

[0071] Based on Table 2 and Figure 7Data analysis revealed significant differences in the economic performance of the three solutions across eight typical disaster scenarios. Case 1, without any reinforcement or location measures, exhibited a high total system cost with large cost fluctuations across different scenarios, indicating the original system's extreme sensitivity to disaster disturbances and its significant vulnerability. Introducing segment location significantly reduced the total cost of Case 2, with an average reduction exceeding 50%, demonstrating that segment location effectively narrows the fault detection range and reduces misjudgment losses. However, in some high-disturbance scenarios, such as Case 3, the cost remained high, indicating that relying solely on segment location without reinforcing the FTU to improve information layer reliability has limitations in risk mitigation capabilities. Under different fault scenarios and reinforcement combinations, the actual total cost of the optimal reinforcement scheme was generally lower than the budget ceiling of 160,000 yuan. This is mainly because, once the number of reinforcements reaches a certain scale, the marginal improvement in segment location accuracy from further increasing reinforcement nodes significantly weakens, and the reduction in misjudgment penalty costs calculated by the model is insufficient to offset the additional reinforcement costs.

[0072] The robust pre-disaster reinforcement method proposed in this invention exhibits optimal overall performance, namely Case 3. Its total cost is further reduced to the range of 43.8 to 64.6, achieving an average additional cost reduction of approximately 35% on top of the significant optimizations already made in Case 2. Crucially, cost fluctuations between different scenarios are significantly narrowed, demonstrating excellent robust stability. The core of this method lies in reinforcing FTU information nodes through the CCG algorithm. With a limited investment of less than 20% of the total cost on average, it significantly improves the reliability of the FTU monitoring network, thereby effectively controlling the penalty costs in most disaster scenarios. The fact that the reinforcement budget is not fully utilized is not due to insufficient model capability, but rather reflects that, under the current network topology and fault scenario settings, limited reinforcement can achieve high localization robustness. Overall, the proposed robust reinforcement scheme can adaptively adjust the reinforcement targets under different disaster scenarios, stably reducing the misjudgment loss in the worst case while keeping reinforcement investment under control, demonstrating a good balance between robustness and economy under multi-scenario uncertainty conditions.

Claims

1. A robust pre-disaster reinforcement method for distribution networks that considers the temporal nature of disasters and the fault tolerance of segment locations, characterized in that... Includes the following steps: Step 1: Establish a time-varying vulnerability model for distribution network components, and generate an uncertain disaster scenario set containing fault states of lines and feeder terminal units across multiple time periods based on the Monte Carlo method; Step 2: Construct a distribution network segment location model, and quantify the location error under various disaster scenarios by comparing the difference between the actual state and the expected state of the nodes; Step 3: Establish a robust pre-disaster reinforcement model with the goal of minimizing the overall system cost, whereby the overall cost includes FTU reinforcement cost and positioning error penalty cost; Step 4: Construct the constraints of the robust pre-disaster reinforcement model, including μPMU observation constraints, circuit breaker protection constraints, fault multiple number constraints, reinforcement budget constraints, FTU immunity constraints, and fault state continuation constraints. Step 5: Combining the constraints in Step 4, the column and constraint generation algorithm is used to iteratively solve the robust pre-disaster reinforcement model and output the optimal pre-disaster reinforcement scheme.

2. The robust pre-disaster reinforcement method for distribution networks considering the timing of disasters and the fault tolerance of section location, as described in claim 1, is characterized in that: In step 1, during a typhoon disaster, high wind speeds generate lateral wind loads on the power distribution lines and towers, causing additional stress and bending moments in the line and tower structures. Based on the basic principles of aerodynamics, acting on the line ij The instantaneous wind load on the surface is expressed as: （1）； In formula (1): Indicates the action on the line ij Instantaneous wind load on the surface; air density; For the line ij The drag coefficient; for t Constantly acting on the line ij Instantaneous wind speed; For the line ij diameter; For adjacent towers m With towers n Between lines ij length; As a supporting structure, the tower is also subject to wind pressure, and its stress can be calculated from the wind-receiving area of ​​the tower: （2）； In formula (2): Indicates pole tower i The force under wind pressure; for t Constantly acting on the tower i Instantaneous wind speed; For towers i The windward coefficient; For towers i The equivalent windward area; Based on the principles of statics, towers i The root bending moment is: （3）； In formula (3): For towers k Equivalent arm; wire ij The lateral stress caused by wind load is: （4）； In equation (4): Indicates wire ij Lateral stress is generated due to wind load; For wires ij The windward cross-sectional area; When wind speed varies with time, both wind load and the resulting stress fluctuate over time. A normalized stress ratio is then introduced: （5）； In equation (5): Reflecting the route during the typhoon ij The percentage of wind intensity received; For wires ij Design limit stress; The impact of heavy rain on the line structure is manifested in the degradation of insulation performance and the reduction of foundation bearing capacity. The former leads to an increased probability of insulator flashover faults, while the latter reduces the stability of the tower structure. line ij The probability of flashover of the upper insulator exhibits an S-shaped relationship with rainfall intensity, which can be represented by a logic function: （6）； In formula (6): for t Timetable ij Probability of flashover of upper insulator; for t Always on the line ij Instantaneous rainfall intensity at the top insulator; For the line ij Critical flashover rainfall intensity for upper insulators; The steepness coefficient reflects the sensitivity of insulation performance to changes in rainfall; This represents the core operation of a logical function, used to map any real number to the interval (0,1); Continuous rainfall will lead to an increase in the moisture content of the foundation soil, resulting in a decrease in bearing capacity. The ultimate bending moment of the tower can be described as a linear decay function with increasing foundation wetting rate. （7）； In equation (7): for t The ultimate bending moment of the tower at any given moment; Design the ultimate bending moment for the tower under dry conditions; This is the humidification sensitivity coefficient; The soil wetting coefficient; （8）； In equation (8): for t Cumulative rainfall at all times; This represents the soil saturation rainfall threshold.

3. The robust pre-disaster reinforcement method for distribution networks considering the timing of disasters and the fault tolerance of section locations, as described in claim 2, is characterized in that: To systematically characterize the combined effects of typhoons and rainstorms, a time-varying damage index based on the principle of multi-source damage superposition is introduced; this index comprehensively considers the effects of wind-induced stress, foundation wetting, and insulation degradation. （9）； In equation (9): For the line ij exist t Comprehensive damage indicators at any given time; Indicates pole tower i Root bending moment; These are the weighting coefficients; Indicates pole tower i The probability of insulator flashover between adjacent lines; At this time, the line ij exist t The failure probability at time t is expressed as: （10）； In formula (10): Indicates the line ij exist t The probability of failure at any given moment; Baseline risk parameters reflect the risk level of the line. ij The probability of natural failure under disaster-free conditions; The damage sensitivity coefficient describes the strength of the impact of changes in damage indicators on the failure probability.

4. The robust pre-disaster reinforcement method for distribution networks considering the timing of disasters and the fault tolerance of section location, as described in claim 3, is characterized in that: The vulnerability of the FTU is quantified by the accumulation of structural strain energy caused by wind pressure; at time... t , No. j The local wind pressure of each FTU is expressed as: （11）； In equation (11): Indicates the first j Local wind pressure of each FTU; Indicates the first j The drag coefficient of each FTU; for t The moment of action at the j Instantaneous wind speed of each FTU; Indicates the first j The equivalent windward area of ​​each FTU; When the wind pressure exceeds the load-bearing threshold of the FTU structure This will lead to misalignment of internal components of the FTU or drift of sensor signals; based on the logistic vulnerability function, the probability of structural damage is defined as: （12）； In equation (12): Indicates the first j The probability of structural damage to an FTU; The wind-induced damage coefficient; Indicates the first j Structural load-bearing threshold of each FTU; Heavy rain affects the dielectric properties of the FTU electronic module through humidity penetration and water ingress short circuits, causing a decrease in sampling accuracy or a shift in the detection threshold; the probability of damage caused by heavy rain is expressed as: （13）； In equation (13): Indicates the first j Probability of damage caused by heavy rain to each FTU; The rain-induced damage coefficient; For the first j Instantaneous rainfall intensity per FTU; For the first j Critical rainfall intensity corresponding to each FTU protection level; Typhoons and torrential rains are positively correlated, defining the first j The probability of each FTU failure is: （14）； In equation (14): Indicates the first j The failure probability of an FTU; The basic component reflects the level of latent damage under normal conditions; , These are the edge effect coefficients for a single disaster cause; This is the disaster coupling coefficient, used to quantify the synergistic amplification effect of typhoons and rainstorms.

5. The robust pre-disaster reinforcement method for distribution networks considering the timing of disasters and the fault tolerance of section locations, as described in claim 4, is characterized in that: Multiple typical typhoon-rainstorm disaster samples were randomly generated using the Monte Carlo method, and an uncertain scenario set was constructed based on their time-varying action process. This uncertain scenario set was directly used in the subsequent robust optimization model as the uncertainty set describing the disaster disturbance. A set of disaster characteristic parameters was defined. （15）； In equation (15): Represents a single set of disaster characteristic parameters; The wind speed at the center of the typhoon; The intensity of rainfall at the center; Indicates the direction of the typhoon's movement; This refers to the typhoon's movement speed; The Monte Carlo method was used to randomly select N groups of disaster samples within their statistical distribution range. , These represent different disaster samples, which include the disaster intensity distribution and spatiotemporal evolution trajectory; This represents the total number of disaster samples drawn in Monte Carlo; each sample Corresponding to a disaster intensity distribution and spatiotemporal evolution trajectory, ; The typhoon was simulated as a circular model, with wind speeds at the maximum wind speed radius, decreasing towards the typhoon eye and outside the typhoon area. The maximum wind speed radius also coincided with the point of maximum rainfall intensity, decreasing towards the typhoon eye and outside the typhoon area. (In the sample...) Below, for distribution network lines ij With the j The local disaster intensity modeling for each FTU is as follows: （16）； In equation (16): Indicates the first n Under a disaster sample t Constantly acting on the line ij or the j Local wind speed intensity of each FTU; Indicates the first n Under a disaster sample t Constantly acting on the line ij or the j The localized rainfall intensity of each FTU; Indicates the first n Under a disaster sample t Timeline or distance from FTU to the disaster center; , These are the spatial attenuation coefficients for wind speed and rainfall intensity, respectively. Combining the previously established line and FTU time-varying vulnerability models, where the line time-varying vulnerability model includes equations (1) to (10) and the FTU time-varying vulnerability model is equations (11) to (14); calculate the failure probability of each component: calculate the line failure probability using equation (10) and calculate the FTU failure probability using equation (14).

6. The robust pre-disaster reinforcement method for distribution networks considering the timing of disasters and the fault tolerance of section locations as described in claim 5, characterized in that: Since disaster scenario analysis is based on a defined failure state, it uses probability quantities. and The fault is transformed into a discrete form, as shown in equations (17) and (18). （17）； In equation (17): For the first i There are several section fault status variables, where 1 indicates a section fault and 0 indicates a section normal. This is the threshold for the line fault probability. （18）； In equation (18): For the first j Each section has a fault status variable, where 1 indicates an FTU fault and 0 indicates a normal FTU. This is the FTU failure probability threshold; Finally, by overlaying state combinations from multiple disaster samples, multiple time periods, and multiple components, a set of decision-related uncertain scenarios was formed. Specifically, for each disaster sample... and each time period t Record the discrete fault states of all lines and all FTUs, and combine them into a complete scenario in chronological order. n The scenario corresponding to each disaster sample can be represented as: （19）； In equation (19): For the first n The scenario corresponding to each disaster sample; For the first n Each sample in the time period t Discrete fault state vectors for each section; For the first n Each sample in the time period t Discrete state vectors of each FTU; To set the number of time periods; Therefore, the overall set of uncertain scenarios can be written as: （20）； In equation (20): This represents a set of uncertain scenarios as a whole.

7. The robust pre-disaster reinforcement method for distribution networks considering the timing of disasters and the fault tolerance of section locations as described in claim 6, characterized in that: In step 2, the desired state of the node is calculated by the switching function, the actual state of the node is collected by the FTU, and the minimum set theory is used to construct an approximation model between the desired state and the actual state of the node, thereby realizing the fault-tolerant location of the fault section. The switching function is a logic function that calculates the desired state of the distribution network FTU based on the segment status and distribution network topology. Its construction mechanism is as follows: （21）； In equation (21): FTU j Upstream power supply reachability discrimination quantity, i.e., used to determine FTU. j Are there any faulty sections along the path to the upstream power source? FTU j Downstream fault presence discriminant, i.e., used to determine the presence of FTU. j Are there faulty sections in the downstream network? FTU j The theoretical expected state; For FTU j Number of power sources in the upstream network; For FTU j Number of power sources in the downstream network; For FTU j Upstream power The set of segments along the path; For FTU j The set of all segments in the downstream network; For FTU j to downstream power supply The set of segments along the path; For FTU j The set of all segments in the upstream network; This is a section fault status variable, where 1 indicates a section fault and 0 indicates a normal section. Represents the logical AND. Represents the logical "NOT"; Indicates the first k The first path i Fault status variables for each section; Indicates the first l Fault state variables of each section This indicates the power supply number, which is the serial number of the upstream or downstream power supply. express Path or The segment number in the path; express Path or The segment number in the path; Under normal operating conditions, FTU j The following situations may occur: （22）； Based on the fault-tolerant principle of segment positioning, the positioning function is as follows: （23）； In equation (23): This represents the set of FTU nodes in the distribution network; This indicates the actual status of the FTU received by the distribution network operation center; This indicates the expected status of the FTU received by the distribution network operation center; Meanwhile, when the FTU malfunctions, the signal it transmits to the control center will be distorted, resulting in either missed alarms or false alarms; therefore, the first... j FTU underreporting indicator variable False alarm indicator variable The formula is as follows: （24）； （25）。 8. The robust pre-disaster reinforcement method for distribution networks considering the timing of disasters and the fault tolerance of section locations as described in claim 7, characterized in that: In step 3, based on the established segment location model and the set of uncertain scenarios, a robust pre-disaster reinforcement model is constructed; the objective function of the robust pre-disaster reinforcement model is expressed as: （26）； In equation (26): n This represents the number of FTU nodes in the system. For the first i Unit reinforcement cost of an FTU; The penalty coefficient for misjudging segment positioning; s This is a pre-disaster reinforcement plan; For the first i The enhancement variable for each FTU is set to 1 if it is enhanced and 0 if it is not enhanced. For the scene u Next i The actual status of each segment; The first output of the segment positioning model i The expected state of each segment.

9. The robust pre-disaster reinforcement method for distribution networks considering the timing of disasters and the fault tolerance of section location, as described in claim 8, is characterized in that: Step 4 includes: 1) μPMU observation branch constraints: To improve the ability to identify feeder conditions under extreme weather conditions, μPMUs are introduced as high-precision condition observation points, and each μPMU can provide real-time voltage and current phasor information of its branch. Since the μPMUs have consistent time scales and high accuracy, once they detect fault characteristics, it indicates that the fault must occur within the observed branch. Based on this, the following constraints are established: （27）； In equation (27): For the first j A set of segments on each μPMU installation branch; 2) Circuit breaker constraints: According to the three-stage current protection principle, if the circuit breaker operates, the section fault must be within the protection range of the operating protection device. Therefore, the circuit breaker constraint is expressed as: （28）； In equation (28): For the first j A collection consisting of sections within the protection range of a circuit breaker; 3) Fault multiplicity constraint: To avoid meaningless high-dimensional combinations in the model, the maximum number of faults is limited to a given threshold: （29）； In equation (29): m The number of segments in the system; The maximum number of faults in a given section; 4) Strengthen budget constraints: To characterize the resource constraints of pre-disaster reinforcement decision-making, it is necessary to limit the reinforcement costs: （30）； In equation (30): To strengthen the available total budget cap; 5) Enhanced immune restraint: If a certain FTU is reinforced before a disaster, it will not fail in any time period across all planned scenarios, subject to the following constraints: （31）； In equation (31): Indicates the first i FTU during the period t The underreporting indicator variable; Indicates the first i FTU during the period t False alarm indicator variables; For the first i The enhancement variable for each FTU is 1, which indicates that the FTU has been enhanced, and 0 indicates that the FTU has not been enhanced. 6) Section fault continuation constraints: If a segment is already in a faulty state in a previous time period, it will remain in a faulty state in subsequent time periods, subject to the following constraints: （32）； In equation (32): Indicates the first i Fault status variables of each segment in time period t; Indicates the first i The fault status variables of each segment in time period t+1; In addition, it also includes section positioning switch function constraints and FTU state variable constraints, as shown in equation (21) and equation (22) respectively.

10. A robust pre-disaster reinforcement method for distribution networks considering the timing of disasters and the fault tolerance of section locations, as described in claim 9, is characterized in that: In step 5, since the robust pre-disaster reinforcement model has a typical min-max-min three-layer structure, where the reinforcement decision s and the uncertain scenario set are... There are coupling relationships between them, and direct solution will lead to the curse of dimensionality and exponential computational cost; therefore, this invention introduces the Column and Constraint Generation (CCG) algorithm to solve the robust pre-disaster reinforcement model; The Column and Constraint Generation (CCG) algorithm decomposes the three-level structure into two parts: the Master Problem (MP) and the Subproblems (SP). 1) Main problem MP: Given a finite set of scenarios, find reinforcement decisions s such that the reinforcement cost and the worst penalty cost in these scenarios are minimized; 2) Sub-problem SP: Under a fixed reinforcement scheme, find the worst scenario of the current reinforcement scheme among all disaster scenarios, and add the penalty cost of the worst scenario to the main problem MP to continue iterating; The Column and Constraint Generation (CCG) algorithm continuously generates new worst-case scenarios, gradually approximating the actual worst-case perturbation scenario, thereby completing the search of the uncertainty space; Ultimately, when the subproblem SP cannot find a worse scenario penalty cost than the current one, the solution to the main problem MP is the globally optimal solution. Assume the current main problem MP contains K If there are already generated scenarios, then the main problem MP is written as: （33）； （34）； In the above formula: This is the upper bound of the worst-case localization misjudgment penalty cost for the currently known scenario; Indicates the fault status variable of the section; Indicates the penalty coefficient for misjudging segment location; Indicates the number of FTU nodes in the system; Representing a scene u Next i The actual status of each segment; The output of the segment positioning model represents the first... i The expected state of each segment; Based on the objective function in step 3, the subproblem SP can be written as: （35）； In equation (35): Represents a set of uncertain scenarios One of the scenes; To facilitate solver processing, the absolute value term is standardized linearized, and the minimization problem within the model is transformed into an equivalent maximization form: First, introduce an integer misjudgment indicator variable for each segment: （36）； In equation (36): Indicates the first i The misjudgment indicator variable for each segment is used to measure the true fault status of that segment. With location results The degree of deviation between them; And constraints are added for linearization: （37）； The inner target then becomes: （38）； In equation (38): Indicates the fault state in a given real section. x Below, the minimum total penalty cost corresponding to the segment location model; Then, set a maximum number. M Its value is the penalty cost of locating no faults when all sections are faulty, i.e. （39）； In the formula: This represents the total number of segments in the system. Finally, minimizing the inner layer can be equivalently written as: （40）； Subproblem SP can be transformed into: （41）； After each round of alternating solution of the main problem MP and the subproblem SP, the upper and lower bounds of the maximum loss of the current reinforcement scheme are compared to determine whether to continue iterating. The worst-case penalty cost obtained by the main problem MP under a finite set of scenarios can be regarded as the upper bound (UB), while the minimum penalty cost corresponding to the true worst scenario identified by the subproblem SP in the complete scenario library constitutes the lower bound (LB); when the difference between the two satisfies: （42）； In equation (42): The convergence tolerance of the column and constraint generation algorithm is the maximum allowable error range between the upper bound UB obtained by the main problem MP and the lower bound LB obtained by the subproblem SP. Or it satisfies the relative error criterion: （43）； We can assume that the main problem MP has accurately approximated the worst-case scenario, and the iteration process has converged. At this point, the current enhancement scheme is the robust optimal solution. If it does not meet the requirements, we continue to add the worst-case scenario to the scenario set and enter the next round of iteration.

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