Power distribution network post-disaster collaborative recovery method based on vulnerability perception and dynamic service fee guidance

Abstract

The application provides a power distribution network post-disaster collaborative recovery method based on vulnerability awareness and dynamic service fee guidance, and belongs to the field of power distribution network post-disaster recovery; solves the key problems such as resource fragmentation, traffic static, rough user behavior description and lack of consideration of power grid vulnerability in existing post-disaster dispatching; the application constructs a three-layer optimization architecture of "upper layer dispatching decision-making-middle layer pricing guidance-lower layer behavior response", and takes dynamic service fee as the core coordination mechanism of post-disaster recovery to realize the unification of centralized dispatching and distributed user response; the dynamic service fee is introduced as an independent decision variable, thereby forming a closed-loop feedback system of "dispatching-price-behavior", which provides a systematic technical path for the collaborative optimization of multiple types of mobile resources after the disaster; the application establishes a deep coupling mechanism covering the power system, the traffic system and the user behavior, which significantly improves the efficiency, accuracy and safety of post-disaster recovery.

Description

Technical Field

[0001] This application relates to the field of distribution network post-disaster recovery technology, and in particular to a collaborative post-disaster recovery method for distribution networks based on vulnerability perception and dynamic service fee guidance. Background Technology

[0002] In recent years, global climate change has intensified, and the frequency of extreme natural disasters has increased significantly, placing higher demands on the resilience and power supply continuity of urban energy systems. As a crucial terminal link in the power system, the power distribution network (PDN), due to its decentralized architecture, wide-ranging lines, and complex exposed environments, is highly susceptible to physical damage under disaster scenarios, leading to widespread power outages and consequently affecting the normal operation of critical infrastructure such as communications, water supply, healthcare, and transportation. Therefore, constructing efficient, rapid, and adaptive post-disaster recovery mechanisms for distribution networks has become an important research direction for enhancing power system resilience.

[0003] With the development of mobile energy storage technology, Mobile Energy Storage Systems (MESS) have gradually become an indispensable mobile resource in emergency power supply systems due to their advantages such as high mobility, rapid deployment, and flexible energy allocation. Meanwhile, with the continuous growth of electric vehicle (EV) fleets and the increasing maturity of Vehicle-to-Grid (V2G) technology, the potential of EVs in post-disaster scenarios is becoming increasingly apparent: EVs are not only a component of transportation systems but can also serve as mobile distributed energy storage units, providing support services to damaged power distribution networks. Therefore, integrating MESS and EVs into post-disaster recovery systems to achieve coordinated scheduling of multiple mobile resources has become an important research direction for novel post-disaster recovery methods.

[0004] However, existing literature has significant limitations in post-disaster collaborative recovery. First, in terms of scheduling optimization methods, most studies fail to fully consider the critical safety factor of grid structural vulnerability. Existing models mostly focus on load restoration and network reconfiguration, neglecting vulnerability indicators such as node power supply path redundancy, critical line power flow concentration, and fault propagation risk. This results in blind spots in the safety assessment of scheduling schemes, making it difficult to effectively prevent secondary failure risks in the post-disaster system. Second, most studies are based on static or homogeneous traffic assumptions, failing to accurately characterize the dynamic changes in the post-disaster transportation network and the differentiated behavior of electric vehicles (such as route selection and charging / V2G decisions). This simplifies the coupling relationship between the power and transportation systems and fails to reflect the real interaction mechanism. Third, existing methods typically model and schedule MESS, V2G electric vehicles, and maintenance resources separately, lacking a unified multi-resource collaborative optimization framework, making it difficult to leverage the complementary benefits between resources. This fragmented scheduling approach not only reduces resource allocation efficiency but also ignores the collaborative potential of various mobile resources in the spatiotemporal dimensions. Finally, regarding the coordination mechanism, the traditional charging service fee pricing mechanism often only makes local adjustments based on the load or queuing status within the charging station, without taking into account global information such as the vulnerability of the power grid structure, traffic congestion status, and system recovery needs. Therefore, it cannot effectively guide electric vehicles to form the most favorable spatiotemporal distribution for power grid recovery through economic signals.

[0005] In summary, existing technologies have not yet formed a systematic modeling framework that can uniformly describe the physical coupling between distribution networks and transportation networks, market regulation mechanisms, and user behavior responses. In particular, they lack proactive defense considerations for grid vulnerability in dispatch optimization, making it difficult to meet the collaborative recovery needs of multiple resources, multiple stakeholders, and multiple time periods after a disaster. Therefore, there is an urgent need for a new collaborative recovery method for distribution networks after disasters. This method should introduce a core coordination mechanism to achieve organic integration of centralized dispatch and distributed user decision-making, and incorporate grid vulnerability indicators into the optimization system, thereby comprehensively improving the safety, efficiency, and resilience of the post-disaster recovery process. Summary of the Invention

[0006] To address the aforementioned technical issues, this application proposes a collaborative post-disaster recovery method for distribution networks based on vulnerability perception and dynamic service fee guidance.

[0007] The technical solution adopted in this application is: a method for collaborative post-disaster recovery of distribution networks based on vulnerability perception and dynamic service fee guidance, comprising the following steps:

[0008] Step 1: Post-disaster information collection and initialization of the status of the power distribution network and transportation network;

[0009] Step 2: Construct a power-transportation coupling model based on a three-layer optimization framework, including an upper-layer optimization model as the upper-layer scheduling decision layer, a middle-layer optimization model as the middle-layer pricing guidance layer, and a lower-layer optimization model as the lower-layer behavior response layer. That is, the power-transportation coupling model is a three-layer optimization model.

[0010] The upper-level scheduling and decision-making layer serves as the system control center, responsible for the post-disaster reconstruction of the distribution network and the overall scheduling of various mobile resources. Its decision-making scope includes the access location and path planning of mobile energy storage vehicles, V2G output allocation, scheduling of maintenance personnel and vehicles, virtual line disconnection decisions, and main grid power purchase strategies, with the goal of minimizing the total cost of distribution network restoration.

[0011] The middle-level pricing guidance layer plays a coupling role between the power system and the transportation system. By constructing a dynamic service fee model that comprehensively considers the structural vulnerability of the distribution network, traffic accessibility and the evolution characteristics of charging load, the physical state of the distribution network and the transportation network is mapped into a service fee adjustment signal to guide the behavior of electric vehicles. This guides the spatial distribution of electric vehicles to stations and their charging and discharging behavior, and promotes the evolution of the system operation mode in a direction that is conducive to the safe recovery of the power grid.

[0012] The lower-level behavioral response layer is used to finely depict the micro-decision-making process of electric vehicle users. Under the premise of given dynamic service fees and road conditions, various types of electric vehicles aim to minimize the overall travel and energy costs, and autonomously complete the joint decision-making of route selection, charging station selection, and charging and discharging mode. Their aggregated behavior is fed back to the upper-level scheduling decision-making layer and the middle-level pricing guidance layer through traffic flow distribution and the spatiotemporal characteristics of charging load, forming a closed-loop collaborative mechanism of "price-behavior-scheduling" to achieve the coordinated recovery of the power-transportation system.

[0013] Step 3: Construct the constraints for the power-transportation coupling model;

[0014] Step 4: Solve the power-transportation coupling model;

[0015] Step 5: Implementation and dynamic adjustment of the collaborative recovery plan.

[0016] Furthermore, the post-disaster information collection in step one includes power-side data collection and transportation-side data collection. The power-side data includes: node set, line set, node-line connection relationship matrix set, fault line set, active load at the node, reactive load at the node, electricity purchase price from the main grid, unit load abandonment penalty cost, number of mobile energy storage vehicles, upper limit of output power of mobile energy storage vehicles, number of maintenance personnel, number of charging piles in the charging station, set of all nodes in the distribution network connected to the charging station, set of all charging stations, set of charging stations connected to the node, and set of mapping relationship between distribution network and transportation network nodes.

[0017] Traffic-side data includes: traffic node set, road set, road capacity limit, road free passage time, traffic network travel demand set, number of electric vehicles with insufficient power that need to be charged midway, number of electric vehicles with sufficient power and some of which have the ability to provide V2G services to the power distribution network, number of fuel vehicles and electric vehicles that do not respond to any dispatch signals, and the set of all nodes in the traffic network connected to charging stations.

[0018] Furthermore, the upper-level optimization model uses a virtual network to represent the available topology of the post-disaster distribution network. Its decision variables include line disconnection status, distributed power output, mobile energy storage vehicle access location and operation path, V2G dispatch volume, maintenance path and sequence, and main grid purchased electricity.

[0019] The objective function of the upper-level optimization model aims to minimize the operating cost of the distribution network. The operating cost of the distribution network includes the load abandonment penalty cost, the load abandonment penalty cost incurred by the distribution network during the transfer of electric vehicles providing V2G services to other charging stations in the VCB, the load abandonment penalty cost incurred by the distribution network during the movement of mobile energy storage vehicles, the load abandonment penalty cost incurred by the distribution network during the movement of maintenance personnel, the cost of purchasing electricity from the main grid, and the cost incurred by V2G vehicles supplying power to the distribution network. Here, VCB represents electric vehicles with sufficient power and some vehicles having the ability to provide V2G services to the distribution network.

[0020] Furthermore, the dynamic service fee model is the mid-level optimization model. The mid-level optimization model uses the dynamic service fee as the decision variable and takes the dynamic service fee as the input of the lower-level behavioral response layer to influence the electric vehicle's path and charging and discharging strategy. The behavioral results are then fed back to the upper-level optimization model. The objective function of the mid-level optimization model consists of a charging power deviation adjustment term, a charging accessibility penalty term, a grid vulnerability penalty term, and a service fee smoothing penalty term, which are comprehensively optimized by weighted summation.

[0021] Furthermore, the lower-level optimization model uses traffic behavior response as the decision variable, and its objective function is to minimize the transportation network operating cost. The transportation network operating cost includes the travel cost of electric vehicles in VCA, the travel cost of electric vehicles providing V2G services to the distribution network in VCB, the travel cost of mobile energy storage vehicles, the travel cost of maintenance personnel, the travel cost of fuel vehicles in VCB that do not provide V2G services to the distribution network, and the travel cost of fuel vehicles in VCC. Here, VCA represents electric vehicles that need to be charged midway due to insufficient power, and VCC represents fuel vehicles and electric vehicles that do not respond to any dispatch signals.

[0022] Furthermore, traffic behavior response includes traffic flow for different types of electric vehicles on each OD pair and each optional path, as well as arrival volume and charging / V2G behavior choices at each charging station, where OD is a point pair consisting of origin and destination nodes with travel demand in the transportation network.

[0023] Furthermore, the constraints of the power-transportation coupling model in step three include: transportation network constraints, distribution network constraints, distribution network radial constraints, charging station constraints, mobile energy storage vehicle scheduling constraints, and maintenance personnel inspection constraints.

[0024] Furthermore, after obtaining the power-side dispatch scheme, dynamic service fee sequence, and traffic behavior response results from the three-layer optimization model in step five, the collaborative recovery scheme is implemented in the execution phase. The collaborative recovery scheme is implemented sequentially according to the power-side dispatch scheme, including the gradual reconstruction of the distribution network topology, the path movement and access scheduling of mobile energy storage vehicles, the orderly charging and discharging of electric vehicles with V2G capabilities at designated nodes, the point-to-point dispatch of maintenance personnel, and the synchronous adjustment of the main grid's power purchase.

[0025] Furthermore, as the recovery process unfolds, the voltage of distribution network nodes, line power flow, charging station flow and load distribution, transportation network operation status, and the real-time location of mobile energy storage vehicles and maintenance teams will be continuously monitored, enabling the state variables of the three-layer optimization model to be dynamically updated in the actual environment.

[0026] Furthermore, in step four, the ADMM method is used to solve the power-transportation coupling model.

[0027] The advantages of this application compared to existing technologies are as follows: Compared with traditional methods, this application first solves key problems commonly found in existing post-disaster dispatching, such as resource fragmentation, static traffic, coarse characterization of user behavior, and lack of consideration for grid vulnerability. Existing research typically dispatches mobile energy storage, electric vehicles, and maintenance personnel separately, failing to achieve global coordination among multiple resources; at the same time, most methods simplify the transportation network, making it difficult to reflect the real situation of post-disaster road congestion, reduced accessibility, and uneven vehicle distribution; furthermore, traditional charging station pricing often relies on a single load indicator, failing to map grid structural risks, making it impossible to avoid the phenomenon of vehicles congregating in highly vulnerable areas after a disaster. This application fundamentally overcomes these limitations, establishing a deep coupling mechanism covering the power system, transportation system, and user behavior, significantly improving the efficiency, accuracy, and safety of post-disaster recovery.

[0028] The core innovation of this method lies in the design of a power-transport coupling model based on a three-layer optimization framework: the upper-layer dispatch decision layer is responsible for distribution network topology reconfiguration, mobile energy storage dispatch, V2G output allocation, and maintenance vehicle route planning, with the goal of minimizing the overall system recovery cost while meeting operational constraints. Unlike traditional dispatching, this application introduces indicators such as node power supply path redundancy, power flow concentration, and fault propagation potential at this layer to comprehensively characterize the grid vulnerability of nodes and lines. This enables the dispatching strategy to prioritize the recovery of high-risk areas, avoid power flow concentration and secondary fault propagation, thereby enhancing the safety and resilience of the recovery process.

[0029] The mid-level pricing guidance layer sets the dynamic service fee as an independent optimization variable and constructs a multi-factor pricing model that integrates node vulnerability, traffic conditions, arrival demand deviation, and system recovery targets, achieving a quantitative mapping from physical operating conditions to economic signals. Compared to traditional pricing methods based solely on load adjustment prices, the dynamic service fee mechanism in this application can proactively guide electric vehicles to avoid high-risk nodes or congested paths based on the grid vulnerability index, enabling vehicles to spontaneously form a safe spatial distribution and significantly improving the safety margin and recovery capability of critical nodes.

[0030] The lower-level behavioral response layer simulates the autonomous decision-making process of large-scale electric vehicles under traffic constraints and dynamic service fees. Vehicles make optimal choices among "path-site-charging / discharging modes" based on real-time prices, grid vulnerability constraints, and road accessibility. The resulting load distribution and V2G capabilities are fed back to the upper layer, forming a closed-loop optimization mechanism. Compared to the traditional approach that treats electric vehicles as a single load group, this application optimizes the behavior response layer, making the responses of electric vehicles more realistic and effective, and significantly enhancing the executability of the scheduling scheme.

[0031] In terms of modeling, this application constructs a more refined post-disaster electric vehicle travel and response model, breaking through the traditional assumption that electric vehicles are simply regarded as controllable loads. The model classifies electric vehicles into Class A vehicles requiring charging, Class B vehicles with V2G capabilities, and Class C vehicles that do not participate in scheduling. By characterizing the joint "path-site-charging / discharging" selection behavior of electric vehicles under traffic constraints and price incentives, it achieves bidirectional dynamic coupling between the transportation network and the power network. Based on this, a multi-mobility resource collaborative scheduling model is further proposed, incorporating mobile energy storage systems, V2G-capable electric vehicles, and maintenance vehicles into a unified spatiotemporal optimization system. By clarifying the collaborative relationships and mutual exclusion constraints between resources, it effectively alleviates the independence or fragmentation phenomena existing in traditional scheduling, improving resource allocation efficiency. In particular, this application introduces node grid vulnerability and critical line risk indices into the dynamic service fee mechanism, enabling price signals to guide resource flows and strengthen the support capabilities of critical nodes, which is significantly superior to existing pricing strategies that lack system-level guidance capabilities.

[0032] In terms of solution strategy, this application employs the Alternating Directional Multiplier Method (ADMM) for distributed solution of the strongly coupled three-layer optimization model. By decomposing the overall problem into two sub-problems—the power sector and the transportation-pricing sector—and solving them alternately and iteratively, a near-globally optimal post-disaster recovery scheme is obtained while balancing computational efficiency and model accuracy. Thanks to the introduction of power grid vulnerability indicators, this method can focus more on the recovery and control of critical nodes and high-risk areas during the solution process, making this application not only feasible in large-scale engineering scenarios but also demonstrating significant safety, resilience, and superiority. Attached Figure Description

[0033] The following description, in conjunction with the accompanying drawings, further illustrates this application:

[0034] Figure 1 This is a flowchart illustrating the method provided in an embodiment of this application. Detailed Implementation

[0035] like Figure 1 As shown, this application provides a method for collaborative post-disaster recovery of distribution networks based on vulnerability awareness and dynamic service fee guidance. It constructs a three-layer optimization architecture of "upper-layer scheduling decision-making, mid-layer pricing guidance, and lower-layer behavioral response," using dynamic service fees as the core coordination mechanism for post-disaster recovery to achieve a unification of centralized scheduling and distributed user response. Dynamic service fees are introduced as an independent decision variable, thus forming a closed-loop feedback system of "scheduling-price-behavior," providing a systematic technical path for the collaborative optimization of various mobile resources after a disaster.

[0036] The main implementation steps of the method in this application are as follows:

[0037] Step 1: Post-disaster information collection and initialization of the status of the transportation network and the power distribution network;

[0038] To support the coordinated recovery of power and transportation after a disaster, basic data from both the power and transportation sides needs to be collected, as detailed below:

[0039] (1) The data that needs to be collected on the power side includes: node set Route Collection Node and line connection relationship matrix set Faulty circuit collection ,node Active load ,node reactive load Electricity purchase price from the main grid Unit load abandonment penalty cost Number of Mobile Energy Storage Vehicles (MESS) Maximum output power of mobile energy storage vehicles Number of maintenance personnel Charging stations Number of charging stations included The set of all nodes in the power distribution network connected to the charging station. All charging stations are included. and nodes Connected charging station collection Set of mapping relationships between power distribution network and transportation network nodes The set of mapping relationships between power grid lines and transportation network nodes. By describing the node correspondence between the distribution network and the transportation network, it is used to enable maintenance personnel to know what maintenance paths are available for faulty power lines. Similarly, it can also be used to determine the available paths for MESS to access a certain distribution network node.

[0040] (2) Traffic-side data:

[0041] This embodiment abstracts a complex transportation network as a graph structure, containing a set of transportation nodes. With roads Every road ( It has two key attributes: maximum passage capacity. (i.e., the maximum number of vehicles that can pass through the road without causing congestion) and free passage time (That is, the time it takes for a vehicle to pass through when the current traffic volume on the road does not exceed the maximum capacity). All travel demands in the transportation network consist of a series of OD (Operation-Destination) pairs, represented by a set. This means that any OD pair originates from the starting node. and destination node Composition, using This means that each pair of points can be made up of multiple paths. Composition, using sets This indicates that each path It consists of several roads It is formed by connecting the links. And it is defined. express At this time, starting from the node and destination node The OD pair Total traffic flow.

[0042] To accurately depict the differences in post-disaster traffic flow, this embodiment classifies vehicles into three categories: Category A (VCA) consists of electric vehicles with insufficient battery power requiring charging mid-journey; Category B (VCB) consists of electric vehicles with sufficient battery power, some of which have the capability to provide V2G services to the power grid; and Category C (VCC) consists of gasoline-powered vehicles and electric vehicles that do not respond to any dispatch signals. This embodiment assumes that electric vehicles capable of providing V2G services to the power grid can select the nearest charging station to connect to based on dispatch instructions, or they can move to other charging stations to connect.

[0043] The data that needs to be collected includes: a set of traffic nodes. Road collection ,the way Capacity limit ,the way Free passage time Transportation network travel demand aggregation The number of electric vehicles that need to be charged midway due to insufficient battery power. The number of electric vehicles with sufficient battery power, and some of which have the capability to provide V2G services to the power distribution network. The number of gasoline-powered vehicles and electric vehicles that do not respond to any dispatch signals. The set of all nodes in the transportation network connected to charging stations. wait.

[0044] Step 2: Construct a power-transportation coupling model based on a three-layer optimization framework;

[0045] After completing post-disaster information collection and network initialization, this embodiment constructs a power-transportation coupling model based on a three-layer optimization framework. This model uses dynamic service fees as the core coordination mechanism and achieves coordinated optimization of mobile energy storage systems, electric vehicles, and maintenance resources through a closed-loop feedback loop of "price-behavior-scheduling."

[0046] The three-layer optimization framework includes an upper-layer scheduling decision-making layer, a middle-layer pricing guidance layer, and a lower-layer behavior response layer. The upper-layer scheduling decision-making layer serves as the system control center, responsible for the post-disaster distribution network reconstruction and the overall scheduling of various mobile resources. Its decision-making scope includes the access location and path planning of mobile energy storage vehicles, V2G power output allocation, scheduling of maintenance personnel and vehicles, virtual line disconnection decisions, and main grid power purchase strategies, with the goal of minimizing the total cost of distribution network restoration.

[0047] The mid-level pricing guidance layer plays a coupling role between the power distribution network and the transportation network. By constructing a dynamic service fee model (i.e., the mid-level optimization model) that comprehensively considers the structural vulnerability of the power distribution network, traffic accessibility, and the evolution characteristics of charging load, the system physical state of the power distribution network and the transportation network is mapped into a service fee adjustment signal to guide the behavior of electric vehicles. This guides the spatial distribution of electric vehicles to stations and their charging and discharging behavior, and promotes the evolution of the system operation mode in a direction that is conducive to the safe recovery of the power distribution network.

[0048] The lower-level behavioral response layer is used to finely characterize the micro-decision-making process of electric vehicle users. Given dynamic service fees and road conditions, various types of electric vehicles, with the goal of minimizing overall travel and energy costs, autonomously complete joint decisions on route selection, charging station selection, and charging / discharging modes. Their aggregated behavior is fed back to the upper-level scheduling decision layer and the middle-level pricing guidance layer through traffic flow distribution and the spatiotemporal characteristics of charging load, providing basic data support for closed-loop optimization.

[0049] The power-transportation coupling model based on a three-layer optimization framework achieves tight coupling through consistency constraints on shared variables. Dynamic service fees, as a key coordination variable, are transformed into actual traffic flow and load distribution through lower-layer behavioral responses, thereby influencing the optimization results of upper-layer scheduling schemes. This enables the system to achieve the goal of coordinated power-transportation recovery under multi-time-period and multi-constraint post-disaster scenarios. The modeling framework employs the Alternating Directional Multiplier Method (ADMM) for distributed solution. By decomposing the overall problem into alternating iterations of power-side and transportation-pricing-side sub-problems, it effectively balances solution accuracy and computational efficiency, ensuring the method's engineering feasibility and reliability in large-scale post-disaster scenarios.

[0050] Specifically, the upper-level scheduling decision layer constructs an upper-level optimization model to achieve distribution network restoration and multi-resource collaborative scheduling. The upper-level optimization model focuses on the rapid restoration and operational safety of the distribution network after a disaster. It achieves global optimization of the distribution network restoration plan by jointly scheduling various resources, including mobile energy storage vehicles, V2G electric vehicles, maintenance personnel, and main grid power purchases. This model uses a virtual network to represent the available topology of the distribution network after a disaster. Its decision variables cover key parameters such as line open / closed status, distributed generation output, mobile energy storage vehicle access location and operating path, V2G scheduling volume, maintenance paths and sequences, and main grid power purchases. The objective function of this model aims to minimize the total cost of distribution network restoration, and its mathematical expression is as follows:

[0051] (1);

[0052] In the formula: Total cost of distribution network restoration (including load abandonment penalty cost) The load abandonment penalty cost incurred by the PDN during the transfer of electric vehicles providing V2G services to other charging stations in the VCB. The cost of load abandonment penalty generated by PDN during the movement of mobile energy storage vehicles. The cost of load abandonment penalty incurred by PDN during the relocation of maintenance personnel. Cost of purchasing electricity from the main grid The cost of V2G vehicles supplying power to the PDN ); Penalty cost per unit of abandoned load; for Time Node Discarded load; for time Chinese electric vehicles Starting point This represents the total traffic flow transferred from the destination node to other charging stations. for time Chinese electric vehicles Starting point The minimum travel cost for a single electric vehicle to the destination node; for Mobile energy storage vehicle Starting point The total traffic flow to the destination node; for Mobile energy storage vehicle Starting point Minimum travel cost for a single mobile energy storage vehicle at the destination node; for Maintenance personnel at all times Starting point The total traffic flow to the destination node; for Maintenance personnel at all times Starting point The minimum travel cost for a single maintenance worker at the destination node; for Time Node The active power supplied by V2G vehicles to the PDN; for Time Node Active power purchased from the main power grid; PDN provides electricity price subsidies to V2G vehicle units; The price at which electricity is purchased from the main grid; Power for charging electric vehicles; For the economic parameters of travel time cost; It is the set of nodes in a PDN that are connected to the main power grid; PDN represents a distribution network.

[0053] (2) A mid-level optimization model was constructed in the mid-level pricing guidance layer to provide dynamic service fees;

[0054] The mid-level optimization model, as a key link in the three-layer structure, transforms the distribution network's operating status and traffic flow changes into price signals, guiding electric vehicle route selection, arrival distribution, and V2G participation behavior, thus ensuring that user response aligns with the distribution network's safety recovery goals. This model uses dynamic service fees... Using grid vulnerability, traffic conditions, and market supply-demand discrepancies as decision variables, a multi-factor pricing mechanism is constructed. By setting higher prices for stations near high-risk nodes and maintaining lower prices for stations in low-load or traffic-congested areas, this mechanism promotes a more balanced spatial distribution of electric vehicles, reduces pressure on critical nodes, and improves the operational efficiency of the distribution network. Dynamic service fees, as input to the lower-level behavioral response layer, influence the routes and charging / discharging strategies of electric vehicles, and feed the behavioral results back to the upper-level optimization model, thus forming a closed-loop collaborative mechanism of "price-behavior-scheduling" to achieve coordinated recovery of the power-transportation system. Its mathematical expression is as follows:

[0055] (2);

[0056] (3);

[0057] (4);

[0058] (5);

[0059] (6);

[0060] (7);

[0061] (8);

[0062] (9);

[0063] In the formula: The objective function value for the intermediate-level optimization model; , , , These are the charging power deviation adjustment coefficient, the charging accessibility penalty coefficient, the grid vulnerability penalty coefficient, and the service fee smoothing penalty coefficient, respectively. for Momentary charging station The generated electric vehicle charging power; For charging stations The set charging power threshold; for Always at the charging station Traffic flow at charging stations; For charging station-road adjacency indicator variables, when road To reach the charging station When it is the only way to pass, Otherwise, it is 0; for Road at all times The actual travel time; for Momentary charging station The vulnerability index of the power grid structure at the location; for Momentary charging station The dynamic service fee charged; For charging stations The set basic service fee.

[0064] It should be noted that, Momentary charging station Dynamic service fees charged The service fee structure expression (3) is used to characterize the response relationship of service fees as the system state variables change, providing a price adjustment reference mechanism for mid-level optimization, rather than uniquely determining the service fee; the final service fee level is obtained by comprehensive optimization of the mid-level objective function (2) under the constraints of price smoothness and system coordination. Therefore, the service fee structure expression and the mid-level objective function respectively undertake different functions of describing the pricing mechanism and optimizing the result, and there is no overlap or contradiction between the two.

[0065] , , These are the price sensitivity coefficients of service fees to charging power deviation, demand at the destination, and vulnerability of the power grid structure, respectively. For charging stations The minimum service fee set; For charging stations The set upper limit for service fees;

[0066] for Distribution network nodes at all times The power grid structure vulnerability index; , , These are the weighting coefficients for the impact of power supply path redundancy, critical line power flow concentration, and fault propagation potential on the vulnerability of node structures.

[0067] for Distribution network nodes at all times The number of effective power supply paths to the main power grid; for Time Path The validity indicator variable is determined if all lines on the path are undamaged, nodes are reachable, and the power flow direction is feasible. Otherwise, it is 0; for Distribution network nodes at all times The set of all candidate power supply paths from the main power grid to this node;

[0068] for Distribution network nodes at all times The critical path power flow concentration index reflects whether the power flow is concentrated on a few critical paths; For distribution network nodes The set of critical paths within the region; For the line exist Active power at any given moment; line The upper limit of active power; This is the threshold for the power flow safety margin of the line;

[0069] for Distribution network nodes at all times The fault propagation potential indicator (the potential scope of the fault's impact); For distribution network nodes Importance weighting coefficient; In order to be in Distribution network nodes at all times The number of downstream nodes that may lose power in the event of a failure (determined based on power flow direction and network topology).

[0070] For charging station-node connection indicator variables, when the charging station Connecting distribution network nodes hour, Otherwise, it is 0; It is a set of nodes.

[0071] The effective power supply path refers to the path from the distribution network node under the current post-disaster topology. A continuous node-to-line sequence to the main power grid, and this sequence must simultaneously satisfy the following conditions:

[0072] a) All lines and nodes in the sequence are in operation, without faults or isolation;

[0073] b) The path structure is loopless, and the topological reachability to the main power source can be confirmed by power flow calculation;

[0074] c) Path direction and main power source to distribution network node The trend is in line with the direction of the trend;

[0075] d) The power flow of each line in the path did not exceed its safe operating limit.

[0076] All paths that meet the above conditions are considered valid paths, and their total number is the number of valid power supply paths.

[0077] The critical path is a path that, under a post-disaster power supply topology, satisfies any of the following conditions:

[0078] a) If the line Located at the node from the main power grid to the distribution network A valid power supply path If a path is a necessary branch of a path, then it is considered a critical path.

[0079] b) If the line exist The load factor at any given time satisfies If this indicates that the line has entered a high load or overload risk zone, then the line is determined to be a critical line.

[0080] Lines that meet any of the conditions are assigned to distribution network nodes. The set of critical paths.

[0081] (3) A lower-level optimization model was constructed in the lower-level behavior response layer to realize electric vehicle path selection and charging / V2G response;

[0082] The lower-level optimization model characterizes the autonomous behavioral decisions of electric vehicles (EVs) under given dynamic service fees and road conditions. Based on upper-level scheduling results and mid-level pricing signals, EVs comprehensively consider real-time traffic conditions, charging station prices, grid operation constraints, and their own electricity demand, selecting the lowest-cost travel route, charging station, and corresponding charging / discharging mode from the set of feasible paths and stations. The decision variables of the lower-level optimization model include traffic flow for different types of EVs at each OD pair and on each optional path, as well as arrival volume and charging / V2G behavior choices at each charging station. By minimizing the overall travel and energy costs for individuals or groups, the collective behavior of lower-level vehicles provides feedback to the mid-level service fees and upper-level scheduling schemes, achieving dynamic consistency and behavioral coupling among the three-layer models. Its mathematical expression is as follows:

[0083] (10);

[0084] In the formula: For the operating costs of the transportation network (including the cost of electric vehicle travel in VCA) Electric vehicle travel costs in VCB providing V2G services to PDN Mobile energy storage vehicle travel costs Travel costs for maintenance personnel VCB does not provide V2G services to the distribution network and VCC covers the travel costs of fuel-powered vehicles. ); for time Chinese electric vehicles Starting point The total traffic flow to the destination node. for time Chinese electric vehicles Starting point The minimum travel cost for a single electric vehicle to the destination node; for time Electric vehicles that do not provide V2G services to the power distribution network and The vehicles in Starting point The minimum travel cost for a single vehicle at the destination node; The proportion of electric vehicles in the VCB that can provide V2G services to the power grid; for time Chinese electric vehicles Starting point The total traffic flow to the destination node; for time Chinese electric vehicles Starting point The total traffic flow to the destination node.

[0085] This optimization problem is constrained by factors such as transportation network constraints, distribution network constraints, distribution network radial constraints, charging station constraints, mobile energy storage vehicle scheduling constraints, and maintenance personnel inspection constraints. The specific form is shown in step three.

[0086] Step 3: Construct the constraints for the power-transportation coupling model, including transportation network constraints, distribution network constraints, distribution network radial constraints, charging station constraints, mobile energy storage vehicle dispatch constraints, and maintenance personnel inspection constraints. The specific formulas are as follows:

[0087] (1) Traffic network constraints, including:

[0088] (11);

[0089] (12);

[0090] (13);

[0091] (14);

[0092] (15);

[0093] (16);

[0094] (17);

[0095] (18);

[0096] (19);

[0097] (20);

[0098] (twenty one);

[0099] (twenty two);

[0100] (twenty three);

[0101] In the formula: for The total traffic flow of electric vehicles that can provide V2G services in the VCB at any given moment, choosing the nearest charging station; for Electric vehicles in the VCB at OD path Traffic flow below; for Electric vehicles in the VCA at OD path Traffic flow below; for Electric vehicles in the VCB that do not provide V2G services to the grid and vehicles in the VCC at the OD pair path Traffic flow below;

[0102] for Road at all times Total traffic flow; Choose variables for path-road selection, if OD is... path Passing the road hour, Otherwise, it is 0; Choose variables for path-road selection, if OD is... path Passing the road hour, Otherwise, it is 0;

[0103] For vehicles to pass through the road The actual travel time; For roads Free passage time; For roads Traffic capacity limit;

[0104] for A single electric vehicle in the VCA at OD pair path Lower travel costs; Charging station selection variable, if Electric vehicles in the VCA at OD path Choose the next option When charging at the charging station. Otherwise, it is 0; For the economic parameters of travel time cost; For roads Congestion charges collected; represent , and Constraints;

[0105] for A single electric vehicle providing V2G services to the grid in the VCB at any given time is located at the OD pair. path Lower travel costs; for At any given moment, the electric vehicles providing V2G services to the grid in the VCB and the individual vehicles in the VCC are located at the OD pair. path Reduce travel costs.

[0106] (2) Distribution network constraints, including:

[0107] (twenty four);

[0108] (25);

[0109] In the formula: , Each is based on a node A collection of terminal and beginning lines; for Timetable The active power; for Timetable reactive power; , They are respectively Time Node Injected active and reactive power; , They are respectively PDN Line The active and reactive power; for Time Node The active power generated by the charging station; for Time Node Active power purchased from the main power grid; for At any time, the main power grid to the node Injected reactive power; and They are respectively Time Node The magnitude of active and reactive loads; for Time Node The voltage; for PDN Line The current; , PDN lines Resistance and reactance; for Time Node Discarded load; for Time Node The active power provided by the mobile energy storage vehicle; for Time Node The active power supplied by V2G vehicles to the PDN; and PDN lines Upper limits for active and reactive power; and These are the upper and lower limits of the node voltage amplitude, respectively. This represents the upper limit of the line current amplitude.

[0110] (3) Radial constraints of the distribution network, including:

[0111] (26);

[0112] In the formula: Representing power flow in a virtual network, used to characterize the power flow in the equivalent topology of a distribution network constructed via a virtual network in a post-disaster scenario. exist The trends of the moment; Representing power flow in a virtual network, used to characterize the power flow in the equivalent topology of a distribution network constructed via a virtual network in a post-disaster scenario. exist The trends of the moment; A set of nodes in a virtual network that does not contain distributed power sources; A set of distributed power nodes in a virtual network; for In the virtual network, a 0-1 variable represents the opening and closing of a line; a value of 0 indicates that the line is open, and a value of 1 indicates that the line is closed. for The power emitted by distributed power sources in a virtual network at any given moment; It is a positive number that is arbitrarily large but not infinite; A set of lines in a virtual network.

[0113] 4) Constraints of charging stations:

[0114] In the power-transportation coupled network, charging stations serve as key coupling nodes, enabling physical interconnection and energy transfer between the transportation network and the distribution network. The specific formula is as follows:

[0115] (27);

[0116] (28);

[0117] (29);

[0118] (30);

[0119] (31);

[0120] (32);

[0121] In the formula: for time Chinese electric vehicles in OD path Next, select at the charging station Traffic flow at charging stations; for Always at the charging station Traffic flow at charging stations; for All vehicles at OD at all times path Traffic flow below; Power for charging electric vehicles; for Momentary charging station The active power generated; This refers to the maximum power limit of the charging pile; For charging stations The number of charging stations included; Represents nodes A collection of connected charging stations.

[0122] (5) Mobile energy storage vehicle scheduling constraints:

[0123] Given the transportation network topology, it is essential to ensure that, at any given point in time, through optimal route planning, the mobile energy storage vehicle can only exist in a single geographical location within the transportation network. Specific constraints include:

[0124] (33);

[0125] (34);

[0126] (35);

[0127] (36);

[0128] (37);

[0129] In the formula: for Mobile energy storage vehicles at OD path Traffic flow below; for Mobile energy storage vehicle at OD path Cost of a single vehicle trip; This refers to the number of mobile energy storage vehicles; This refers to the upper limit of the output power of the mobile energy storage vehicle. A collection of mobile energy storage vehicles; For the economic parameters of travel time cost; for Mobile energy storage vehicle Starting point Minimum travel cost for a single mobile energy storage vehicle at the destination node; for Time Node The active power provided by the mobile energy storage vehicle.

[0130] (6) Restraints for maintenance personnel:

[0131] To enhance the resilience and recovery capabilities of power systems during natural disasters or large-scale fault events, it is necessary to rationally prioritize the maintenance of faulty lines during the fault duration phase to optimize system recovery efficiency. The specific mathematical formula is as follows:

[0132] (38);

[0133] (39);

[0134] (40);

[0135] (41);

[0136] (42);

[0137] (43);

[0138] (44);

[0139] (45);

[0140] (46);

[0141] In the formula: A binary variable representing the location of maintenance personnel, if Maintenance personnel Located on the line place, Otherwise, it is 0; for Maintenance personnel are always at OD (Original Device) path Traffic flow below; for Maintenance personnel are always at OD (Original Device) path The cost of traveling for a single maintenance worker; The virtual network representing the lines at the initial moment A 0-1 variable that is interrupted; The first moment represents the line in the virtual network. A 0-1 variable that is interrupted; for In a time-based virtual network, a line is represented. A 0-1 variable that is interrupted; Number of maintenance personnel; Assemble the maintenance personnel; A set of faulty lines; The repair time for each faulty line.

[0142] Step 4: Solve the three-layer coupled optimization model based on ADMM;

[0143] Because the three-layer optimization structure of "upper-layer scheduling decision-making - middle-layer pricing guidance - lower-layer behavior response" constructed in this application involves three types of decision variables: power grid scheduling, dynamic service fee pricing, and traffic behavior response, and the layers are tightly coupled through shared quantities such as service fees, arrival traffic, V2G output, and node load, directly adopting centralized optimization will face problems of high dimensionality, strong coupling, and large computational complexity. To improve the solution efficiency, this application introduces the Alternating Directional Multiplier Method (ADMM), which utilizes the natural separability of the power side and the traffic-pricing side in terms of physical structure to decompose the overall problem into two mutually coupled subproblems, and obtains a near-globally optimal disaster recovery scheme through alternating iterative coordination.

[0144] (1) Subproblem partitioning and coupling relationship representation:

[0145] In the three-layer optimization model of this application, the upper-layer power grid dispatch, the middle-layer dynamic service fee, and the lower-layer traffic behavior are coupled through the following shared variables, including: charging station arrival traffic, V2G output power, node load, and charging station dynamic service fee, etc.

[0146] Based on these shared variables, the original problem can be divided into two separable subproblems:

[0147] Power-side decision variable vector:

[0148] (47);

[0149] This includes node load recovery, main grid electricity purchase, charging station V2G power, mobile energy storage vehicle dispatch, maintenance routes, line open / closed status, and reference amount of service fees used on the power side.

[0150] Transportation-Pricing Side Decision Variable Vector:

[0151] (48);

[0152] It includes variables such as path flow of various types of electric vehicles, arrival volume at each station, mid-level dynamic service fees, and load feedback of traffic flow impact.

[0153] The coupling on both sides is mainly reflected in:

[0154] 1. Power coupling constraints of charging stations:

[0155] The arrival traffic and V2G willingness obtained from the traffic-pricing side determine the charging / discharging capacity of each charging station, thereby constraining the power allocation on the power side.

[0156] 2. Service fee-path selection coupling:

[0157] The power supply side uses the dynamic service fee given by the middle layer to enter the user cost function of the lower layer, which affects the path and site selection;

[0158] 3. Node load changes caused by traffic flow:

[0159] Charging and V2G behavior on the transportation side cause changes in node load, affecting power flow distribution and power balance on the power side.

[0160] The above coupling relationship can be abstractly represented as a linear or approximately linear form:

[0161] ;

[0162] in, , It is a coefficient matrix composed of relationships such as charging station-node mapping and path-road mapping. It is a constant vector.

[0163] (2) Construction of augmented Lagrange function:

[0164] Based on the subproblem partitioning, Lagrange multiplier vectors are introduced. and penalty parameters Construct the augmented Lagrangian function for the power-transportation coupled optimization problem:

[0165] (49);

[0166] In the formula, and The objective functions are for the electricity side and the transportation-pricing side, respectively. For vectors The square of the Euclidean norm is the result of summing the squares of each component.

[0167] The augmented Lagrangian function strengthens the coupling constraints through a quadratic penalty term. The convergence of this makes it possible to achieve the desired result through alternating optimization. and This allows for the coordinated optimization of issues on both sides.

[0168] (3) Alternating iterative update based on ADMM algorithm

[0169] This application employs the alternating direction multiplier method to iteratively solve the augmented Lagrange function, dividing each iteration into three steps: power-side update, transportation-pricing-side update, and Lagrange multiplier update.

[0170] 1. Update on power supply issues ( renew)

[0171] Given a traffic-pricing solution and the vehicle Under the premise of solving the following power-side optimization subproblem:

[0172] (50);

[0173] In the formula: This represents the feasible region on the power side, which consists of the power flow constraints of the distribution network, the scheduling constraints of the mobile energy storage vehicle, the maintenance constraints of the maintenance personnel, and the capacity constraints of the charging station, as described in step three.

[0174] 2. Update on transportation-pricing issues ( renew)

[0175] After obtaining a new power side solution After that, fix and Solve the traffic-pricing optimization subproblem:

[0176] (51);

[0177] In the formula: This represents the traffic-side feasible region formed by traffic network constraints such as traffic flow conservation constraints and road capacity constraints in step three.

[0178] 3. Lagrange multiplier update ( renew)

[0179] After updating the variables on the power side and the transportation-pricing side, update the Lagrange multiplier vector based on the residuals of the current coupling constraints:

[0180] (52);

[0181] This step gradually reduces the inconsistency in the coupling between the power side and the transportation-pricing side, thereby achieving coordination between the two sub-problems.

[0182] (4) Convergence Criterion and Stopping Condition

[0183] This embodiment uses a combination of the original residual and the dual residual to determine whether the ADMM iterative process has converged, as detailed below:

[0184] Original residuals:

[0185] (53);

[0186] Dual residuals:

[0187] (54);

[0188] The algorithm is considered convergent and the iteration terminates when the following conditions are met simultaneously:

[0189] (55);

[0190] In the formula: , These are the pre-defined allowable thresholds for the original and dual residuals, respectively. Representative matrix Transpose of; and These are the original residual vector and the dual residual vector for this iteration, respectively. , It is the 2-norm of the corresponding vector.

[0191] Step 5: Implementation and dynamic adjustment of the collaborative recovery plan;

[0192] After completing the three-layer coupled optimization solution and obtaining the power-side dispatch scheme, dynamic service fee sequence, and traffic behavior response results, this application enters the execution phase of the collaborative recovery scheme. The collaborative recovery scheme is implemented sequentially according to the power-side dispatch scheme, including the gradual reconstruction of the distribution network topology, the path movement and access scheduling of mobile energy storage vehicles, the orderly charging and discharging of electric vehicles with V2G capabilities at designated nodes, the point-to-point dispatch of maintenance personnel, and the synchronous adjustment of the main grid's power purchase. As the recovery process unfolds, the method of this application will also continuously monitor the voltage of distribution network nodes, line power flow, charging station flow and load distribution, traffic network operating status, and the real-time location of mobile energy storage vehicles and maintenance teams, so that the state variables of the three-layer optimization model can be dynamically updated in the actual environment.

[0193] During operation, this application employs a rolling time-domain optimization strategy, re-executing the three-layer optimization solution for each new time period. This strategy updates the initial values ​​of the model based on real-time collected data and uses the ADMM iterative solution from the previous time period as the starting point to improve computational efficiency. This allows the recovery plan to be dynamically adjusted according to changes in traffic conditions, charging load, and grid operation, ensuring that the recovery path always remains close to optimal. As faulty lines are gradually repaired, node power supply capacity is gradually restored, and the transportation-power system enters a stable state, this application evaluates the recovery process based on indicators such as load recovery rate, recovery time, resource utilization efficiency, and overall cost. When the network power supply capacity and operating status meet preset stability conditions, the collaborative recovery process can be considered complete, thereby achieving efficient collaborative recovery of the power system and transportation system in a post-disaster environment.

[0194] Compared with existing technologies, this application has significant advantages in the operational robustness and risk management capabilities of post-disaster distribution networks, particularly in enhancing grid security through the dynamic service fee mechanism. By introducing key structural indicators such as node vulnerability, power flow concentration, power supply path redundancy, and fault propagation potential, this application transforms post-disaster recovery scheduling from traditional operational optimization to a structured optimization framework that also considers risk control. More importantly, the dynamic service fee mechanism proposed in this application breaks through the limitations of traditional "load-based pricing," quantitatively mapping grid structural risks into economic signals, enabling node vulnerability and power flow pressure to be transmitted to the user side in real time. Through this mechanism, electric vehicles, guided by price, will automatically avoid highly vulnerable nodes and high-risk lines, migrating their spatial distribution to areas with higher safety margins, thereby reducing the operational pressure on critical nodes and lines from the source and achieving proactive risk sharing and rapid response by users.

[0195] Building upon this foundation, the multi-mobile resource unified collaborative scheduling method in this application further enhances the robustness of the power grid structure. Mobile energy storage vehicles and electric vehicles with V2G capabilities can be rapidly deployed to vulnerable areas under the dual influence of dynamic service fee signals and upper-level scheduling strategies, providing direct support to highly vulnerable nodes, improving local power supply redundancy, and reducing the propagation range of potential risks. Throughout the recovery process, rolling time-domain optimization and ADMM distributed solution strategies enable the system to continuously track vulnerability indices, power flow changes, and traffic conditions, and adjust scheduling schemes, service fee levels, and user behaviors in a coordinated manner at the first sign of increased risk, thereby constructing a dynamic risk mitigation mechanism that runs through the entire recovery process.

[0196] In summary, this application not only surpasses traditional methods in recovery efficiency but also achieves qualitative breakthroughs in dynamic risk perception, improved node safety margins, reduced pressure on critical lines, and enhanced grid structural resilience. In particular, the core role of the dynamic service fee mechanism in grid security enables this application to deeply unify vulnerability assessment, behavioral guidance, and resource allocation, constituting a system-level advantage that is difficult to achieve with traditional methods. Therefore, this application demonstrates higher reliability, controllability, and engineering application value in collaborative recovery under complex post-disaster environments.

[0197] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A method for collaborative post-disaster recovery of distribution networks based on vulnerability perception and dynamic service fee guidance, characterized in that: Includes the following steps: Step 1: Post-disaster information collection and initialization of the status of the power distribution network and transportation network; Step 2: Construct a power-transportation coupling model based on a three-layer optimization framework, including an upper-layer optimization model as the upper-layer scheduling decision layer, a middle-layer optimization model as the middle-layer pricing guidance layer, and a lower-layer optimization model as the lower-layer behavior response layer. That is, the power-transportation coupling model is a three-layer optimization model. The upper-level scheduling and decision-making layer serves as the system control center, responsible for the post-disaster reconstruction of the distribution network and the overall scheduling of various mobile resources. Its decision-making scope includes the access location and path planning of mobile energy storage vehicles, V2G output allocation, scheduling of maintenance personnel and vehicles, virtual line disconnection decisions, and main grid power purchase strategies, with the goal of minimizing the total cost of distribution network restoration. The upper-level optimization model uses a virtual network to represent the available topology of the post-disaster distribution network. Its decision variables include line disconnection status, distributed power output, mobile energy storage vehicle access location and operation path, V2G dispatch volume, maintenance path and sequence, and main grid purchase of electricity. The objective function of the upper-level optimization model aims to minimize the distribution network operating cost, which includes the load abandonment penalty cost, the load abandonment penalty cost incurred by the distribution network during the transfer of electric vehicles providing V2G services to other charging stations in the VCB, the load abandonment penalty cost incurred by the distribution network during the movement of mobile energy storage vehicles, the load abandonment penalty cost incurred by the distribution network during the movement of maintenance personnel, the cost of purchasing electricity from the main grid, and the cost incurred by V2G vehicles supplying power to the distribution network. Here, VCB represents electric vehicles with sufficient power and some vehicles having the ability to provide V2G services to the distribution network. The middle-level pricing guidance layer plays a coupling role between the power system and the transportation system. By constructing a dynamic service fee model that comprehensively considers the structural vulnerability of the distribution network, traffic accessibility and the evolution characteristics of charging load, the physical state of the distribution network and the transportation network is mapped into a service fee adjustment signal to guide the behavior of electric vehicles. This guides the spatial distribution of electric vehicles to stations and their charging and discharging behavior, and promotes the evolution of the system operation mode in a direction that is conducive to the safe recovery of the power grid. The dynamic service fee model is a mid-level optimization model. The mid-level optimization model uses the dynamic service fee as a decision variable and takes the dynamic service fee as the input of the lower-level behavioral response layer to influence the electric vehicle's path and charging and discharging strategy. The behavioral results are fed back to the upper-level optimization model. The objective function of the mid-level optimization model consists of a charging power deviation adjustment term, a charging accessibility penalty term, a grid vulnerability penalty term, and a service fee smoothing penalty term, and is comprehensively optimized by weighted summation. The lower-level behavioral response layer is used to finely depict the micro-decision-making process of electric vehicle users. Under the premise of given dynamic service fees and road conditions, various types of electric vehicles aim to minimize the overall travel and energy costs, and autonomously complete the joint decision-making of route selection, charging station selection, and charging and discharging mode. Their aggregated behavior is fed back to the upper-level scheduling decision-making layer and the middle-level pricing guidance layer through traffic flow distribution and the spatiotemporal characteristics of charging load, forming a closed-loop collaborative mechanism of "price-behavior-scheduling" to achieve the coordinated recovery of the power-transportation system. The lower-level optimization model uses traffic behavior response as the decision variable, and its objective function is to minimize the operation cost of the transportation network. The operation cost of the transportation network includes the travel cost of electric vehicles in VCA, the travel cost of electric vehicles providing V2G services to the distribution network in VCB, the travel cost of mobile energy storage vehicles, the travel cost of maintenance personnel, the travel cost of fuel vehicles in VCB that do not provide V2G services to the distribution network, and the travel cost of fuel vehicles in VCC. Here, VCA represents electric vehicles that need to be charged midway due to insufficient power, and VCC represents fuel vehicles and electric vehicles that do not respond to any dispatch signals. Step 3: Construct the constraints for the power-transportation coupling model; Step 4: Solve the power-transportation coupling model; Step 5: Implementation and dynamic adjustment of the collaborative recovery plan.

2. The method for collaborative post-disaster recovery of distribution networks based on vulnerability perception and dynamic service fee guidance as described in claim 1, characterized in that: The post-disaster information collection in step one includes power-side data collection and transportation-side data collection. The power-side data includes: node set, line set, node-line connection relationship matrix set, fault line set, active load at node, reactive load at node, electricity purchase price from the main grid, unit load abandonment penalty cost, number of mobile energy storage vehicles, upper limit of output power of mobile energy storage vehicles, number of maintenance personnel, number of charging piles in charging stations, set of all nodes in the distribution network connected to charging stations, set of all charging stations, set of charging stations connected to nodes, and set of mapping relationship between distribution network and transportation network nodes. Traffic-side data includes: traffic node set, road set, road capacity limit, road free passage time, traffic network travel demand set, number of electric vehicles with insufficient power that need to be charged midway, number of electric vehicles with sufficient power and some of which have the ability to provide V2G services to the power distribution network, number of fuel vehicles and electric vehicles that do not respond to any dispatch signals, and the set of all nodes in the traffic network connected to charging stations.

3. The method for collaborative post-disaster recovery of distribution networks based on vulnerability perception and dynamic service fee guidance as described in claim 1, characterized in that: Traffic behavior response includes traffic flow for different types of electric vehicles on each origin-destination (OD) pair and each alternative path, as well as arrival volume and charging / V2G behavior choices at each charging station. Here, OD is a point pair consisting of origin and destination nodes with travel demand in the transportation network.

4. The method for collaborative post-disaster recovery of distribution networks based on vulnerability perception and dynamic service fee guidance as described in claim 1, characterized in that: The constraints of the power-transportation coupling model in step three include: transportation network constraints, distribution network constraints, distribution network radial constraints, charging station constraints, mobile energy storage vehicle dispatch constraints, and maintenance personnel inspection constraints.

5. The method for collaborative post-disaster recovery of distribution networks based on vulnerability perception and dynamic service fee guidance as described in claim 1, characterized in that: In step five, after obtaining the power-side dispatch scheme, dynamic service fee sequence, and traffic behavior response results based on the three-layer optimization model, the collaborative recovery scheme is implemented in sequence according to the power-side dispatch scheme. This includes the gradual reconstruction of the distribution network topology, the path movement and access scheduling of mobile energy storage vehicles, the orderly charging and discharging of electric vehicles with V2G capabilities at designated nodes, the point-to-point dispatch of maintenance personnel, and the synchronous adjustment of the main grid's power purchase.

6. The method for collaborative post-disaster recovery of distribution networks based on vulnerability perception and dynamic service fee guidance as described in claim 5, characterized in that: As the recovery process unfolds, the system will continuously monitor the voltage of distribution network nodes, line power flow, charging station flow and load distribution, transportation network operation status, and the real-time location of mobile energy storage vehicles and maintenance teams, enabling the state variables of the three-layer optimization model to be dynamically updated in the actual environment.

7. The method for collaborative post-disaster recovery of distribution networks based on vulnerability perception and dynamic service fee guidance as described in claim 1, characterized in that: In step four, the ADMM method is used to solve the power-transportation coupling model.

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