A bi-level robust optimization method for resilient distribution network section location considering failure probability and reinforcement strategy

Abstract

A double-layer robust optimization method for section location in resilient distribution network considering failure probability and reinforcement strategy is proposed, including: establishing a failure probability-aware chance constraint model to quantify the failure probability and its spatial correlation of each section and generate a high-confidence failure scenario set; establishing a reinforcement strategy optimization model to select key sections for pre-disaster reinforcement by genetic algorithm and change the underlying failure risk distribution; establishing a basic model for failure section location under information distortion; combining the chance constraint model, the reinforcement strategy optimization model and the basic model for failure section location, a double-layer robust optimization model for "defense and location" coordination is constructed, and a hybrid intelligent optimization method is used to solve it. Through the coordination of probability awareness, spatial correlation modeling and reinforcement strategy, the method significantly improves the positioning accuracy and robustness of the distribution network under multiple failure and information distortion scenarios, providing a coordinated optimization decision basis for pre-disaster defense and disaster location in resilient distribution network.

Description

Technical Field

[0001] This invention relates to the field of power system fault diagnosis and location technology, specifically to a two-layer robust optimization method for resilient distribution network segment location that considers fault probability and reinforcement strategies. Background Technology

[0002] To achieve rapid power grid recovery, "resilient distribution networks" have become an important research direction. Rapid and accurate fault isolation during the disaster phase is crucial for curbing the spread of accidents. The accuracy and timeliness of fault isolation directly depend on the reliability of fault location technology.

[0003] Currently, fault location based on fault current direction information collected by feeder terminal units (FTUs) is the mainstream approach. However, in harsh operating environments caused by extreme disasters, FTU equipment and its communication links are easily damaged, resulting in a high probability of missed and false alarms in remote signaling information, severely impacting the accuracy of traditional location models. Furthermore, extreme disasters can easily trigger large-scale, interconnected multiple faults in the distribution network, further increasing the difficulty of fault location. Improving the fault location method's fault tolerance under conditions of incomplete information and interference has become an important direction for solving practical engineering problems.

[0004] To improve the fault tolerance of positioning, scholars both domestically and internationally have conducted extensive research. Existing research mainly includes improved methods based on intelligent optimization algorithms (such as genetic algorithms and particle swarm optimization), as well as uncertainty modeling methods that introduce probabilistic frameworks (such as Bayesian networks and data-driven probabilistic models). However, these methods are essentially still within the "passive positioning during disasters" paradigm, and their performance is limited by the inherent vulnerability distribution of the power grid. When faced with large-scale, interconnected multiple faults and severe FTU information distortion caused by extreme disasters, the positioning accuracy drops significantly or even fails.

[0005] In recent years, research perspectives have shifted towards proactive disaster prevention, encompassing differentiated hardening, preventative reconfiguration, and other aspects. However, these optimization objectives typically focus on overall system reliability, connectivity, or load recovery capabilities, without directly and quantitatively optimizing fault location performance as an endogenous decision variable. There is a lack of a complete closed-loop optimization theoretical model and methodology that extends from "hardening strategies" to "probability distributions" and then to "fault location robustness."

[0006] Therefore, there is an urgent need for a new method that can coordinate proactive pre-disaster defense with robust mid-disaster location to fundamentally improve the accuracy and fault tolerance of power distribution network fault location under extreme disasters. Summary of the Invention

[0007] To address the issue of decreased accuracy in distribution network fault location under extreme disasters due to severe information distortion and complex multiple faults, this invention proposes a two-layer robust optimization method for resilient distribution network segment location that considers fault probability and reinforcement strategies. This method significantly improves the location accuracy and robustness of distribution networks under scenarios of multiple faults and information distortion through the synergy of probability perception, spatial correlation modeling, and reinforcement strategies. This provides a collaborative optimization decision-making basis for pre-disaster defense and in-disaster location of resilient distribution networks. The technical solution adopted in this invention is as follows: A two-layer robust optimization method for resilient distribution network segment location considering both fault probability and reinforcement strategies includes the following steps: Step 1: Establish a chance constraint model for fault probability perception, quantify the fault probability of a section and its spatial correlation, and generate a set of high-confidence fault scenarios; Step 2: Establish a reinforcement strategy optimization model, use a genetic algorithm to screen key sections for pre-disaster reinforcement, and change the underlying failure risk distribution; Step 3: Establish a basic model for fault segment location under information distortion, which serves as a general mathematical model for handling information distortion and adapting to complex topologies, and provides a unified interface for subsequent integration of probabilistic information, evaluation of strategy effectiveness, and participation in two-level optimization. Step 4: Combining the opportunity constraint model for fault probability perception established in Step 1, the reinforcement strategy optimization model established in Step 1, and the basic model for fault segment localization under information distortion established in Step 3, construct a "defense" system. A two-layer robust optimization model for "positioning" collaboration is proposed, and a hybrid intelligent optimization method combining genetic algorithm and improved particle swarm optimization algorithm is used to solve it.

[0008] In step 1, the occurrence of distribution network faults under extreme disasters exhibits significant spatial and temporal correlations. Traditional deterministic fault location models struggle to accurately describe the probabilistic characteristics of such complex fault scenarios, leading to decreased location accuracy. Therefore, this invention introduces probability-aware opportunity constraint modeling, constructing a fault probability database and a scenario probability calculation model to achieve accurate descriptions of fault scenarios under extreme disasters. The specific construction method is as follows: 1) Construction of the failure probability database: Traditional research on fault location in distribution networks is mostly based on deterministic models, failing to fully consider the uncertainty of fault occurrence under extreme disaster conditions. To overcome this theoretical limitation, a basic fault probability model based on stochastic fluctuation theory is constructed, and its mathematical expression is as follows: (1); In formula (1): For section j The basic failure probability; The baseline failure probability is the benchmark reference value for the failure probability of all sections. The probability fluctuation coefficient is set to 0.2, meaning the failure probability has a fluctuation range of 20%.

[0009] Considering the spatiotemporal propagation characteristics of extreme disasters, a spatial correlation matrix of failure probability is established: (2); In formula (2): express Corresponding "section" i and j The correlation coefficient of "physical adjacency" is set to 0.2, which reflects the degree of correlation between the failure probabilities of adjacent sections under extreme disasters. Corresponding "section" i and j The correlation coefficient for "belonging to the same feeder branch" is set to 0.1, which quantifies the correlation of fault probabilities between different sections of the same feeder. Corresponding "section" i and j The correlation coefficient for "critical connection nodes" is set to 0.06, which describes the probability association of failures in the critical connection node segment; the correlation coefficient for other cases is 0, indicating that there is no obvious spatial correlation between the failure probabilities of such segments.

[0010] 2) Scene probability calculation model: Under extreme disasters, multiple faults in the distribution network are affected not only by the probability of basic faults in each independent section, but also by the spatial correlation and electrical connectivity between sections. Traditional probabilistic models based on the assumption of independent faults are difficult to accurately describe such complex fault scenarios, leading to biased probability estimates. Therefore, this invention proposes a scenario probability calculation model that considers correlations, providing an accurate probabilistic basis for chance-constrained optimization. Let the sets of faulted sections and normal sections be respectively... , , Indicates a section i State variables; i The index representing the segment number, i.e., the... i Each section.

[0011] The probability of the scenario is: (3); In formula (3): Faulty section j Failure probability The product of consecutive products; Considering the spatial correlation between faulty sections, for all faulty sections that are not themselves... j Summation, "1+" reflects the enhancing effect of correlation on failure probability; Normal sectionj Probability of no failure The product of consecutive products; Indicates a section j The basic failure probability.

[0012] To avoid combinatorial explosion, a probability threshold is set for scene filtering: (4); In equation (4): To extract from all scene sets In this process, scenarios that meet the probability conditions are selected. This indicates the scenario number, which represents a specific fault scenario. A pre-set confidence threshold is used to filter out scenarios with extremely low probabilities. This refers to the number of fault demerits; the higher the number of fault demerits, the more likely it is to occur. The smaller the value, the more lenient the screening criteria, thus avoiding missing potential multi-fault scenarios that require attention.

[0013] 3) Opportunity constraint modeling: Chance constraints are an effective method for handling stochastic optimization problems. In distribution network fault location under extreme disasters, traditional deterministic constraints are insufficient to accurately describe the uncertainty characteristics due to the potential for missed and false alarms in FTU information. Based on robust optimization theory, chance constraints allow constraints to be satisfied with a certain probability level, thereby establishing a balance between optimization objectives and risk control. Chance-constrained fault location model considering information distortion probability: (5); In formula (5): Represents the probability distribution for failure scenarios. Conditional distribution of FTU signal after information distortion Seeking expectations reflects a comprehensive consideration of the uncertainties of failure scenarios and information distortion. This represents the FTU observation signal vector after information distortion, i.e., the set of FTU signals actually obtained during positioning; This represents the true signal vector of the FTU, that is, the true FTU signal that the system should have obtained when there is no information distortion.

[0014] This represents the calculation of the desired signal for M FTUs. With the actual distorted signal The absolute error is used to measure the degree of fit between the positioning result and the actual signal. This indicates the total number of FTUs configured in the distribution network. This is the weighting coefficient, set to 0.5; This indicates the number of faulty sections in the location results, which is used to avoid the unreasonable situation of assuming multiple faulty sections without any restrictions, and to balance the reasonableness of signal matching and the number of faults. This indicates the total number of sections to be located in the distribution network; Indicates the first i The fault status determination variables for each section, namely Indicates the first i One section was identified as faulty. Indicates the first i The section was determined to be normal.

[0015] Required location results Equivalent to real-world fault scenarios The probability is at least ,in, This is the allowable probability of location errors, thereby ensuring the reliability of fault location.

[0016] To address multiple faults, a compensation factor is introduced to improve robustness: (6); In formula (6): This represents the compensation factor for multiple fault scenarios. This is the compensation coefficient, used to control the magnitude of the compensation, and is set to 0.1. The number of faulty sections; This means that compensation will only be triggered when the fault count is greater than 1, and compensation will be 0 when the fault count is 1. This is specifically designed for multi-fault scenarios.

[0017] The opportunity constraint model for fault probability perception specifically includes formulas (1) to (6).

[0018] In step 2, traditional research on fault location in distribution networks mainly focuses on improving fault location algorithms during disasters, while rarely considering the proactive improvement of location performance through pre-disaster reinforcement measures. This invention innovatively introduces pre-disaster reinforcement strategies into the field of fault location, improving the overall performance of the location system by proactively reducing the probability of faults in key sections, thus realizing a paradigm shift from passive location to proactive prevention. The specific construction method is as follows: 1) Define reinforcement strategy: Based on system reliability theory, reinforcement strategies indirectly affect the performance boundary of the localization algorithm by altering the underlying failure probability distribution. A reinforcement strategy vector is defined. , These represent reinforcement strategies. The components are the decision variables for whether reinforcement is implemented in segments 1 to N. Among them: (7); The probability of section failure after reinforcement is reduced to the original level. Times: (8); In equation (8): For section j Enhanced failure probability; To enhance the effect coefficient, a value of 0.1 is set.

[0019] 2) Establish a multi-objective optimization problem: The goal of reinforcement strategy optimization is to achieve the highest positioning accuracy with the minimum reinforcement cost, and it establishes a multi-objective optimization problem: (9); In equation (9): This represents the total enhancement cost of all enhanced sections. For section j The cost of strengthening; This is the negative of the positioning accuracy; minimizing this objective is equivalent to maximizing the positioning accuracy. This indicates that the total number of segments that can be enhanced cannot exceed the maximum number of enhancements. .

[0020] The positioning accuracy rate is defined as follows: (10); In formula (10): This represents the accuracy of fault segment location under the enhanced strategy r; For the indicator function, if the positioning result Compared to real-world failure scenarios If the values ​​match, the function value is 1; otherwise, it is 0. For test scenario set The scale, i.e., the number of scenarios; The enhanced strategy optimization model specifically includes formulas (7) to (10); 3) Solving using a genetic algorithm: Transform the multi-objective optimization problem into a single-objective optimization problem, and design the fitness function: (11); In equation (11): This represents the fitness function value of the reinforcement policy r; This represents the accuracy of fault segment location under the enhanced strategy r; This is the accuracy threshold; This is the fault multiplicity penalty factor, which increases as the fault multiplicity increases; The penalty coefficient is used. A genetic algorithm is employed to solve the reinforcement strategy optimization problem. The complete algorithm flow design is as follows:Figure 1 As shown.

[0021] In step 3, to support the effectiveness evaluation of the above model, a basic model for fault segment location under information distortion needs to be established as a carrier. Together, these three elements form a complete modeling system of "risk perception - proactive defense - decision execution," laying the foundation for subsequent collaborative optimization research. The specific construction method is as follows: 1) Objective function and improved switching function: Based on the principle of distribution network segment location, the objective function established in this invention is as follows: (12); (13); In the above formula: The fitness value corresponding to each solution (segment state vector) in the solution set; This represents the total number of FTUs and also the total number of feeder sections. Twice the number of FTUs; For the first j FTU (i.e., FTU) j The actual fault current information transmitted; For the calculated FTU j Expected fault current information; For section LS j The state; The weighting coefficients, set according to the minimum set theory of fault diagnosis, are generally set to 0.5 to avoid misjudgment. This is the sum of the number of all faulty sections; The penalty coefficient for critical sections is set to 0.15. This is the sum of the number of all critical segments; Indicates the first k State variables of key sections; Indicates the index number of the key section; This represents the set of key segments.

[0022] Traditional switching functions directly superimpose forward and reverse expected states, making it difficult to accurately calculate the node expected states when the fault currents supplied by the main power source and distributed generation (DG) reverse. This results in existing fault location models being unsuitable for complex multiple faults under extreme disasters. An improved switching function is constructed using the fault section assumption and distribution network topology: (14); In equation (14): FTU j The node's expected positive state; For FTU j Number of power sources in the upstream network; For FTU j Upstream power The set of segments along the path; for Inner section i The state; For FTU j The set of all segments in the downstream network; Indicates the logical "OR"; This represents the logical AND operator; Indicates the logical "NOT"; This indicates the segment index, that is, the number of a certain segment; Indicates a section State variables; FTU j The reverse expected state of the node; For FTU j Number of power sources in the downstream network; For FTU j to downstream power supply The set of segments along the path; for Inner section i The state; For FTU j The set of all segments in the upstream network; FTU j The overall expected state of the node; FTU j The node's expected positive state; FTU j The reverse expected state of the node.

[0023] 2) Multi-source information fusion and physical operational constraints: 2.1) Fault branch constraints: The configuration of a miniature synchronous phasor measurement unit (μPMU) can identify faulty branches, thereby defining the extent of the faulty section. Let the monitoring domain of the μPMU be... Therefore, the faulty section must be located on the faulty branch determined by the μPMU, that is: (15); In equation (15): The set of sections on the faulty branch determined by the μPMU, i.e. the range of potential faulty sections detected by the μPMU.

[0024] 2.2) Circuit breaker protection domain constraints: According to the three-stage current protection principle, circuit breaker tripping can determine the power outage area, and the faulty section must be within the protection range of the activated protection device. That is: (16); In equation (15): This refers to the set of sections within the protection range of the circuit breaker.

[0025] 2.3) FTU signal distortion constraint: Considering the harsh operating environment of FTUs under extreme disasters, the missed and false alarms of FTU remote signaling information become the biggest adverse factors for the application of positioning methods. A signal distortion model is constructed as follows: (17); In equation (17): Indicates the first j The signal values ​​ultimately used by each FTU for fault location; Indicates the first j Distortion observation signal of one FTU; Indicating the candidate fault state vector Next, the j The expected signal of each FTU.

[0026] 2.4) Fault multiplicity constraint: Even under extreme weather conditions, the probability of multiple failures occurring is very small; therefore, the maximum number of failures under extreme weather conditions is limited as follows: (18); In formula (18): The set consisting of segments LS; The maximum number of faults is set to 3 in this invention.

[0027] 2.4) Section state constraints: Since the distribution network topology changes due to the connection of the DG (Distribution Current Generation) system, encoding is performed based on the direction of the fault current. (19).

[0028] In step 4, to address the uncertainty and reliability issues in fault location within the distribution network under extreme disasters, this invention proposes constructing a "defense" system. A two-layer robust optimization model for "location" collaboration is proposed. This model, through a master-slave hierarchical structure, deeply integrates pre-disaster defense and in-disaster location, aiming to obtain a method that maintains high location performance under probabilistic uncertainty. Its core lies in the bidirectional coupling and iterative verification between the upper and lower layers, achieving collaborative optimization of policy robustness and de-robustness. The specific construction method is as follows: 1) Overall structure: The two-layer robust optimization model constructed in this invention adopts a typical master-slave hierarchical structure, and its mathematical expression is as follows: (20); In equation (20): Represents the upper-level reinforcement policy vector The feasible region is the set of values ​​for the upper-level decision variables; For upper-level binary decision variables, in the form of , representing the reinforcement strategy vector These represent the reinforcement decision variables for each segment; Indicates transpose; Each represents the total number of segments; Costs associated with upper-level decision-making; It is a set of uncertainties that depend on reinforcement strategies; For uncertain parameters, in the form of Includes fault scenarios and FTU signal distortion Characterizes the uncertain interference factors of the system; For hierarchical relationships, it indicates that given a higher-level strategy... and uncertainty parameters When, the optimal objective value of the lower-level subproblem; The lower feasible region is the basis for lower-level decision-making. The range of valid values; The lower-level objective function; For lower-level binary decision variables, in the form of Characterize the fault location results. These represent the vectors of the lower-level fault location results. Each component, i.e., the fault state variable of each section.

[0029] The upper planning layer influences the lower operating environment through probability adjustments, and the performance of the lower operating layer guides the optimization of upper-level strategies through accuracy feedback, forming a complete "planning-operation" collaborative optimization chain. The architecture is as follows: Figure 2 As shown.

[0030] 2) Upper layer: Strengthening the robust optimization model of the strategy: The upper-level planning layer is built upon a reinforcement strategy optimization model. It introduces a worst-case scenario optimization mechanism and fault probability spatial correlation modeling through a fault probability-aware opportunity constraint model, establishing a dynamic coupling relationship between the reinforcement strategy and the probability distribution. This ensures that the system maintains reliable positioning capability even under the most unfavorable conditions within budget constraints. The modeling process is as follows: (twenty one); In equation (21): This is the risk aversion coefficient; the higher the value, the more conservative the decision-making. The positioning accuracy function is used to evaluate the positioning results of the lower layer. Compared to real faults Consistency; This indicates that, given a reinforcement policy Uncertain scenarios and real-world failure scenarios Under the given conditions, the optimal solution to the subproblem of locating the lower-level fault section. This represents the feasible region of the upper-level reinforcement strategy, which is the set of all reinforcement schemes that satisfy the constraints. Indicates the first i Strengthening decision variables for each segment; This indicates the maximum number of enhancement sections allowed, which can also be understood as the upper limit of the enhancement budget. For the set of key segments; Mandatory constraints for critical sections; This refers to the minimum reinforcement requirement for key sections.

[0031] 3) Lower layer: Probability-aware robust localization model: The lower-level operational layer integrates a basic model for fault segment localization under information distortion and an opportunity-constrained model for fault probability perception. Addressing the performance degradation of traditional deterministic localization in FTU signal distortion environments, it enhances uncertainty handling capabilities through opportunity-constrained robustness and multi-source information fusion, achieving high-precision localization under signal distortion interference. The modeling process is as follows: (twenty two).

[0032] 4) Solution steps: The two-layer robust optimization model constructed in this invention considers the uncertainty of the probability distribution of fault scenarios through chance constraints in the upper planning layer, and the uncertainty of FTU signal distortion in the lower operation layer, unifying the two within a probability-aware framework. The upper planning layer generates a high-confidence scenario set using probability distributions, and the lower operation layer achieves robust localization on this scenario set, thus constructing both layers as probability-aware optimization problems. Methods that transform the two-layer robust optimization model into a single-layer model (such as KKT, C&CG) are difficult to effectively handle discrete decision variables and complex chance constraints when applied to this optimization problem. Furthermore, the reinforcement strategy and fault localization form an interactive game process of strategy optimization and localization response through probability adjustment, which is difficult to effectively map using a single-layer model. Therefore, this invention employs a hybrid intelligent optimization method combining genetic algorithm and improved particle swarm optimization algorithm to solve the two-layer robust optimization model constructed in this invention. The algorithm solution process is as follows: Figure 3 As shown.

[0033] 1) In the upper planning layer of the two-layer robust optimization model, based on the requirements of fault probability perception and system reliability, a genetic algorithm is used to optimize and solve the reinforcement strategy. Specific steps include: The initial population includes multiple reinforcement schemes, and the offspring population is generated through roulette wheel selection, single-point crossover, and uniform mutation. 1.1) Initialize a population containing multiple enhancement schemes, including: The enhancement strategy vectors defined in equations (20) to (21) As the individual encoding for the genetic algorithm, the population containing multiple feasible reinforcement schemes is initialized, and the specific formula is as follows: (twenty three).

[0034] In equation (23): This is the initial population of generation 0; Each individual within the population; For the first q There are 1 candidate reinforcement strategy, and each entity satisfies the feasible region constraint in equation (21). ; This indicates the population size of the upper-level genetic algorithm, that is, how many individuals with reinforcement strategies are in the initial population.

[0035] 1.2) Generate the parent population through roulette wheel selection: For each candidate reinforcement strategy in the initial population Construct the fitness function according to equation (21) Calculate individual merits and demerits. Indicates candidate reinforcement strategy The objective function value in the robust optimization model of the upper-level reinforcement strategy shown in equation (21) is determined. A roulette wheel selection mechanism is used to select parent individuals. q The probability of an individual being selected is: (twenty four).

[0036] In equation (24): For the first q The probability of an individual being selected; For the first q The fitness function value of an individual using a reinforcement strategy; It is a very small positive number; This represents the summation over all individuals in the entire population; Index representing an individual in the population; Population size.

[0037] 1.3) Single-point crossover generates offspring population: The parent individuals obtained by roulette wheel selection and Let the random intersection point be... m Then, two offspring individuals are generated through a single-point crossover: (25).

[0038] In equation (25): , These are the two offspring individuals generated after crossover; , Reinforcement strategies for both parent generations; Assign a parent generation individual number; , Indicates the parent individual in the first generation i Strengthened decision-making in each segment; Represents a random intersection point that satisfies ; To enhance the policy vector dimension, the length of the individual encoding is determined.

[0039] 1.4) Uniform mutation generates new candidate enhancement strategies: Uniform mutation is performed on each reinforcement decision variable of the offspring individuals, with the mutation rule as follows: (26).

[0040] In equation (26): For the mutated first i Strengthen decision variables; For the first time before the mutation i Strengthen decision variables; Toggles the values ​​of 0 and 1; 1 indicates the probability of mutation; others indicate that the original value is retained if no mutation occurs.

[0041] 1.5) Evaluate the worst-case localization performance of each strategy in a high-confidence fault scenario set using parallel computing: including: For any candidate reinforcement strategy First, update the segment failure probability according to equation (8), then calculate the scenario probability according to equation (3). Based on equation (4), filter high-confidence failure scenarios to obtain the high-confidence scenario set corresponding to this reinforcement strategy: (27).

[0042] In equation (27): For the first q A set of high-confidence fault scenarios corresponding to each reinforcement strategy; This represents a specific fault scenario; The scenario probability is calculated based on equation (3); The scene filtering threshold in expression (4).

[0043] In each scene Next, the lower-level probabilistic perception robust localization model of equation (22) is invoked to obtain the optimal localization result: (28).

[0044] In equation (28): To represent the reinforcement policy given Uncertain scenarios and real-world failure scenarios Under the given conditions, the optimal positioning result obtained by the lower layer; This represents the vector of the lower-level fault location results; Let be the lower feasible region in equations (20) and (22); Let be the lower-level objective function in equations (20) and (22).

[0045] Furthermore, the positioning accuracy under each high-confidence scenario is calculated according to equation (10), and the minimum value is taken as the worst positioning performance of this enhancement strategy: (29).

[0046] Equivalently, it can also be written as the performance loss in the worst-case scenario: (30).

[0047] In equations (29) to (30): For the first q The worst localization accuracy of each reinforcement strategy on a high-confidence scenario set; For the first q The worst-case localization performance loss of each reinforcement strategy in a high-confidence scenario set; The positioning accuracy function defined by equation (10); This refers to the positioning loss in the corresponding scenario; The solution obtained from equation (28) is the optimal fault location scheme under the current strategy and scenario; Generated by Equation (27), it only includes fault scenarios that meet the probability standard and require key prevention; This indicates an uncertain scenario.

[0048] Due to different scenarios The lower-level solutions are independent of each other, so parallel computing can be used to improve the evaluation efficiency of high-confidence fault scenario sets.

[0049] 1.6) And combine the reinforcement cost to construct the upper-level fitness function for environment selection: including: Based on Equation (21), a robust optimization model for strengthening strategies is constructed, and the fitness function is then defined as follows: (31).

[0050] In equation (31): For the first qThe fitness function value of each reinforcement strategy; Indicates the total reinforcement cost; For section i The cost of strengthening; Indicates the first q In the reinforcement strategy, the first i Strengthening decision variables for each segment; This represents the risk aversion coefficient; the higher the value, the more conservative the decision-making. Indicates the first q The worst-case localization performance loss in high-confidence scenarios of the reinforcement strategy.

[0051] During environmental selection, parent and offspring individuals are merged and selected based on fitness function values. Sort the individuals from smallest to largest, and retain those with better fitness for the next generation.

[0052] 1.7) The final iteration obtains the optimal combination of reinforced sections that can maintain high positioning reliability even under severe fault conditions, including: After multiple iterations, the optimal reinforcement strategy is output: (32).

[0053] The corresponding optimal combination of enhancement sections is: (33).

[0054] In equations (32) to (33): This is the optimal reinforcement strategy ultimately output by the upper planning layer; Indicates in the feasible region Inside, find the fitness function Minimal reinforcement strategy That is, the solution that best combines cost and robustness; This represents the optimal set of enhanced sections. The optimal reinforcement strategy is represented by the first... i The optimal decision value for the segment. i The index representing the segment number, i.e., the... i Each section.

[0055] 2) In the lower running layer of the two-layer robust optimization model, an improved particle swarm optimization algorithm is used to solve the fault section location model: 2.1) Based on the given optimal enhancement scheme at the upper level, initialize the particle swarm position and velocity, including: The optimal reinforcement scheme at the upper level Based on this, the lower-level decision variables in equations (20) and (22) are... As particle position encoding, and to initialize the particle swarm: (34).

[0056] Simultaneously, initialize a velocity vector for each particle: (35).

[0057] In equations (34) to (35): For the initial particle swarm; Indicates the first p The position of each particle; Particle swarm size; Given an enhancement scheme and failure scenarios The next feasible region; Indicates the first p The velocity vector of each particle; Indicates the first p The first particle i A velocity vector of dimension; For the first i The fault state variables of each section are defined in equation (13).

[0058] 2.2) Updating particle positions based on Sigmoid probability, including: In the t In the nth iteration, the 1st p The first particle i The speed of the dimension update is: (36).

[0059] In equation (36): Indicates the first p The first particle i Vi in the Speed ​​during the next iteration; Indicates the first p The first particle i Vi in the Speed ​​during the next iteration; Indicates the first Inertia weights in the next iteration; Represents an individual's learning factor; Represents the group learning factor; , express Random numbers within the interval; Indicates the first p The best historical position of each particle i Dimensional components; The first position representing the group's historical best position i Dimensional components; Indicates the first p The first particle iVi in the Position components at the next iteration.

[0060] Then, the sigmoid function is used to map the velocity to the position update probability: (37).

[0061] In equation (37): This represents the Sigmoid probability mapping function; Represents the natural exponential function; The updated velocity components are obtained from equation (36); Indicates the first i The probability of updating the dimension position to 1.

[0062] Update particle positions accordingly: (38).

[0063] In equation (38): This represents the Sigmoid probability mapping function; Indicate Random numbers within the interval; For the updated number i Dimensional segment state variables; From equation (37), we obtain that the first... i The probability of updating the dimension position to 1.

[0064] 2.3) Accelerate convergence through adaptive inertia weights and early stopping mechanisms, including: For the inertia weight in equation (36) Adaptive decreasing method: (38).

[0065] In equation (38): Indicates the first t Inertia weights in the next iteration; Indicates the upper bound of the inertia weight; Indicates the lower bound of the inertia weight; Indicates the maximum number of iterations; This indicates the current iteration number.

[0066] At the same time, when continuous L The improvement of the global optimal objective function in the iteration is less than the threshold. ε When the iteration is terminated early, this is the stopping criterion in the solution process of the lower-level model in equation (22): (39).

[0067] In equation (39): Indicates the firstt The globally optimal objective function value at the next iteration; Indicates the preceding L The globally optimal objective function value at time; Represents continuous observation algebra; Indicates the early stopping threshold; This represents absolute value operations.

[0068] 2.4) The localization accuracy is evaluated by combining the high-confidence fault scenario set generated by chance constraints, including: For the high-confidence fault scenario set generated by equation (27) In every scene The following outputs the optimal fault location result: (40).

[0069] In equation (40): Representing a scene The optimal fault location result is as follows; This represents the optimal reinforcement strategy obtained by the upper layer; This indicates a high-confidence fault scenario; Represents a real-world fault scenario; This represents the lower-level feasible region, which is the basis for lower-level decision-making. The range of valid values; This represents the lower-level objective function.

[0070] Finally, the localization accuracy is statistically analyzed on the high-confidence fault scenario set according to equation (10): (41).

[0071] In equation (41): Represents the optimal reinforcement strategy Overall positioning accuracy; Indicates the size of the set of high-confidence failure scenarios; This represents the summation over all high-confidence scenarios; Indicates an indicator function. (The text inside the parentheses is incomplete and likely refers to a function or instruction.) If true, set the value to 1 (correct positioning); otherwise, set the value to 0 (incorrect positioning).

[0072] 2.5) Finally, output the fault segment location results that are robust under various interference scenarios. This includes: The optimal localization results obtained by combining Equation (40) under various high-confidence fault scenarios, and the overall accuracy evaluation given by Equation (41), are used to finally output the fault segment localization results that are robust under information distortion, multiple faults, and the most unfavorable disturbance conditions. The specific results are shown in Table 2.

[0073] This invention presents a two-layer robust optimization method for resilient distribution network segment location that considers both fault probability and reinforcement strategies. The beneficial effects are as follows: 1) This invention innovatively introduces a proactive pre-disaster reinforcement strategy into the field of fault location, and proactively improves the boundary of location performance by changing the distribution of system vulnerability, thereby realizing a paradigm shift from "passive response" to "proactive defense-robust location" collaboration.

[0074] 2) This invention quantifies faults and their spatial correlation through a probabilistic perception model and uses chance constraints to handle information distortion, making the positioning model more adaptable and robust to extreme uncertainty environments.

[0075] 3) The two-layer robust optimization model constructed in this invention realizes a direct and quantitative correlation between reinforcement measures and positioning performance in the mathematical model, which can systematically improve the lower limit of positioning reliability in the worst scenario with limited disaster prevention resources.

[0076] 4) The genetic-improved particle swarm optimization hybrid intelligent algorithm used in this invention can effectively solve high-dimensional, nonlinear, and discrete bi-level optimization problems, ensuring the feasibility and efficiency of the method in practical applications.

[0077] 5) In scenarios with multiple faults and severe distortion of FTU information, the method of the present invention can significantly improve the positioning accuracy and fault tolerance compared with traditional methods, providing an economical and reliable decision support tool for the planning and operation of resilient distribution networks. Attached Figure Description

[0078] The present invention will be further described below with reference to the accompanying drawings and examples; Figure 1 This is a flowchart of the distribution network reinforcement strategy optimization based on genetic algorithms.

[0079] Figure 2 Diagram of the two-layer robust optimization model architecture.

[0080] Figure 3 This is a flowchart for solving the two-layer robust model.

[0081] Figure 4 This is a topology diagram of a 14-node dual-end power supply network.

[0082] Figure 5 A comparison chart of the fault location capabilities of different fault location methods.

[0083] Figure 6 A comparison chart of false negative rates for segment location methods.

[0084] Figure 7 A comparison chart of false alarm rates for segment positioning methods. Detailed Implementation

[0085] This paper proposes a two-layer robust optimization method for resilient distribution network segment location, considering both fault probability and reinforcement strategies. First, a chance-constrained model for fault probability perception is established to quantify segment fault probabilities and their spatial correlations, generating a high-confidence fault scenario set. Second, a reinforcement strategy optimization model is constructed, utilizing a genetic algorithm to select key segments for pre-disaster reinforcement, thereby altering the underlying fault risk distribution. Finally, a two-layer robust optimization model framework is designed, coordinating upper-layer reinforcement strategies with lower-layer probabilistic robust location, to achieve "defense..." "Location" closed-loop optimization, and the use of genetics An improved particle swarm optimization hybrid intelligent algorithm is used for solving the problem. This invention significantly improves the location accuracy and robustness of distribution networks under multiple faults and information distortion scenarios through the synergy of probability perception, spatial correlation modeling, and reinforcement strategies, providing a collaborative optimization decision-making basis for pre-disaster defense and in-disaster location of resilient distribution networks.

[0086] Example: To verify the effectiveness of the proposed two-layer robust optimization method for resilient distribution network segment location considering both fault probability and reinforcement strategies, a simulation analysis is performed on a 14-node distribution network system with one distributed generation (DG) as an example. Figure 4 As shown, the feeder has 14 FTUs with directional elements, installed at each node. Three μPMU measuring devices are installed at nodes 6, 12, and 14, respectively. Three circuit breakers are installed at nodes 1, 2, and 8, respectively. A distributed generation (DG) is connected at node 14. The direction from the main power supply to the end of the feeder or the DG is defined as the positive direction of the entire network. The line segment between two adjacent FTUs is called the feeder segment, and the feeder segment number is consistent with its adjacent upstream switch. Simulations were performed in MATLAB R2025a environment, and the effectiveness of the proposed two-layer robust optimization method was verified based on this topology.

[0087] In the proposed genetic-improved particle swarm optimization (PSO) hybrid algorithm framework, the mutation rate of the upper-level genetic algorithm is a key parameter controlling the global search capability of the reinforcement strategy. Specifically, the mutation rate adjustment algorithm balances the exploration of new strategies and the maintenance of superior patterns in the solution space, and its value directly affects the diversity, robustness, and final localization performance of the obtained strategies. Table 1 shows the reinforcement schemes and localization performance corresponding to different mutation rates.

[0088]

[0089] As shown in Table 1, when the mutation rate is low (0.05), the algorithm's global exploration capability is insufficient, leading to premature convergence and a low localization accuracy (49.61%) in the worst-case scenario. When the mutation rate increases to 0.15, the algorithm achieves a better balance between global search and local exploration, obtaining a higher average localization accuracy (86.99%) and a worst-case scenario accuracy (65.89%), while maintaining a reasonable convergence time. Further increasing the mutation rate (0.20, 0.30) introduces too much random perturbation, disrupting the inheritance of excellent strategy patterns and resulting in performance degradation and prolonged convergence time. In conclusion, the hybrid algorithm exhibits the best overall optimization performance when the mutation rate is 0.15. To verify the effectiveness and fault tolerance of the distribution network fault location method proposed in this invention, simulations were performed on single and multiple faults in the distribution network, as well as scenarios involving intact, missed, and false FTU remote signaling information. The fault location results under information distortion conditions are shown in Table 2.

[0090]

[0091] Table 2 shows that the pre-disaster reinforcement strategy optimized by the upper-level genetic algorithm can effectively reduce the failure probability of key sections, thereby improving the lower limit of the system's localization model's performance in the worst-case scenario. As the number of reinforced sections increases, the overall system localization accuracy shows a monotonically increasing trend (from 71.01% to 92.37%), and the FTU information distortion rate decreases synchronously, verifying the effectiveness of the synergistic optimization of the chance-constrained model and the reinforcement strategy. The worst-case failure scenario localization accuracy, as a core robustness indicator, reveals the marginal effect of performance improvement: when the reinforcement strategy covers the key section combination shown in Scheme 3 (including the backbone, information hub, and DG end), the spatial distribution of the failure probability is reshaped, and the lower limit of system robustness significantly increases; further expanding the reinforcement scope significantly narrows the improvement in performance for the worst-case scenario.

[0092] A comprehensive comparison of various schemes reveals that Scheme 3 (strengthening 6 sections) achieves the optimal balance between cost and robustness, improving the overall location accuracy to 86.99%, with both the dual and triple worst-case scenarios maintaining accuracy above 65%. This result validates the advancement of the proposed method: by quantifying fault probability and its spatial correlation through a probabilistic perception model, and utilizing a two-layer optimization framework to select key sections for targeted reinforcement, it achieves a paradigm shift from "passive fault location" to "active probabilistic defense" with limited disaster prevention resources, providing an economical and reliable decision-making basis for the planning and operation of resilient distribution networks.

[0093] To verify the effectiveness and superiority of the method of this invention in complex and uncertain environments, it is compared with several typical methods. The comparison methods are shown in Table 3, including the traditional analytical method based on switching functions (M1), the intelligent localization method based on particle swarm optimization (M2), the probabilistic localization method based on Bayesian networks (M3), the probabilistically aware robust localization method (M4), and the method proposed in this invention (M5).

[0094]

[0095] The selected methods constitute a technological evolution chain from traditional inference to system resilience optimization. M1 and M2 are based on deterministic assumptions. Although the latter improves convergence and average accuracy through intelligent search, neither characterizes the randomness of faults, spatial correlation, and uncertainty in information acquisition, limiting their performance in scenarios with multiple faults and signal distortion. M3 and M4 introduce uncertainty modeling, with M4 integrating probability awareness, spatial correlation, and robust optimization, representing the current advanced level of passive disaster location. M5, comprehensively covering all technical dimensions of M4, further introduces upper-level reinforcement strategies, extending the decision-making object from the location algorithm to the system's vulnerable structures, achieving "pre-disaster proactive hardening." Enhanced collaborative resilience through "robust positioning during disasters".

[0096] Simulations M1-M5 run independently under the same fault scenario scale, FTU distortion conditions, and test sample set, differing only in their localization mechanisms. M1 and M2 use randomly generated fault scenarios, M3 uses Bayesian prior-based fault scenario generation, and M4 and M5 use probability-aware chance-constrained scenario generation. Simulation results are as follows: Figures 5-7 As shown.

[0097] Figure 5 The localization accuracy of different methods under single, dual, and triple fault conditions was compared. The method of this invention (M5) maintained high accuracy under all fault conditions: an average of 97.01% (82.95% in the worst-case scenario) for single faults, 85.58% (67.44% in the worst-case scenario) for dual faults, and 73.51% (65.89% in the worst-case scenario) for triple faults. In contrast, the accuracy of M1 and M2 decreased significantly with increasing fault severity; M3's accuracy dropped to 0% in the worst-case scenario of multiple faults, indicating insufficient robustness; while M4 outperformed the first three methods, it still lagged behind M5 in worst-case scenario protection, demonstrating the synergistic effect of reinforcement strategies and probabilistic modeling in improving robustness.

[0098] Figure 6 and Figure 7The false alarm rate and false alarm rate of each method were compared. The method of this invention (M5) maintained a low level even under multiple faults, with a false alarm rate of 11.41% and a false alarm rate of 2.42% under triple faults, showing the best performance. The false alarm rate of traditional methods (M1, M2) increased significantly with the number of faults; M3 had a false alarm rate as high as 12.86% under triple faults, showing high sensitivity to information distortion. M4 showed improvement in information distortion control, and M5 further improved the positioning stability under false alarm and false alarm interference by fusing multi-source information and reinforcement mechanisms.

[0099] In summary, traditional methods have limited overall performance under complex fault conditions; Bayesian network-based probabilistic localization methods lack the ability to adapt to multiple faults and information distortion; while probabilistically aware robust localization methods offer some improvement at the level of single uncertainty, they lack reinforcement mechanisms, leaving room for improvement in worst-case scenario reliability. The method proposed in this invention demonstrates the best performance in terms of localization accuracy, worst-case robustness, and tolerance to information distortion, especially maintaining reliable localization capabilities even under conditions of multiple faults and signal distortion.

Claims

1. A two-layer robust optimization method for resilient distribution network segment location considering fault probability and reinforcement strategies, characterized in that... Includes the following steps: Step 1: Establish a chance constraint model for fault probability perception, quantify the fault probability of a section and its spatial correlation, and generate a set of high-confidence fault scenarios; Step 2: Establish a reinforcement strategy optimization model, use a genetic algorithm to screen key sections for pre-disaster reinforcement, and change the underlying failure risk distribution; Step 3: Establish a basic model for locating fault sections under information distortion; Step 4: Combining the opportunity constraint model for fault probability perception established in Step 1, the reinforcement strategy optimization model established in Step 1, and the basic model for fault segment localization under information distortion established in Step 3, construct a "defense" system. A two-layer robust optimization model for "positioning" collaboration is proposed and solved using a hybrid intelligent optimization method.

2. The two-layer robust optimization method for resilient distribution network segment location considering fault probability and reinforcement strategy as described in claim 1, characterized in that: In step 1, probability-aware opportunity constraint modeling is introduced. By constructing a fault probability database and a scenario probability calculation model, an accurate description of fault scenarios under extreme disasters is achieved. The specific construction method is as follows: 1) Construction of the failure probability database: A basic failure probability model based on stochastic fluctuation theory was constructed, and its mathematical expression is as follows: （1）； In formula (1): For section j The basic failure probability; The baseline failure probability is the benchmark reference value for the failure probability of all sections. It is the probability fluctuation coefficient; Considering the spatiotemporal propagation characteristics of extreme disasters, a spatial correlation matrix of failure probability is established: （2）； In formula (2): express Corresponding "section" i and j The correlation coefficient of "physical adjacency" reflects the degree of correlation between the failure probabilities of adjacent sections under extreme disasters; Corresponding "section" i and j The correlation coefficient of "belonging to the same feeder branch" quantifies the correlation of fault probabilities in different sections of the same feeder; Corresponding "section" i and j The correlation coefficient for "critical connection nodes" describes the probability association of failures in critical connection point segments; otherwise, the correlation coefficient is 0, indicating that there is no obvious spatial correlation between the failure probabilities of such segments. 2) Scene probability calculation model: A scenario probability calculation model considering correlation is proposed, providing an accurate probabilistic basis for chance-constrained optimization; let the index sets of faulty sections and normal sections be respectively... , , Indicates a section i State variables; i The index representing the segment number, i.e., the... i Each section; The probability of the scenario is: （3）； In formula (3): Faulty section j Failure probability The product of consecutive products; Considering the spatial correlation between faulty sections, for all faulty sections that are not themselves... j Summation, "1+" reflects the enhancing effect of correlation on failure probability; Normal section j Probability of no failure The product of consecutive products; Indicates a section j The basic failure probability; To avoid combinatorial explosion, a probability threshold is set for scene filtering: （4）； In equation (4): To extract from all scene sets In this process, scenarios that meet the probability conditions are selected. Indicates the scene number; A pre-set confidence threshold is used to filter out scenarios with extremely low probabilities. This refers to the number of fault demerits; the higher the number of fault demerits, the more likely it is to occur. The smaller the value, the more lenient the screening criteria, avoiding missing potential multi-fault scenarios that require attention; 3) Opportunity constraint modeling: Chance-constrained fault location model considering information distortion probability: （5）； In formula (5): Represents the probability distribution for failure scenarios. Conditional distribution of FTU signal after information distortion Seeking expectations reflects a comprehensive consideration of the uncertainties of failure scenarios and information distortion. This represents the FTU observation signal vector after information distortion; This represents the actual signal vector of the FTU; This represents the calculation of the desired signal for M FTUs. With the actual distorted signal The absolute error is used to measure the degree of fit between the positioning result and the actual signal. This indicates the total number of FTUs configured in the distribution network; These are the weighting coefficients; This indicates the number of faulty sections in the location results, which is used to avoid the unreasonable situation of assuming multiple faulty sections without any restrictions, and to balance the reasonableness of signal matching and the number of faults. This indicates the total number of sections to be located in the distribution network; Indicates the first i The fault status determination variables for each section, namely Indicates the first i One section was identified as faulty. Indicates the first i Each section was determined to be normal; Required location results Equivalent to real-world fault scenarios The probability is at least ,in, This is the allowable probability of location errors, thereby ensuring the reliability of fault location.

3. The two-layer robust optimization method for resilient distribution network segment location considering fault probability and reinforcement strategy as described in claim 2, characterized in that: To address multiple faults, a compensation factor is introduced to improve robustness: （6）； In formula (6): This represents the compensation factor for multiple fault scenarios. This is the compensation coefficient, used to control the magnitude of the compensation. The number of faulty sections; This means that compensation will only be triggered when the fault count is greater than 1, and compensation will be 0 when the fault count is 1.

4. The two-layer robust optimization method for flexible distribution network segment location considering fault probability and reinforcement strategy as described in claim 3, characterized in that: In step 2, a pre-disaster enhancement strategy is introduced into the fault segment location domain. By actively reducing the probability of faults in key segments, the overall performance of the location system is improved. The specific construction method is as follows: 1) Define reinforcement strategy: Based on system reliability theory, reinforcement strategies indirectly affect the performance boundary of the localization algorithm by changing the underlying failure probability distribution; a reinforcement strategy vector is defined. , These represent reinforcement strategies. The various components; where: （7）； The probability of section failure after reinforcement is reduced to the original level. Times: （8）； In equation (8): For section j Enhanced failure probability; To enhance the effect coefficient; 2) Establish a multi-objective optimization problem: The goal of reinforcement strategy optimization is to achieve the highest positioning accuracy with the minimum reinforcement cost, and it establishes a multi-objective optimization problem: （9）； In equation (9): This represents the total enhancement cost of all enhanced sections. For section j The cost of strengthening; This is the negative of the positioning accuracy; minimizing this objective is equivalent to maximizing the positioning accuracy. This indicates that the total number of segments that can be enhanced cannot exceed the maximum number of enhancements. ; The positioning accuracy rate is defined as follows: （10）； In formula (10): This represents the accuracy of fault segment location under the enhanced strategy r; For the indicator function, if the positioning result Compared to real-world failure scenarios If the values ​​match, the function value is 1; otherwise, it is 0. For test scenario set The scale, i.e. the number of scenarios.

5. The two-layer robust optimization method for resilient distribution network segment location considering fault probability and reinforcement strategy as described in claim 4, characterized in that: Transform the multi-objective optimization problem into a single-objective optimization problem, and design the fitness function: （11）； In equation (11): This represents the fitness function value of the reinforcement policy r; This represents the accuracy of fault segment location under the enhanced strategy r; This is the accuracy threshold; This is the fault multiplicity penalty factor, which increases as the fault multiplicity increases; This is the penalty coefficient.

6. The two-layer robust optimization method for resilient distribution network segment location considering fault probability and reinforcement strategy as described in claim 5, characterized in that: Step 3 involves establishing a basic model for locating fault sections under information distortion, specifically including: Based on the principle of distribution network segment location, the objective function is established as follows: （12）； （13）； In the above formula: The fitness value corresponding to each solution in the solution set; This represents the total number of FTUs and also the total number of feeder sections. Twice the number of FTUs; For the first j FTU, i.e., FTU j The actual transmitted fault current information; For the calculated FTU j Expected fault current information; For section LS j The state; The weighting coefficients are set according to the minimum set theory of fault diagnosis to avoid misjudgment. This is the sum of the number of all faulty sections; This refers to the penalty coefficient for critical sections. This is the sum of the number of all critical segments; Indicates the first k State variables of key sections; Indicates the index number of the key section; Represents the set of key segments; Based on the fault section assumption and distribution network topology, an improved switching function is constructed: （14）； In equation (14): FTU j The node's expected positive state; For FTU j Number of power sources in the upstream network; For FTU j Upstream power The set of segments along the path; for Inner section i The state; For FTU j The set of all segments in the downstream network; This represents the logical "OR" operator. This represents the logical AND operator; Represents the logical "NOT"; This indicates the segment index, that is, the number of a certain segment; Indicates a section State variables; FTU j The reverse expected state of the node; For FTU j Number of power sources in the downstream network; For FTU j to downstream power supply The set of segments along the path; for Inner section i The state; For FTU j The set of all segments in the upstream network; FTU j The overall expected state of the node; FTU j The node's expected positive state; FTU j The reverse expected state of the node.

7. The two-layer robust optimization method for resilient distribution network segment location considering fault probability and reinforcement strategy as described in claim 6, characterized in that: Step 3 includes multi-source information fusion and physical operational constraints: 2.1) Fault branch constraints: The configuration of a miniature synchronous phasor measurement unit (μPMU) can identify faulty branches, thereby defining the range of the faulty section; let the monitoring domain of the μPMU be... Therefore, the faulty section must be located on the faulty branch determined by the μPMU, that is: （15）； In equation (15): The set of sections on the faulty branch determined by μPMU, i.e. the range of potential faulty sections detected by μPMU; 2.2) Circuit breaker protection domain constraints: Based on the three-stage current protection principle, circuit breaker tripping can determine the power outage area, and the faulty section must be within the protection range of the activated protection device; that is: （16）； In equation (15): This refers to the set of sections within the protection range of the circuit breaker. 2.3) FTU signal distortion constraint: Considering the harsh operating environment of FTUs under extreme disasters, the missed and false alarms of FTU remote signaling information become the biggest adverse factors for the application of positioning methods. A signal distortion model is constructed as follows: （17）； In equation (17): Indicates the first j The signal values ​​ultimately used by each FTU for fault location; Indicates the first j Distortion observation signal of one FTU; Indicating the candidate fault state vector Next, the j The expected signal of each FTU; 2.4) Fault multiplicity constraint: Maximum number of faults under extreme weather conditions: （18）； In formula (18): The set consisting of segments LS; This represents the maximum number of faults. 2.4) Section state constraints: Since the distribution network topology changes due to the connection of the DG (Distribution Current Generation) system, encoding is performed based on the direction of the fault current. （19）。 8. The two-layer robust optimization method for resilient distribution network segment location considering fault probability and reinforcement strategy as described in claim 7, characterized in that: In step 4, a "defense" is constructed. A two-layer robust optimization model for "location" collaboration is proposed. This model deeply integrates pre-disaster defense and in-disaster location through a master-slave hierarchical structure. Through bidirectional coupling and iterative verification between the upper and lower layers, it achieves collaborative optimization of policy robustness and de-robustness. The specific construction method is as follows: 1) The constructed two-layer robust optimization model adopts a master-slave hierarchical structure, and its mathematical expression is as follows: （20）； In equation (20): Represents the upper-level reinforcement policy vector The feasible region is the set of values ​​for the upper-level decision variables; For upper-level binary decision variables, in the form of , representing the reinforcement strategy vector These represent the reinforcement decision variables for each segment; Indicates transpose; Each represents the total number of segments; Costs associated with upper-level decision-making; It is a set of uncertainties that depend on reinforcement strategies; For uncertain parameters, in the form of Includes fault scenarios and FTU signal distortion Characterizes the uncertain interference factors of the system; For hierarchical relationships, it indicates that given a higher-level strategy... and uncertainty parameters When, the optimal objective value of the lower-level subproblem; The lower feasible region is the basis for lower-level decision-making. The range of valid values; The lower-level objective function; For lower-level binary decision variables, in the form of Characterize the fault location results. These represent the vectors of the lower-level fault location results. Each component, i.e., the fault state variables of each section; 2) Upper layer: Strengthening the robust optimization model of the strategy: The upper-level planning layer is built upon a reinforcement strategy optimization model. It introduces a worst-case scenario optimization mechanism and fault probability spatial correlation modeling through a fault probability-aware opportunity constraint model, establishing a dynamic coupling relationship between the reinforcement strategy and the probability distribution. This ensures that the system maintains reliable positioning capability even under the most unfavorable conditions within budget constraints. The modeling process is as follows: （21）； In equation (21): This is the risk aversion coefficient; the higher the value, the more conservative the decision-making. The positioning accuracy function is used to evaluate the positioning results of the lower layer. Compared to real faults Consistency; This indicates that, given a reinforcement policy Uncertain scenarios and real-world failure scenarios Under the given conditions, the optimal solution to the subproblem of locating the lower-level fault section; This represents the feasible region of the upper-level reinforcement strategy, which is the set of all reinforcement schemes that satisfy the constraints. Indicates the first i Strengthening decision variables for each segment; This indicates the maximum number of enhancement sections allowed, which can also be understood as the upper limit of the enhancement budget. For the set of key segments; Mandatory constraints for critical sections; Minimum reinforcement quantity requirement for key sections; 3) Lower layer: Probability-aware robust localization model: The lower-level operational layer integrates a basic model for fault segment localization under information distortion and an opportunity-constrained model for fault probability perception. Addressing the performance degradation of traditional deterministic localization in FTU signal distortion environments, it enhances uncertainty handling capabilities through opportunity-constrained robustness and multi-source information fusion, achieving high-precision localization under signal distortion interference. The modeling process is as follows: （22）。 9. The two-layer robust optimization method for resilient distribution network segment location considering fault probability and reinforcement strategy as described in claim 8, characterized in that: In the upper planning layer of the two-layer robust optimization model, based on the requirements of fault probability perception and system reliability, a genetic algorithm is used to optimize and solve the reinforcement strategy. The specific steps include: 1.1) Initialize a population containing multiple enhancement schemes, including: The enhancement strategy vectors defined in equations (20) to (21) As the individual encoding for the genetic algorithm, the population containing multiple feasible reinforcement schemes is initialized, and the specific formula is as follows: （23）； In equation (23): This is the initial population of generation 0; Each individual within the population; For the first q There are 1 candidate reinforcement strategy, and each entity satisfies the feasible region constraint in equation (21). ; This indicates the population size of the upper-level genetic algorithm, that is, how many individuals with reinforcement strategies are in the initial population; 1.2) Generate the parent population through roulette wheel selection: For each candidate reinforcement strategy in the initial population Construct the fitness function according to equation (21) Calculate individual merits and demerits. Indicates candidate reinforcement strategy The objective function value in the robust optimization model of the upper-level reinforcement strategy shown in equation (21) is determined; and a roulette wheel selection mechanism is used to select parent individuals; the first q The probability of an individual being selected is: （24）； In equation (24): For the first q The probability of an individual being selected; For the first q The fitness function value of an individual using a reinforcement strategy; It is a very small positive number; This represents the summation over all individuals in the entire population; Index representing an individual in the population; Population size; 1.3) Single-point crossover generates offspring population: The parent individuals obtained by roulette wheel selection and Let the random intersection point be... m Then, two offspring individuals are generated through a single-point crossover: （25）； In equation (25): , These are the two offspring individuals generated after crossover; , Reinforcement strategies for both parent generations; Assign a parent generation individual number; , Indicates the parent individual in the first generation i Strengthened decision-making in each segment; Represents a random intersection point that satisfies ; To enhance the strategy vector dimension, the length of the individual encoding is determined; 1.4) Uniform mutation generates new candidate enhancement strategies: Uniform mutation is performed on each reinforcement decision variable of the offspring individuals, with the mutation rule as follows: （26）； In equation (26): For the mutated first i Strengthen decision variables; For the first time before the mutation i Strengthen decision variables; Toggles the values ​​of 0 and 1; Indicates the probability of mutation; others indicate that the original value is retained if no mutation occurs. 1.5) Evaluate the worst-case localization performance of each strategy in a high-confidence fault scenario set using parallel computing, including: For any candidate reinforcement strategy First, update the segment failure probability according to equation (8), then calculate the scenario probability according to equation (3); based on equation (4), filter high-confidence failure scenarios to obtain the high-confidence scenario set corresponding to this reinforcement strategy: （27）； In equation (27): For the first q A set of high-confidence fault scenarios corresponding to each reinforcement strategy; This represents a specific fault scenario; The scenario probability is calculated based on equation (3); The scene filtering threshold in expression (4); In each scene Next, the lower-level probabilistic perception robust localization model of equation (22) is invoked to obtain the optimal localization result: （28）； In equation (28): To represent the reinforcement policy given Uncertain scenarios and real-world failure scenarios Under the given conditions, the optimal positioning result obtained by the lower layer; This represents the vector of the lower-level fault location results; Let be the lower feasible region in equations (20) and (22); Let be the lower-level objective function in equations (20) and (22); Furthermore, the positioning accuracy under each high-confidence scenario is calculated according to equation (10), and the minimum value is taken as the worst positioning performance of this enhancement strategy: （29）； Equivalently, it can also be written as the performance loss in the worst-case scenario: （30）； In equations (29) to (30): For the first q The worst localization accuracy of each reinforcement strategy on a high-confidence scenario set; For the first q The worst-case localization performance loss of each reinforcement strategy in a high-confidence scenario set; The positioning accuracy function defined by equation (10); This refers to the positioning loss in the corresponding scenario; The solution obtained from equation (28) is the optimal fault location scheme under the current strategy and scenario; Generated by Equation (27), it only includes fault scenarios that meet the probability standard and require key prevention; Indicates an uncertain scenario; Due to different scenarios The lower-level solutions are independent of each other, so parallel computing can be used to improve the evaluation efficiency of high-confidence fault scenario sets; 1.6) Combined with reinforcement cost to construct an upper-level fitness function for environment selection, including: Based on Equation (21), a robust optimization model for strengthening strategies is constructed, and the fitness function is then defined as follows: （31）； In equation (31): For the first q The fitness function value of each reinforcement strategy; Indicates the total reinforcement cost; For section i The cost of strengthening; Indicates the first q In the reinforcement strategy, the first i Strengthening decision variables for each segment; This represents the risk aversion coefficient; the higher the value, the more conservative the decision-making. Indicates the first q The worst-case localization performance loss in high-confidence scenarios of the reinforcement strategy; During environmental selection, parent and offspring individuals are merged and selected based on fitness function values. Sort the individuals from smallest to largest, retaining those with better fitness for the next generation; 1.7) The final iteration obtains the optimal combination of reinforced sections that maintains high positioning reliability even under severe fault conditions; including: After multiple iterations, the optimal reinforcement strategy is output: （32）； The corresponding optimal combination of enhancement sections is: （33）； In equations (32) to (33): This is the optimal reinforcement strategy ultimately output by the upper planning layer; Indicates in the feasible region Inside, find the fitness function Minimal reinforcement strategy That is, the solution that best combines cost and robustness; This represents the optimal set of enhanced sections. The optimal reinforcement strategy is represented by the first... i The optimal decision value for the segment. i The index representing the segment number, i.e., the... i Each section.

10. The two-layer robust optimization method for resilient distribution network segment location considering fault probability and reinforcement strategy as described in claim 9, characterized in that: In the lower layer of the two-layer robust optimization model, an improved particle swarm optimization algorithm is used to solve the fault segment location model: 2.1) Based on the given optimal enhancement scheme at the upper level, initialize the particle swarm position and velocity, including: The optimal reinforcement scheme at the upper level Based on this, the lower-level decision variables in equations (20) and (22) are... As particle position encoding, and to initialize the particle swarm: （34）； Simultaneously, initialize a velocity vector for each particle: （35）； In equations (34) to (35): For the initial particle swarm; Indicates the first p The position of each particle; Particle swarm size; Given an enhancement scheme and failure scenarios The next feasible region; Indicates the first p The velocity vector of each particle; Indicates the first p The first particle i A velocity vector of dimension; For the first i The fault state variables of each section are defined in equation (13). 2.2) Updating particle positions based on Sigmoid probability, including: In the t In the nth iteration, the 1st p The first particle i The speed of the dimension update is: （36）； In equation (36): Indicates the first p The first particle i Vi in the Speed ​​during the next iteration; Indicates the first p The first particle i Vi in the Speed ​​during the next iteration; Indicates the first Inertia weights in the next iteration; Represents an individual's learning factor; Represents the group learning factor; , express Random numbers within the interval; Indicates the first p The best historical position of each particle i Dimensional components; The first position representing the group's historical best position i Dimensional components; Indicates the first p The first particle i Vi in the Position components at the next iteration; Then, the sigmoid function is used to map the velocity to the position update probability: （37）； In equation (37): This represents the Sigmoid probability mapping function; Represents the natural exponential function; The updated velocity components are obtained from equation (36); Indicates the first i The probability that the dimension position is updated to 1; Update particle positions accordingly: （38）； In equation (38): This represents the Sigmoid probability mapping function; Indicate Random numbers within the interval; For the updated number i Dimensional segment state variables; From equation (37), we obtain that the first... i The probability that the dimension position is updated to 1; 2.3) Accelerate convergence through adaptive inertia weights and early stopping mechanisms, including: For the inertia weight in equation (36) Adaptive decreasing method: （38）； In equation (38): Indicates the first t Inertia weights in the next iteration; Indicates the upper bound of the inertia weight; Indicates the lower bound of the inertia weight; Indicates the maximum number of iterations; Indicates the current iteration number; At the same time, when continuous L The improvement of the global optimal objective function in the iteration is less than the threshold. ε When the iteration is terminated early, this is the stopping criterion in the solution process of the lower-level model in equation (22): （39）； In equation (39): Indicates the first t The globally optimal objective function value at the next iteration; Indicates the preceding L The globally optimal objective function value at time; Represents continuous observation algebra; Indicates the early stopping threshold; This represents the absolute value operation; The accuracy of localization is evaluated by combining a high-confidence fault scenario set generated by chance constraints, including: 2.4) Evaluate the localization accuracy by combining the high-confidence fault scenario set generated by chance constraints: For the high-confidence fault scenario set generated by equation (27) In every scene The following outputs the optimal fault location result: （40）； In equation (40): Representing a scene The optimal fault location result is as follows; This represents the optimal reinforcement strategy obtained by the upper layer; This indicates a high-confidence fault scenario; Represents a real-world fault scenario; This represents the lower-level feasible region, which is the basis for lower-level decision-making. The range of valid values; This represents the lower-level objective function; Finally, the localization accuracy is statistically analyzed on the high-confidence fault scenario set according to equation (10): （41）； In equation (41): Represents the optimal reinforcement strategy Overall positioning accuracy; Indicates the size of the set of high-confidence failure scenarios; This represents the summation over all high-confidence scenarios; Indicates an indicator function; the part within the parentheses If the condition is met, the value is 1, indicating that the positioning is correct; otherwise, the value is 0, indicating that the positioning is incorrect. 2.5) Output fault segment location results that are robust under various interference scenarios, including: The optimal location results obtained by combining Equation (40) under various high-confidence fault scenarios, and the overall accuracy evaluation given by Equation (41), are finally output as fault segment location results that are robust under information distortion, multiple faults and the most unfavorable disturbance conditions.

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