A power distribution network resilience improvement method and system considering electric vehicle v2g willingness

Abstract

A power distribution network resilience improvement method and system considering electric vehicle V2G willingness, comprising: constructing a linear decay model of weather influence coefficient, a wind-induced road physical damage model and a water depth penalty model, calculating the shortest travel time of mobile energy storage vehicle MESS from an access node to another node based on all models; based on the comprehensive utility, the response probability of electric vehicle EV participating in grid interaction V2G is calculated, and the EV cluster response coefficient of each node is calculated through the response probability and the maximum discharge power; combined with the EV cluster response coefficient, a pre-disaster pre-layout two-stage robust optimization model is constructed to solve the pre-disaster mobile energy storage vehicle MESS pre-configuration position and pre-disaster scheduling variable, and combined with the shortest travel time, a post-disaster multi-source collaborative recovery model is constructed to solve the post-disaster mobile energy storage vehicle MESS position and post-disaster scheduling variable. The present application ensures the timeliness and rationality of post-disaster MESS scheduling, and improves the post-disaster recovery efficiency of the power distribution network.

Description

Technical Field

[0001] This invention belongs to the technical field of power distribution network operation under extreme disaster environments, and more specifically, relates to a method and system for improving the resilience of power distribution networks that takes into account the V2G willingness of electric vehicles. Background Technology

[0002] In recent years, extreme weather events such as typhoons, torrential rains, and ice storms have occurred frequently, posing severe challenges to the safe operation of urban power distribution networks. Compared with transmission systems, distribution networks typically exhibit greater vulnerability to extreme events. This is fundamentally due to their relatively low level of automation, insufficient network redundancy, and limited control measures, making them more susceptible to failures and power outages under external disturbances. Therefore, comprehensively enhancing the resilience of power systems—that is, the system's ability to withstand, absorb, rapidly recover from, and adapt to such major disturbances—has become extremely important and urgent.

[0003] Currently, domestic and international scholars mainly conduct related research from the perspectives of pre-disaster resource planning and allocation, and post-disaster recovery and scheduling. In the pre-disaster phase, measures such as line reinforcement, pre-deployment of mobile energy storage, and emergency resource site selection are used to strengthen the system's ability to withstand disasters. In the post-disaster phase, strategies such as optimized allocation of distributed power sources, dispatch of maintenance personnel, and network reconfiguration are used to provide protection for critical loads and reduce losses caused by power outages. Existing research often makes independent decisions regarding pre-disaster prevention and post-disaster recovery processes, facing inherent shortcomings such as low resource utilization efficiency, poor decision-making effectiveness, and prolonged post-disaster recovery. Therefore, pre-disaster collaborative scheduling of distributed power sources such as wind turbines, energy storage, and diesel engine generators (DEGs) is proposed, while post-disaster consideration of a microgrid networking model with master-slave distributed resources is needed to improve the resilience of the power distribution system in emergency situations.

[0004] With the accelerated construction of urban electric vehicle charging stations (EVCS), electric vehicles (EVs) connected to EVCS can not only meet travel needs but also leverage vehicle-to-grid (V2G) mechanisms to achieve coordinated optimization of resources on the transportation and power sides, thereby improving grid stability. However, the availability of private electric vehicles is affected by various uncertainties such as individual psychological factors, battery health, and road conditions, which can significantly weaken their dispatchability and reliability in emergency situations. Existing research typically treats electric vehicles participating in V2G after a disaster as deterministically available resources, neglecting the impact of user response willingness on the actual output of EVs, which may overestimate the system's post-disaster recovery capabilities. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method and system for improving the resilience of power distribution networks that takes into account the V2G willingness of electric vehicles.

[0006] The present invention adopts the following technical solution.

[0007] The first aspect of this invention proposes a method for improving the resilience of a distribution network that considers the V2G willingness of electric vehicles, comprising: A linear decay model of the weather impact coefficient, a wind-induced road physical damage model, and a water depth penalty model were constructed respectively. Based on all the constructed models, the shortest travel time for the mobile energy storage vehicle (MESS) to transfer from one access node to another was calculated. Based on the comprehensive utility of electric vehicles (EVs) participating in grid-connected V2G, taking into account discharge benefits, battery life loss costs, and time anxiety costs, the response probability of corresponding EVs participating in grid-connected V2G is calculated, and the EV cluster response coefficient of each node is calculated by using the response probability and the maximum discharge power of the EVs. With the goal of minimizing the sum of mobile energy storage configuration costs and load reduction costs under the most severe line fault scenarios, a two-stage robust optimization model for pre-disaster pre-deployment is constructed to solve for the pre-disaster mobile energy storage vehicle MESS pre-configuration location and pre-disaster scheduling variables. The constraint function of the two-stage robust optimization model for pre-disaster pre-deployment includes the pre-disaster electric vehicle call capability constraint constructed based on the pre-disaster EV cluster response coefficient. With the goal of minimizing load reduction costs during the recovery period, a multi-source collaborative recovery model is constructed to solve for the post-disaster location of mobile energy storage vehicles (MESS) and post-disaster scheduling variables. The constraint function of the multi-source collaborative recovery model includes cross-node transfer constraints of mobile energy storage vehicles (MESS) based on the shortest travel time.

[0008] Preferably, a linear decay model for the weather impact coefficient, a wind-induced road physical damage model, and a water depth penalty model are constructed respectively, specifically as follows: The linear decay model for the weather impact coefficient is as follows: divide real-time rainfall intensity and real-time wind speed by their respective thresholds, then sum them up with weights. Subtract the weighted sum from 1 to obtain the weather impact coefficient. The wind-induced physical damage model for roads is as follows: Calculation cutoff time period The maximum historical wind speed experienced by the road is obtained by using the ln function. The difference between the ln function result and the logarithmic mean of the critical wind speed for infrastructure failure along the road is divided by the logarithmic standard deviation of the critical wind speed for infrastructure failure along the road. The result of the division is then input into the standard normal cumulative distribution function to obtain the probability of road damage in the power distribution network. The water depth penalty model is as follows: First, a continuous physical resistance function is constructed, and then a time period is used. The maximum value of the sum of the squares of the results of the division between the depth of the accumulated water and the initial water depth at which the accumulated water begins to affect the normal driving of vehicles and 0 is divided by the critical water depth at which the road section loses its effective traffic capacity and the initial water depth at which the accumulated water begins to affect the normal driving of vehicles. The minimum value of the sum of the squares of the results of the division is the result of the continuous physical resistance function. Will The difference between the water depth during a given period and the critical water depth that causes a road segment to lose its effective traffic capacity is input into the Sigmoid function to obtain the nonlinear transition weight; The depth penalty coefficient is obtained by multiplying the continuous physical resistance function by 1 and the difference between it and the nonlinear transition weight, and then adding 1 to the nonlinear transition weight.

[0009] Preferably, the shortest travel time for a Mobile Energy Storage Vehicle (MESS) to transfer from one access node to another is calculated based on all the constructed models, specifically as follows: For a road segment, subtract the water depth penalty coefficient from 1 and add the set minimum number to obtain the water depth correction coefficient. Divide the free passage time of the road segment by the product of the weather influence coefficient and the water depth correction coefficient to obtain the basic passage time. Multiply the road section's design capacity, weather impact coefficient, the difference between 1 and the probability of road damage to the power distribution network, and the water depth correction coefficient, and then multiply the time period... The real-time traffic flow is divided by the product as the base, and the second set coefficient is used as the exponent for exponential calculation. The product of the exponential calculation result and the first set coefficient is added by 1 to obtain the total correction coefficient. Multiply the basic travel time by the total correction factor to obtain the disaster travel time for the corresponding road segment; Obtain all feasible paths between the access node and another node. For each feasible path, sum the disaster travel times of all road segments included in the corresponding feasible path to obtain the travel time of the corresponding feasible path. The minimum travel time among all feasible paths is the shortest travel time from the access node to another node.

[0010] Preferably, the comprehensive utility of electric vehicles (EVs) participating in grid-connected V2G, taking into account discharge benefits, battery life depreciation costs, and time anxiety costs, is as follows: The overall utility is the discharge benefit minus the battery life loss cost, and then minus the time anxiety cost; Discharge benefit is time period The V2G incentive electricity price multiplied by the corresponding electric vehicle (EV) during the time period The actual discharge capacity within; Battery life loss cost is the product of unit capacity battery investment cost, battery rated capacity and equivalent full cycle count, divided by cycle life under standard test conditions; The time anxiety cost is calculated as follows: the product of the user's sensitivity coefficient to time occupation and the actual continuous online time of the electric vehicle (EV) participating in V2G is divided by the maximum online time that the user can accept, and the natural base e is used as the base to perform the exponential operation. The result of the exponential operation is used as the first exponent. The sensitivity coefficient of users to time consumption is indexed, with the natural base e as the base, and the result of the exponentiation is used as the second exponent. Divide the difference between the first exponent and 1 by the difference between the second exponent and 1, and multiply the result by the set user time anxiety coefficient to obtain the time anxiety cost. .

[0011] Preferably, the response probability of the corresponding electric vehicle (EV) participating in grid-to-grid interaction (V2G) is calculated, and the EV cluster response coefficient of each node is calculated using the response probability and the maximum discharge power of the electric vehicle (EV). Specifically: The difference between the overall utility and the set psychological threshold parameter for user participation in V2G is input into the Logistic function to obtain the response probability; Node i in the time period The product of the response probability of all electric vehicles (EVs) participating in grid-connected V2G and the maximum discharge power of the corresponding EV is summed, and the summation result is divided by the number of nodes i in the time period. The sum of the maximum discharge power of all electric vehicles (EVs) is used to obtain the node. During the period The EV cluster response coefficient.

[0012] Preferably, the two-stage robust optimization model for pre-disaster layout is as follows: The decision variables for the first stage of the two-stage robust optimization model for pre-disaster pre-deployment are the pre-configuration locations of mobile energy storage vehicles (MESS) and the decision variables for the second stage are the pre-disaster scheduling variables, which include load reduction power, diesel generator output, electric vehicle (EV) aggregated discharge power, and power distribution network flow variables.

[0013] Preferably, the objective is to minimize the sum of the mobile energy storage configuration cost and the load reduction cost under the most severe line fault scenario, specifically: The cost of pre-configuring a pre-disaster mobile energy storage vehicle (MESS) on all nodes is added together with the product of the state variables of the pre-configured MESS on the corresponding node at the time of the disaster as the mobile energy storage configuration cost; if the corresponding node has pre-configured a pre-disaster mobile energy storage vehicle (MESS) at the time of the disaster, the corresponding state variable is 1, otherwise it is 0. Reduce the cost of unit load across all nodes during the time period The product of the active power load reduction and the scheduling time interval is added together to obtain the time period. The load reduction cost is obtained by summing the load reduction costs of all failure periods. For each fault scenario, the line fault parameters of the fault scenario are obtained to form the line fault uncertainty vector; the first-stage decision variables and the line fault uncertainty vector simultaneously determine the feasible region of the second-stage decision variables. For each fault scenario's line fault uncertainty vector, the sum of the minimum fault period load reduction costs in the feasible domain of the corresponding second-stage decision variables is obtained as the sum of fault period load reduction costs under the corresponding line fault uncertainty vector conditions. Then, the maximum value of the sum of fault period load reduction costs under the line fault uncertainty vector conditions for all fault scenarios is obtained as the sum of load reduction costs under the most severe line fault scenario. The sum of the mobile energy storage configuration cost and the load reduction cost under the most severe line fault scenario is used as the objective function of the two-stage robust optimization model for pre-disaster pre-deployment.

[0014] Preferably, the pre-disaster electric vehicle dispatch capability constraint constructed based on the pre-disaster EV cluster response coefficient is as follows: For nodes configured with grid-connected V2G charging piles (EVCS), pre-disaster The expected EV discharge power during the period is greater than or equal to 0 and less than or equal to the EV cluster response coefficient and the theoretical maximum discharge power of the EV cluster during the corresponding period before the disaster. The expected available battery power of electric vehicles (EVs) is greater than or equal to 0 and less than or equal to the pre-disaster EV cluster response coefficient and the theoretical maximum available battery power of the EV cluster. The pre-disaster EV cluster response coefficient is greater than or equal to the lower limit of the EV cluster response coefficient and less than or equal to the upper limit of the EV cluster response coefficient.

[0015] Preferably, the objective is to minimize the cost of load reduction during the recovery period, specifically: Reduce the cost of unit load across all nodes during the time period The product of the active power load reduction and the scheduling time interval is added together to obtain the time period. The load reduction cost is calculated by summing the load reduction costs of all post-disaster recovery periods to obtain the sum of load reduction costs during the recovery period; the sum of load reduction costs during the recovery period is used as the objective function of the post-disaster multi-source collaborative recovery model.

[0016] Preferably, the cross-node transfer constraint of the mobile energy storage vehicle MESS based on the shortest travel time is as follows: Divide the shortest travel time by the scheduling interval and round up to obtain the discrete time period travel time. The MESS cross-node transfer constraint for mobile energy storage vehicles is: when the first node... MESS vehicles during the time period By node Transfer to target node At that time, before the discrete time period travel time is reached, the first The MESS vehicle cannot access the target node.

[0017] Preferably, the two-stage robust optimization model for pre-disaster layout is solved using a column constraint generation algorithm, and the post-disaster multi-source collaborative recovery model is solved by transforming it into a linear model using mixed integer second-order cone programming.

[0018] The second aspect of this invention proposes a distribution network resilience enhancement system based on the method described in the first aspect of this invention, considering the V2G willingness of electric vehicles, including a shortest travel time calculation module, an EV cluster response coefficient calculation module, a pre-disaster pre-layout two-stage robust optimization model construction module, and a post-disaster multi-source collaborative recovery model construction module, specifically: The shortest travel time calculation module is used to construct a linear decay model of the weather impact coefficient, a wind-induced road physical damage model, and a water depth penalty model, respectively, and calculate the shortest travel time for the mobile energy storage vehicle (MESS) to transfer from one access node to another based on all the constructed models. EV Cluster Response Coefficient Calculation Module: This module is used to calculate the response probability of electric vehicles (EVs) participating in grid interaction (V2G) based on the comprehensive utility of EVs participating in grid interaction (V2G) taking into account discharge benefits, battery life loss costs, and time anxiety costs. The module calculates the EV cluster response coefficient of each node by using the response probability and the maximum discharge power of the EVs. The pre-disaster pre-deployment two-stage robust optimization model construction module is used to construct a pre-disaster pre-deployment two-stage robust optimization model with the goal of minimizing the sum of mobile energy storage configuration cost and load reduction cost under the most severe line fault scenario. It solves the pre-disaster mobile energy storage vehicle MESS pre-configuration location and pre-disaster scheduling variables. The constraint function of the pre-disaster pre-deployment two-stage robust optimization model includes pre-disaster electric vehicle call capability constraints based on the pre-disaster EV cluster response coefficient. The post-disaster multi-source collaborative recovery model construction module is used to construct a post-disaster multi-source collaborative recovery model with the goal of minimizing load reduction costs during the recovery period. It solves for the post-disaster location of mobile energy storage vehicles (MESS) and post-disaster scheduling variables. The constraint functions of the post-disaster multi-source collaborative recovery model include cross-node transfer constraints of mobile energy storage vehicles (MESS) based on the shortest travel time.

[0019] The beneficial effects of this invention are that, compared with the prior art, 1) A two-stage collaborative resilience enhancement framework considering dynamic road resistance and the V2G willingness of electric vehicles is proposed, encompassing pre-disaster and post-disaster phases. Unlike traditional single-stage resilience enhancement models, this framework treats pre-disaster planning and post-disaster recovery as an organic whole, constructing a collaborative optimization system. The pre-disaster phase focuses on the rational pre-configuration of mobile energy storage vehicles (MESS) to mitigate disaster risks in advance; the post-disaster phase emphasizes multi-source collaborative scheduling to rapidly restore grid functionality. Through the close connection between the two phases, a comprehensive and systematic improvement of distribution network resilience is achieved, solving the problems of disconnect between pre-disaster and post-disaster approaches and insufficient efficiency in resilience enhancement found in traditional methods.

[0020] 2) Incorporate electric vehicle (EV) users' V2G response willingness into the post-disaster recovery model, rather than treating EVs as fully callable resources. Breaking away from the idealized assumption in traditional models that EVs can fully participate in grid interaction (V2G), this model fully considers users' actual willingness to participate in V2G, combining core user concerns such as discharge benefits, battery degradation, and time anxiety. It quantifies user response probability and EV cluster response capabilities, integrating these into pre-disaster scheduling constraints and the post-disaster recovery model. This makes the model more aligned with real-world application scenarios, improving the feasibility and practicality of grid scheduling, and avoiding the problem of scheduling schemes being difficult to implement due to neglecting user willingness.

[0021] 3) Considering the hindering effect of typhoons and rainstorms on the traffic capacity of the transportation network, a dynamic road resistance constraint-based MESS time-space scheduling model was established. Addressing issues such as road damage and flooding caused by typhoons and rainstorms, the traditional assumption of fixed road resistance was abandoned. The dynamic impact of severe weather on the transportation network was fully considered, incorporating factors such as weather, physical road damage, and flooding into the road resistance calculation. This enabled the dynamic calculation of the shortest travel time for mobile energy storage vehicles (MESS) to transfer across nodes, and used this as the core constraint for MESS time-space scheduling. This ensures the timeliness and rationality of post-disaster MESS scheduling and improves the post-disaster recovery efficiency of the power distribution network. Attached Figure Description

[0022] Figure 1 This is a diagram showing the coupling relationship between the power distribution network and the transportation network. Figure 2 This is a graph showing the relationship between the probability of road damage in the power distribution network and wind speed. Figure 3 A graph showing the relationship between the water depth penalty coefficient and the water depth in MESS; Figure 4 Flowchart for solving the pre-disaster-post-disaster collaborative resilience enhancement model; Figure 5 The topology diagram of the power distribution network-transportation network in the example is shown below. Figure 6 A schematic diagram of time-varying fault rates for distribution network lines; Figure 7 This is a diagram illustrating the weather penalty coefficient. Figure 8 This is a schematic diagram illustrating the probability of road damage in the power distribution network. Figure 9 This is a diagram illustrating the water wading penalty coefficient. Figure 10 A schematic diagram of a typical fault scenario for IEEE 33 nodes. Figure 11 This is a schematic diagram showing the location of access nodes during the MESS post-disaster dynamic scheduling process; Figure 12 A schematic diagram of charging and discharging power during the MESS post-disaster dynamic dispatch process; Figure 13 This is a schematic diagram of the charge status during the MESS post-disaster dynamic dispatch process. Figure 14 A schematic diagram of the active power output of each EVCS during the post-disaster recovery process; Figure 15 This is a schematic diagram of the active power output of DEG during the post-disaster recovery process. Figure 16 This is a schematic diagram of the active power recovery rate at different times after the disaster. Figure 17 This diagram illustrates the changes in average willingness to pay and actual EV discharge capacity under different compensation prices. Figure 18 A schematic diagram showing the changes in average willingness to participate and actual EV discharge capacity under different user anxiety levels; Figure 19 A schematic diagram showing the changes in average willingness and actual EV discharge capacity under different psychological thresholds; Figure 20 This is a schematic diagram of the critical load recovery rate for each strategy in Scenario 1. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of this invention. The embodiments described in this application are merely some embodiments of this invention, and not all embodiments. Based on the spirit of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of this invention.

[0024] Example 1 of this embodiment proposes a method for improving the resilience of the distribution network that considers the V2G intentions of electric vehicles, including: 1. Line fault and dynamic road resistance model under typhoon and rainstorm disasters In typhoon and rainstorm disaster scenarios, the high degree of physical overlap and functional dependence between power distribution networks and transportation networks significantly amplifies the vulnerability of the system. Figure 1 It demonstrates the coupling relationship between the power distribution network and the transportation network.

[0025] As the final extension of the transmission network, the distribution network contains a large number of exposed poles and conductors, making it highly susceptible to extreme wind loads and rain-induced moisture damage, which can lead to line breaks or insulation failures. This can result in large-scale power outages during disasters due to loss of power from the upstream grid. Such outages directly paralyze traffic signal systems, weakening the real-time throughput of traffic flow. Simultaneously, physical damage such as collapsed distribution poles, broken lines, or fallen trees along the route can directly encroach on lanes, creating structural roadblocks. This significantly impacts the dispatch efficiency of mobile emergency resources such as mobile energy storage, delaying the post-disaster recovery process of the entire system. Therefore, when modeling extreme disaster scenarios, it is necessary to consider the damage to both the distribution network and the transportation network.

[0026] 1.1 Typhoon wind field and rainfall distribution model Typhoons often bring secondary disasters such as torrential rains, and their impact on power distribution networks and transportation networks cannot be ignored. This embodiment uses the Batts wind field model to simulate the typhoon wind field. This model calculates the maximum gradient wind speed at different times using parameters such as the pressure difference at the typhoon center, the moving speed, and the attenuation intensity. Combined with the attenuation relationship of wind speed with distance from the typhoon center, it obtains the wind speed experienced by each node of the power distribution network.

[0027] The intensity of typhoon-induced heavy rainfall is spatially closely related to the typhoon's wind field structure, exhibiting a radially decreasing distribution with the typhoon center as the core. To obtain the time-varying rainfall intensity at each node of the transportation network and ensure the physical consistency between rainfall data and wind field data, this embodiment uses the R-CLIPER model to describe the radial rainfall rate as a piecewise function of the distance from the typhoon center. Within the maximum rainfall radius... Within this range, the rainfall rate increases linearly from the typhoon center outwards; In addition, the rainfall rate decreases exponentially. The specific expression is: (1) In the formula: Distance from the center of the typhoon Rainfall rate at the location, in mm / h; for Rainfall rate at the location; for The maximum rainfall rate at the location; The unit is the rainfall attenuation scale, measured in km.

[0028] The above parameters R 0、 R m , r m , r e All are related to typhoon intensity and can be expressed as equations (2)-(6): (2) (3) (4) (5) (6) In the formula: The maximum wind speed of the typhoon is expressed in m / s. Normalized wind speed index; , ( 1,2,3,4) are the coefficients to be fitted, and their values ​​can be obtained by statistical regression of historical typhoon rainfall samples using satellite rainfall data.

[0029] For a node in a power distribution network or transportation network, let it be... The distance from the center of the typhoon at any time is Then the node Rainfall intensity at any time for: (7) The above model can be used to obtain the typhoon wind speed and rainfall intensity at each node of the power distribution network and transportation network at each time period during the disaster, providing data input for subsequent line failure rate calculation and transportation network resistance analysis.

[0030] 1.2 Line Failure Rate Model under Typhoon and Rainstorm Disasters Typhoons primarily cause faults in power distribution network conductors and towers. Any line breakage or tower collapse will disrupt the power transmission of the entire line. The probability model for conductor and tower faults follows a normal distribution. Simultaneously, the torrential rains accompanying typhoons can cause insulator flashovers and transformer dampness, leading to line and transformer faults. This embodiment models the fault probabilities of the aforementioned components under typhoon and torrential rain disasters, yielding the overall line fault rate as follows: (8) (9) (10) In the formula: The overall failure rate of power lines under typhoon and rainstorm disasters; The line failure rate caused by typhoon wind load; The line failure rate caused by heavy rain; For the first The probability of failure of the conductor; For the first The probability of failure of the tower; , These refer to the number of conductor spans and the number of towers on the line, respectively. For the first The flashover probability of an insulator; , The first The probability of moisture absorption of insulating oil and oil-impregnated paper in a distribution transformer; , These represent the number of insulators and the number of distribution transformers, respectively.

[0031] 1.3 Dynamic Road Resistance Model under Typhoon and Rainstorm Disasters 1.3.1 Traditional Road Resistance Model The volume-delay function (VDF) is the core of traffic assignment models, used to describe the relationship between travel time on a road segment and traffic flow. The most classic VDF model is the BPR (bureau of public roads) function. The standard BPR function has the following form: (11) In the formula: For road section The actual travel time; For free circulation time; For road section Real-time traffic flow; For road section Design traffic capacity; , These are the regression parameters.

[0032] In disaster scenarios, the limitations of this function are mainly reflected in the following aspects: 1) Traffic capacity is not a constant: Severe weather reduces the road friction coefficient and driver visibility, leading to a decrease in effective traffic capacity. 2) Free-flow time failure: Even without traffic flow, vehicles cannot reach the design speed on roads affected by heavy rain or flooding. 3) Lack of description of physical damage: Fallen utility poles or trees can block lanes, making it impossible to measure traffic capacity using a simple flow ratio. 4) Lack of water depth penalty: The effect of water depth on vehicle speed is non-linear, and there are situations where vehicles cannot pass due to their wading limits.

[0033] 1.3.2 Dynamic Road Resistance Model under Disaster To overcome the above shortcomings, we need to introduce three key correction factors: weather impact coefficient. Probability of damage to power distribution network roads and water depth penalty coefficient .

[0034] 1) Linear decay model of weather impact coefficient The weather coefficient primarily reflects the impact of rainfall intensity and wind speed on driver visibility and road surface friction coefficient. Studies have shown a significant negative correlation between rainfall intensity and free-flow velocity. Based on regression analysis of microscopic traffic simulation and measured data, its dimensionless model is constructed as follows: (12) In the formula: The weather impact coefficient, when This indicates that the road is completely impassable. for Real-time rainfall intensity for a given period, in units . for Real-time wind speed for a given period of time, in units ; , The thresholds for extreme rainfall and wind speeds that would cause a road to become completely impassable; , This is a sensitivity coefficient, which depends on the road grade. Considering that the transportation network topology is urban roads, which are more sensitive to water depth, we take... , .

[0035] 2) Wind-induced physical damage model of roads Extreme wind speeds during typhoons can cause structural failures in roadside infrastructure, leading to physical disruptions to road traffic. These disruptions directly impact post-disaster emergency response and road network connectivity; therefore, quantifying the physical damage to roads caused by typhoons is crucial. (Road Physical Damage Probability) Used to assess the integrity of road infrastructure, describing situations where utility poles, trees, or other building debris obstruct lanes. The higher the typhoon wind speed in the area during a disaster, the greater the probability of severe physical road blockage.

[0036] This embodiment introduces the infrastructure vulnerability mechanism from the field of structural engineering, and uses a log-normal vulnerability function to construct a road physical damage model, which measures the probability of road damage in the power distribution network. It can be represented as: (13) In the formula: Represents the standard normal cumulative distribution function; As of The highest historical wind speed experienced by the road during that period; , These are the logarithmic mean and logarithmic standard deviation of the critical wind speeds for failure of key infrastructure along the road, respectively. In this embodiment, these values ​​are 3.92 and 0.214.

[0037] The relationship between the probability of damage to power distribution network and road infrastructure and wind speed is as follows: Figure 2 As shown; 3) Water depth penalty model Urban flooding has a significant nonlinear reduction effect on the capacity of transportation networks. This embodiment proposes a water depth-interruption function to construct a piecewise water depth penalty model. When the water depth exceeds the safe wading depth, the Big M method is used to set the road segment impedance to a maximum value, thereby forcing the path planning algorithm to actively avoid deep-water sections during the optimization process. Water depth penalty time The mathematical model is defined as follows: (14) In the formula: It is the water depth impedance sensitivity coefficient, which reflects the rate at which road capacity decreases nonlinearly with water depth; for The water depth during a given time period is approximately assumed to be... The difference between the cumulative rainfall and the road drainage rate at any given time; The initial water depth at which accumulated water begins to affect the normal operation of vehicles; The critical water depth at which a road section loses its effective traffic capacity.

[0038] Although equation (14) can effectively characterize the physical blocking effect of a vehicle when it exceeds the wading limit, it is non-differentiable and discontinuous at the critical point, which can easily lead to numerical oscillations or difficulty in convergence during the solution process of the optimization algorithm. Therefore, this embodiment introduces the Sigmoid function to smooth the original model, thus... Expressed as dimensionless coefficients First, a locally normalized continuous physical resistance function is constructed. Measuring the continuous deceleration process when the water level has not yet submerged the vehicle's chassis: (15) Secondly, construct a nonlinear transition weight operator. : (16) In the formula: This is the kurtosis parameter, used to control the steepness of the function; in this embodiment, it is set to 2.

[0039] Finally, the Sigmoid-type water depth penalty coefficient is obtained. As shown in equation (17), This indicates that there is no water accumulation. This indicates that the road section is completely impassable. (17) Considering that mobile energy storage devices are significantly superior to ordinary vehicles in terms of chassis height and electrical protection level during disaster recovery, this embodiment sets the critical wading depth of the mobile energy storage vehicle to [specific value missing] based on relevant standards for the safety requirements of electric buses and current procurement specifications for special rescue vehicles. The relationship between the water depth penalty coefficient of MESS and the water depth can be expressed as follows: Figure 3 As shown; In typhoon and rainstorm disaster scenarios, the actual traffic capacity of transportation networks is simultaneously affected by severe weather, physical road damage, and water depth. Traditional BPR road resistance functions are insufficient to accurately describe the traffic status of mobile emergency resources under disaster conditions. Therefore, this embodiment introduces a weather impact coefficient, the probability of power grid and road damage, and a water depth penalty coefficient into the classic BPR model to correct the road segment travel time under disaster conditions.

[0040] Set up road section During the period The weather impact coefficient, the probability of power grid road damage, and the water depth penalty coefficient are respectively , and Then mobile energy storage vehicles on the road section Disaster travel time It can be represented as: (18) In the formula: For road section Free circulation time; For time period Real-time traffic flow; Design the traffic capacity for the road section; to reflect the impact of disaster scenarios on the travel time of mobile energy storage vehicles. , For the first and second coefficients set; take , ; To prevent the minimum value where the denominator is zero.

[0041] To reflect the spatial transfer characteristics of mobile energy storage in transportation networks during disasters, the time period of MESS is further defined. From the access node Transfer to node Shortest travel time for: (19) In the formula: For nodes in the transportation network To the node The set of feasible paths This is a feasible path.

[0042] 2. Strategies for Enhancing Resilience in the Pre-Disaster and Post-Disaster Phases In extreme disaster scenarios such as typhoons and torrential rains, electric vehicles (EVs) participating in V2G (Vehicle-to-Grid) interaction as distributed flexible resources connected to charging pile nodes are an important way to enhance the resilience of the power distribution network after a disaster. However, whether private EV users are willing to participate in post-disaster regulation is closely related to battery life depletion, vehicle usage time flexibility, and bounded rationality behavior, in addition to being influenced by electricity price incentives. To this end, this embodiment first constructs a response willingness model for EV users to participate in V2G, and on this basis, establishes a two-stage collaborative resilience enhancement model before and after a disaster. In the pre-disaster stage, mobile energy storage systems are pre-deployed considering the most severe line fault scenarios. In the post-disaster stage, dynamic road resistance and EV user response willingness factors are comprehensively considered to coordinate the scheduling of multiple types of distributed resources to maximize the restoration of power supply to important loads and improve system resilience.

[0043] 2.1 Electric Vehicle V2G Response Willingness Model To more accurately characterize the response characteristics of electric vehicle users in post-disaster scenarios, this embodiment constructs a comprehensive user utility function from three aspects: EV battery wear anxiety cost, time anxiety cost, and discharge benefit. Furthermore, it establishes a response willingness model based on bounded rationality to evaluate the possibility of EV users participating in V2G and its aggregation adjustability.

[0044] For nodes First EVs, defined as their time period The discharge charge and depth of discharge are as follows: (20) (twenty one) In the formula: For the first electric vehicles during the period The actual discharge capacity within; Its discharge power; The scheduling time interval; Depth of discharge; This refers to the battery's rated capacity.

[0045] Considering the impact of depth of discharge and initial state of charge on battery life, the equivalent total cycle number of a single emergency discharge is... It can be represented as: (twenty two) In the formula: The standard value for the depth of discharge is taken as 0.8; The initial state of charge of an electric vehicle before it participates in V2G; The standard value for the state of charge is taken as 0.8; , The fitting parameters for the experiment were set to 1.98 and 2.79, respectively.

[0046] Therefore, the first electric vehicles during the period Battery life loss cost due to internal factors involved in V2G It can be represented as: (twenty three) In the formula: The investment cost per unit capacity battery is set at 1500 yuan / kWh; The cycle life under standard test conditions is taken as 1500 cycles.

[0047] Besides battery degradation, the participation of electric vehicles in post-disaster energy supply also occupies users' free travel time, reducing their vehicle usage flexibility. To reflect users' time anxiety caused by travel uncertainty, a time anxiety cost is defined. for: (twenty four) In the formula: The actual continuous online time of electric vehicles participating in V2G; The maximum acceptable online time for users; The user's time anxiety level; The sensitivity coefficient for user time occupancy is set to 3 in this embodiment. As can be seen from equation (24), as the proportion of V2G participation time to the maximum acceptable duration increases, the time anxiety cost shows a monotonically increasing trend.

[0048] Taking into account the discharge benefits, battery life loss costs, and time anxiety costs, the first electric vehicles during the period Integrated utility function of intrinsic components in V2G It can be represented as: (25) In the formula: For time period V2G incentive electricity price.

[0049] Considering that users are not entirely rational in post-disaster scenarios, but rather exhibit certain bounded rationality characteristics, the Logistic function is used to describe the probability of user responses, i.e. (26) In the formula: For the first electric vehicles during the period The probability of internal participation in V2G response; The rationality tendency parameter is used to reflect the user's sensitivity to changes in returns; in this embodiment, it is set to 2. The psychological threshold parameter for users to participate in V2G is set to 0.5 in this embodiment.

[0050] To facilitate unified scheduling of EV clusters in the distribution network recovery optimization model, user response probabilities are further aggregated by node, and nodes are defined. During the period The EV cluster response coefficient is: (27) In the formula: For nodes A collection of electric vehicles that can be accessed; For the first The maximum discharge power of an electric vehicle; Represents a node EV cluster during time period The overall willingness to respond. The larger the value, the more likely the electric vehicle at that node is to participate in V2G response in a post-disaster scenario.

[0051] 2.2 Two-stage robust optimization model for pre-disaster planning 2.2.1 Objective Function The core task in the pre-disaster phase is to pre-deploy a limited number of mobile energy storage devices based on the risk of line faults under typhoon and rainstorm disasters, in order to improve the rapid response capability after the disaster occurs. To this end, this embodiment aims to minimize the sum of the mobile energy storage configuration cost and the load reduction cost under the most severe line fault scenario, establishing a two-stage robust optimization model. The decision variables in the first stage are the connection status of mobile energy storage devices and nodes; the decision variables in the second stage are the load reduction power, diesel generator output, aggregated discharge power of electric vehicles, and power flow variables of the distribution network under the fault scenario. The objective function can be expressed as: (28) In the formula: This is a set of candidate access nodes for mobile energy storage. For the set of fault periods; For the set of distribution network nodes; This is the pre-deployment vector for mobile energy storage (i.e., the decision variable for the first stage). for The feasible domain; The line fault parameters, representing the fault scenarios, are used to form a line fault uncertainty vector. This is the set of line fault uncertainty vectors under all fault scenarios; For the second stage of distribution network decision variables, This represents the feasible region of the decision variables in the second stage, which is also affected by the decision variables in the first stage. and line fault uncertainty vector The combined effects; It consists of equations (29) and (30); Composed of equations (31)-(44); the parameters of the line fault uncertainty vector include: active power and reactive power in the pre-disaster stage; active load reduction power, reactive load reduction power, active and reactive power of diesel generators, expected EV discharge power in the pre-disaster stage, expected EV available power in the pre-disaster stage, EV response coefficient, active and reactive power flow of branches and node voltage amplitude. For the node The cost of pre-configuring a MESS unit; Pre-disaster moment nodes MESS pre-configured state variables, Represents a node MESS is configured there; For nodes Reduce unit load cost; For nodes During the period The reduction in active power load.

[0052] 2.2.2 Constraints 1) Constraints on the pre-deployment of mobile energy storage In the pre-disaster phase, it is necessary to determine the pre-layout locations of a limited number of MESSs, and the constraints can be expressed as follows: (29) (30) (31) (32) In the formula: This represents the maximum number of MESS that can be pre-configured during the pre-disaster phase. and Pre-disaster nodes The active and reactive power outputs of the pre-configured MESS are displayed. and These represent the maximum discharge power and reactive power output limits of the MESS, respectively. Equation (29) limits the number of pre-configured MESSs. Equation (30) indicates that each candidate node can pre-connect a maximum of one MESS. Equations (31) and (32) limit the active and reactive power outputs of mobile energy storage.

[0053] 2) Load reduction constraints Assuming a fixed load power factor, the load reduction power constraint is: (33) (34) In the formula: For nodes During the period The amount of reactive load reduction; and They are nodes The maximum values ​​of active and reactive loads.

[0054] 3) Diesel generator output constraints For diesel generators that are subject to unified dispatch, their active and reactive power outputs must meet the following constraints: (35) (36) In the formula: A collection of diesel generators; and Diesel generators During the period The meritorious and the ineffective contributions; , Diesel generators During the period The lower limit of both meritorious and non-meritorious contributions; Diesel generators During the period The upper limit of both active and passive output.

[0055] 4) Pre-disaster electric vehicle deployment capacity constraints Considering that electric vehicles have not yet entered the actual discharge process in the pre-disaster stage, user psychological factors mainly affect the upper limit of EV resource availability, rather than real-time charging and discharging decisions. Furthermore, this embodiment assumes that electric vehicles can only participate in V2G operation when connected to charging piles with "vehicle-to-grid interaction" functionality. Therefore, EVs only participate in scheduling as distributed flexible resources at fixed charging pile nodes and do not possess the spatial transfer capability similar to mobile energy storage systems. Based on the EV cluster response coefficient obtained from equation (27), the EV cluster response coefficient calculated in the pre-disaster stage is defined as the pre-disaster predicted response coefficient. This is used to quantify the availability of EV resources at charging station nodes during the pre-disaster phase. The pre-disaster EV availability constraint, considering user psychological factors, can be expressed as: (37) (38) (39) In the formula: The set of nodes for configuring V2G charging stations; Before the disaster Time period nodes The expected EV discharge power at the location (i.e., the aggregate discharge power of electric vehicles in the optimized decision variables; since it is before the disaster and has not yet entered the actual discharge state, it is expected). This refers to the expected available battery capacity for the EV. and These represent the theoretical maximum discharge power and available power of the EV cluster, respectively. and These are the lower and upper limits of the EV cluster response coefficient, respectively.

[0056] 5) Distribution network operation constraints This embodiment uses the DistFlow model to describe the power flow equations of the distribution network. Let... For branch (node) To the node ), For nodes The set of child nodes Given a fault scenario Lower branch road The available status parameter is set to 1 when the line is available and 0 when there is a fault. To avoid forcing the voltage drop relationship to still be satisfied on the faulty line, a sufficiently large positive number is introduced. Then the operating constraints of the distribution network can be expressed as: (40) (41) (42) (43) (44) In the formula: For distribution network branch collection; For nodes A collection of diesel generators; and Branch roads During the period The trend of meritorious and ineffective actions; and They are nodes During the period The active and reactive load demand; and Branch roads Resistance and reactance; branch road Maximum permissible apparent power; For nodes During the period The voltage amplitude; , They are nodes During the period The lower and upper limits of the voltage amplitude; branch road During the period The positive trend.

[0057] 2.3 Post-disaster multi-source collaborative recovery model 2.3.1 Objective Function Following a disaster, the distribution network loses support from the main grid and enters the post-disaster recovery phase. Considering that the duration of the fault can be estimated based on the disaster intensity and available repair resources, this embodiment aims to minimize the load reduction cost during the recovery period. A multi-source collaborative recovery model is constructed, taking into account the time-of-use scheduling of mobile energy storage, the responsiveness of electric vehicles, and the support of diesel generators. The objective function is as follows: (45) In the formula: This is a collection for the post-disaster recovery period; For time period node The active load at the location is reduced in power.

[0058] Post-disaster multi-source collaborative recovery model: Part 1 Mobile energy storage vehicles During the period With nodes Connection state variables Travel time during discrete periods ; During the period charging status and discharge state variables ; During the period charging power Discharge power and reactive power Time period Energy storage status EV cluster discharge power and charging power ; EV's state of charge EV cluster charging and discharging state variables Post-disaster real-time scheduling variables , and .

[0059] 2.3.2 Constraints 1) Scheduling constraints for mobile energy storage set up For the first Mobile energy storage vehicles During the period With nodes The connection state variable, when Time indicates docked at the node It can also participate in charging and discharging. The shortest travel time of MESS in the disaster transportation network is obtained according to equation (19). Further define its discrete time travel time. for: (46) The uniqueness of the position and the cross-node transfer constraint of MESS can then be expressed as: (47) (48) In the formula: For mobile energy storage devices. Equation (47) indicates that each MESS can be connected to at most one node at any given time period; For the first Mobile energy storage vehicles During the period With nodes The connection state variable; Equation (48) represents when the first MESS vehicles during the time period By node Transfer to node At that time, access to the target node cannot be made before the travel time determined by dynamic road resistance is reached.

[0060] Further definition and They are respectively During the period Given the charging and discharging state variables, we have: (49) (50) (51) (52) Define the injected power of MESS at the node as: (53) (54) Furthermore, the energy state constraint of MESS can be expressed as: (55) (56) (57) In the formula: For the MESS collection; , and They are respectively During the period The charging, discharging, and reactive power; Its time period Energy storage status; and They are respectively The charging and discharging efficiency; , and These represent the minimum energy storage capacity, maximum energy storage capacity, and initial energy storage state, respectively. Equation (49) is used to constrain the charging and discharging state of the MESS. Equations (50) and (51) limit the charging and discharging power of the MESS, respectively. Equation (52) limits the reactive power output range of the MESS. Equations (53) and (54) define the active power injection and reactive power injection of the MESS at the node, respectively. Equation (55) is used to calculate the state of charge of the MESS at each moment. Equation (56) constrains the upper and lower limits of the MESS state of charge. Equation (57) is used to give the energy storage state of the MESS at the moment of recovery.

[0061] 2) Post-disaster charging and discharging constraints for electric vehicles During the post-disaster recovery phase, user psychology directly influences whether electric vehicles are willing to connect, the duration of V2G participation, and the actual discharge power released. Therefore, this embodiment incorporates a post-disaster real-time response coefficient into the EV cluster real-time scheduling model. The electric vehicle charging and discharging constraints considering user willingness during the post-disaster phase can be expressed as: (58) (59) (60) (61) (62) (63) In the formula: and They are nodes During the period The discharge power and charging power of the EV cluster; The state of charge of the EV; For the charging and discharging state variables of the EV cluster, when When it indicates charging, Time indicates discharge; and These are the charging and discharging efficiencies of the EV, respectively. and These are the maximum charging and discharging power of the EV cluster, respectively. and These are the minimum reserved power and maximum available power for the EV cluster, respectively. The minimum battery power required to meet users' basic travel needs; For safety redundancy, Equation (58) is used to calculate the net active power output of the EV cluster. Equation (59) is used to calculate the state of charge of the EV cluster at each moment. Equation (60) limits the charging power of the EV cluster.

[0062] Equation (61) limits the discharge power of the EV cluster, reflecting the impact of the willingness to respond in real time after a disaster on the actual discharge capacity of EVs. Equation (62) limits the state of charge of the EV cluster. Equation (63) imposes a constraint on the minimum reserve capacity of the EV cluster when participating in post-disaster recovery.

[0063] 3) Other constraints In addition to the aforementioned constraints on mobile energy storage scheduling and electric vehicle charging / discharging, the load reduction constraints, diesel generator output constraints, and distribution network operation constraints at various times during the post-disaster recovery phase still need to meet corresponding limitations. These can be expressed by equations (33)-(36) and (40)-(44), respectively. In the post-disaster power flow equations, only the pre-disaster decision variables need to be included. , and Replace them with post-disaster real-time scheduling variables respectively , and That's all.

[0064] 3. Model transformation and solution 3.1 Model Transformation and Solution Method The two-stage collaborative resilience enhancement model constructed in this embodiment includes a pre-disaster pre-layout robust optimization model and a post-disaster multi-source collaborative recovery optimization model. The former belongs to a two-stage robust optimization problem, while the latter belongs to a mixed-integer nonlinear programming problem containing a product term of binary and continuous variables and second-order cone constraints. Considering the structural characteristics of the two models, this embodiment uses the column-and-constraint generation (C&CG) algorithm to solve the pre-disaster pre-layout two-stage robust optimization model, and transforms and solves the post-disaster multi-source collaborative recovery model using the mixed-integer second-order cone programming (MISOCP) method.

[0065] For the pre-disaster planning stage, equation (28) can be further written in the following compact form: (64) (65) In the formula: The variables for the second phase of operational decisions mainly include load reduction power, diesel generator output, aggregated discharge power of electric vehicles, support power of pre-configured MESS, and power flow variables of the distribution network; among them, It consists of equations (29) and (30); It consists of equations (31) to (44).

[0066] The C&CG algorithm is used to iteratively solve equations (64) and (65). Let the first equation be... The set of most severe line fault scenarios generated in the next iteration is Then the main problem can be written as: (66) (67) (68) In the formula: The auxiliary variable introduced is used to characterize the upper bound of the worst-case operating cost of the second stage under the current scenario set; No. Scene generated in the next iteration The corresponding second-stage decision variables are as follows. The role of the main problem MP is to find the current optimal pre-disaster MESS pre-layout scheme under the known set of most severe line fault scenarios.

[0067] Given the optimal solution to the main problem Then, the subproblem SP is used to search for the most severe line fault scenario under the current pre-layout scheme. The expression is: (69) Accordingly, the lower bound in the iteration process and the Upper Realm Updated to: (70) (71) fixed Afterwards, the inner minimization problem of the subproblem only contains the continuously running variables and their constraints described by equations (31)-(44), which is a convex optimization problem. It can be transformed into a single-layer subproblem for solution using its dual form. When the following conditions are met... hour, If the minimum value is not reached, the algorithm terminates; otherwise, the most severe line fault scenario obtained from the subproblem is added to the main problem scenario set, and the algorithm continues to iterate until convergence.

[0068] For the post-disaster multi-source collaborative recovery phase, the nonlinearity in the original model mainly comes from the binary location variables in equations (53) and (54). With continuous variables , and The product term, and the quadratic term in the line capacity constraint. To transform this model into the MISOCP model, the following is introduced: , and Auxiliary variables corresponding to the variables , , : (72) The product relationship between the above binary variable and the continuous variable can be equivalently transformed through the following linear constraint: (73) (74) Accordingly, the injection power of MESS at the node, equations (53) and (54), can be rewritten as equations (75) and (76): (75) (76) Given representative fault scenarios, the available state parameters of the line Since the line capacity constraint equation (43) is a known constant, it can be further written in the standard second-order cone form: (77) After the above transformation, the post-disaster multi-source collaborative recovery model can be reconstructed into the MISOCP model for solution.

[0069] The solution process for the pre-disaster and post-disaster collaborative resilience enhancement model for distribution networks proposed in this embodiment is as follows: Figure 4 As shown.

[0070] 4. Case Analysis 4.1 Basic Information of the Example This embodiment uses a coupled distribution network-transportation network system consisting of a 33-node IEEE distribution network and a 12-node transportation network as a case study to verify the effectiveness of the proposed two-stage pre-disaster and post-disaster collaborative resilience enhancement strategy. Distribution network nodes 9, 22, 24, and 30 are connected to transportation network nodes T4, T6, T9, and T8. The topology of the distribution network-transportation network is as follows: Figure 5 As shown in the figure, the distribution network is equipped with 5 diesel generators, connected to nodes 6, 14, 19, 25, and 31; and 3 electric vehicle charging piles, with 25, 30, and 25 electric vehicles respectively, connected to nodes 9, 24, and 30. The battery capacity of each electric vehicle is 50 kWh, the maximum charge / discharge power is 7 kW, the initial state of charge (SOC) is 0.90, the minimum retained SOC is 0.40, the maximum SOC is 0.95, and the charge / discharge efficiency is 0.95. In addition, this embodiment configures 3 identical mobile energy storage vehicles, with a pre-disaster configuration cost of 500 yuan per vehicle. Each vehicle has a rated active power of 250 kW, a rated capacity of 600 kWh, an initial SOC of 0.95, a minimum SOC of 0.2, a maximum SOC of 1.0, and a charge / discharge efficiency of 0.95. Other distributed power parameters are shown in Table 1. Meanwhile, to highlight the effect of important load restoration, nodes 7, 8, 12, 14, 19, 24, 25, 29, 30, and 32 are designated as critical nodes, while the remaining nodes are non-critical nodes. The unit load reduction cost for critical nodes is 10 yuan / kWh, and the unit load reduction cost for non-critical nodes is 1 yuan / kWh. The relevant parameters of distributed power generation are shown in Table 1.

[0071] Table 1. Parameters related to distributed power sources

[0072] 4.2 Scene Generation Result Analysis This embodiment uses the Batts model to simulate the typhoon wind field, and the rainfall intensity at each time period is calculated based on the R-CLIPER model. To reflect the dynamic evolution of typhoon storm disasters, this embodiment uses the typhoon landfall time t=0h as the time origin and sets the simulation time domain to 12h. The system is established with reference to the IEEE 33-node system, where node 1 at the feeder head is located at (2,7), the typhoon landfall point is located at (-16,-13), the initial pressure difference at the typhoon center is 50hPa, the initial maximum wind speed is 43.92m / s, and the initial maximum wind speed radius is approximately 8.55km. It moves approximately 35° in the positive direction of its axis. As the typhoon makes landfall and gradually moves inland, its central intensity gradually weakens, while the radius of its maximum wind speed gradually increases.

[0073] The typhoon's wind field evolution results indicate that the typhoon completely left the power distribution network and transportation network areas around t=3.50h and t=3.83h, respectively. It should be noted that the typhoon's departure from the area does not mean the disaster's impact immediately ends. The lag effects of the outer wind circle, the tail of rainfall, and the clearing of road flooding and obstacles will continue to cause changes in line failure rates and dynamic road resistance coefficients in subsequent periods. The time-varying failure rate of power distribution network lines is shown below. Figure 6 (The failure rate is calculated using formulas (8)-(10)). The time-varying values ​​of the weather penalty coefficient, the probability of road damage in the distribution network, and the water wading penalty coefficient in the dynamic road resistance function are shown in [reference]. Figure 7 , Figure 8 and Figure 9 .

[0074] To provide a disaster scenario involving the distribution network and transportation network for subsequent pre-disaster and post-disaster collaborative resilience enhancement strategies, this embodiment uses the Monte Carlo method to generate 2000 sets of random line failure scenarios based on the time-varying failure rate of the lines. Ten typical failure scenarios and their probabilities of occurrence are extracted using the K-means clustering algorithm. Specific parameters are shown in Table 2. This embodiment selects scenario 1, which has the highest line failure probability, as a typical scenario for subsequent research on the multi-source collaborative recovery process after the disaster. Its topology is as follows: Figure 10 As shown.

[0075] Table 2 Typical Failure Scenarios and Probabilities

[0076] 4.3 Analysis of Pre-Disaster Layout Results To verify the effectiveness of the robust pre-disaster layout method proposed in this embodiment, two pre-disaster layout schemes were set up for comparative analysis: Scheme 1 is a robust pre-layout scheme that considers the uncertainties of multiple scenarios, and Scheme 2 is a deterministic pre-layout scheme based on scenario 2. The two schemes were compared by combining the combination of pre-deployed nodes, the load reduction cost corresponding to the scheme, the load reduction cost of the worst scenario, and the load reduction cost after weighting the occurrence probability of the 10 scenarios in Table 2. The results are shown in Table 3.

[0077] Table 3 Comparison of Pre-Disaster Deployment Results

[0078] As shown in Table 3, in Scheme 2, mobile energy storage is deployed at nodes 6, 8, and 29. Since this scheme is only optimized for scenario 2, its corresponding load reduction cost is 1265 yuan. However, from the perspective of multi-scenario application results, the worst-case load reduction cost of this scheme reaches 5625 yuan, and the probability-weighted load reduction cost is 2401 yuan. In contrast, Scheme 1 pre-configures mobile energy storage at nodes 7, 8, and 24, with a worst-case load reduction cost of 2605 yuan and a probability-weighted load reduction cost of 1827 yuan, which are 3020 yuan and 574 yuan lower than Scheme 2, respectively, representing reductions of 53.69% and 23.91%. This indicates that although robust pre-deployment does not obtain the optimal solution for a single scenario, it exhibits better overall recovery adaptability under multi-scenario uncertainty conditions.

[0079] 4.4 Analysis of Post-Disaster Multi-Source Collaborative Recovery Strategies After completing the pre-disaster layout, this embodiment selects nodes 7, 8, and 24 as the starting points for MESS post-disaster recovery and analyzes the operation process of the multi-source collaborative recovery strategy in scenario 1. It is assumed that the upstream power grid and distribution network are disconnected, and the distribution network mainly relies on local mobile and distributed resources such as DEG, MESS, and EVCS for isolated recovery. Considering that the typhoon will completely leave the distribution network area and the transportation network area at approximately t=3.50h and t=3.83h respectively, to ensure the safe passage of mobile energy storage devices, this embodiment sets the post-disaster recovery start time to t=4h, with an estimated total recovery time of 8 hours.

[0080] To demonstrate the practical role of dynamic road resistance coefficient in post-disaster scheduling, Table 4 presents some of the optimal paths and travel times of MESS from pre-deployed nodes to candidate support nodes in disaster-stricken areas.

[0081] Table 4. Candidate Support Paths and Travel Time for MESS under Dynamic Road Resistance

[0082] As shown in Table 4, dynamic road obstruction significantly prolonged the actual transfer time of the MESS, and the degree of impact varied significantly among different travel routes. Taking the support from node 24 to the disaster-stricken area 27 as an example, its free-flow time was only 20 minutes, but under the influence of dynamic road obstruction, the shortest travel time increased to 52.76 minutes, an increase of 32.76 minutes. This indicates that under typhoon and rainstorm disaster conditions, road flooding, physical obstacles, and weather deterioration work together to directly affect the arrival time and recovery pace of the MESS. Based on the spatiotemporal location and charging / discharging results of the MESS, the three MESS units exhibited characteristics of rapid initial response, localized energy replenishment in the middle stage, and concentrated discharge in the final stage during the post-disaster recovery process. The corresponding MESS access node locations, charging / discharging power, and state of charge during the post-disaster dynamic scheduling process are shown in Table 5. Figure 11 , Figure 12 and Figure 13 .

[0083] Table 5. MESS Mobility Paths and Travel Times under Actual Post-Disaster Dispatch

[0084] It should be noted that this embodiment focuses on the early emergency recovery process after a typhoon, when the distribution network is still operating under conditions of main grid outage and power supply shortages. Therefore, the EVCS mainly provides reverse support to the system through V2G. This embodiment only focuses on the discharge behavior of aggregated resources of electric vehicles and does not separately model the charging process during the recovery period. Although the theoretical callable capacity of the three EVCSs is higher than the upper limit after intention correction, due to user V2G intention constraints, their actual cumulative discharge capacity is only 2030kWh, which still provides an effective supplement to the recovery of critical loads. The active power output of each EVCS during the post-disaster recovery process is shown in the figure. Figure 14 Based on the DEG output results, all five diesel generators operated at high load levels for most of the time. The active power output of each DEG during the post-disaster recovery process is shown in the table below. Figure 15 .

[0085] Figure 16 The active power recovery rate at different time points after the disaster is shown. It can be seen that the critical load recovery rate remained between 77% and 82% throughout the recovery process, while the non-critical load recovery rate remained stable at around 19% for most periods, only decreasing to about 8% between t=9.5h and t=10h, before recovering to 24% at the end. Notably, the critical load recovery rate reached 82.08% at t=4h, 8h, 8.5h, 9h, 11.5h, and 12h, indicating that the multi-source collaborative recovery strategy consistently prioritized power supply to critical loads. Overall, the proposed strategy effectively prioritized the recovery of critical loads, but the recovery effect is still constrained by both the fault topology and the process of transferring moving resources.

[0086] 4.5 Analysis of V2G Willingness and Method Effectiveness 4.5.1 Sensitivity Analysis of V2G Willingness Parameters for Electric Vehicles To further analyze the impact of electric vehicle user behavior parameters on V2G support capabilities, this embodiment selects compensation price. User time anxiety coefficient and psychological threshold Sensitivity analysis was conducted on three key parameters, with average willingness and actual EV discharge capacity used as evaluation indicators. The results are as follows: Figure 17 , Figure 18 and Figure 19 As shown.

[0087] Depend on Figure 16It can be seen that as the compensation price increased from 0.30 yuan / kWh to 0.70 yuan / kWh, the average willingness to participate increased from 0.42 to 0.89, and the actual EV discharge capacity increased from 584kWh to 1232kWh. This indicates that increasing the economic compensation level can significantly enhance users' enthusiasm for participating in V2G and further unleash the supporting capacity of electric vehicle aggregation resources. Figure 17 , Figure 18 and Figure 19 It can be seen that the compensation price is positively correlated with the V2G support capacity, while the increase in user anxiety coefficient and psychological threshold will significantly inhibit user participation and weaken the post-disaster support capacity of EVCS, indicating that it is necessary to model the characteristics of electric vehicle user willingness in the post-disaster recovery analysis of distribution network.

[0088] 4.5.2 Method Validity Analysis To verify the effectiveness of the pre-disaster and post-disaster two-stage resilience enhancement strategy proposed in this embodiment, five recovery strategies were set up for comparative analysis. Strategy S1: Only DEG support is considered, without MESS or EV participation. Strategy S2: Post-disaster MESS scheduling is considered, but pre-disaster pre-deployment is not performed, and EV participation is not considered. Strategy S3: Pre-disaster MESS pre-deployment and post-disaster MESS scheduling are considered, but EV participation is not considered. Strategy S4: Pre-disaster pre-deployment and post-disaster multi-source collaboration are considered, with EV participation in discharge, but a fixed willingness coefficient is used. Strategy S5: The method proposed in this embodiment considers pre-disaster robust pre-deployment, dynamic road resistance, and V2G response willingness. The key load recovery rates for each strategy under scenario 1 are shown in [reference needed]. Figure 20 Load reduction costs under different recovery strategies and Figure 5 Table 6 shows the weighted load reduction costs for the five scenarios with the highest probability.

[0089] As shown in Table 6, the load reduction costs of S2 to S5 are significantly lower than those of S1, indicating that relying solely on the fixed DEG is insufficient to meet post-disaster recovery needs, while the system recovery capability is significantly improved after the introduction of MESS.

[0090] Table 6 Comparison of results from different recovery strategies

[0091] Compared to S1, S2 reduces load reduction costs by 28.95% and weighted load reduction costs by 29.12% in Scenario 1, indicating that mobile energy storage is a key resource for improving the system's post-disaster support capabilities. Further consideration of pre-disaster deployment improves load reduction costs in all scenarios, but the benefits are relatively limited under the current scenario and resource allocation.

[0092] Building upon this, S4 introduces EVCS, further reducing the load reduction cost in Scenario 1 by 18.25% compared to S3, and the weighted load reduction cost by 18.45%, demonstrating that the aggregation of electric vehicle resources can significantly enhance the system's flexible support capabilities during the post-disaster recovery period. In contrast, the strategy S5 proposed in this embodiment further considers the dynamic willingness model of electric vehicles based on S4, further reducing the load reduction cost and probability-weighted load reduction cost in Scenario 1 by 0.51% and 0.26%, respectively. Although the improvement is not significant, S5 achieves the best result among the five strategies, indicating that the dynamic willingness model can more accurately characterize the actual support capabilities of V2G, thereby improving the overall performance of the multi-source collaborative recovery strategy after a disaster.

[0093] This disclosure can be a system, method, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of this disclosure.

[0094] Computer-readable storage media can be tangible devices capable of holding and storing instructions for use by an instruction execution device. Computer-readable storage media can be, for example—but not limited to—electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination of the foregoing. The computer-readable storage media used herein are not to be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses through fiber optic cables), or electrical signals transmitted through wires.

[0095] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0096] Computer program instructions used to perform the operations of this disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The computer-readable program instructions may execute entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing the status information of the computer-readable program instructions to implement various aspects of this disclosure.

[0097] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the claims of the present invention.

Claims

1. A method for improving the resilience of a distribution network considering the V2G willingness of electric vehicles, characterized in that, include: A linear decay model of the weather impact coefficient, a wind-induced road physical damage model, and a water depth penalty model were constructed respectively. Based on all the constructed models, the shortest travel time for the mobile energy storage vehicle (MESS) to transfer from one access node to another was calculated. Based on the comprehensive utility of electric vehicles (EVs) participating in grid-connected V2G, taking into account discharge benefits, battery life loss costs, and time anxiety costs, the response probability of corresponding EVs participating in grid-connected V2G is calculated, and the EV cluster response coefficient of each node is calculated by using the response probability and the maximum discharge power of the EVs. With the goal of minimizing the sum of mobile energy storage configuration costs and load reduction costs under the most severe line fault scenarios, a two-stage robust optimization model for pre-disaster pre-deployment is constructed to solve for the pre-disaster mobile energy storage vehicle MESS pre-configuration location and pre-disaster scheduling variables. The constraint function of the two-stage robust optimization model for pre-disaster pre-deployment includes the pre-disaster electric vehicle call capability constraint constructed based on the pre-disaster EV cluster response coefficient. With the goal of minimizing load reduction costs during the recovery period, a multi-source collaborative recovery model is constructed to solve for the post-disaster location of mobile energy storage vehicles (MESS) and post-disaster scheduling variables. The constraint function of the multi-source collaborative recovery model includes cross-node transfer constraints of mobile energy storage vehicles (MESS) based on the shortest travel time.

2. The method for improving distribution network resilience considering the V2G willingness of electric vehicles according to claim 1, characterized in that: A linear decay model for the weather impact coefficient, a wind-induced road physical damage model, and a water depth penalty model are constructed respectively, as follows: The linear decay model for the weather impact coefficient is as follows: divide real-time rainfall intensity and real-time wind speed by their respective thresholds, then sum them up with weights. Subtract the weighted sum from 1 to obtain the weather impact coefficient. The wind-induced physical damage model for roads is as follows: Calculation cutoff time period The maximum historical wind speed experienced by the road is obtained by using the ln function. The difference between the ln function result and the logarithmic mean of the critical wind speed for infrastructure failure along the road is divided by the logarithmic standard deviation of the critical wind speed for infrastructure failure along the road. The result of the division is then input into the standard normal cumulative distribution function to obtain the probability of road damage in the power distribution network. The water depth penalty model is as follows: First, a continuous physical resistance function is constructed, and then a time period is used. The maximum value of the sum of the squares of the results of the division between the depth of the accumulated water and the initial water depth at which the accumulated water begins to affect the normal driving of vehicles and 0 is divided by the critical water depth at which the road section loses its effective traffic capacity and the initial water depth at which the accumulated water begins to affect the normal driving of vehicles. The minimum value of the sum of the squares of the results of the division is the result of the continuous physical resistance function. Will The difference between the water depth during a given period and the critical water depth that causes a road segment to lose its effective traffic capacity is input into the Sigmoid function to obtain the nonlinear transition weight; The depth penalty coefficient is obtained by multiplying the continuous physical resistance function by 1 and the difference between it and the nonlinear transition weight, and then adding 1 to the nonlinear transition weight.

3. The method for improving the resilience of a distribution network considering the V2G willingness of electric vehicles according to claim 2, characterized in that: Based on all the constructed models, the shortest travel time for a Mobile Energy Storage Vehicle (MESS) to transfer from one access node to another is calculated as follows: For a road segment, subtract the water depth penalty coefficient from 1 and add the set minimum number to obtain the water depth correction coefficient. Divide the free passage time of the road segment by the product of the weather influence coefficient and the water depth correction coefficient to obtain the basic passage time. Multiply the road section's design capacity, weather impact coefficient, the difference between 1 and the probability of road damage to the power distribution network, and the water depth correction coefficient, and then multiply the time period... The real-time traffic flow is divided by the product as the base, and the second set coefficient is used as the exponent for exponential calculation. The product of the exponential calculation result and the first set coefficient is added by 1 to obtain the total correction coefficient. Multiply the basic travel time by the total correction factor to obtain the disaster travel time for the corresponding road segment; Obtain all feasible paths between the access node and another node. For each feasible path, sum the disaster travel times of all road segments included in the corresponding feasible path to obtain the travel time of the corresponding feasible path. The minimum travel time among all feasible paths is the shortest travel time from the access node to another node.

4. The method for improving distribution network resilience considering the V2G willingness of electric vehicles according to claim 1, characterized in that: The comprehensive utility of electric vehicles (EVs) participating in grid-connected V2G, taking into account discharge benefits, battery life depreciation costs, and time anxiety costs, is as follows: The overall utility is the discharge benefit minus the battery life loss cost, and then minus the time anxiety cost; Discharge benefit is time period The V2G incentive electricity price multiplied by the corresponding electric vehicle (EV) during the time period The actual discharge capacity within; Battery life loss cost is the product of unit capacity battery investment cost, battery rated capacity and equivalent full cycle count, divided by cycle life under standard test conditions; The time anxiety cost is calculated as follows: the product of the user's sensitivity coefficient to time occupation and the actual continuous online time of the electric vehicle (EV) participating in V2G is divided by the maximum online time that the user can accept, and the natural base e is used as the base to perform the exponential operation. The result of the exponential operation is used as the first exponent. The sensitivity coefficient of users to time consumption is indexed, with the natural base e as the base, and the result of the exponentiation is used as the second exponent. Divide the difference between the first exponent and 1 by the difference between the second exponent and 1, and multiply the result by the set user time anxiety coefficient to obtain the time anxiety cost. .

5. The method for improving distribution network resilience considering the V2G willingness of electric vehicles according to claim 1, characterized in that: Calculate the response probability of electric vehicles (EVs) participating in grid-to-grid (V2G) interaction, and then calculate the EV cluster response coefficient for each node using the response probability and the maximum discharge power of the EVs. Specifically: The difference between the overall utility and the set psychological threshold parameter for user participation in V2G is input into the Logistic function to obtain the response probability; Node i in the time period The product of the response probability of all electric vehicles (EVs) participating in grid-connected V2G and the maximum discharge power of the corresponding EV is summed, and the summation result is divided by the number of nodes i in the time period. The sum of the maximum discharge power of all electric vehicles (EVs) is used to obtain the node. During the period The EV cluster response coefficient.

6. The method for improving distribution network resilience considering the V2G willingness of electric vehicles according to claim 1, characterized in that: The two-stage robust optimization model for pre-disaster layout is as follows: The decision variables for the first stage of the two-stage robust optimization model for pre-disaster pre-deployment are the pre-configuration locations of mobile energy storage vehicles (MESS) and the decision variables for the second stage are the pre-disaster scheduling variables, which include load reduction power, diesel generator output, electric vehicle (EV) aggregated discharge power, and power distribution network flow variables.

7. A method for improving the resilience of a distribution network considering the V2G willingness of electric vehicles, as described in claim 6, characterized in that: The objective is to minimize the sum of the mobile energy storage configuration cost and the load reduction cost under the most severe line fault scenario, specifically: The cost of pre-configuring a pre-disaster mobile energy storage vehicle (MESS) on all nodes is added together with the product of the state variables of the pre-configured MESS on the corresponding node at the time of the disaster as the mobile energy storage configuration cost; if the corresponding node has pre-configured a pre-disaster mobile energy storage vehicle (MESS) at the time of the disaster, the corresponding state variable is 1, otherwise it is 0. Reduce the cost of unit load across all nodes during the time period The product of the active power load reduction and the scheduling time interval is added together to obtain the time period. The load reduction cost is obtained by summing the load reduction costs of all failure periods. For each fault scenario, the line fault parameters of the fault scenario are obtained to form a line fault uncertainty vector; The decision variables in the first stage and the uncertainty vector of line faults simultaneously determine the feasible region of the decision variables in the second stage. For each fault scenario's line fault uncertainty vector, the sum of the minimum fault period load reduction costs in the feasible domain of the corresponding second-stage decision variables is obtained as the sum of fault period load reduction costs under the corresponding line fault uncertainty vector conditions. Then, the maximum value of the sum of fault period load reduction costs under the line fault uncertainty vector conditions for all fault scenarios is obtained as the sum of load reduction costs under the most severe line fault scenario. The sum of the mobile energy storage configuration cost and the load reduction cost under the most severe line fault scenario is used as the objective function of the two-stage robust optimization model for pre-disaster pre-deployment.

8. A method for improving distribution network resilience considering the V2G willingness of electric vehicles according to claim 1, characterized in that: The pre-disaster electric vehicle call capability constraints, constructed based on the pre-disaster EV cluster response coefficients, are as follows: For nodes configured with grid-connected V2G charging piles (EVCS), pre-disaster The expected EV discharge power during the period is greater than or equal to 0 and less than or equal to the EV cluster response coefficient and the theoretical maximum discharge power of the EV cluster during the corresponding period before the disaster. The expected available battery power of electric vehicles (EVs) is greater than or equal to 0 and less than or equal to the pre-disaster EV cluster response coefficient and the theoretical maximum available battery power of the EV cluster. The pre-disaster EV cluster response coefficient is greater than or equal to the lower limit of the EV cluster response coefficient and less than or equal to the upper limit of the EV cluster response coefficient.

9. A method for improving distribution network resilience considering the V2G willingness of electric vehicles according to claim 1, characterized in that: The objective is to minimize the cost of load reduction during the recovery period, specifically: Reduce the cost of unit load across all nodes during the time period The product of the active power load reduction and the scheduling time interval is added together to obtain the time period. The load reduction cost is calculated by summing up the load reduction costs during all post-disaster recovery periods to obtain the total load reduction cost during the recovery period. The sum of load reduction costs during the recovery period is used as the objective function of the post-disaster multi-source collaborative recovery model.

10. A method for improving the resilience of a distribution network considering the V2G willingness of electric vehicles, as described in claim 1, characterized in that: The cross-node transfer constraints for mobile energy storage vehicles based on the shortest travel time (MESS) are as follows: Divide the shortest travel time by the scheduling interval and round up to obtain the discrete time period travel time. The MESS cross-node transfer constraint for mobile energy storage vehicles is: when the first node... MESS vehicles during the time period By node Transfer to target node At that time, before the discrete time period travel time is reached, the first The MESS vehicle cannot access the target node.

11. A method for improving the resilience of a distribution network considering the V2G willingness of electric vehicles, as described in claim 1, characterized in that: The two-stage robust optimization model for pre-disaster layout is solved using a column constraint generation algorithm, while the post-disaster multi-source collaborative recovery model is solved by transforming it into a linear model using mixed integer second-order cone programming.

12. A distribution network resilience enhancement system considering the V2G willingness of electric vehicles based on the method of any one of claims 1-11, comprising a shortest travel time calculation module, an EV cluster response coefficient calculation module, a pre-disaster pre-layout two-stage robust optimization model construction module, and a post-disaster multi-source collaborative recovery model construction module, characterized in that: The shortest travel time calculation module is used to construct a linear decay model of the weather impact coefficient, a wind-induced road physical damage model, and a water depth penalty model, respectively, and calculate the shortest travel time for the mobile energy storage vehicle (MESS) to transfer from one access node to another based on all the constructed models. EV Cluster Response Coefficient Calculation Module: This module is used to calculate the response probability of electric vehicles (EVs) participating in grid interaction (V2G) based on the comprehensive utility of EVs participating in grid interaction (V2G) taking into account discharge benefits, battery life loss costs, and time anxiety costs. The module calculates the EV cluster response coefficient of each node by using the response probability and the maximum discharge power of the EVs. The pre-disaster pre-deployment two-stage robust optimization model construction module is used to construct a pre-disaster pre-deployment two-stage robust optimization model with the goal of minimizing the sum of mobile energy storage configuration cost and load reduction cost under the most severe line fault scenario. It solves the pre-disaster mobile energy storage vehicle MESS pre-configuration location and pre-disaster scheduling variables. The constraint function of the pre-disaster pre-deployment two-stage robust optimization model includes pre-disaster electric vehicle call capability constraints based on the pre-disaster EV cluster response coefficient. The post-disaster multi-source collaborative recovery model construction module is used to construct a post-disaster multi-source collaborative recovery model with the goal of minimizing load reduction costs during the recovery period. It solves for the post-disaster location of mobile energy storage vehicles (MESS) and post-disaster scheduling variables. The constraint functions of the post-disaster multi-source collaborative recovery model include cross-node transfer constraints of mobile energy storage vehicles (MESS) based on the shortest travel time.

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