Power distribution network post-disaster collaborative repair path optimization method and system considering infrastructure interdependence

Abstract

The application discloses a power distribution network post-disaster collaborative repair path optimization method and system considering infrastructure interdependence, and the method comprises the following steps: acquiring a node set and a damaged node set containing at least two types of lifeline networks; configuring a repair center and the number of repair teams for each type of infrastructure network, and collecting or estimating the standardized repair operation time of each damaged node, and combining the damaged nodes and the repair center to form a set of accessible routing nodes; obtaining a functional dependence matrix according to the functional dependence relationship between any two nodes in the set, constructing a target function with the total recovery time of all nodes as the core, and solving to obtain a vehicle path sequence and an arrival schedule and a functional recovery schedule that meet the constraint relationship. The application establishes a unified optimization model of "road driving-repair operation-dependence propagation-function recovery", shortens the overall recovery process, improves the recovery efficiency of key services after a disaster, and forms an auditable and interpretable recovery schedule.

Description

Technical Field

[0001] This invention belongs to the field of disaster relief and emergency recovery scheduling and operations optimization technology for power distribution networks. It relates to the collaborative path planning, arrival-repair-power / service restoration time assessment, and scheduling decisions for power distribution network repair teams after a disaster. Specifically, it involves establishing a multi-repair team vehicle path optimization model and a rapid solution method under road traffic constraints, comprehensively considering the functional interdependence and cascading effects between the power distribution network and critical infrastructure such as communications, transportation, fuel / material supply, and water utilities. This model generates interpretable repair paths and restoration schedules to support post-disaster command and dispatch and post-disaster assessment. Background Technology

[0002] Extreme disasters such as typhoons, earthquakes, floods, and freezing rains often cause simultaneous damage to multiple parts of the power distribution network, including power lines, switchgear, ring main units, and transformer substations, accompanied by worsening external conditions such as road interruptions, communication degradation, and limited fuel and material supplies. In this context, the "completion of repairs" and "restoration of function (ability to supply power to loads)" of the power distribution network are not equivalent. For example, even after maintenance of a section of the line, if upstream power sources, key switches, or communication links are not restored, power supply may still be impossible. Furthermore, remote switching, feeder automation, and emergency repair command rely on communication infrastructure, while communication base stations and dispatch terminals, in turn, depend on the power supply from the power distribution network, creating a circular dependency that may trigger cascading failures.

[0003] Current disaster relief decision-making often adopts a single-system perspective of the power distribution network: each unit separately formulates the repair sequence and vehicle routes, usually aiming to minimize travel time, work completion time, or latest arrival time. Dependencies on cross-infrastructure systems are often handled retrospectively based on empirical rules, which has the following main shortcomings:

[0004] 1. Ignoring inter-infrastructure dependencies and circular dependencies: Prioritizing the repair of equipment does not necessarily lead to priority load recovery, and may cause long-term delays in critical dependent nodes.

[0005] 2. Confusing "repair completed" with "power / service restored": It fails to depict the waiting and recovery surge caused by the propagation of the dependency chain, affecting the recovery curve and critical load supply assessment.

[0006] 3. Lack of a unified and interpretable timeline: It is difficult to simultaneously provide the routes of multiple repair teams and the three types of timestamps: "arrival - repair completion - function restoration", and to explain the systemic reasons for the repair priorities.

[0007] 4. Difficulty in scaling up solutions: When the number of damaged locations and the size of the teams increase and the dependencies become more complex, the calculation time of the precise mixed integer model is too long, making it difficult to meet the emergency response time. Summary of the Invention

[0008] The purpose of this invention is to provide a method and system for optimizing the collaborative repair path of a power distribution network after a disaster, taking into account the interdependence of infrastructure. Under the condition of a known disaster damage list, repair resources, road travel time, and cross-infrastructure dependencies, a unified optimization model is established that can simultaneously characterize "road travel - repair operation - dependency propagation - function restoration". The access sequence and repair priority of multiple repair teams are optimized to minimize the total time for critical nodes / critical loads of the power distribution network to enter a power-available state. The path of each repair team, as well as the node arrival time, repair completion time, and function restoration time, are output, thereby shortening the overall recovery process, improving the efficiency of post-disaster critical service restoration, and forming an auditable and interpretable recovery schedule.

[0009] To achieve the above objectives, the solution of the present invention is:

[0010] A method for optimizing the post-disaster collaborative repair path of a power distribution network that considers the interdependence of infrastructure includes,

[0011] Obtain a node set containing at least two types of lifeline networks. With damaged node set ,in, Represents a collection of infrastructure networks. Indicates infrastructure network The set of all nodes in , Indicates infrastructure network The set of damaged nodes;

[0012] For each type of infrastructure network Configure emergency repair center With the number of repair teams and for each damaged node Collect or estimate the duration of its standardized repair operations. The damaged nodes and the repair center are combined to form a set of accessible routing nodes. ;

[0013] Based on any two nodes in the set of routing nodes The functional dependencies are determined to obtain the functional dependency matrix. ;

[0014] Based on the functional dependency matrix We construct an objective function with the sum of all node recovery times as the core, and solve it to obtain the vehicle path sequence, arrival timetable, and function recovery timetable that meet the constraints.

[0015] Specifically, the functional dependency matrix is ​​obtained based on the functional dependency relationship between any two nodes in the routing node set. ,include,

[0016] For any two nodes in the set of routing nodes The functional dependency matrix is ​​constructed by defining that the functional dependency value is 1 when a node is self-dependent and 0 when there is no dependency between the two nodes. .

[0017] Wherein, based on the functional dependency matrix Construct an objective function with the sum of all node recovery times as its core, including:

[0018] For each type of infrastructure network Define binary routing variables ,in and If and only if the repair team is on the infrastructure network From node on a certain path Direct transfer to node The value is set to 1; at the same time, a continuous variable for arrival time is defined. With continuous variables of function recovery time ;

[0019] The objective function is based on the sum of the recovery times of all nodes. And expanded into a weighted form The weight Used to characterize the importance of critical loads, emergency facilities, population coverage, or key dependency hubs.

[0020] The solution process yields vehicle route sequences, arrival schedules, and function recovery schedules that satisfy the constraints. These constraints include:

[0021] For any node With any damaged node Apply constraints and for any node pair Apply constraints ;

[0022] In every infrastructure network Internal routing—time recursion constraints are established to calculate arrival time. , including, for any Apply constraints For any Apply constraints ,in Take no less than the infrastructure network The upper bound of the maximum possible arrival time. For infrastructure networks The repair team started from the damaged node Drive to the damaged node Time;

[0023] For each infrastructure network Apply an upper bound to the number of starting arcs at the repair center. .

[0024] The solution yields vehicle route sequences and arrival schedules, as well as function recovery schedules, that satisfy the constraints.

[0025] Given a set of path sequences, obtain the arrival time of each damaged node based on time recursion constraints. Then, at the fixed arrival time Solving under the condition that only contains For a linear inequality system, the function recovery time vector is obtained. ;

[0026] Based on the aforementioned function recovery time vector To obtain the target value .

[0027] The solution yields vehicle route sequences and arrival schedules, as well as function recovery schedules, that satisfy the constraints.

[0028] Based on the priority of dependency criticality, an initial solution for multiple vehicles is obtained;

[0029] Based on the initial solution, simulated annealing optimization is performed, setting the initial temperature, termination temperature, and geometric cooling coefficient. At each temperature level, a local search iteration with a length equal to the number of temperature layer iterations is executed. The acceptance of candidate solutions follows the Metropolis criterion: when the candidate solution's objective value... Better than the current solution Accept directly if it is true, otherwise accept based on probability. accept;

[0030] In each iteration of simulated annealing, multiple neighborhood operators are executed for each infrastructure network, and a "best improvement" strategy is used for each neighborhood to generate several candidate solutions with optimal evaluation. Then, the evaluation subroutine is called to calculate... As an output candidate for this neighborhood;

[0031] For each neighborhood operator, the candidate solution set is sorted according to the objective value, and the top [number] solutions are selected. The candidate sets are composed of several candidates. When there is an improved solution in the preferred set, the improved solution is accepted first. When the preferred set consists of no improved solutions, a candidate is randomly selected from the preferred set and then the Metropolis criterion is used to decide whether to accept it.

[0032] Based on the priority of dependencies, a preliminary solution for multiple vehicles is obtained, including:

[0033] Calculate the out-degree dependency index for each damaged node and use it as a key score for "how many nodes directly depend on it";

[0034] The sequence of damaged nodes is arranged from high to low according to the criticality score;

[0035] Set a travel time threshold, and sequentially assign high-critical nodes to the end of the existing vehicle path. If the travel time between a node and the current end node of any vehicle is less than the travel time threshold, select the vehicle with the smallest increment to add; otherwise, activate a new vehicle until the upper limit of the number of starting arcs of the repair center is reached.

[0036] For the remaining unassigned nodes, the criterion of "minimizing the latest recovery time increment of each vehicle's last node" is used for insertion.

[0037] The method further includes dynamically increasing the number of temperature layer iterations or increasing the number of local searches near the current temperature when a new historical optimal solution appears during the solution process.

[0038] A post-disaster collaborative repair path optimization system for power distribution networks that considers the interdependence of infrastructure includes,

[0039] The data access module is configured to acquire a node set containing at least two types of lifeline networks. With damaged node set ,in, Represents a collection of infrastructure networks. Indicates infrastructure network The set of all nodes in , Indicates infrastructure network The set of damaged nodes;

[0040] The routing initialization module is configured for each type of infrastructure network. Configure emergency repair center With the number of repair teams And for each damaged node Collect or estimate the duration of its standardized repair operations. The damaged nodes and the repair center are combined to form a set of accessible routing nodes. ;

[0041] The dependency modeling module is configured to base its model on any two nodes in the set of routing nodes. The functional dependencies are used to obtain the functional dependency matrix. ;as well as,

[0042] The data solving module is configured to be based on the functional dependency matrix. We construct an objective function with the sum of all node recovery times as the core, and solve it to obtain the vehicle path sequence, arrival timetable, and function recovery timetable that meet the constraints.

[0043] By adopting the above solution, the present invention has the following advantages compared with existing methods of independent emergency repair or methods that only determine routes based on driving convenience:

[0044] 1. Explicitly introduce cross-network functional dependencies and circular dependencies, and separate and characterize repair and function recovery by "repair completion lower bound + dependency propagation lower bound" to avoid misjudging "repair completion = restoration of energy / gas / water supply".

[0045] 2. With the goal of minimizing the total recovery time of all nodes, it automatically reflects the systemic benefit of "repairing key upstream nodes first can bring about a large-scale recovery" and can support a key node weight priority strategy.

[0046] 3. The evaluation subroutine of "fixed route - fast solution of recovery time" supports simulated annealing iteration, which is suitable for rapid decision-making in large-scale, strongly coupled scenarios.

[0047] 4. Output three types of timestamps: "arrival - repair completed - function restored" and vehicle load statistics, which can be directly used for emergency command and dispatch and review audit.

[0048] In post-disaster scenarios, there is a high degree of coupling between infrastructures (such as power distribution networks, communication base stations, and gas pressurization stations). To accurately characterize this coupling, this invention establishes a unified data model of "infrastructure network layer—road and traffic layer—functional dependency layer" and formulates the following strict subscript naming rules to eliminate semantic confusion:

[0049] : Represents a global set of nodes that includes all infrastructure nodes. elements in

[0050] : Represents the set of damaged nodes that have failed. elements in )

[0051] : Indicates that it includes damaged nodes and repair centers ( The elements in the set of routing nodes, including ).

[0052] For each type of infrastructure network Configure a corresponding emergency repair center and the number of repair teams of the same structure For any damaged node in the set of damaged nodes The estimated time for its standardized repair work. . Detailed Implementation

[0053] This invention relates to the field of post-disaster emergency recovery and operations optimization technology, and discloses a collaborative emergency repair path optimization method and system for interdependent infrastructure networks. This method addresses situations where various infrastructure networks, such as power and gas, are damaged after a disaster and exhibit cross-network functional dependencies, cyclic dependencies, and cascading failures. It constructs a multi-repair team path decision model based on road travel time and repair operation time, introduces node functional dependency parameters, and establishes a coupled constraint of "arrival time—repair completion time—functional recovery time," ensuring that the node functional recovery time is simultaneously constrained by its own repair progress and the recovery status of nodes in its dependent chain. The optimization objective is to minimize the total functional recovery time of all network nodes, outputting the multi-vehicle repair access sequence and node recovery time for each infrastructure. To improve the efficiency of solving large-scale scenarios, an initial solution construction strategy based on dependency criticality priority is further adopted, combined with a simulated annealing search framework including path 2-opt, swapping, and cross-path shifting insertion. A balance between global exploration and local convergence is achieved through probabilistic acceptance criteria and diversified / reinforcement strategies. Compared with independent emergency repairs that do not consider cross-network dependencies, this invention can significantly reduce the overall system recovery time and improve the recovery efficiency and coordination level of critical services after a disaster.

[0054] In the embodiments provided by this invention, in order to improve the post-disaster recovery efficiency of interdependent infrastructure networks, a unified data model of "infrastructure network layer - road traffic layer - functional dependency layer" is established, wherein the infrastructure network layer contains node sets of at least two types of lifeline networks. With damaged node set ,in, Represents a collection of infrastructure networks. Indicates infrastructure network The set of all nodes, which may include power equipment (such as substations and lines), gas pipeline interface nodes, communication facility nodes, etc. Indicates infrastructure network The set of damaged nodes.

[0055] The road traffic layer provides emergency repair teams with access to routing nodes. and Travel time matrix between This matrix can be calculated from the road topology map using the shortest path algorithm.

[0056] The functional dependency layer uses a binary dependency matrix. Represents the global node set any node For nodes This establishes functional dependencies and allows for cross-network and circular dependencies, enabling subsequent optimizations to explicitly characterize cascading non-functional and dependency-driven recovery order constraints. Lifeline networks refer to two or more infrastructure network types involved in post-disaster recovery, typically including but not limited to the following two categories:

[0057] Power network (power system): encompasses transmission lines, substations, and distribution stations in the power transmission and distribution system. It is usually one of the infrastructure networks that needs to be prioritized for restoration during disaster recovery.

[0058] Gas network: including natural gas pipelines, pressure regulating stations, etc. The gas supply network also plays a key role in post-disaster recovery, especially after extreme weather and disasters, when restoring gas supply is crucial to ensuring people's livelihood.

[0059] In addition to these, other common lifeline networks include:

[0060] 1. Communication networks: such as telephones and the Internet, are crucial for information transmission and emergency command during the post-disaster recovery process.

[0061] 2. Transportation network: including roads, bridges, railways, etc. Restoring the transportation network is crucial to ensuring the smooth transport of supplies and the smooth progress of rescue operations.

[0062] In the embodiments provided by this invention, in order to improve the accuracy of post-disaster damage information modeling, specific measures are taken for each type of infrastructure network. Configure emergency repair center With the number of repair teams And for each damaged node Collect or estimate the duration of its standardized repair operations. ,in This can be obtained by decomposing the work order process (such as the sum of the time for sub-processes like on-site safety handling, isolation, repair, replacement, and acceptance), and the damaged node and the emergency repair center together form an accessible set of routing nodes. To ensure subsequent routing nodes , Routing variables are defined only on the accessible set, thus effectively reducing the size of unnecessary decision variables.

[0063] In the embodiments provided by this invention, in order to improve the computability of cross-network functional dependencies, the functional dependency matrix is... Construct a sparse representation of "direct dependencies" and optionally compute its transitive closure or a dependency propagation sequence based on topological sorting to accelerate recovery time computation, wherein the following is specified: Used to uniformly represent "node self-dependency (the node itself must complete the repair / maintenance function)", and to assign a dependency to nodes that do not have a dependency relationship. This allows the recovery time constraint to be written as a unified set of linear inequalities and adapted to mixed-integer linear programming and heuristic evaluation subroutines.

[0064] In the embodiments provided by this invention, in order to improve the consistency of emergency repair path decision expression, for each infrastructure network Define binary routing variables ,in and If and only if the repair team is on the network From node on a certain path Direct transfer to node The value is set to 1; at the same time, a continuous variable for arrival time is defined. (Only for damaged nodes) ) and continuous variables of functional recovery time (For global nodes) ), and The timestamp indicating "first arrival and commencement of operation" is... The timestamp indicates that "the node has been restored to a functional state that can provide services", which semantically distinguishes between "repair completed" and "functional restoration (including dependency satisfaction)".

[0065] In the embodiments provided by this invention, in order to improve the accuracy of recovery time characterization under dependency constraints, two types of linear constraints are constructed to jointly determine the recovery time: "repair completion driven lower bound constraint" and "dependency propagation driven lower bound constraint". For any node With any damaged node Apply constraints To ensure if Depends on damaged nodes ,but Functional recovery must not be earlier than "Arrival + Repair Complete"; and for any node pair Apply constraints To ensure if Dependency Nodes ,but Functional recovery must not be earlier than The function is restored, thus enabling the overall recovery time to be "raised" backward through linear constraints even when cross-network dependencies and circular dependencies exist, achieving a unified expression of cascading effects; among which, Damaged node The arrival time refers to the time when the repair team first arrives at the node. And the timestamp for when the repair work begins; Damaged node The repair operation duration is the time required from arrival and commencement of work until the physical repair of the node is completed. For nodes Function recovery time refers to the node's recovery time. The timestamp of recovery from a non-functional state to a "serviceable / available" state after a disaster. This is not equivalent to the "repair completion time," because even if a node itself is repaired, if its dependent nodes have not yet recovered, then... It will still be postponed due to dependency constraints; This is a function-dependent indicator parameter, typically taking a binary value. Represents a node Functional dependency nodes , express Not dependent .

[0066] In the embodiments provided by this invention, in order to improve the routing and time consistency of multiple repair teams, in each infrastructure network Internal routing—time recursion constraints are established to calculate arrival time. This includes (1) constraints originating from the emergency repair center: for any Imposing constraints, whereby, for the infrastructure network The emergency repair team departed from the emergency repair center. Drive to the damaged node (2) Big-M constraint on arc selection and time recursion: for any Apply constraints ,in Take no less than the network An upper bound on the maximum possible arrival time is set to ensure that constraints fail when no arc is selected. For infrastructure networks The repair team started from the damaged node Drive to the damaged node Time; Choose variables for the path, if the infrastructure network On a certain emergency repair route, the repair team started from node Go directly to the node ,but Otherwise, it is 0; and combined with the flow conservation constraint, each damaged node satisfies "exactly one predecessor and one successor" to form several paths originating from the vehicle base and suppress the generation of sub-loops.

[0067] In the embodiments provided by this invention, in order to improve the expression of multi-vehicle departure constraints, for each infrastructure network... Apply an upper bound to the number of starting arcs at the repair center. Optionally, a closed-loop constraint for returning to the vehicle base or a soft constraint for "free return to the end node" can be further applied (e.g., by adding a virtual return arc and incorporating time recursion) to express engineering operation rules such as "must return to the site / can be terminated in place / transfer to another site for continued repair" under different emergency strategies.

[0068] In the embodiments provided by this invention, in order to improve the goal orientation of post-disaster recovery, an objective function with the sum of the recovery times of all nodes as the core is adopted. It can be expanded into a weighted form. The weight It is used to characterize the importance of critical loads, emergency facilities, population coverage, or key dependent hubs; the objective function makes the optimization process tend to prioritize the restoration of nodes that can bring greater systemic benefits, while automatically reflecting the synergistic effect of "restoring critical upstream nodes can bring about large-scale restoration" under the influence of dependency constraints.

[0069] In the embodiments provided by this invention, in order to improve the solvability of large-scale scenarios, a decomposition and calculation mechanism of "fixed route, solving recovery time" is adopted in the heuristic evaluation stage, that is, given a set of path sequences (equivalently determined) After that, the arrival time of each damaged node is first calculated or solved using time recursion constraints. Then fix Solving under the condition that only contains The linear inequality system (by and (Composition) to obtain a consistent functional recovery time vector Finally, the target value is calculated. This transforms the complex "routing + dependency coupling" evaluation into a fast, reusable subroutine to support simulated annealing iterations.

[0070] In the embodiments provided by the present invention, in order to improve the quality of the initial feasible solution, a criticality priority is constructed and a multi-vehicle initial solution is generated accordingly, specifically including (1) for each damaged node Calculate its dependency out-degree index (2) Arrange the sequence of damaged nodes from high to low according to the criticality score; (3) Set the travel time threshold. (The average travel time between damaged nodes or a quantile threshold can be used), and highly critical nodes are sequentially assigned to the end of the existing vehicle path. If the travel time between a node and any vehicle's current end node is less than... If the vehicle with the smallest increment is selected for addition, otherwise a new vehicle is activated until the target is reached. (4) For the remaining unassigned nodes, the criterion of "minimizing the latest recovery time increment of each vehicle's end node" is adopted for insertion to achieve an initial balance between path length and recovery benefits.

[0071] In the embodiments provided by this invention, in order to improve the global search capability and local convergence stability, simulated annealing optimization is performed based on the initial solution, and an initial temperature is set. Termination temperature With geometric cooling coefficient And at each temperature level, a local search iteration of length equal to the number of temperature layer iterations is performed; where candidate solutions are accepted using the Metropolis criterion: when the objective value of the candidate solution is... Better than the current solution Accept directly if it is true, otherwise accept based on probability. Acceptance is necessary to ensure that local optima are allowed to be crossed during the high-temperature phase and that convergence is strengthened during the low-temperature phase.

[0072] In the embodiments provided by the present invention, in order to improve the coverage of the neighborhood search, multiple neighborhood operators are executed for each infrastructure network in each iteration of the simulated annealing, including at least (1) 2-opt: disconnecting and reconnecting two edges in the same path to change the order of the segments; (2) exchanging neighborhoods: swapping the positions of two nodes in the same path; (3) exchanging between paths: swapping the nodes of two different vehicle paths; (4) relocating neighborhoods: removing a node from one path and inserting it into a specified position in another path; and using the "best improvement" strategy for each type of neighborhood to generate several candidate solutions with the best evaluation, and then calling the evaluation subroutine to calculate As output candidates for this neighborhood, search efficiency is improved while ensuring evaluation consistency.

[0073] In the embodiments provided by this invention, in order to improve search diversity and prevent premature convergence, the candidate solution set generated by each neighborhood operator is sorted according to the target value, and the top [number] solutions are selected. The candidate sets are composed of several candidates. When there is an improved solution in the preferred set, the improved solution is accepted first. When the preferred set consists of non-improved solutions, a candidate is randomly selected from the preferred set and then the Metropolis criterion is used to decide whether to accept it. This is to introduce controlled random perturbation in the "near local optimum" to avoid getting stuck in a fixed cyclic path structure and to enhance the ability to migrate across neighborhoods.

[0074] In the embodiments provided by the present invention, in order to improve the fine-grained search capability after the optimal solution is discovered, an enhancement strategy is introduced. When a new historical optimal solution appears, the number of temperature layer iterations is dynamically increased or the number of local searches is increased near the current temperature to deepen the exploration of the neighborhood of the optimal solution. Furthermore, a threshold of "not enabling enhancement in the first few iterations" can be set to avoid wasting computational budget in the early high-temperature stage, thereby achieving better time allocation and solution quality improvement under the condition of limited overall computation time.

[0075] Through the above processing, the "arrival time" of each damaged node u can be finally output as (1). Repair completion time global node Function recovery time "Three types of timestamps; (2) Provide system-level indicators such as total recovery time" Weighted recovery time of critical nodes Statistics on the route length and workload of each vehicle are compiled to facilitate explanations during emergency reviews of "why this node must be repaired first / why this vehicle takes this route".

[0076] This invention also provides a post-disaster collaborative repair path optimization system for power distribution networks that considers the interdependence of infrastructure, comprising,

[0077] The data access module is configured to acquire a node set containing at least two types of lifeline networks. With damaged node set This is used to import disaster damage lists, emergency repair resources, road travel times, and dependency matrices.

[0078] The routing initialization module is configured for each type of infrastructure network. Configure emergency repair center With the number of repair teams and for each damaged node Collect or estimate the duration of its standardized repair operations. to integrate various infrastructure networks Set of damaged nodes Its emergency repair center Together they form a set of accessible routing nodes. ;

[0079] The dependency modeling module is configured to obtain a functional dependency matrix based on the functional dependency relationship between any two nodes in the routing node set. And calculate key indicators; and,

[0080] The data solving module is configured to be based on the functional dependency matrix. The module constructs an objective function with the sum of all node recovery times as its core, and solves it to obtain the vehicle route sequence, arrival timetable, and function recovery timetable that meet the constraints. Specifically, this module includes an objective evaluation module, a simulated annealing optimization module, and a result output module. The objective evaluation module is used to solve the problem under a fixed route. and and output The simulated annealing optimization module is used to call the neighborhood operator and the acceptance criterion to iteratively update the path; the result output module is used to output the vehicle path sequence, arrival timetable, node recovery timetable and optional key node priority repair list for each infrastructure, so as to interface with the emergency command and dispatch system.

[0081] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, various improvements and modifications can be made without departing from the spirit and principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for optimizing the post-disaster collaborative repair path of a power distribution network considering the interdependence of infrastructure, characterized in that: include, Obtain a node set containing at least two types of lifeline networks. With damaged node set ,in, Represents a collection of infrastructure networks. Indicates infrastructure network The set of all nodes in , Indicates infrastructure network The set of damaged nodes; For each type of infrastructure network Configure emergency repair center With the number of repair teams and for each damaged node Collect or estimate the duration of its standardized repair operations. The damaged nodes and the repair center are combined to form a set of accessible routing nodes. ; Based on any two nodes in the set of routing nodes The functional dependencies are determined to obtain the functional dependency matrix. ; Based on the functional dependency matrix We construct an objective function with the sum of all node recovery times as the core, and solve it to obtain the vehicle path sequence, arrival timetable, and function recovery timetable that meet the constraints.

2. The method as described in claim 1, characterized in that: Based on the functional dependency relationship between any two nodes in the routing node set, the functional dependency matrix is ​​obtained. ,include, For any two nodes in the set of routing nodes The functional dependency matrix is ​​constructed by defining that the functional dependency value is 1 when a node is self-dependent and 0 when there is no dependency between the two nodes. .

3. The method as described in claim 1, characterized in that: Based on the functional dependency matrix Construct an objective function with the sum of all node recovery times as its core, including: For each type of infrastructure network Define binary routing variables ,in and If and only if the repair team is on the infrastructure network From node on a certain path Direct transfer to node The value is set to 1; at the same time, a continuous variable for arrival time is defined. With continuous variables of function recovery time ; The objective function is based on the sum of the recovery times of all nodes. And expanded into a weighted form The weight Used to characterize the importance of critical loads, emergency facilities, population coverage, or key dependency hubs.

4. The method as described in claim 3, characterized in that: The solution yields vehicle route sequences, arrival schedules, and function recovery schedules that satisfy the constraints. These constraints include: For any node With any damaged node Apply constraints and for any node pair Apply constraints ; In every infrastructure network Internal routing—time recursion constraints are established to calculate arrival time. , including, for any Apply constraints For any Apply constraints ,in Take no less than the infrastructure network The upper bound of the maximum possible arrival time. For infrastructure networks The repair team started from the damaged node Drive to the damaged node Time; For each infrastructure network Apply an upper bound to the number of starting arcs at the repair center. .

5. The method as described in claim 4, characterized in that: The solution yields the vehicle route sequence and arrival timetable, and the function recovery timetable, which satisfy the constraints. Given a set of path sequences, obtain the arrival time of each damaged node based on time recursion constraints. Then, at the fixed arrival time Solving under the condition that only contains For a linear inequality system, the function recovery time vector is obtained. ; Based on the aforementioned function recovery time vector To obtain the target value .

6. The method as described in claim 4, characterized in that: The solution yields the vehicle route sequence and arrival timetable, and the function recovery timetable, which satisfy the constraints. Based on the priority of dependency criticality, an initial solution for multiple vehicles is obtained; Based on the initial solution, simulated annealing optimization is performed, setting the initial temperature, termination temperature, and geometric cooling coefficient. At each temperature level, a local search iteration with a length equal to the number of temperature layer iterations is executed. The acceptance of candidate solutions follows the Metropolis criterion: when the candidate solution's objective value... Better than the current solution Accept directly if it is true, otherwise accept based on probability. accept; In each iteration of simulated annealing, multiple neighborhood operators are executed for each infrastructure network, and a "best improvement" strategy is used for each neighborhood to generate several candidate solutions with optimal evaluation. Then, the evaluation subroutine is called to calculate... As an output candidate for this neighborhood; For each neighborhood operator, the candidate solution set is sorted according to the objective value, and the top [number] solutions are selected. The candidate sets are composed of several candidates. When there is an improved solution in the preferred set, the improved solution is accepted first. When the preferred set consists of no improved solutions, a candidate is randomly selected from the preferred set and then the Metropolis criterion is used to decide whether to accept it.

7. The method as described in claim 6, characterized in that: Based on the dependency criticality priority, an initial solution for multiple vehicles is obtained. include, Calculate the out-degree dependency index for each damaged node and use it as a key score for "how many nodes directly depend on it"; The sequence of damaged nodes is arranged from high to low according to the criticality score; Set a travel time threshold, and sequentially assign high-critical nodes to the end of the existing vehicle path. If the travel time between a node and the current end node of any vehicle is less than the travel time threshold, select the vehicle with the smallest increment to add; otherwise, activate a new vehicle until the upper limit of the number of starting arcs of the repair center is reached. For the remaining unassigned nodes, the criterion of "minimizing the latest recovery time increment of each vehicle's last node" is used for insertion.

8. The method as described in claim 6, characterized in that: It also includes dynamically increasing the number of temperature layer iterations or increasing the number of local searches near the current temperature when a new historical optimal solution appears during the solution process.

9. A post-disaster collaborative emergency repair path optimization system for power distribution networks that considers the interdependence of infrastructure, characterized in that: include, The data access module is configured to acquire a node set containing at least two types of lifeline networks. With damaged node set ,in, Represents a collection of infrastructure networks. Indicates infrastructure network The set of all nodes in , Indicates infrastructure network The set of damaged nodes; The routing initialization module is configured for each type of infrastructure network. Configure emergency repair center With the number of repair teams and for each damaged node Collect or estimate the duration of its standardized repair operations. The damaged nodes and the repair center are combined to form a set of accessible routing nodes. ; The dependency modeling module is configured to base its model on any two nodes in the set of routing nodes. The functional dependencies are determined to obtain the functional dependency matrix. ;as well as, The data solving module is configured to be based on the functional dependency matrix. We construct an objective function with the sum of all node recovery times as the core, and solve it to obtain the vehicle path sequence, arrival timetable, and function recovery timetable that meet the constraints.

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