Power distribution network fault section positioning method considering pre-disaster reinforcement information

Abstract

A power distribution network fault section positioning method considering pre-disaster reinforcement information comprises the following steps: step 1, establishing a first-stage pre-disaster reinforcement model used for determining a reinforcement scheme of a feeder line section and FTU nodes, calculating corresponding investment cost, and generating a fault scene set based on the reinforcement scheme; step 2, establishing a second-stage section positioning model for fusing multi-source information to perform fault section identification and calculating positioning deviation penalty cost; 3, integrating the pre-disaster reinforcement model in the step 1 and the second-stage section positioning model in the step 2, and constructing a two-stage collaborative optimization model with the aim of minimizing the total expected cost of the system; and 4, solving the two-stage collaborative optimization model constructed in the step 3, and finally outputting an optimal pre-disaster reinforcement scheme. According to the method, through collaborative optimization of pre-disaster reinforcement and fault positioning, the fault positioning fault-tolerant capability and the system toughness of the power distribution network under extreme disasters are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of power distribution network segment location technology, and specifically to a method for locating faulty segments in power distribution networks that takes into account pre-disaster reinforcement information. Background Technology

[0002] The distribution network is a crucial link connecting the transmission system and users. Its resilience and fault response capabilities directly affect the reliability of power supply and the safety of electricity use for users. Fault location, as the foundation for fault isolation and network reconstruction during disasters and rapid power restoration after disasters, is one of the core means to improve the resilience of the distribution network. With the improvement of the automation level of the distribution network, fault location methods based on feeder terminal unit (FTU) remote signaling are widely used due to their speed and versatility. However, FTUs are often in harsh environments, which can easily lead to missed or false alarms in remote signaling information, seriously affecting the accuracy of location. Therefore, improving the fault tolerance of location—that is, the ability to accurately determine the fault section when information is incomplete—has become the most direct and effective way to deal with FTU anomalies. However, existing distribution network segment location methods suffer from severe deficiencies in fault tolerance due to information loss when large-scale FTU failures are triggered by extreme disasters. Simply increasing information sources, improving models, or optimizing algorithms cannot fundamentally solve this problem. On the other hand, pre-disaster reinforcement of FTUs and lines can significantly improve the fault tolerance of the location system. Therefore, building a model that coordinates pre-disaster reinforcement and fault segment location is a key support and technical guarantee for improving the resilience of the distribution network. Summary of the Invention

[0003] To address the issues of significantly reduced fault tolerance in distribution network location during large-scale FTU failures caused by extreme disasters, as well as the lack of pre-disaster reinforcement and coordinated fault location, this invention provides a method for fault location in distribution networks that considers pre-disaster reinforcement information. This method significantly improves the fault location tolerance and system resilience of distribution networks under extreme disasters by coordinating and optimizing pre-disaster reinforcement and fault location.

[0004] The technical solution adopted in this invention is as follows: A method for locating fault sections in a distribution network that considers pre-disaster reinforcement information includes the following steps: Step 1: Establish the first-stage pre-disaster reinforcement model to determine the reinforcement scheme for feeder sections and FTU nodes, calculate the corresponding investment costs, and generate a set of failure scenarios based on the reinforcement scheme; Step 2: Establish a second-stage segment location model to integrate multi-source information for fault segment identification and calculate the location deviation penalty cost; Step 3: Integrate the pre-disaster hardening model from Step 1 with the second-stage segment location model from Step 2 to construct a two-stage collaborative optimization model with the goal of minimizing the total expected cost of the system. Step 4: Solve the two-stage collaborative optimization model constructed in Step 3, and finally output the optimal pre-disaster reinforcement scheme.

[0005] In step 1, the relevant constraints of the first-stage pre-disaster reinforcement model include reinforcement logic, physical resources, and investment budget constraints. The first-stage pre-disaster reinforcement model is as follows: (1); In formula (1): The intensification state of the described section; Indicates the enhanced state of a node; This indicates the reinforcement scheme for the feeder section; For the first The status of each FTU node; ①: The hardened logic constraints are expressed as follows: After reinforcing the feeder section The FTU node is considered absolutely reliable and will not fail in fault scenarios, as expressed mathematically below: (2); In formula (2): and The fault status of a segment and node is represented by: (3); Investment costs It is a core indicator of the pre-disaster reinforcement model, and its specific description is as follows: (4); In equation (4): , These are the reinforcement cost coefficients for sections and nodes, respectively; The number of feeder sections to be reinforced; The number of FTU nodes to be reinforced; The intensification state of the described section; This indicates the enhanced state of a node.

[0006] ②: Simultaneously, the reinforcement of the power distribution network must adhere to the principle of resource constraints, specifically limited by physical resources and investment budget. The physical resource constraint is reflected in the constraint on the quantity of reinforcement required: (5); In formula (5): and These are the upper limits for the number of reinforcements required for feeder sections and FTU nodes, respectively.

[0007] Investment budget constraints are reflected in: The reinforcement cost must not exceed the total budget, specifically stated as: investment cost. It cannot exceed its upper limit. ,Right now: .

[0008] Based on the aforementioned reinforcement scheme, Monte Carlo simulation is used to generate fault scenarios for evaluating the localization effect; the core of each fault scenario is a segment fault state vector. With node FTU fault state vector ,in, Section 1 to Section The fault status; For FTU node 1 to FTU node The fault status.

[0009] The generation process includes the following steps: S1: Initialization parameters: Input system parameters: Predefined reinforcement scheme , The intensification state of the described section; This indicates the enhanced state of a node.

[0010] Set probability parameters: Section fault probability FTU underreporting probability FTU false alarm probability ; Setting constraints and objectives: Maximum number of faults in a given section Maximum FTU fault count Number of target scenarios ; And initialize an empty scene library. ; S2: Generation section fault status: Traverse all segments and FTU nodes to generate their states; For a section: If the section has been reinforced, force it into a fault state. Otherwise, generate random numbers. ,like ,but Otherwise, it is 0; For FTU nodes: If the FTU has been hardened, force it into a fault state. Otherwise, generate random numbers. And its state is determined according to equation (6). : (6); In formula (6): For a random number, .

[0011] S3: Scenario Validation: Calculate the fault count for the current candidate scenario: number of faults in the section. FTU failure count If satisfied and If the scenario is successful, execute S4; otherwise, discard the scenario and return to S2 to regenerate.

[0012] S4: Record valid scenarios: Current valid fault status Store in scene library .

[0013] S5: Loop termination check. If the number of scenes in the scene library... Target value reached If the loop terminates, output the result. Otherwise, return to S2 and continue generating.

[0014] In obtaining the fault state vector This needs to be converted into input information for the positioning phase, namely the current information reported by each FTU. ,in This indicates that a positive fault current has been detected. This indicates that a reverse fault current has been detected, and This indicates that no fault current was detected.

[0015] In distribution network fault analysis, when the FTU is operating normally, the current information can be defined as the expected state of the FTU. This desired state is calculated using section fault information and switching functions, and its mathematical expression is as follows: (7); In equation (7): , These are the switching functions for the upstream and downstream parts of the node, respectively; The number of power sources in the FTU's upstream network; The number of power sources in the downstream network of FTUj; For FTU to upstream power supply The set of segments along the path; This is the set of all segments in the downstream network of the FTU; For FTUj to downstream power supply The set of segments along the path; This is the set of all segments in the upstream network of FTUj; for or A segment of a collection; No. Possible section failures are possible; Indicates the section number; Indicates the power supply designation; Indicates the logical AND. It represents the logical "NOT".

[0016] However, in real-world operating environments, FTUs may malfunction due to equipment aging, communication interference, or external factors, causing their reported information to deviate from the expected state. Common FTU malfunctions manifest in two main forms: missed reports and false reports. A missed report occurs when the FTU fails to detect a fault current and incorrectly reports a "0" state; a false report occurs when the FTU incorrectly reports a "1" or "-1" signal when there is no fault current, or incorrectly reports the current direction, as detailed below: (8).

[0017] In step 2, a second-stage segment location model is established, and based on the deviation between the location result and the actual fault state, the location deviation penalty cost is calculated. The objective function of the second-stage segment location model is: (9); In equation (9): This represents the difference between the expected state and the actual state of the FTU. This represents the optimal fault prediction state; The weighting coefficients, set according to the minimum set theory of fault diagnosis, are generally set to 0.5 to avoid misjudgment. Total number of FTU switches; For fault scenarios The FTU node state is calculated below.

[0018] The optimal fault prediction state is obtained by solving the problem. Then, the positioning performance can be quantified by comparing the inferred results with the actual state, and the positioning deviation can be defined. for: (10); In formula (10): The optimal fault inference state segment The fault status; No. The first type of failure scenario The fault status of each location segment.

[0019] The expected value of this positioning deviation across the entire set of failure scenarios constitutes the expected positioning penalty cost of the second stage. : (11); In equation (11): This indicates a penalty for failure to locate the fault. For the scene The probability of occurrence; This represents a set of fault scenarios.

[0020] This expectation positions the cost of punishment. As a collaborative link connecting the two stages, it serves as a key feedback signal and is incorporated into the global optimization objective.

[0021] The second-stage segment location model includes the following constraints: 1) μPMU branch constraints: Based on the μPMU configuration location, when a ground fault occurs in the distribution network, the fault branch can be determined using the fault information collected by the μPMU. Therefore, the faulty section must be located on the faulty branch, and the μPMU branch constraint can be expressed as: (12); In equation (12): The optimal fault inference state is the fault state of segment 1; What is the optimal fault inference state for segment 2? This represents the optimal fault inference state segment. The fault status; This represents the set of segments on the faulty branch determined by μPMU.

[0022] 2) Circuit breaker constraints: The specific location of the circuit breaker tripping determines the power outage area. Therefore, a section fault must be within the protection range of the operating protective equipment, and the constraints on the power outage area are expressed as follows: (13); In equation (13): Representative protective equipment The set of segments LS within the defined protection area; This indicates a logical OR.

[0023] 3) Fault multiple number constraint for section: Maximum number of faults under extreme events 2: (14); In equation (14): Represents the set of fault locations; The optimal fault inference state segment The fault status.

[0024] 4) FTU section state constraints: (15); 5) FTU Real-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. (16).

[0025] In step 3, the two-stage collaborative optimization model is constructed by integrating the pre-disaster hardening model of step S2 and the segment location model of step S3. The constructed collaborative optimization model aims to minimize the total expected cost of the system. In the two-stage collaborative optimization model, the total expected cost of the system is the sum of the expected values ​​of the investment cost in step 1 and the positioning deviation penalty cost in step 2, specifically expressed as follows: (17); In equation (17): Indicates the total cost; Expressed as investment cost; It is a very large penalty coefficient; This indicates a penalty for positioning deviation; Indicates the reinforcement cost coefficient for the section; This represents the reinforcement cost coefficient for FTU nodes; Indicates a section The reinforced state; Indicates FTU node The reinforced state; This indicates a penalty for positioning deviation; Indicates the number of reinforced sections; This indicates the number of nodes that have been reinforced.

[0026] To quantitatively evaluate the positioning reliability of different schemes, positioning accuracy is defined. as follows: (18); In equation (18): It is an indicator function, in the scene The value is 1 when the location is perfectly accurate, and 0 otherwise. This represents a set of fault scenarios.

[0027] In step 4, the two-stage co-optimization model constructed in step 3 is linearized using a logistic-algebraic transformation method, transforming it into a mixed-integer linear programming model for efficient solution. Specifically: Equations (18) and (2) involve nonlinear absolute value operations. To integrate them into the mixed-integer linear programming model, a standard linearization method is adopted, and auxiliary variables are introduced. and Transform it into equations (19), (20), and (21): (19); In equation (19): This indicates a penalty for positioning deviation; Represents a binary auxiliary variable.

[0028] (20); In equation (20): No. Section under various fault scenarios Optimal fault inference; Indicates the first Section under various fault scenarios The actual fault condition.

[0029] (twenty one); In equation (21): Represents a binary auxiliary variable; This indicates the enhanced state of the FTU node.

[0030] The linearization of the positioning model objective function in equation (9) first requires removing the absolute value sign on the right side of the equation. According to the definition rules of the expected FTU state and the actual FTU state, there are nine possible differences between them, as shown in Table 1. For each case, the function value corresponding to the positioning model objective function in equation (9) is calculated, and intermediate variables are given. and All possible combinations.

[0031] The objective function of the localization model can be transformed into a linear function (22) and a conditional function (23): (twenty two); In equation (22): This represents the difference between the expected state and the actual state of the FTU. This represents the set of FTU nodes in the distribution network; This represents the set consisting of all feeder sections in a distribution network; This represents a weighting coefficient used to prevent misjudgments, typically set to 0.5; Indicates the segment status.

[0032] (twenty three); The logical relations are transformed into algebraic relations, as shown in equations (24) to (26). This allows all nonlinear logical relation constraints to be converted into linear algebraic relation constraints. (twenty four); In equation (24): Represents any value; Represents any value Component 1; Represents any value Composition ; This indicates that it is equivalent to; Represents any value Composition .

[0033] (25); In equation (25): Represents any value; Represents any value Composition ; This indicates the number of components in B.

[0034] (26); In equation (26): Represents any value; express Composition values Invert; express The composition values.

[0035] According to the linear transformation principle of equation (24), the nonlinear logical relations (12) and (13) can be transformed into the following linear algebraic relations: (27); In equation (27): This represents the set of segments on the faulty branch determined by μPMU.

[0036] (28); Introducing intermediate variables , , , , and ,make: , This is a binary intermediate variable used to linearize the positioning function; This represents the set of FTU nodes in the distribution network; This is a binary intermediate variable used to linearize the positioning function; This is a binary intermediate variable used to linearize the positioning function.

[0037] , For FTU to upstream power supply The set of segments along the path; This is a binary intermediate variable used to linearize the positioning function.

[0038] , The number of power sources in the FTU's upstream network; , For FTU j The set of all segments in the downstream network; This is a binary intermediate variable used to linearize the positioning function; , This is a binary intermediate variable used to linearize the positioning function; This is a binary intermediate variable used to linearize the positioning function; This is a binary intermediate variable used to linearize the positioning function; ; , The number of power sources in the downstream network of FTUj; This is a binary intermediate variable used to linearize the positioning function; This is the set of all segments in the upstream network of FTUj; Indicates the fault scenario lower section The fault status.

[0039] Then the desired state equation (7) of FTU can be transformed into: (29); In equation (29): Upstream switching function; Indicates the downstream switching function; This represents the actual node current information.

[0040] The forward current state of the FTU can be transformed into: (30); The negative current state of the FTU can be transformed into: (31).

[0041] This invention provides a method for locating fault sections in a distribution network that considers pre-disaster reinforcement information. The technical advantages are as follows: 1) Step 1 of this invention is the first to consider physical layer reinforcement (feeder section) and information layer reinforcement (FTU node) in a unified model, and constructs a "physical-information" dual-layer protection system. This breaks through the limitation of traditional reinforcement of only one layer. The Monte Carlo method is used to generate an effective set of fault scenarios that take into account the impact of reinforcement, making the model more in line with the uncertainty of actual disasters and providing real and reliable input for the subsequent positioning stage.

[0042] 2) Step 2 of this invention proposes a multi-source information fusion positioning model, which combines multi-source information such as μPMU, circuit breaker, and FTU for comprehensive judgment, significantly improving the fault tolerance capability in the case of missing or incorrect information, and introduces positioning deviation penalty cost as a quantitative evaluation index, transforming positioning accuracy into an economic goal, which is convenient for coordinated optimization with reinforcement cost.

[0043] 3) Step 3 of this invention constructs a collaborative optimization framework based on two-stage stochastic programming, organically integrating reinforcement decision-making (pre-event) and positioning decision-making (in-event) in terms of time sequence and objectives to achieve global optimality. The total expected cost of the system comprehensively considers reinforcement investment and positioning deviation penalty, reflecting the trade-off between economy and reliability, and providing a scientific basis for decision-makers.

[0044] 4) Step 4 of this invention transforms the complex nonlinear mixed-integer programming problem into a mixed-integer linear programming problem through the Boolean-algebraic transformation and linearization techniques, which greatly improves the solution efficiency and stability. Commercial solvers (such as Gurobi) can be used to efficiently solve large-scale practical systems, and it has good engineering applicability and scalability. Attached Figure Description

[0045] The present invention will be further described below with reference to the accompanying drawings and examples; Figure 1 This is a diagram of the two-stage collaborative optimization framework of the present invention.

[0046] Figure 2 This is a schematic diagram of the 14-node simulation system of the present invention.

[0047] Figure 3 This is a schematic diagram of the reinforcement location.

[0048] Figure 4 The effect of strengthening a single information layer.

[0049] Figure 5 This is a schematic diagram of a fault in section 9.

[0050] Figure 6 This is a schematic diagram of the faults in sections 9 and 10.

[0051] Figure 7 The diagram shows the optimal reinforcement scheme under different investment constraints.

[0052] Figure 8 This is a comparison chart of hardening strategies based on the maximum number of faults. Detailed Implementation

[0053] A method for locating fault sections in a distribution network considering pre-disaster reinforcement information is proposed. First, a collaborative decision-making strategy for pre-disaster reinforcement and fault section location is designed. Second, a pre-disaster reinforcement model is established to determine reinforcement schemes for feeder sections and FTU nodes and calculate investment costs, while simultaneously generating a set of fault scenarios based on the reinforcement schemes. Next, a multi-source information fusion-based section location model is established for fault identification and calculation of location deviation penalties. Then, the aforementioned models are integrated to construct a two-stage collaborative optimization model with the objective of minimizing the total expected cost of the system. Finally, this model is transformed into a mixed-integer linear programming problem and solved efficiently to output the optimal reinforcement scheme. The method includes the following steps: Step S1: Design a collaborative decision-making strategy for pre-disaster reinforcement and distribution network fault location: By strengthening key information nodes to improve perception reliability and narrowing the search range for faulty sections, a two-stage collaborative optimization framework is constructed with the goal of minimizing the total expected cost of the system.

[0054] Step S2: Establish a pre-disaster hardening model: Based on the strategy in step S1, a first-stage pre-disaster reinforcement model is established. The model is used to determine the reinforcement scheme for feeder sections and FTU nodes and calculate the corresponding investment costs. Based on the reinforcement scheme, a set of fault scenarios is generated using the Monte Carlo simulation method to evaluate the positioning effect.

[0055] Step S3: Establish a segment location model based on multi-source information fusion. Based on the strategy in step S1, a second-stage segment location model is established; the model is used to fuse multi-source information to identify fault segments, and to calculate the location deviation penalty cost based on the deviation between the location result and the actual fault state.

[0056] Step S4: Construct a two-stage collaborative optimization model: By integrating the pre-disaster hardening model of step S2 and the segment positioning model of step S3, a collaborative optimization model is constructed with the goal of minimizing the total expected cost of the system; the total expected cost of the system is the sum of the expected values ​​of the investment cost in step S2 and the positioning deviation penalty cost in step S3.

[0057] Step S5: Model linearization and solution: The two-stage collaborative optimization model constructed in step S4 is linearized using the logistic-algebraic transformation method, transforming it into a mixed-integer linear programming model and solving it efficiently, ultimately outputting the optimal pre-disaster reinforcement scheme.

[0058] In step S1, a collaborative decision-making strategy is designed for pre-disaster reinforcement and fault location in the distribution network. By reinforcing key information nodes to improve perception reliability and narrowing the search range for fault sections, a two-stage collaborative optimization framework is constructed with the goal of minimizing the total expected cost of the system. To achieve collaborative optimization of pre-disaster reinforcement and fault location in the distribution network, this invention constructs a unified decision-making framework based on two-stage stochastic programming. This framework organically integrates the two stages of equipment reinforcement and fault location through a time-series-connected decision-making mechanism, and its logical structure is as follows: Figure 1 As shown.

[0059] The pre-disaster reinforcement phase involves forward-looking decision-making, requiring the determination of a reinforcement plan for the feeder section before a failure occurs. reinforcement scheme reinforcement scheme for FTU nodes Then, based on the determined reinforcement scheme, the investment cost is calculated and a set of valid failure scenarios is generated using the Monte Carlo method. The fault segment localization phase involves adaptive decision-making. First, a localization model based on multi-source information fusion is established. Then, the fault segment is determined after the fault scenario is realized. The model sets a positioning deviation penalty based on the positioning effect. With the goal of minimizing the total expected cost of the system, this collaborative model enhances sensing reliability by reinforcing the FTU at the information source and strengthens the feeder structure to narrow the fault search range. Ultimately, it outputs a collaborative reinforcement strategy that balances economy and accuracy, providing decision support for the scientific allocation of disaster prevention and mitigation resources in the distribution network.

[0060] In step S2, based on the strategy of step S1, a first-stage pre-disaster hardening model is established. This model is used to determine the hardening scheme for the feeder section and FTU node, and calculate the corresponding investment cost. Relevant constraints are established, including hardening logic, physical resources, and investment budget constraints. Based on the hardening scheme, a Monte Carlo simulation method is used to generate fault scenarios for evaluating the positioning effect. The pre-disaster hardening model is as follows: (1); In the formula: and The feeder section reinforcement schemes are as follows reinforcement scheme reinforcement scheme for FTU nodes This method constructs a comprehensive protection system through differentiated hardening of the physical and information layers. Physical layer hardening aims to improve the physical resilience of the feeder section, and its core function is to achieve lateral fault isolation and directly reduce the section's own outage risk. Information layer hardening, on the other hand, focuses on vertically improving the fault tolerance performance of the FTU and ensuring the accuracy of state awareness.

[0061] The improvement in information quality and the reduction in fault space are specifically reflected in: reinforced feeder sections. The FTU node is considered absolutely reliable and will not fail in fault scenarios, thus physically limiting the range of possible fault combinations. At the same time, it ensures the reliability of state awareness at the information source. The mathematical expression is as follows: (2); In the formula: and The fault status of a segment and node is represented by: (3); Investment costs It is a core indicator of the pre-disaster model, and its specific description is as follows: (4); In the formula: , These are the reinforcement cost coefficients for sections and nodes, respectively. The number of feeder sections to be reinforced; The number of FTU nodes to be reinforced.

[0062] Meanwhile, the reinforcement of the power distribution network must adhere to the principle of resource constraints. Specifically, it is limited by physical resources and investment budget. The physical resource constraint is reflected in the constraint on the quantity of reinforcement: (5); In the formula: and These are the upper limits for the number of reinforcements required for feeder sections and FTU nodes, respectively.

[0063] The investment budget constraint is reflected in the fact that reinforcement costs cannot exceed the total budget, specifically in terms of investment costs. It cannot exceed its upper limit. ,Right now: .

[0064] The generation of fault scenarios is based on the reinforcement scheme. This section uses the Monte Carlo method for random generation. The core of each fault scenario is the section fault state vector. With node FTU fault state vector The generation process follows these steps: Step 1: Initialize parameters: Input system parameters: Predefined reinforcement scheme Set probability parameters: section fault probability FTU underreporting probability FTU false alarm probability ;Set constraints and objectives: Maximum number of faults in a given section Maximum FTU fault count Number of target scenarios And initialize an empty scene library. .

[0065] Step 2: Generate Segment Fault States: Traverse all segments and FTU nodes to generate their states: For a segment: If the segment has been hardened, force its fault state. Otherwise, generate random numbers. ,like ,but Otherwise, it is 0.

[0066] For FTU nodes: If the FTU has been hardened, force it into a fault state. Otherwise, generate random numbers. And its state is determined according to equation (6). : (6); Step 3: Scenario Validity Verification: Calculate the fault count of the current candidate scenario: number of faults in the segment. FTU failure count If satisfied and If the scenario is successful, proceed to Step 4; otherwise, discard the scenario and return to Step 2 to regenerate.

[0067] Step 4: Record valid scenarios: Record the current valid fault states. Store in scene library .

[0068] Step 5: Loop Termination Check: If the number of scenes in the scene library is insufficient... Target value reached If the loop terminates, output the result. Otherwise, return to Step 2 to continue generating.

[0069] In obtaining the fault state vector This needs to be converted into input information for the positioning phase, namely the current information reported by each FTU. ,in This indicates that a positive fault current has been detected. This indicates that a reverse fault current has been detected, and This indicates that no fault current was detected.

[0070] In distribution network fault analysis, when the FTU is operating normally, the theoretically required current information it should report can be defined as the FTU's expected state. This desired state can be calculated using section fault information and switching functions, and its mathematical expression is as follows: (7); In the formula: Indicates the logical AND. Indicates the logical "NOT"; , These are the switching functions for the upstream and downstream parts of the node, respectively; The number of power sources in the FTU's upstream network; For FTU to upstream power supply The set of segments along the path; This is the set of all segments in the downstream network of the FTU; 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 FTU j The set of all segments in the upstream network.

[0071] However, in real-world operating environments, FTUs may malfunction due to equipment aging, communication interference, or external factors, causing their reported information to deviate from the expected state. Common FTU malfunctions manifest in two main forms: missed reports and false reports. A missed report occurs when the FTU fails to detect a fault current and incorrectly reports a "0" state; a false report occurs when the FTU incorrectly reports a "1" or "-1" signal when there is no fault current, or incorrectly reports the current direction, as detailed below: (8); In step S3, based on the strategy of step S1, a fault segment location model is established by fusing multi-source information, and a location deviation penalty cost is calculated based on the deviation between the location result and the actual fault state. The location function is: (9); In the formula: This represents the difference between the expected state and the actual state of the FTU. 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; Indicates a section fault Desired state of FTU; To prevent misjudgments, the weighting coefficient is usually set to 0.5; It represents the set of all feeder sections in a distribution network.

[0072] The optimal fault prediction state is obtained by solving the problem. Then, the positioning performance can be quantified by comparing the inferred results with the actual state, and the positioning deviation can be defined. for: (10); The expected value of this deviation across the entire set of failure scenarios constitutes the expected localization penalty cost of the second stage. : (11); In the formula: For the scene The probability of occurrence.

[0073] This expected penalty cost It serves as a collaborative link between the two stages. As a key feedback signal, it is incorporated into the global optimization objective.

[0074] The multi-source information-based fault location model includes the following constraints: 1) μPMU branch constraints: Based on the μPMU configuration location, when a ground fault occurs in the distribution network, the fault branch can be determined using the fault information collected by the μPMU. Therefore, the faulty section must be located on the faulty branch, and the μPMU branch constraint can be expressed as: (12); In the formula, This is the set of segments on the faulty branch determined by μPMU.

[0075] 2) Circuit breaker constraints; According to the principle of three-stage current protection, the power outage area can be determined from the specific location of the circuit breaker tripping. Therefore, a section fault must be within the protection range of the operating protection device, and thus the constraint of the power outage area can be expressed as: (13); In the formula: Representative protective equipment The set consisting of segments LS within the defined protection range, Represents logical OR, A collection of protective equipment.

[0076] 3) Section fault multiple number constraint: Even under extreme events, the probability of triple or higher failures is extremely small; therefore, the maximum number of failures under extreme events is limited. The value is 2.

[0077] (14); 4) FTU section state constraints: (15); 5) FTU Real-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. (16); In step S4, the collaborative optimization model is described as follows: integrating the pre-disaster hardening model of step S2 and the segment location model of step S3, a collaborative optimization model is constructed with the objective of minimizing the total expected cost of the system; the total expected cost of the system is the sum of the expected values ​​of the investment cost in step S2 and the location deviation penalty cost in step S3, specifically described as follows: (17); In the formula: It is a very large penalty coefficient used to characterize the severe consequences of positioning failure. Equation (10) clearly shows that the investment decision in the first stage... No longer just pursuing its own cost Instead of minimizing, it is necessary to proactively assess how it can be mitigated by changing the effective scenario set. Alarm information affects the inference performance in the second stage. Ultimately, the total expected cost of the system is achieved. The global optimum.

[0078] Meanwhile, in order to quantitatively evaluate the positioning reliability of different schemes in the numerical example analysis, this invention defines positioning accuracy. as follows: (18); In the formula: It is an indicator function, in the scene Completely and accurately located (i.e., for all segments) The value is 1 when the condition is met, and 0 otherwise.

[0079] In step S5: the collaborative optimization model constructed in step S4 is linearized using a logistic-algebraic transformation method, transforming it into a mixed-integer linear programming model for efficient solution. Specifically: Equations (11) and (2) involve nonlinear absolute value operations. To integrate them into the mixed-integer linear programming framework, this invention adopts a standard linearization method and introduces auxiliary variables. and Transform it into equations (19), (20), and (21).

[0080] (19); (20); (twenty one); The linearization of the positioning function in equation (9) first requires removing the absolute value sign on the right side of the equation. According to the definition rules of the expected FTU state and the actual FTU state, there are nine possible differences between them. For each case, the function value corresponding to the positioning function in equation (9) needs to be calculated, and intermediate variables need to be given. and For all possible combinations, please refer to Table 1.

[0081]

[0082] According to Table 1, the logical relation positioning function can be converted into a linear function (22) and a conditional function (23).

[0083] (twenty two); (twenty three); There are three principles for transforming logical relations into algebraic relations, as shown in equations (9) to (26). Based on these three principles, all nonlinear logical relation constraints can be transformed into linear algebraic relation constraints.

[0084] (twenty four); (25); (26); According to the linear transformation principle of equation (24), the nonlinear logical relations (12) and (13) can be transformed into the following linear algebraic relations: (27); (28); Introducing intermediate variables , , , , and , make: ,

[0085] Then, the expected state equation (7) of FTU can be transformed into: (29); The forward current state of the FTU can be transformed into: (30); The negative current state of the FTU can be transformed into: (31).

[0086] Detailed solution process: S1: Model Initialization and Parameter Input. Input the distribution network topology, including the set of feeder sections. With FTU node set Input economic parameters, including section reinforcement costs. FTU reinforcement cost Penalty coefficient and investment budget Input reliability parameters, including the probability of section failure. FTU underreporting probability With false alarm probability And load the fault scenario library generated in advance using the Monte Carlo method. Each of the scenes Includes actual fault conditions Information actually reported by FTU .

[0087] S2: Constructing a mixed-integer linear programming model. The co-optimization problem is constructed as a standard mixed-integer linear programming model: First, define all decision variables, including the binary variables for the first stage. and Second-stage binary variables And the auxiliary variables introduced during the linearization process; then set the linear objective function as shown in equation (11) to minimize the total expected cost of the system. Finally, add all constraints, including the budget and quantity constraints for the first stage, and the linearization constraint group for the second stage.

[0088] S3: Model Solving and Result Output. The commercial mathematical programming solver Gurobi is invoked, the constructed complete model is input, and the solution is executed. After the solver finishes running, the optimal first-stage collaborative reinforcement scheme is extracted and output. Simultaneously record the optimal investment cost Positioning accuracy .

[0089] Verification Example: (a): Example parameters: This invention employs, as follows Figure 3The 14-node distribution network system with distributed generation shown is used as a test case to simulate and verify the proposed model. This system is configured with 14 FTUs (Feeder Transmission Units) with directional elements. The main power source is located on the side containing the transformer, and a distributed generation is connected at node 14. The positive direction of the entire network is defined as the direction from the main power source to the end of the feeder or the distributed generation, and the feeder section number is consistent with its adjacent upstream switch number. μPMU (μm-to-μm measurement unit) devices (a~e) are connected at the power source outlet, topology end node, and important nodes, and the distribution network is divided into 5 monitoring domains based on the location of each μPMU (a~e). P a ~ P e The configuration locations of the instantaneous overcurrent protection circuit breaker (Fa), the time-limited instantaneous overcurrent protection circuit breaker (Fb1~Fb3), and the overcurrent protection circuit breaker (Fc1~Fc4) are as follows: Figure 2 As shown. The simulation was performed in the MATLAB R2024a environment.

[0090] Regarding parameter settings, set the maximum number of faults in a given section. Both the maximum number of FTU faults and the maximum number of faults are set to 2, and the reinforcement cost of a single feeder section is... The fee is set at 20,000 yuan, which covers the purchase, installation, and system integration costs of physical isolation equipment; for a single FTU node. The reinforcement cost is set at 10,000 yuan, mainly used to improve its communication reliability and fault tolerance performance; The amount is 100,000 yuan. The disciplinary coefficient is... The value is 1 million yuan. Section fault probability. FTU underreporting probability and false alarm probability They are 3%, 10%, and 8%, respectively.

[0091] (II) Optimization Result Configuration Analysis: Figure 3 Using the 14-node distribution network topology adopted in this invention as a background, the optimal reinforcement scheme calculated by the collaborative optimization model is intuitively demonstrated. The figure clearly marks the specific spatial locations of the selected feeder sections and FTU nodes. The results clearly show that the reinforcement resources are not evenly distributed, but concentrated on several key line corridors and information nodes, which confirms the effectiveness of the collaborative model in identifying weak links and key nodes in the system.

[0092] As shown in Table 2, to achieve the optimal goal, reinforcement is required for two critical line sections (numbered 11 and 4) and six FTU nodes (numbered 13, 8, 14, 9, 7, and 3) in the system. Section reinforcement mainly reduces the probability of failure through physical reinforcement; node reinforcement focuses on hardware reinforcement and software fault tolerance upgrades for FTU terminals to reduce information omissions and false alarms during disasters. The total reinforcement cost of this scheme is 100,000 yuan. After reinforcement, the fault location accuracy of the system under extreme disaster scenarios increased from the initial 45% to 91%, significantly enhancing the resilience of the distribution network.

[0093]

[0094] As shown in Table 2, the number of FTU nodes requiring reinforcement is significantly greater than that of feeder sections. This is because node reinforcement directly improves the reliability of the information source for the fault location system. The accuracy of distribution network fault location highly depends on the quality of fault information uploaded by FTUs. Node reinforcement significantly reduces the false alarm and missed alarm rates of FTUs through hardware reinforcement and software fault tolerance upgrades, thereby directly ensuring the reliability of fault diagnosis from the information source. In contrast, section reinforcement mainly improves the disaster resistance of physical components. Although it can reduce the probability of fault occurrence, its effect on improving the accuracy of fault location after it has occurred is relatively indirect. In addition, the cost of node reinforcement is significantly lower than that of section reinforcement, and the implementation cycle is shorter and the results are faster. With the same resource investment, it can generate greater marginal benefits, thus having a better cost-effectiveness ratio. This difference in benefits is particularly evident in scenarios where extreme disasters cause severe distortion of FTU data. Node reinforcement can provide more direct and effective technical support for rapid fault isolation during disasters and power restoration after disasters.

[0095] However, relying solely on node hardening exhibits significant diminishing returns and performance bottlenecks. Once all critical FTUs have been hardened, the marginal return on further investment will decrease significantly, and the system's positioning performance will tend to saturate. Figure 4 The study demonstrates the effectiveness of a solution that only reinforces nodes under the same cost constraints. Its positioning accuracy is significantly lower than that of the combined solution, confirming the limitations of single-information-layer reinforcement.

[0096] To evaluate the effectiveness of the single FTU node hardening strategy, 10 nodes were selected with an investment cost of 100,000 and configured in the optimal hardening order. Specifically, the hardening order was nodes 13, 8, 14, 5, 9, 11, 4, 7, 10, and 3. Figure 4The accuracy growth trend shown indicates that as the number of nodes reinforced increases, the system fault location accuracy gradually improves, but the rate of increase decreases. Initially, when nodes 13, 8, and 14 are reinforced, the accuracy significantly improves, with increases of 11% and 6%, respectively. Subsequently, when nodes 5, 9, and 11 are reinforced, the rate of increase gradually narrows to 5%–3%. Further reinforcement of nodes 4, 7, 10, and 3 further reduces the rate of increase to 1% or even lower, ultimately achieving an accuracy of only 80%.

[0097] This diminishing reinforcement effect primarily stems from the inherent limitations of switching functions in handling multiple fault scenarios. Even with all FTU nodes sufficiently reinforced and no information omissions or false alarms, traditional switching functions still struggle to accurately describe the fault current direction characteristics under multi-power supply coupling conditions when dealing with complex current paths formed by multiple faults, thus reducing the fault tolerance of the localization model. For example, when only segment 9 experiences a fault. Figure 5 As shown, the fault current information reported by the FTU is [1 1 0 0 0 0 1 1 1 0 0 0 -1 -1]; while when both section 9 and section 10 are faulty at the same time, as shown... Figure 6 As shown, the information returned by the FTU is still the same set of data. Because the information characteristics are completely identical in both cases, the positioning system cannot effectively identify multiple faults, resulting in missed detections.

[0098] To verify the sensitivity of the proposed pre-disaster reinforcement optimization model to key parameters, this section conducts sensitivity analysis on the maximum investment cost and the maximum number of failures, respectively, and evaluates their impact on the final reinforcement scheme, total cost, and system performance.

[0099] Table 3 and Figure 7 This study reveals the inherent relationship between investment costs and fault location accuracy from different dimensions. Data shows that system location accuracy exhibits a typical step-like growth pattern with increasing investment scale, reflecting a non-linear relationship between resource input and performance improvement.

[0100]

[0101] During periods of low investment intensity ( The initial investment of 50,000 yuan focused on hardening FTU nodes. At this stage, funds were prioritized for hardening critical FTU nodes, achieving a rapid improvement in positioning accuracy at a relatively low cost, demonstrating the significant initial marginal benefits of information layer hardening. When the investment increased to 60,000 yuan, segment hardening was introduced for the first time, forming a collaborative protection architecture between the information and physical layers, resulting in a significant leap in accuracy.

[0102] With further investment, the system achieved a steady improvement in accuracy through precise configuration of the hardening combination of the information layer and the physical layer. In the highest investment plan (160,000 yuan), the system ultimately achieved a 96% positioning accuracy by building a comprehensive collaborative protection network. The above evolution path shows that the optimization logic for achieving high-reliability positioning lies in: prioritizing performance breakthroughs through information layer hardening, and then introducing physical layer hardening to achieve higher goals. This conclusion provides an important reference for the formulation of differentiated investment strategies.

[0103] The number of fault duplications in a section is one of the important factors affecting the accuracy of fault location in a distribution network. Its changes are directly related to the complexity of fault scenarios during disasters and the fault tolerance requirements of the location model. This invention sets a maximum number of fault duplications in a section. This section simulates typical multiple failure scenarios under extreme disasters. To systematically evaluate the sensitivity of failure multiples to pre-disaster hardening strategies, this section further examines single-segment failures (...). ) and triple section faults ( In investment costs A reinforcement scheme under the constraint of 10,000, and a comparison with the baseline scenario ( A comparison was made to reveal the impact of changes in fault multiplicity on the effectiveness of hardening resource allocation and system resilience enhancement.

[0104]

[0105] From Table 4 and Figure 8 It is evident that increasing the number of fault layers in a section significantly increases the difficulty and cost of pre-disaster reinforcement. Under a single fault condition, reinforcing 10 FTU nodes can achieve 100% positioning accuracy. In this case, the fault scenario is simple, and traditional switching functions can accurately determine the fault current. The performance bottleneck mainly lies in the reliability of FTU information, and node reinforcement can effectively suppress false alarms and missed alarms.

[0106] When the fault severity increases to 2 or 3, the hardening strategy undergoes a fundamental change, typically characterized by the inclusion of feeder sections in the hardening combination. This is because multiple faults create complex current paths, and even if FTU information is reliable, traditional location models are prone to failure due to their inherent limitations.

[0107] Therefore, as the number of multiple faults increases, the focus of hardening needs to shift from simply improving information reliability to a comprehensive hardening solution that integrates the physical and information layers: this requires both segment hardening to reduce the probability of high-multiple faults and expanding node hardening to enhance information fault tolerance. This conclusion indicates that under mild risk conditions dominated by single faults, node hardening can be emphasized; however, under extreme risk conditions with a high incidence of multiple faults, comprehensive hardening of both the physical and information layers is necessary, incurring the corresponding costs. This provides a basis for differentiated defense resource allocation.

[0108] In summary, the collaborative optimization model of pre-disaster hardening and fault location significantly improves the fault tolerance of distribution network fault location and provides decision support for differentiated disaster prevention strategies. This invention aims to address the shortcomings of existing distribution network fault location methods in terms of insufficient fault tolerance under large-scale failures of feeder terminal units, and the lack of effective coordination between existing pre-disaster hardening research and the fault location process. The proposed method, through collaborative optimization of pre-disaster hardening and fault location, significantly improves the fault location tolerance and system resilience of distribution networks under extreme disasters.

Claims

1. A method for locating fault sections in a distribution network that considers pre-disaster reinforcement information, characterized in that... Includes the following steps: Step 1: Establish the first-stage pre-disaster reinforcement model to determine the reinforcement scheme for feeder sections and FTU nodes, calculate the corresponding investment costs, and generate a set of failure scenarios based on the reinforcement scheme; Step 2: Establish a second-stage segment location model to integrate multi-source information for fault segment identification and calculate the location deviation penalty cost; Step 3: Integrate the pre-disaster hardening model from Step 1 with the second-stage segment location model from Step 2 to construct a two-stage collaborative optimization model with the goal of minimizing the total expected cost of the system. Step 4: Solve the two-stage collaborative optimization model constructed in Step 3, and finally output the optimal pre-disaster reinforcement scheme.

2. The method for locating fault sections in a distribution network considering pre-disaster reinforcement information as described in claim 1, characterized in that: In step 1, the first-stage pre-disaster reinforcement model is as follows: （1）； In formula (1): The intensification state of the described section; Indicates the enhanced state of a node; This indicates the reinforcement scheme for the feeder section; For the first The status of each FTU node.

3. The method for locating fault sections in a distribution network considering pre-disaster reinforcement information according to claim 2, characterized in that: The constraints of the first-phase pre-disaster reinforcement model include reinforcement logic, physical resources, and investment budget constraints. ①: The hardened logic constraints are expressed as follows: After reinforcing the feeder section The FTU node is considered absolutely reliable and will not fail in fault scenarios, as expressed mathematically below: （2）； In formula (2): and The fault status of a segment and node is represented by: （3）； Investment costs It is a core indicator of the pre-disaster reinforcement model, and its specific description is as follows: （4）； In equation (4): , These are the reinforcement cost coefficients for sections and nodes, respectively; The number of feeder sections to be reinforced; The number of FTU nodes to be reinforced; The intensification state of the described section; Indicates the enhanced state of a node; ②: At the same time, the reinforcement of the power distribution network must follow the principle of resource constraints, specifically, it is limited by physical resources and investment budget; among which, the physical resource constraint is reflected in the constraint of the quantity of reinforcement: （5）； In formula (5): and These are the maximum number of reinforcements required for feeder sections and FTU nodes, respectively. Investment budget constraints are reflected in: The reinforcement cost must not exceed the total budget, specifically stated as: investment cost. It cannot exceed its upper limit. ,Right now: .

4. The method for locating fault sections in a distribution network considering pre-disaster reinforcement information as described in claim 3, characterized in that: Based on the reinforcement scheme, Monte Carlo simulation method is used to generate fault scenarios for evaluating the localization effect; the core of each fault scenario is the segment fault state vector. With node FTU fault state vector ,in, Section 1 to Section The fault status; For FTU node 1 to FTU node The fault status.

5. The method for locating fault sections in a distribution network considering pre-disaster reinforcement information as described in claim 4, characterized in that: The fault scenario generation process includes the following steps: S1: Initialization parameters: Input system parameters: Predefined reinforcement scheme , The intensification state of the described section; Indicates the enhanced state of a node; Set probability parameters: Section fault probability FTU underreporting probability FTU false alarm probability ; Setting constraints and objectives: Maximum number of faults in a given section Maximum FTU fault count Number of target scenarios ; And initialize an empty scene library. ; S2: Generation section fault status: Traverse all segments and FTU nodes to generate their states; For a section: If the section has been reinforced, force it into a fault state. ; Otherwise, generate random numbers. ,like ,but Otherwise, it is 0; For FTU nodes: If the FTU has been hardened, force it into a fault state. Otherwise, generate random numbers. And its state is determined according to equation (6). : （6）； In formula (6): For a random number, ; S3: Scenario Validation: Calculate the fault count for the current candidate scenario: number of faults in the section. FTU failure count If satisfied and If the condition is met, then execute S4; otherwise, discard the scene and return to S2 to regenerate. S4: Record valid scenarios: Current valid fault status Store in scene library ; S5: Loop termination check; If the number of scenes in the scene library Target value reached If the loop terminates, output the result. ; Otherwise, return to S2 and continue generating; In obtaining the fault state vector This needs to be converted into input information for the positioning phase, namely the current information reported by each FTU. ,in This indicates that a positive fault current has been detected. This indicates that a reverse fault current has been detected, and This indicates that no fault current was detected.

6. The method for locating fault sections in a distribution network considering pre-disaster reinforcement information as described in claim 5, characterized in that: In distribution network fault analysis, when the FTU is operating normally, the current information can be defined as the expected state of the FTU. This desired state is calculated using section fault information and switching functions, and its mathematical expression is as follows: （7）； In equation (7): , These are the switching functions for the upstream and downstream parts of the node, respectively; The number of power sources in the FTU's upstream network; The number of power sources in the downstream network of FTUj; For FTU to upstream power supply The set of segments along the path; This is the set of all segments in the downstream network of the FTU; For FTUj to downstream power supply The set of segments along the path; This is the set of all segments in the upstream network of FTUj; for or A segment of a collection; No. Possible section failures are possible; Indicates the section number; Indicates the power supply designation; Represents the logical AND. Represents the logical "NOT"; FTU malfunctions manifest in two forms: missed alarms and false alarms; A missed alarm occurs when the FTU fails to detect a fault current and incorrectly reports a "0" status. A false alarm occurs when the FTU incorrectly reports a "1" or "-1" signal when there is no fault current, or incorrectly reports the current direction. The specific manifestations are as follows: （8）。 7. The method for locating fault sections in a distribution network considering pre-disaster reinforcement information as described in claim 6, characterized in that: In step 2, a second-stage segment location model is established, and based on the deviation between the location result and the actual fault state, the location deviation penalty cost is calculated. The objective function of the second-stage segment location model is: （9）； In equation (9): This represents the difference between the expected state and the actual state of the FTU. This represents the optimal fault prediction state; These are the weighting coefficients set according to the minimum set theory of fault diagnosis; Total number of FTU switches; For fault scenarios The calculated FTU node status; The optimal fault prediction state is obtained by solving the problem. Then, the positioning performance can be quantified by comparing the inferred results with the actual state, and the positioning deviation can be defined. for: （10）； In formula (10): The optimal fault inference state segment The fault status; No. The first type of failure scenario Fault status of each location segment; The expected value of this positioning deviation across the entire set of failure scenarios constitutes the expected positioning penalty cost of the second stage. : （11）； In equation (11): This indicates a penalty for failure to locate the fault. For the scene The probability of occurrence; This represents a set of failure scenarios; the expected location penalty cost. As a collaborative link connecting the two stages, it serves as a key feedback signal and is incorporated into the global optimization objective.

8. The method for locating fault sections in a distribution network considering pre-disaster reinforcement information according to claim 7, characterized in that: The second-stage segment location model includes the following constraints: 1) μPMU branch constraints: Based on the μPMU configuration location, when a ground fault occurs in the distribution network, the fault branch can be determined using the fault information collected by the μPMU. Therefore, the faulty section must be located on the faulty branch, and the μPMU branch constraint can be expressed as: （12）； In equation (12): The optimal fault inference state is the fault state of segment 1; What is the optimal fault inference state for segment 2? This represents the optimal fault inference state segment. The fault status; This represents the set of segments on the faulty branch determined by μPMU; 2) Circuit breaker constraints: The specific location of the circuit breaker tripping can determine the power outage area; therefore, a section fault must be within the protection range of the operating protective equipment. Thus, the constraint on the power outage area is expressed as: （13）； In equation (13): Representative protective equipment The set of segments LS within the defined protection area; Indicates logical OR; 3) Fault multiple number constraint for section: Maximum number of faults under extreme events 2: （14）； In equation (14): Represents the set of fault locations; The optimal fault inference state segment The fault status; 4) FTU section state constraints: （15）； 5) FTU Real-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. （16）。 9. The method for locating fault sections in a distribution network considering pre-disaster reinforcement information as described in claim 8, characterized in that: In step 3, in the two-stage collaborative optimization model, the total expected cost of the system is the sum of the expected values ​​of the investment cost in step 1 and the positioning deviation penalty cost in step 2, specifically expressed as follows: （17）； In equation (17): Indicates the total cost; Expressed as investment cost; This is the penalty coefficient; This indicates a penalty for positioning deviation; Indicates the reinforcement cost coefficient for the section; This represents the reinforcement cost coefficient for FTU nodes; Indicates a section The reinforced state; Indicates FTU node The reinforced state; This indicates a penalty for positioning deviation; Indicates the number of reinforced sections; Indicates the number of reinforced nodes; To quantify the positioning reliability of different schemes, positioning accuracy is defined. as follows: （18）； In formula (18): It is an indicator function, in the scene The value is 1 when the location is completely and accurately determined, and 0 otherwise. This represents a set of fault scenarios.

10. The method for locating fault sections in a distribution network considering pre-disaster reinforcement information according to claim 9, characterized in that: In step 4, the two-stage co-optimization model constructed in step 3 is linearized using a logistic-algebraic transformation method, transforming it into a mixed-integer linear programming model for efficient solution. Specifically: Equations (18) and (2) involve nonlinear absolute value operations. To integrate them into the mixed-integer linear programming model, a standard linearization method is adopted, and auxiliary variables are introduced. and Transform it into equations (19), (20), and (21): （19）； In equation (19): This indicates a penalty for positioning deviation; Represents a binary auxiliary variable; （20）； In equation (20): No. Section under various fault scenarios Optimal fault inference; Indicates the first Section under various fault scenarios The actual fault condition; （21）； In equation (21): Represents a binary auxiliary variable; Indicates the enhanced state of the FTU node; To linearize the objective function of the positioning model in equation (9), the absolute value sign on the right side of the equation needs to be removed. According to the definition rules of the expected FTU state and the actual FTU state, there are 9 possible differences between them, as shown in Table 1. For each case, the function value corresponding to the objective function of the positioning model in equation (9) is calculated, and intermediate variables are given. and All possible combinations; The objective function of the localization model can be transformed into a linear function (22) and a conditional expression (23): （22）； In equation (22): This represents the difference between the expected state and the actual state of the FTU. This represents the set of FTU nodes in a distribution network; This represents the set consisting of all feeder sections in a distribution network; This represents a weighting coefficient used to prevent misjudgments, typically set to 0.5; Indicates the segment status; （23）； The logical relations are transformed into algebraic relations, as shown in equations (24) to (26); all nonlinear logical relation constraints can be transformed into linear algebraic relation constraints: （24）； In equation (24): Represents any value; Represents any value Component 1; Represents any value Composition ; This indicates that it is equivalent to; Represents any value Composition ; （25）； In equation (25): Represents any value; Represents any value Composition ; Indicates the number of components in B; （26）； In equation (26): Represents any value; express Composition values Invert; express The composition values; According to the linear transformation principle of equation (24), the nonlinear logical relations (12) and (13) can be transformed into the following linear algebraic relations: （27）； In equation (27): This represents the set of segments on the faulty branch determined by μPMU; （28）； Introducing intermediate variables , , , , and ,make: , This is a binary intermediate variable used to linearize the positioning function; This represents the set of FTU nodes in the distribution network; This is a binary intermediate variable used to linearize the positioning function; This is a binary intermediate variable used to linearize the positioning function; , For FTU to upstream power supply The set of segments along the path; This is a binary intermediate variable used to linearize the positioning function; , The number of power sources in the FTU's upstream network; , For FTU j The set of all segments in the downstream network; This is a binary intermediate variable used to linearize the positioning function; , This is a binary intermediate variable used to linearize the positioning function; This is a binary intermediate variable used to linearize the positioning function; This is a binary intermediate variable used to linearize the positioning function; ； , The number of power sources in the downstream network of FTUj; This is a binary intermediate variable used to linearize the positioning function; This is the set of all segments in the upstream network of FTUj; Indicates the fault scenario lower section The fault status; Then the desired state equation (7) of FTU can be transformed into: （29）； In equation (29): Upstream switching function; Indicates the downstream switching function; This represents the actual node current information; The forward current state of the FTU can be transformed into: （30）； The negative current state of the FTU can be transformed into: （31）。

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