Dynamic damage sensing collaborative recovery method for power distribution network to cope with flood disaster

Abstract

The invention belongs to the technical field of power distribution network restoration, and particularly relates to a dynamic damage sensing collaborative restoration method for a power distribution network to cope with flood disasters, which comprises the following steps: S1, acquiring local data of a target area; s2, constructing a disaster scene deduction model, a search and fault perception model, a random maintenance time model, an unmanned aerial vehicle-maintenance team cooperative scheduling model, a communication recovery and switch control model, a waterlogging development model and an operation constraint model based on the local data collected in S1; s3, taking maximum recovery of weighted load energy, reduction of flood drainage cost and improvement of fault information FI perception efficiency as target functions, and establishing a dynamic damage perception collaborative recovery model of the distribution network coping with flood disasters under fault information loss; and S4, an event-driven rolling optimization framework is established and solved, and a power supply recovery strategy is obtained. The method can sense the damage state in real time, dynamically adjust the recovery strategy, and cooperatively dispatch the unmanned aerial vehicle and maintenance resources in a complex environment of dynamic development of waterlogging.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of power distribution network repair, and particularly relates to a dynamic damage perception and collaborative recovery method for power distribution network in response to flood disasters. BACKGROUND

[0002] As a key link in the power system directly facing users to distribute electric energy, the power distribution system bears the important responsibility of guaranteeing the normal operation of national daily life, industrial and commercial operation and urban infrastructure. With the continuous development of power grid construction in China, the power distribution network has evolved from a traditional single physical network into an information-physical power distribution system (Cyber-Physical Distribution System, CPDS) integrating power flow, information flow and control flow, and its structure is increasingly complex and covers a wide range. However, with the intensification of global warming trend, extreme rainstorm weather events occur frequently and intensively, and the secondary disasters such as urban waterlogging caused thereby pose a serious challenge to the safe and stable operation of the power distribution network.

[0003] In extreme rainstorm flood disasters, rainwater backflow, road waterlogging and underground facility submergence not only directly lead to physical damage such as short circuit, insulation breakdown and tower collapse of power distribution equipment, but also often cause power outage of communication base stations, damage of optical cables and interruption of signals, thereby causing large-area paralysis of communication networks. At the same time, the traffic network is blocked due to waterlogging, which seriously affects the accessibility and scheduling efficiency of repair teams and emergency resources. More importantly, there is a serious risk of electric leakage after the power equipment is submerged by water, and the power restoration operation must be carried out after the water level recedes and safety detection, which further prolongs the power outage time. Under this background, it is difficult for operators to obtain accurate key information such as fault location, damage degree and equipment state in time, forming a large number of "perception blind areas", resulting in serious lack of fault information. If the coupling influence of multiple factors such as communication interruption, road blockage and waterlogging evolution is ignored, the traditional power supply restoration strategy will lose the basis for decision-making, causing unreasonable repair sequence, resource scheduling mismatch, power restoration delay and other problems, which seriously affect the overall efficiency and social and economic benefits of power supply restoration. At present, the research on post-disaster restoration of power distribution network under extreme weather mainly focuses on network reconfiguration and repair priority sequencing based on known fault information, and usually makes optimization decisions according to parameters such as fault location, load importance and estimated repair time. Some advanced methods have begun to consider the influence of communication system failure on power distribution network control services (such as remote switch operation and state monitoring), and model the restoration of communication network and power supply restoration collaboratively to improve the overall restoration ability of the system. However, these methods are mostly based on the premise that operators can obtain complete fault information in time, ignoring the loss of fault information perception ability caused by large-scale damage of communication infrastructure under extreme disasters.

[0004] Specifically, the prior art has the following two significant defects: (1) Ignoring the dynamic lack of fault information acquisition capability. Traditional recovery methods rely on the real-time perception and centralized decision of the dispatch center on the whole network state, but in extreme flood disasters, the widespread destruction of the communication network causes the SCADA, AMI and other data acquisition systems to fail, and the operator cannot obtain the fault information of the disaster area (such as which line is out of power, whether the equipment is flooded, and how damaged) in time, resulting in a large number of "information blind areas". In this case, the traditional optimization model based on complete information cannot effectively operate, and the recovery decision lacks data support, which is prone to misjudgment or delay. (2) Lack of modeling and response mechanism for the dynamic evolution process of secondary disasters. Existing methods mostly regard disaster impact as a static or one-time event, ignoring the fact that flood disasters have significant spatiotemporal dynamic characteristics - the processes of continuous rainfall, water spread, water level rise and fall, and road gradual flooding or recovery will change over time and continuously affect equipment availability, repair feasibility and resource accessibility. If the development process of waterlogging and the recovery process of the distribution network are not coupled, the generated recovery strategy may not be implemented due to road interruptions or equipment still being flooded, causing a gap between planning and reality and reducing the practicality and robustness of the strategy.

[0005] Therefore, how to construct a power distribution network post-disaster power restoration method that can perceive damage state in real time, dynamically adjust recovery strategy, and coordinate the scheduling of unmanned aerial vehicles and maintenance resources in the complex environment of missing fault information, communication interruption, traffic obstruction, and dynamic development of waterlogging, so as to significantly improve the power restoration speed and efficiency under extreme flood disasters, has become a problem to be solved. SUMMARY

[0006] In view of the above problems of the prior art, the present application provides a dynamic damage perception and coordinated recovery method for power distribution network in response to flood disasters, which can perceive damage state, dynamically adjust recovery strategy, and coordinate the scheduling of unmanned aerial vehicles and maintenance resources in the complex environment of missing fault information, communication interruption, traffic obstruction, and dynamic development of waterlogging.

[0007] To solve the above technical problems, the present application adopts the following technical solutions:

[0008] A dynamic damage perception and coordinated recovery method for power distribution network in response to flood disasters, comprising the following steps:

[0009] S1, obtaining local data of the target area; the local data includes electrical and structural parameters of the information-physical power distribution system, topographic and traffic network data of the area where the power distribution network is located, and rainfall intensity information during extreme rainstorms;

[0010] S2, based on the local data collected in S1, constructing a disaster scenario deduction model, a search and fault perception model, a random repair time model, a UAV-repair team collaborative scheduling model, a communication recovery and switch control model, an internal flooding development model, and an operation constraint model;

[0011] The disaster scenario deduction model is used for simulating the spatial and temporal distribution of flood disasters, the search and fault perception model is used for describing the line set belonging to the blind area, the random repair time model is used for estimating the repair time of the fault scenario, the UAV-repair team collaborative scheduling model is used for simulating the collaborative scheduling of the UAV and the repair team, the communication recovery and switch control model is used for describing the communication recovery constraint and the control service constraint, the internal flooding development model is used for simulating the dynamic spatial and temporal development process of flood, and the operation constraint model is used for describing the operation constraint of the distribution network in the recovery process.

[0012] S3, taking the models constructed in S2 as constraint conditions, and taking the maximized recovery of the weighted load energy, the reduced flood drainage cost and the improved fault information FI perception efficiency as objective functions, a dynamic damage perception collaborative recovery model for the distribution network responding to flood disasters under the condition of missing fault information is established.

[0013] S4, considering the dynamic characteristics of the recovery process, an event-driven rolling optimization framework is established based on the dynamic damage perception collaborative recovery model, and is solved, so that a power supply recovery strategy is obtained.

[0014] Compared with the prior art, the present application has the following beneficial effects:

[0015] 1. Active perception and blind area identification under the condition of missing fault information are realized. Unlike the traditional recovery method which relies on complete communication and real-time monitoring data, the present method constructs a "search and fault perception model", combines UAV inspection path planning and communication interruption area analysis, and actively detects the "information blind area" formed due to communication interruption. By simulating the search behavior of the UAV in the complex post-disaster environment, the set of lines that may be damaged but lack reported information is dynamically identified, which makes up for the defects of the traditional method caused by information missing, and enhances the state perception ability of the system under extreme conditions.

[0016] 2. The dynamic evolution process of flood disasters and its influence on recovery are effectively described. The existing technology usually regards the disaster influence as a static or one-time impact, and it is difficult to reflect the real process of internal flooding spreading and receding over time. The present method introduces an "internal flooding development model" to simulate the spatial and temporal changes of water depth based on terrain, rainfall intensity and drainage capacity, and then judges whether the equipment can be repaired and whether the road is passable. The model is linked with repair scheduling and power restoration operation, which avoids blindly dispatching repair tasks when the equipment is still flooded or the road is not passable, and improves the feasibility and timeliness of the recovery strategy.

[0017] 3. Efficient coordination and scheduling of UAVs and repair teams The method establishes a "UAV-repair team coordination and scheduling model" to address the problem of traffic congestion and difficult human scheduling after a disaster. The model takes full advantage of the rapid patrol and obstacle-crossing flight of UAVs to obtain the status information of key nodes and guide the accurate deployment of ground repair resources. Compared with the traditional method of relying solely on manual inspection, this coordination mechanism significantly shortens the fault location time and optimizes the allocation efficiency of limited repair resources.

[0018] 4. Considering the coupling relationship between communication recovery and power supply control, the overall controllability of the system is improved. Traditional methods often ignore the constraints of communication network damage on remote switch operation and load control functions. The method combines communication link repair priority with power distribution network topology reconstruction through the "communication recovery and switch control model" to gradually rebuild control capabilities while restoring power supply, ensuring that important loads can be quickly connected through remote control, avoiding the situation of "power not delivered" due to communication failure.

[0019] 5. Building an event-driven rolling optimization framework to enhance the dynamic adaptability of recovery strategies. Unlike traditional static optimization or single-solution methods, the method establishes an event-driven rolling optimization mechanism based on the "dynamic damage perception and collaborative recovery model". Whenever new perception information (such as UAV feedback, water level changes, communication recovery) arrives, the system automatically triggers re-optimization to dynamically adjust the subsequent repair sequence and power supply path. This closed-loop feedback mechanism significantly improves the response capability of the recovery process to environmental changes, overcoming the "rigid planning" problem of traditional methods.

[0020] In summary, in the complex environment of missing fault information, communication interruption, traffic congestion, and dynamic development of waterlogging, the method can realize real-time perception of damage state, dynamic adjustment of recovery strategy, and collaborative scheduling of UAVs and repair resources, significantly improving the speed and efficiency of power supply recovery under extreme flood disasters.

[0021] Preferably, the construction process of the disaster scenario deduction model comprises:

[0022] The research area is gridded based on a triangular grid, and the obtained rainfall intensity information during extreme heavy rain is modeled as a high-dimensional rainfall matrix as shown in (1):

[0023]

[0024] wherein, represents the rainfall information of triangular grid point i at time period t, including the position Cartesian coordinates and rainfall intensity ; represents the set of triangular grid points in the research area; Represents the temporal distribution set of extreme rainfall intensity;

[0025] remember , and They represent Time period coordinates The water depth and average vertical velocity in the x and y directions of the flood on the grid; water level height. b represents the terrain elevation; the two-dimensional shallow water equations are obtained as shown in (2)-(4);

[0026]

[0027]

[0028] (4)

[0029] in, , , and These are vectors representing fluid variables, flow rate in the x-direction, flow rate in the y-direction, and source term, respectively. Represents gravitational acceleration; It is the runoff coefficient, which represents the proportion of rainfall that can reach the ground without being blocked by trees or buildings; and These represent the terrain slopes in the x and y directions, respectively. This indicates the intensity of excess rainfall, determined by rainfall intensity. Infiltration rate and evaporation rate calculate: ; and Let x and y represent the friction slopes respectively, and calculate them using Manning's formula as shown in (5):

[0030]

[0031] in, This represents the empirical Manning coefficient, reflecting the degree of terrain roughness.

[0032] The governing equations are solved using a semi-implicit finite volume method based on triangular mesh discretization; the integral form of equation (2) is obtained by applying Green's theorem as shown in (6):

[0033]

[0034] in, Indicates the control volume; Represents the boundary of the volume; This represents the unit normal vector perpendicular to the boundary and pointing outwards; and Represent the area element and the arc element respectively; Indicates the outward normal flow, where Discretizing formula (6) in a triangular mesh yields (7):

[0035]

[0036] in, This represents the average fluid variable vector of grid i. Represents the area of ​​grid i; This represents the flow vector on the k-th edge of grid i; and These represent the fluid variables on the left and right sides of the boundary, respectively. Indicates arc length; This represents the unit normal vector perpendicular to the boundary and pointing outwards;

[0037] Source Item Divided into friction terms and bed slope item As shown in formula (4); assuming the terrain within the grid changes linearly, and The calculation formula is:

[0038]

[0039]

[0040] in, and Indicates the slope of grid i; , and subscript It is the vertex index of the triangular mesh that satisfies the counterclockwise direction;

[0041] Using the rotational invariance of the two-dimensional shallow water equation, the first term on the right-hand side of equation (7) is transformed into:

[0042]

[0043] in, , These are the rotation matrix and its inverse matrix, respectively; and They represent the unit normal vectors respectively. The components in the x and y directions; let ,have:

[0044]

[0045] in, and Let represent velocities perpendicular to and parallel to the boundary, respectively; formulas (10) and (11) introduce variables... The two-dimensional shallow water equations are transformed into a one-dimensional Riemann problem; the boundary flows are calculated using the HLLC approximate Riemann solution, as shown below:

[0046]

[0047]

[0048]

[0049] in, Calculated using formula (11); and These represent the flow rates on the left and right sides of the middle region of the Riemann solution, respectively. , and These represent the velocity estimates for the left wave, contact wave, and right wave at the grid boundary, respectively; where, and These represent the fastest speed at which the fluid propagates from the left and right sides of the boundary toward the middle, respectively, and represent the maximum potential contribution of the fluid on both sides to the flow rate at the boundary. It is the intermediate wave velocity of the fluid at the boundary, reflecting the physical characteristic of pressure discontinuity caused by the different fluid states on both sides of the boundary. and Indicates normal flow The first and second components;

[0050] According to formula (7) and boundary normal flow , source item The calculation, through the time-progression formula, will... Time grid points Fluid variables updated to The time frame is used to simulate the spatiotemporal distribution of flood disasters, as shown in (18):

[0051]

[0052] In the formula, This represents the fluid variables in the nth time period of grid i.

[0053] This approach, through the comprehensive application of advanced numerical techniques such as two-dimensional shallow water equations, the finite volume method, and Riemann solutions, enables high-precision simulation and dynamic prediction of the spatiotemporal distribution of flood disasters. Its superior performance in handling complex boundary conditions, source term effects, and variable disaster scenarios significantly enhances the scientific rigor and effectiveness of disaster risk assessment and emergency response.

[0054] Preferably, , and Calculated using the following formula:

[0055]

[0056]

[0057]

[0058] in, and This represents the average quantity of Roy. , .

[0059] This setup allows for precise calculation of wave speed. , and This significantly improves the stability and accuracy of numerical simulations. It also demonstrates excellent performance in capturing contact waves and adapting to various fluid conditions.

[0060] Preferably, the process of constructing the search and fault perception model includes:

[0061] The communication network PN and the physical network CN are modeled as undirected graphs. and Each electrical node is mapped to a network node;

[0062] The affected lines are defined as network blind zone lines (CBL), forming a blind zone line set. ; The lines in the system are isolated from the substation and communication is interrupted, meeting the following conditions:

[0063]

[0064]

[0065]

[0066] Among them, binary variables It is a line belong The flag bit, when set to 1, indicates that it belongs to binary variables and Representing network nodes Communication status and corresponding electrical nodes The isolation status is set to 1 if communication is connected or not isolated; a binary constant. , express The status of communication / power distribution lines between them is assumed to be zero for faults; it is assumed that the communication system between the substation and the command center is well protected and does not experience faults, satisfying the following conditions. ;

[0067] Based on time-varying failure probabilities, multiple random failure scenarios are generated using the Monte Carlo method. This indicates the possible fault conditions and degree of damage; when the rainfall intensity exceeds the threshold, flashover of the insulator leads to insulation damage, while the mud and sand carried by the flood impacting the tower causes collapse; the fault probability is calculated as follows:

[0068]

[0069]

[0070] in, This indicates that during time period t, the line The probability of the kth insulator / tower experiencing a flashover / collapse fault; and These are the mean and standard deviation of the critical rainfall intensity; Indicates flow rate; This is the flood capacity threshold curve, which represents the relationship between the flow velocity and flood depth that leads to tower collapse; Indicates the line The rainfall intensity experienced by the k-th insulator during time period t; It represents the differential sign of rainfall intensity; Indicates the line The flood depth at the location of the kth tower.

[0071] The random damage scenario s generated by the Monte Carlo method divides the network blind zone lines (CBLs) into two sets: , and These respectively represent faulty lines in network dead zones and lines with potential faults; lines Upper The simulated damage state of an insulator / tower is defined as follows: The subscripts ij, s, and k represent the lines respectively. 1. Random damage scenario s; 2. The k-th recovery event.

[0072] This setup, through the construction of a search and fault perception model, enables the accurate identification of potentially faulty lines in the distribution network during floods and the scientific assessment of fault probabilities. It demonstrates excellent performance in accurately delineating network blind spots, effectively assessing fault probabilities, enhancing the robustness and reliability of the model, and optimizing resource allocation and emergency response.

[0073] Preferably, the process of constructing the stochastic maintenance time model includes:

[0074] Two approximations, a coarse approximation and a precise approximation, are constructed to estimate maintenance time. The coarse approximation uses a statistical method, based on the mean value of s. and variance To describe repair time; an accurate approximation is based on accurate FI processing, providing an accurate approximation of repair time by truncating the normal distribution, including the mean. ,variance The upper limit of exact approximation and lower limit Repair time estimates are used for both pessimistic and optimistic scenarios; based on these, the average of two approximate estimates is calculated as follows:

[0075]

[0076] in, / This represents the average repair time per unit for damaged insulators / towers, derived from historical maintenance team data; , They represent the lines respectively. The number of insulators and towers; , These represent the status of the insulator and the tower, respectively; the value is 1 if there is a fault.

[0077] Random repair time This is represented as having an ideal probability level. Opportunity constraints:

[0078]

[0079] in, It is the cumulative distribution function (CDF); maintenance time The formulas for the rough approximation and the exact approximation are (26) and (27), respectively:

[0080]

[0081]

[0082]

[0083] in, and These are the CDF and inverse CDF of the standard normal distribution; κ, These are the introduced parameters;

[0084] An additional chance constraint is introduced to limit robustness, minimizing the probability of adverse situations;

[0085]

[0086] in, Indicates the probability of an unfavorable situation; Used to calculate random events The probability of;

[0087] Applying the sample mean approximation SAA, by... Sampling is performed on each scene, and the frequency of scenes that satisfy the constraints is used to approximate the probability of the constraints being satisfied; the SAA of formula (29) is written as (30):

[0088]

[0089] in, ; It is a number greater than the preset value; when When, constraint (26) is satisfied in scenario s; when At that time, the constraint is relaxed by making the first formula in (30) redundant; the second formula in (30) limits the number of violations of the rough approximation to no more than .

[0090] This setup, combining precise and coarse approximation methods, enables the model to provide comprehensive data support for maintenance scheduling and resource allocation. Maintenance teams can select the appropriate approximation method based on actual needs to formulate reasonable maintenance plans. In practical applications, this model helps optimize the coordinated scheduling of UAVs and maintenance resources, improve emergency response efficiency, reduce unnecessary resource waste, and ensure the rapid repair of critical lines and equipment.

[0091] Preferably, the construction process of the UAV-maintenance team collaborative scheduling model includes:

[0092] (1) Scheduling problem; using This refers to the coordination and scheduling problem between the maintenance team and the drones. If the first... Step in the first Each recovery event corresponds to the repair team. or drone At work If the superscript is 1, then take 1; , These represent the maintenance team and the drone, respectively; the subscripts q and k represent the working point q and the kth recovery event, respectively.

[0093] The scheduling model is constructed as follows:

[0094]

[0095] C and D represent a combination of maintenance teams and drones; Represents a collection of recovery events; and These represent the work sites of the maintenance team and the drones, respectively. , ; and These represent the sets of observable faulty lines and network blind spots, respectively. This represents the set of network blind spots, faulty lines, and potentially faulty lines. This represents a set of faulty lines in network dead zones.

[0096] (2) Target path problem; by defining The path relationship between work points p and q is represented, and the target path problem is modeled as follows:

[0097]

[0098]

[0099]

[0100] Where the subscript 0 indicates the starting point; the first equation of constraint (32) represents and The relationship between the two equations is such that the second equation prevents the path from being at the same work point; constraint (33) indicates that only when the maintenance team or the drone arrives... Then arrive at the work site hour, Talent is 1;

[0101] (3) Time schedule problem; First, determine the completion time of step k. The model is as follows:

[0102]

[0103] in, and The completion times for the incidents involving the repair team and the drone are respectively. Indicates the start time of the step;

[0104] The maintenance time is given by formulas (27) and (30). ; It consists of three terms in formula (36): 1) the past time before reaching q. 2) Maintenance time; 3) Time required for inspection q ;

[0105]

[0106]

[0107] in, This represents the travel time required for the maintenance team to travel from work point p to work point q; Indicates the time for line inspection;

[0108] Drone line inspection completion time and the time required to restore communication functionality as follows:

[0109]

[0110]

[0111] in, Indicates the dwell time of the drone; Indicates the travel time for the drone;

[0112] (4) Traffic time problem; model the traffic network TN as an undirected graph. ,in and Represent traffic nodes and edge sets, respectively;

[0113] A dynamic adjacency traffic time matrix is ​​proposed. To reflect Dynamic changes in indirect connectivity and corresponding travel time As shown in formula (40); this matrix is ​​used to improve the performance of the Floyd algorithm in calculating traffic time in the Honglai scenario;

[0114]

[0115]

[0116] in, Indicates passing through the edge Minimum travel time;

[0117] Modeling is considered for expressways, arterial roads, and secondary roads; the depth destruction function in formula (43) models the mesh for each road type. Medium speed limit With the depth of waterlogging The relationship; accordingly, The calculation is as shown in formula (42):

[0118]

[0119]

[0120] in, , and These are parameters related to road type; Represents a grid Middle Length;

[0121] Then, the minimum travel time between any two work points is determined using the Floyd algorithm. And the corresponding route, where the unreachable fault point j satisfies ;

[0122] Ignoring factors such as flight altitude and energy consumption, we assume that the drone's flight speed is constant. The flight time of the UAV is determined by the nearest neighbor path selection principle. The Euclidean distance between any two working points divided by .

[0123] This setup, which constructs a drone-maintenance team collaborative scheduling model, achieves comprehensive optimization of emergency response and maintenance scheduling for flood disasters. It effectively enhances scheduling decision support, comprehensively considers multiple time factors, optimizes dynamic traffic time matrices, and efficiently calculates drone flight times.

[0124] Preferably, the process of constructing the communication recovery and switching control model includes:

[0125] The worst-case scenario is defined as communication recovery relying entirely on EC provided by the UAV, as shown in Equation (47). All maintenance resources are allocated to PN fault repair to improve load recovery efficiency. The communication recovery constraints are as follows:

[0126]

[0127]

[0128]

[0129]

[0130] in, Indicates whether the communication function of node i has been restored by drone d; This represents the straight-line distance from node i to the center of EC; The coordinates of the EC center; This indicates the communication status of node i; r represents the preset distance threshold. The preset network node threshold;

[0131] In CPDS, both communication status and physical faults affect switching control; observable and controllable distributed generation (DGs) restores critical loads in fault-free areas through unplanned islanding, while DGs with communication interruptions rely on planned islanding operation by the local controller; planned islanding of DGs divides the PN into internal lines. Boundary lines and external lines The control service model is as follows:

[0132]

[0133]

[0134]

[0135] in, Indicates the line The on / off state; DG Network status; A collection representing intact lines; This represents the set of potentially faulty lines.

[0136] This setup, through comprehensive management and optimization of communication recovery and switching control, significantly improves the power system's disaster resistance and recovery speed under extreme weather conditions, providing strong support for ensuring the continuity and reliability of power supply.

[0137] Preferably, the process of constructing the urban flooding development model includes:

[0138] Based on the principle of water balance, the dynamic process of flood dynamics in time and space is represented by mathematical formula (51), where the total drainage volume is the sum of pump drainage volume, infiltration volume, and evaporation volume; the waterlogged area Net infiltration rate Evaporation rate Calculated using formula (52);

[0139]

[0140]

[0141] in, and The flooded areas The water pumps and grid assembly in the middle; This indicates the average decrease in water depth. The time interval between events; For water pumps The drainage rate; Represents a grid The dry and wet state; C is the drainage rate of underground pipelines; C is an empirical coefficient. and These represent the saturated vapor pressure and the actual vapor pressure, respectively. Wind speed; Represents thermodynamic temperature;

[0142] Water pump power With drainage rate The relationship is shown in (53);

[0143]

[0144]

[0145] in, The density of water; For still water lift; For water pump efficiency; Indicates power status; and These represent the upper and lower limits of the water pump power, respectively.

[0146] This setup accurately simulates the spatiotemporal changes in water volume during floods, providing a scientific basis for flood control and drainage. By comprehensively considering factors such as pump drainage, infiltration, and evaporation, the model can predict the development trend of urban flooding, helping decision-makers formulate effective response measures and reduce losses caused by floods.

[0147] Preferably, the process of constructing the constraint model includes:

[0148] Define the coefficient of recovery The proportion of recoverable load in quantized zn is determined by the average unit load density of grid m or region zn. and security depth threshold Control measures are implemented to ensure that areas with water depths below this threshold can be restored; recovery coefficient. The calculation formula is:

[0149]

[0150] For each recovery event, possible system state transitions are controlled by formulas (56)-(58);

[0151]

[0152]

[0153]

[0154] in, and They are nodes or region Active and reactive loads at the location; and They represent the lines respectively. The active and reactive power flows on the surface; in formula (56), nodes o and j represent the upstream and downstream nodes of i, respectively; and These represent the active power generation and reactive power generation of the DG or substation at point i, respectively. This represents the square of the voltage value at point i; and They are respectively Resistance and reactance; To pass Maximum permissible apparent power; and These represent the upper and lower limits of the square node voltage amplitude, respectively;

[0155] During the recovery process, the faulty line and PFLs are isolated, the command center reconstructs the PN, and the load in the fault-free area is restored. To maintain the radial topology, a single-commodity flow method is used, as shown below:

[0156]

[0157] in, Indicates the root node; Indicates the line The connected state; Represents the flow of virtual goods; It is a number that is greater than the preset large value.

[0158] This setup effectively manages the power system's fault recovery process, ensuring proper load distribution and system stability. By precisely controlling power flow and state transitions, the model improves the power system's recovery efficiency and reliability, reducing the impact of faults on users.

[0159] Preferably, in S3, the objective function is:

[0160]

[0161] in, Let be the weight coefficient of node i; This is a conservative estimate of the recovery time; denoted as energy cost per drainage pump; r is the reward factor perceived by FI. This represents the time interval between the completion of perception and the termination of the model predictive control step. N represents the completion time of event k; D This represents the set of distribution network nodes.

[0162] This setup can effectively improve the efficiency and economy of the power system recovery process. By rationally allocating resources and optimizing time management, it ensures the priority recovery of critical nodes, reduces energy consumption costs, and incentivizes the timeliness and accuracy of FI sensing. Attached Figure Description

[0163] To make the objectives, technical solutions, and advantages of the invention clearer, the invention will now be described in further detail with reference to the accompanying drawings, wherein:

[0164] Figure 1 This is a flowchart of the method;

[0165] Figure 2 This is a schematic diagram of the network blind spot and the network blind spot line in Example 1;

[0166] Figure 3 This is a schematic diagram of the improved IEEE 33-node CPDS in Example 2;

[0167] Figure 4 This is a schematic diagram comparing the weighted load recovery schemes of the four schemes in Example 2;

[0168] Figure 5 This is a schematic diagram comparing the weighted unload energy of the four schemes in Example 2. Detailed Implementation

[0169] The following detailed explanation illustrates the specific implementation methods:

[0170] Example 1

[0171] like Figure 1 As shown in the figure, this embodiment discloses a dynamic damage perception and collaborative recovery method for power distribution networks in response to flood disasters, including the following steps:

[0172] S1. Obtain local data for the target area; the local data includes electrical and structural parameters of the information-physical distribution system, topographic and transportation network data of the area where the distribution network is located, and rainfall intensity information during extreme rainstorms;

[0173] S2. Based on the local data collected in S1, construct disaster scenario simulation model, search and fault perception model, random maintenance time model, UAV-maintenance team collaborative scheduling model, communication restoration and switch control model, urban flooding development model, and operation constraint model.

[0174] In practice, the process of constructing a disaster scenario simulation model includes:

[0175] The study area was modeled as a triangular grid, and a high-dimensional rainfall matrix was created based on the acquired rainfall intensity information during extreme rainstorms. As shown in (1):

[0176]

[0177] in, This represents the rainfall information for point i in the triangular grid during time period t, including its Cartesian coordinates. and rainfall intensity ; Represents the triangular grid point set of the study area; Represents the temporal distribution set of extreme rainfall intensity;

[0178] remember , and They represent Time period coordinates The water depth and average vertical velocity in the x and y directions of the flood on the grid; water level height. b represents the terrain elevation; the two-dimensional shallow water equations are obtained as shown in (2)-(4);

[0179]

[0180]

[0181]

[0182] in, , , and These are vectors representing fluid variables, flow rate in the x-direction, flow rate in the y-direction, and source term, respectively. Represents gravitational acceleration; It is the runoff coefficient, which represents the proportion of rainfall that can reach the ground without being blocked by trees or buildings; and These represent the terrain slopes in the x and y directions, respectively. This indicates the intensity of excess rainfall, determined by rainfall intensity. Infiltration rate and evaporation rate calculate: ; and Let x and y represent the friction slopes respectively, and calculate them using Manning's formula as shown in (5):

[0183]

[0184] in, This represents the empirical Manning coefficient, reflecting the degree of terrain roughness.

[0185] The governing equations are solved using a semi-implicit finite volume method based on triangular mesh discretization; the integral form of equation (2) is obtained by applying Green's theorem as shown in (6):

[0186]

[0187] in, Indicates the control volume; Represents the boundary of the volume; This represents the unit normal vector perpendicular to the boundary and pointing outwards; and Represent the area element and the arc element respectively; Indicates the outward normal flow, where Discretizing formula (6) in a triangular mesh yields (7):

[0188]

[0189] in, This represents the average fluid variable vector of grid i. Represents the area of ​​grid i; This represents the flow vector on the k-th edge of grid i; and These represent the fluid variables on the left and right sides of the boundary, respectively. Indicates arc length; The unit normal vector perpendicular to the boundary and pointing outwards.

[0190] Source Item Divided into friction terms and bed slope item As shown in formula (4); assuming the terrain within the grid changes linearly, and The calculation formula is:

[0191]

[0192]

[0193] in, and Indicates the slope of grid i; , and subscript It is the vertex index of the triangular mesh that satisfies the counterclockwise direction;

[0194] Using the rotational invariance of the two-dimensional shallow water equation, the first term on the right-hand side of equation (7) is transformed into:

[0195]

[0196] in, , These are the rotation matrix and its inverse matrix, respectively; and They represent the unit normal vectors respectively. The components in the x and y directions; let ,have:

[0197]

[0198] in, and Let represent velocities perpendicular to and parallel to the boundary, respectively; formulas (10) and (11) introduce variables... The two-dimensional shallow water equations are transformed into a one-dimensional Riemann problem; the boundary flows are calculated using the HLLC approximate Riemann solution, as shown below:

[0199]

[0200]

[0201]

[0202] in, Calculated using formula (11); and These represent the flow rates on the left and right sides of the middle region of the Riemann solution, respectively. , and These represent the velocity estimates for the left wave, contact wave, and right wave at the grid boundary, respectively; where, and These represent the fastest speed at which the fluid propagates from the left and right sides of the boundary toward the middle, respectively, and represent the maximum potential contribution of the fluid on both sides to the flow rate at the boundary. It is the intermediate wave velocity of the fluid at the boundary, reflecting the physical characteristic of pressure discontinuity caused by the different fluid states on both sides of the boundary. and Indicates normal flow The first and second components;

[0203] , and Calculated using the following formula:

[0204]

[0205]

[0206]

[0207] in, and This represents the average quantity of Roy. , .

[0208] According to formula (7) and boundary normal flow , source item The calculation, through the time-progression formula, will... Time grid points Fluid variables updated to The time frame is used to simulate the spatiotemporal distribution of flood disasters, as shown in (18):

[0209]

[0210] In the formula, This represents the fluid variables in the nth time period of grid i.

[0211] The process of building a search and fault perception model includes:

[0212] Cyber-Physical Distribution Systems (CPDS) typically deploy both a Cyber ​​Network (CN) and a Physical Network (PN) in parallel, exhibiting topological consistency, such as... Figure 2 As shown, PN and CN are modeled as undirected graphs respectively. and Each electrical node maps to a network node. Extreme rainstorms cause communication facility failures, creating network blind spots. This leads to the failure of power distribution system (PDN) monitoring and fault information (FI) perception, making recovery decisions impossible. Affected lines are defined as cyber blind lines (CBLs), forming a set of blind lines. and in Figure 2 The middle part is marked in red.

[0213] Specifically, communication line or equipment failures create two sensing blind spots. For blind spot 1, due to the isolation of L6-7 faults, the control center cannot determine whether L7-8 and L8-9 have failed. For blind spot 2, the control center can determine and isolate L2-3 faults through power flow analysis, but cannot determine whether L3-4 and L4-5 have failed. Furthermore, the control center cannot assess the repair time required for blind spot line faults, such as L2-3. In summary, the incomplete information flow (FI) of CBLs introduces uncertainty regarding the fault state or extent of damage. Therefore, this method establishes a... The search and fault perception model.

[0214] The affected lines are defined as network blind zone lines (CBL), forming a blind zone line set. ; The lines in the system are isolated from the substation and communication is interrupted, meeting the following conditions:

[0215]

[0216]

[0217]

[0218] Among them, binary variables It is a line belong The flag bit, when set to 1, indicates that it belongs to binary variables and Representing network nodes Communication status and corresponding electrical nodes The isolation status is set to 1 if communication is connected or not isolated; a binary constant. , express The status of communication / power distribution lines between them is assumed to be zero for faults; it is assumed that the communication system between the substation and the command center is well protected and does not experience faults, satisfying the following conditions. ;

[0219] FI sensing methods capture the command center's activity during the recovery process. The evolution of perception capabilities. First, based on time-varying fault probabilities, multiple random damage scenarios are generated using the Monte Carlo method. This indicates the possible fault conditions and degree of damage; when the rainfall intensity exceeds the threshold, flashover of the insulator leads to insulation damage, while the mud and sand carried by the flood impacting the tower causes collapse; the fault probability is calculated as follows:

[0220]

[0221]

[0222] in, This indicates that during time period t, the line The probability of the kth insulator / tower experiencing a flashover / collapse fault; and These are the mean and standard deviation of the critical rainfall intensity; Indicates flow rate; This is the flood capacity threshold curve, which represents the relationship between the flow velocity and flood depth that leads to tower collapse; Indicates the line The rainfall intensity experienced by the k-th insulator during time period t; It represents the differential sign of rainfall intensity; Indicates the line The flood depth at the location of the kth tower.

[0223] The random damage scenario s generated by the Monte Carlo method divides the network blind zone lines (CBLs) into two sets: , and These respectively represent faulty lines in network dead zones and lines with potential faults; lines Upper The simulated damage state of an insulator / tower is defined as follows: The subscripts ij, s, and k represent the lines respectively. 1. Random damage scenario s; 2. The k-th recovery event.

[0224] Therefore, the simulated fault location and damage extent constitute a rough system FI (Fixed Insulation Data). Drones conduct aerial reconnaissance for flood control, establishing Emergency Communications (ECs) and transmitting real-time telemetry data. Their imaging capabilities enable precise identification of insulation faults and tower collapses. Based on this rough fault information, the command center formulates recovery strategies and deploys drone maintenance teams to conduct coordinated inspections of the CBL (Cybersecurity Blind Spot). Once the drones or maintenance teams have inspected the network blind spots... This allows us to obtain accurate FI and damage status. The collaborative integration of drone-assisted perception and recovery-oriented inspection optimizes damage detection and recovery efficiency.

[0225] The process of constructing a stochastic maintenance time model includes:

[0226] Based on the sensing-based FI, two approximations, a coarse approximation and a precise approximation, are constructed to estimate maintenance time. The coarse approximation uses a statistical method, based on the mean value of s. and variance To describe repair time; an accurate approximation is based on accurate FI processing, providing an accurate approximation of repair time by truncating the normal distribution, including the mean. ,variance The upper limit of exact approximation and lower limit Repair time estimates are used for both pessimistic and optimistic scenarios; based on these, the average of two approximate estimates is calculated as follows:

[0227]

[0228] in, / This represents the average repair time per unit for damaged insulators / towers, derived from historical maintenance team data; , They represent the lines respectively. The number of insulators and towers; , These represent the status of the insulator and the tower, respectively; the value is 1 if there is a fault.

[0229] Random repair time This is represented as having an ideal probability level. Opportunity constraints:

[0230]

[0231] in, It is the Cumulative Distribution Function (CDF); maintenance time The formulas for the rough approximation and the exact approximation are (26) and (27), respectively:

[0232]

[0233]

[0234]

[0235] in, and These are the CDF and inverse CDF of the standard normal distribution; κ, The parameter is introduced; Equation (26) is a deterministic substitution of (25), expressed by the Cantelli-Chebyshev inequality, applicable to any distribution with known mean and variance, avoiding the need for a specific distribution. Equation (27) is based on an exact approximation obtained by inverse convexification of both sides of (25).

[0236] Monte Carlo-based repair time estimates can become overly robust when coarsely sampling a large number of failure scenarios. This includes rare, large-scale component failures that may overestimate actual repair times. To address this, an additional chance constraint is introduced to limit robustness and minimize the probability of adverse events.

[0237]

[0238] in, Indicates the probability of an adverse situation occurring; Used to calculate random events The probability of [the probability]. Typically, evaluating the probability under joint chance constraints involves high-dimensional integrals without explicit form. Therefore, the Sample Average Approximation (SAA) is applied to [the probability of the probability]. Sampling is performed on each scene, and the frequency of scenes that satisfy the constraints is used to approximate the probability of the constraints being satisfied; the SAA of formula (29) is written as (30):

[0239]

[0240] in, ; It is a number greater than the preset value; when When, constraint (26) is satisfied in scenario s; when At that time, the constraint is relaxed by making the first formula in (30) redundant; the second formula in (30) limits the number of violations of the rough approximation to no more than .

[0241] The construction process of the drone-maintenance team collaborative scheduling model includes:

[0242] (1) Scheduling problem;

[0243] In the proposed framework, Mobile Recovery Resources (MRRs) consist of maintenance teams and drones. Maintenance teams repair faulty lines, while drones establish Emergency Recovery Centers (ECs) and inspect Common Line Baselines (CBLs) to obtain Initial Response Points (FIs). Given the dynamic nature of the recovery process, only a limited number of future actions are considered. Therefore, the scheduling model is based on a set of recovery events. To solve this, that is, to determine in each MPC step. A future event. Then,

[0244] use This refers to the coordination and scheduling problem between the maintenance team and the drones. If the first... Step in the first Each recovery event corresponds to the repair team. or drone At work If the value is 1, then the value is 1. (Superscript) , Let represent the maintenance team and the drone, respectively; the subscripts q and k represent the working point q and the k-th recovery event, respectively. For simplicity, the subscripts will not be repeated. Omitted. The scheduling model is constructed as follows:

[0245]

[0246] C and D represent a combination of maintenance teams and drones; Represents a collection of recovery events; and These represent the work sites of the maintenance team and the drones, respectively. , ; and These represent the sets of observable faulty lines and network blind spots, respectively. This represents the set of network blind spots, faulty lines, and potentially faulty lines. Let represent the set of faulty lines in the network dead zone; in equation (31), the first equation indicates that a faulty line can only be repaired once. The second equation indicates that inspections of CBFLs can only be performed before maintenance. The third equation stipulates that each CBFL must be inspected no more than once. The fourth equation restricts the assignment of only one task in each recovery event.

[0247] (2) Target path problem; In order to ensure that the MRR path follows the basic logic, by defining The path relationship between work points p and q is represented, and the target path problem is modeled as follows:

[0248]

[0249]

[0250]

[0251] Where the subscript 0 indicates the starting point; the first equation of constraint (32) represents and The relationship between the two equations is such that the second equation prevents the path from being at the same work point; constraint (33) indicates that only when the maintenance team or the drone arrives... Then arrive at the work site hour, Talent is 1;

[0252] (3) Time schedule problem; First, determine the completion time of step k. The model is as follows:

[0253]

[0254] in, and The completion times for the incidents involving the repair team and the drone are respectively. Indicates the start time of the step;

[0255] The maintenance time is given by formulas (27) and (30). ; It consists of three terms in formula (36): 1) the past time before reaching q. 2) Maintenance time; 3) Time required for inspection q ;

[0256]

[0257]

[0258] in, This represents the travel time required for the maintenance team to travel from work point p to work point q; This indicates the line inspection time. In formula (37), the first equation represents the time during which the line is inspected. hour The second equation indicates that drones can replace maintenance teams in performing line inspection tasks, reducing the need for maintenance teams to search for line faults in blind spots. Furthermore, maintenance teams do not need to conduct inspections when repairing lines with significant faults.

[0259] Drone line inspection completion time and the time required to restore communication functionality as follows:

[0260]

[0261]

[0262] in, Indicates the dwell time of the drone; This represents the travel time of the drone. In emergency communications, the network service time of the drone is usually in the range of milliseconds to seconds, which is ignored in formula (38). Unlike the maintenance process, formula (27) indicates that the drone can hover to provide continuous emergency communications for critical network nodes.

[0263] (4) Travel time issues;

[0264] To ensure optimal paths for scheduling MRRs during floods, this problem is modeled. This invention models the Transportation Network (TN) as an undirected graph. ,in and Let represent traffic nodes and edge sets, respectively. In formula (40), a dynamic adjacency traffic time matrix is ​​proposed. To reflect Dynamic changes in indirect connectivity and corresponding travel time As shown in formula (40); this matrix is ​​used to improve the performance of the Floyd algorithm in calculating traffic time in the Honglai scenario.

[0265]

[0266]

[0267] in, Indicates passing through the edge Minimum travel time;

[0268] Modeling is considered for expressways, arterial roads, and secondary roads; the depth destruction function in formula (43) models the mesh for each road type. Medium speed limit With the depth of waterlogging The relationship; accordingly, The calculation is as shown in formula (42):

[0269]

[0270]

[0271] in, , and These are parameters related to road type; Represents a grid Middle The length. Formula (42) indicates that when the depth of waterlogging exceeds a threshold ( When, on the side Unable to pass ( Then, the minimum travel time between any two work points is determined using the Floyd algorithm. And the corresponding route, where the unreachable fault point j satisfies .

[0272] Then, the minimum travel time between any two work points is determined using the Floyd algorithm. And the corresponding route, where the unreachable fault point j satisfies ;

[0273] Ignoring factors such as flight altitude and energy consumption, we assume that the drone's flight speed is constant. The flight time of the UAV is determined by the nearest neighbor path selection principle. The Euclidean distance between any two working points divided by .

[0274] The process of constructing the communication recovery and switching control model includes:

[0275] The worst-case scenario is defined as communication recovery relying entirely on EC provided by the UAV, as shown in Equation (47), where all maintenance resources are allocated to PN fault repair to improve load recovery efficiency; this situation typically occurs after extreme disasters severely damage both PN and CN. Therefore, the communication recovery constraints are as follows:

[0276]

[0277]

[0278]

[0279]

[0280] in, Indicates whether the communication function of node i has been restored by drone d; This represents the straight-line distance from node i to the center of EC; The coordinates of the EC center; This indicates the communication status of node i; r represents the preset distance threshold. This is a preset network node threshold.

[0281] In formula (44), the first equation indicates that the drone can only restore the functionality of network nodes within the EC coverage area; the second equation indicates that one drone is needed to restore the functionality of a network node, and one drone can restore the functionality of a maximum of [number missing]. Network nodes. Formula (46) indicates that the EC center and the UAV are located at the same position. When When, the coordinates are updated to the working position of q; when At that time, the coordinates remain unchanged.

[0282] In CPDS, both communication status and physical faults affect switching control; observable and controllable distributed generators (DGs) restore critical loads in fault-free areas through unplanned islanding, while DGs with communication interruptions rely on planned islanding operation by the local controller; planned islanding of distributed generators (DGs) divides the PN into internal lines. Boundary lines and external lines The control service model is as follows:

[0283]

[0284]

[0285]

[0286] in, Indicates the line The on / off state; DG Network status; A collection representing intact lines; This represents the set of potentially faulty lines. In formula (48), the first equation represents the situation when DG communication is interrupted. Disconnect; the second equation represents It can be corresponding DG The local controller controls the system. In equation (49), the first equation allows for free control. The second equation requires an inspection of PFLs before closure; the third equation requires a complete repair of the faulty line before closure. Equation (50) indicates that... The switching state of the internal CBLs can only be changed when communication is normal or when the RCs are manually operated.

[0287] The process of constructing an urban flooding development model includes:

[0288] Flooding inundates roads and power facilities, disrupts the dispatch routes of MRRs (Medium- and Long-Term Responsible Responses), and reduces the recoverable load capacity of affected areas. To quantify the adverse effects of flooding on recovery, this invention models the dynamic spatiotemporal evolution of flooding.

[0289] Based on the principle of water balance, the dynamic process of flood dynamics in time and space is represented by mathematical formula (51), where the total drainage volume is the sum of pump drainage volume, infiltration volume, and evaporation volume; the waterlogged area Net infiltration rate Evaporation rate Calculated using formula (52);

[0290]

[0291]

[0292] in, and The flooded areas The water pumps and grid assembly in the middle; This indicates the average decrease in water depth. The time interval between events; For water pumps The drainage rate; Represents a grid The dry and wet state; C is the drainage rate of underground pipelines; C is an empirical coefficient. and These represent the saturated vapor pressure and the actual vapor pressure, respectively. Wind speed; Represents thermodynamic temperature;

[0293] Water pump power With drainage rate The relationship is shown in (53);

[0294]

[0295]

[0296] in, The density of water; For still water lift; For water pump efficiency; Indicates power status; and These represent the upper and lower limits of the water pump power, respectively.

[0297] The process of building a constraint model includes:

[0298] In practice, the command center will proactively cut off power to severely flooded areas to prevent electrical hazards (such as leakage or short circuits). Define the recovery coefficient. The proportion of recoverable load in quantized zn is determined by the average unit load density of grid m or region zn. and security depth threshold Control measures are implemented to ensure that areas with water depths below this threshold can be restored; recovery coefficient. The calculation formula is:

[0299]

[0300] For each recovery event, possible system state transitions are controlled by formulas (56)-(58); formulas (56) and (57) are the power flow equations of the linearized DistFlow model, used to calculate line power flow and voltage magnitude. The line power flow and voltage magnitude limits in formula (58) ensure the safety of the system.

[0301]

[0302]

[0303]

[0304] in, and They are nodes or region Active and reactive loads at the location; and They represent the lines respectively. The active and reactive power flows on the surface; in formula (56), nodes o and j represent the upstream and downstream nodes of i, respectively; and These represent the active power generation and reactive power generation of the DG or substation at point i, respectively. This represents the square of the voltage value at point i; and They are respectively Resistance and reactance; To pass Maximum permissible apparent power; and These represent the upper and lower limits of the square node voltage amplitude, respectively;

[0305] During the recovery process, the faulty line and PFLs are isolated, the command center reconstructs the PN, and the load in the fault-free area is restored. To maintain the radial topology, a single-commodity flow method is used, as shown below:

[0306]

[0307] in, Indicates the root node; Indicates the line The connected state; Represents the flow of virtual goods; It is a number greater than the preset large value. In formula (59), the first equation designates the substation as the root node, and the DG and the isolated line endpoints as candidate root nodes; the second equation is based on the root node through... The first equation relaxes the flow balance while imposing a single net inflow constraint elsewhere; the second equation restricts the virtual flow to only through closed loops; and the third equation sets the number of closed loops to the total number of nodes minus the number of root nodes.

[0308] S3. Using the models constructed in S2 (Equations (1)-(59)) as constraints, and taking the maximization of the recovery of weighted load energy, the reduction of drainage costs, and the improvement of fault information FI perception efficiency as objective functions, a dynamic damage perception collaborative recovery model for distribution network to cope with flood disasters under the condition of missing fault information is established.

[0309] In practical implementation, the objective function is:

[0310]

[0311] in, Let be the weight coefficient of node i; This is a conservative estimate of the recovery time; denoted as energy cost per drainage pump; r is the reward factor perceived by FI. This represents the time interval between the completion of perception and the termination of the model predictive control step. N represents the completion time of event k; D Let represent the set of distribution network nodes. In (60), c and r are assigned sufficiently small values ​​to prioritize load recovery. Meanwhile, the third term emphasizes the importance of minimizing completion time when the number of precisely sensed FIs remains constant.

[0312] S4. Considering the dynamic characteristics of the recovery process, an event-driven rolling optimization framework is established based on the dynamic damage perception collaborative recovery model, and the solution is obtained to obtain the power supply recovery strategy.

[0313] This invention considers the impact of large-scale communication facility failures and secondary disasters following extreme weather events. It proposes a dynamic damage perception and collaborative recovery method for distribution networks responding to floods under conditions of missing fault information. This addresses the problem that traditional recovery methods are unusable due to operators' inability to quickly obtain fault information from disaster-stricken areas caused by communication interruptions. Furthermore, it models the development and impact of urban flooding to improve the performance of the recovery method in responding to extreme rainstorm disasters and accelerate the recovery process.

[0314] Extreme disasters can cause large-scale communication facility failures, leading to a lack of distribution network fault information. Addressing the issue that most existing recovery methods fail under such conditions, this invention establishes a two-stage fault information perception and stochastic maintenance time model to support operators' recovery decisions. Furthermore, this invention establishes an improved Floyd algorithm adapted to the dynamic development of urban flooding and a load recovery influencing factor model to quantify the long-term dynamic impact of floods on the distribution network recovery process, providing a model reference for power grid operation and maintenance during torrential rain and flood disasters.

[0315] When a power distribution network encounters floods or physical or communication networks suffer large-scale failures due to extreme disasters, this invention can take into account the dynamic impact of floods even when fault information is missing, effectively reducing the time required for power restoration and the cost of power outages.

[0316] Example 2

[0317] To better illustrate the effectiveness of this method, the following example is provided.

[0318] This example uses a CPDS system in a specific city to verify the effectiveness of this method. Figure 3 As shown, the CPDS covers an area of ​​20×20km, with terrain data resolution of 30m. The city's TN model includes three road types with corresponding depth damage function parameters: expressways are set to 0.0008, -0.5070, and 80; arterial roads are set to 0.0005, -0.3459, and 60; and secondary roads are set to 0.0002, -0.1848, and 40. It is assumed that maintenance teams move at road speed limits. The PDN uses a modified IEEE 33-node test system with a base voltage of 12.66kV and a base power of 10MW. The voltage limit is [0.9-1.1]pu, and the total load requirement is 3.715MW + 2.30Mvar. The weighting coefficients for critical load and normal load are set to 10 and 1, respectively. The test system consists of a warehouse, a substation, and three DGs. The warehouse is equipped with two maintenance teams and two UAVs. The EC radius of the UAVs is 500 meters. Each DG has a rated capacity of 400kW + 2.45kvar, assuming its planned islanding is located at its respective node. PN and CN use the same topology, and virtual nodes in TN represent the geographical locations of CBLs or points of failure.

[0319] To simulate the impact of extreme rainstorms and floods on CPDS, we assume network infrastructure failures and divide the system into three network blind zones (I, II, and III) using the search method proposed in this paper. The command center has precise FI (Fixed Information Function) for six physical lines: D3-4, D7-8, D9-10, D1-18, D2-22, and D26-27, whose locations are... Figure 3 The damage is marked with a red circle. The actual extent of damage to the physical lines is shown in Table 1. It is worth noting that the FI (Fixed Indicator) of CBLs is unavailable before the inspection. Assume the average repair time for insulators and towers is 0.2 hours and 0.3 hours, respectively. The variances of the rough and precise approximations are 15% and 10%, respectively. The ideal confidence level for the chance constraint of random repair time is... Set to 0.5. Parameters in the Joint Probability Constraint (SAA). Set to 0.4, the number of damage scenarios generated. Set it to 100.

[0320] Table 1 Actual damage level of the faulty circuit

[0321]

[0322] To prevent damage to power facilities from prolonged flooding, loads in flood-prone areas are considered critical loads. The Manning coefficient is set to... Pump model parameters Set to 1060kW, 0kW, 85%, 7m Since urban groundwater drainage data was unavailable, the groundwater volume was assumed to be equivalent to the post-disaster rainwater accumulation in low-lying areas. Infiltration and evaporation effects were ignored. To reflect different insulator contamination levels and tower aging conditions, the 50% breakdown voltage and flood capacity thresholds were randomly adjusted. All simulations were performed in GUROBI.

[0323] Four comparative schemes were implemented to evaluate the effectiveness of the proposed recovery strategy: 1) Scheme 1, the recovery strategy of this invention, deploys water pumps in flooded areas where the fault point is inaccessible due to road flooding and where the initial recovery coefficient is low; 2) Scheme 2, also the recovery strategy of this invention, deploys water pumps only in flooded areas with low initial recovery coefficients; 3) Scheme 3, a conventional recovery strategy, employs a parallel damage assessment-repair method under incomplete FI, combined with open-loop dynamic FI sensing and decision updates; 4) Scheme 4, after obtaining complete FI, coordinates maintenance teams to simultaneously repair PN and CN faults, representing conventional network-physical collaborative recovery. The results of the four schemes are as follows:

[0324] Table 2. Route and timetable for resource recovery in Option 1

[0325]

[0326] Figure 4 and Figure 5 The weighted load recovery and cumulative weighted load loss energy under schemes 1-4 are presented. Table 2 shows the routes and completion times of the maintenance team and drones in scheme 1. Scheme 1 achieved 99.06% weighted load recovery without verifying the actual damage extent of network blind zone lines D30-31, D13-14, and D14-15. This confirms the performance of the present invention, minimizing time-sensitive recovery costs by avoiding redundant FI sensing in emergency situations.

[0327] In Option 2, the maintenance paths for maintenance team 1 are D20-21, D7-8, D1-18, and D13-14; for maintenance team 2, they are D26-27, D3-4, D19-20, D9-10, D16-17, and D14-15. The path for drone 1 is D31-32, C17, D16-17, D15-16, C15, D19-20, C15, C20, and C15; and for drone 2, it is D20-21 and C31. Because accessibility limitations caused by flooding were ignored and water pumps were not deployed, Option 2 could not repair D2-22, achieving only 94.62% weighted load recovery within 403 minutes, and a cumulative weighted load loss of 16.39 at 420 minutes. In comparison, Scheme 1 achieved 99.06% weighted load recovery within 234 minutes, representing a 5.8% improvement in load recovery and a 41.94% reduction in recovery time. Within 420 minutes, Scheme 1 reduced the cumulative weighted load loss energy to 14.93, a 9.45% reduction compared to Scheme 2. These performance differences underscore the necessity of modeling accessibility to flood-induced faults, demonstrating the advantages of the proposed method in reducing recovery delays and cumulative energy losses compared to methods that ignore accessibility dynamics.

[0328] Option 3, which involves parallel scheduling of inspection and maintenance teams, restores the weighted load for all faults except for the flood-blocked D2-22 fault within 412 minutes, but accumulates 20.3 units of weighted load loss energy within 420 minutes. In contrast, Option 1 improves the weighted load restoration efficiency by 6.32%, reduces time costs by 43.2%, and lowers the cumulative weighted load loss energy by 35.95%, demonstrating higher restoration efficiency.

[0329] Option 4 completes blind spot line checks within 98 minutes, implementing a globally optimized recovery strategy based on full FI, while considering the interdependence between CN and PN. Option 4 achieves 94.65% weighted load recovery within 396 minutes after dispatching the maintenance team, improving weighted load recovery by 2.06% and reducing time by 16 minutes compared to Option 3 through global network-physical collaborative optimization. However, in large-scale CN-PN damage scenarios, Option 4's joint network and physical fault repair strategy suffers reduced efficiency due to competition for limited maintenance resources, and its neglect of flooding effects further limits its practical applicability. Compared to Option 1, where UAVs provide temporary EC to restore network functionality while the maintenance team focuses on PN repair, Option 4's weighted load recovery is reduced by 4.41%, but the time taken is extended by 69.23%, despite relying on full FI. Furthermore, the additional FI sensing time results in a cumulative weighted load loss energy of 38.27 within 420 minutes, which is 156.31%, 133.55%, and 88.53% higher than Options 1, 2, and 3, respectively.

[0330] Therefore, the closed-loop sensing-recovery collaborative optimization method for distribution networks under incomplete FI proposed in this invention can not only reduce the load loss penalty during the power supply restoration process and improve the restoration efficiency, but also alleviate the severity of urban flooding disasters.

[0331] 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 the technical solutions. Those skilled in the art should understand that any modifications or equivalent substitutions to the technical solutions of the present invention without departing from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. A method for dynamic damage sensing and collaborative recovery of power distribution networks in response to flood disasters, characterized in that, Includes the following steps: S1. Obtain local data for the target area; the local data includes electrical and structural parameters of the information-physical distribution system, topographic and transportation network data of the area where the distribution network is located, and rainfall intensity information during extreme rainstorms; S2. Based on the local data collected in S1, construct disaster scenario simulation model, search and fault perception model, random maintenance time model, UAV-maintenance team collaborative scheduling model, communication restoration and switch control model, urban flooding development model, and operation constraint model. Among them, the disaster scenario simulation model is used to simulate the spatiotemporal distribution of flood disasters; the search and fault perception model is used to describe the set of lines belonging to blind spots; the stochastic maintenance time model is used to estimate the maintenance time of fault scenarios; the UAV-maintenance team collaborative scheduling model is used to simulate the collaborative scheduling of UAVs and maintenance teams; the communication restoration and switch control model is used to describe communication restoration constraints and control service constraints; the urban flooding development model is used to simulate the dynamic spatiotemporal development process of floods; and the operation constraint model is used to describe the distribution network operation constraints during the restoration process. S3. Using the models constructed in S2 as constraints, and taking the maximization of weighted load energy recovery, reduction of drainage costs, and improvement of fault information FI perception efficiency as objective functions, a dynamic damage perception collaborative recovery model for distribution network to cope with flood disasters under the condition of missing fault information is established. S4. Considering the dynamic characteristics of the recovery process, an event-driven rolling optimization framework is established based on the dynamic damage perception collaborative recovery model, and the solution is obtained to obtain the power supply recovery strategy.

2. The dynamic damage perception and collaborative recovery method for power distribution networks in response to flood disasters as described in claim 1, characterized in that: The process of constructing a disaster scenario simulation model includes: The study area was modeled as a triangular grid, and a high-dimensional rainfall matrix was created based on the acquired rainfall intensity information during extreme rainstorms. As shown in (1): Among them, R i,t This represents the rainfall information for point i in the triangular grid during time period t, including its Cartesian coordinate x. i ,y i and rainfall intensity R i,t ; Represents the triangular grid point set of the study area; Represents the temporal distribution set of extreme rainfall intensity; Let h(x,y,t), u(x,y,t) and v(x,y,t) represent the water depth of the flood and the average vertical velocity in the x and y directions on the grid of coordinates (x,y) during time period t, respectively; water level height η = h + b, where b represents the topographic elevation; the two-dimensional shallow water equations are shown in (2)-(4); Where U, E, G, and S represent the fluid variables, the flow rate in the x-direction, the flow rate in the y-direction, and the source term vector, respectively; g represents gravitational acceleration; c r R is the runoff coefficient, representing the proportion of rainfall that reaches the ground without being blocked by trees or buildings; α and β represent the terrain slope in the x and y directions, respectively; ex The excess rainfall intensity is represented by rainfall intensity R and infiltration rate K. inf and evaporation rate K eva Calculate: R ex =R-(K) inf +K eva );S fx and S fy Let x and y represent the friction slopes in the x and y directions, respectively, and calculate them using Manning's formula as shown in (5): Where n represents the empirical Manning coefficient, which reflects the roughness of the terrain; The governing equations are solved using a semi-implicit finite volume method based on triangular mesh discretization; the integral form of equation (2) is obtained by applying Green's theorem as shown in (6): Where Ω represents the control volume; The boundary represents the volume; n represents the unit normal vector perpendicular to the boundary outwards; dΩ and dl represent the area element and arc element, respectively; F·n represents the outward normal flux, where F=[E,G] T Discretizing formula (6) in a triangular mesh yields (7): Among them, U i Ω represents the average fluid variable vector of grid i. i F represents the area of ​​grid i; i,k (U L U R U represents the flow vector on the k-th edge of grid i; L and U R L represents the fluid variables on the left and right sides of the boundary, respectively. i,k Indicates arc length; n i,k This represents the unit normal vector perpendicular to the boundary and pointing outwards; Source Item S i Divided into friction term S i,f and bed slope item As shown in formula (4); assuming the terrain within the grid changes linearly, S i,0x and S i,0y The calculation formula is: S i,(0x / 0y) =-∫ i g(h i +b i )(a i / b i )dΩ=-g(h i +b i )(a i / b i )Oh i (8) Where, α i and β i Indicates the slope of grid i; x i,k y i,k and b i,k The index k is the vertex index of the triangle mesh that satisfies the counterclockwise direction; Using the rotational invariance of the two-dimensional shallow water equation, the first term on the right-hand side of equation (7) is transformed into: Among them, T n , These are the rotation matrix and its inverse matrix, respectively; n x and n y Let represent the components of the unit normal vector n in the x and y directions, respectively; let have: Among them, u ⊥ and u / / Let represent velocities perpendicular to and parallel to the boundary, respectively; formulas (10) and (11) introduce variables... The two-dimensional shallow water equations are transformed into a one-dimensional Riemann problem; the boundary flows are calculated using the HLLC approximate Riemann solution, as shown below: Among them, F L / R =F(U L / R )·n is calculated by formula (11); F *L and F *R s1, s2, and s3 represent the flow rates on the left and right sides of the middle region of the Riemann solution, respectively; s1, s2, and s3 represent the velocity estimates of the left wave, contact wave, and right wave at the grid boundary, respectively; where s1 and s3 are the fastest propagation speeds of the fluid from the left and right sides of the boundary towards the middle, representing the maximum potential contribution of the fluid on both sides to the flow rate at the boundary; s2 is the middle wave velocity of the fluid at the boundary, reflecting the physical characteristic of pressure discontinuity caused by the different fluid states on both sides of the boundary; (E HLL ) 1 and (E) HLL ) 2 Indicates normal flow rate E HLL The first and second components; According to formula (7) and boundary normal flow F(U) L U R )·n、Source Term S i The calculation updates the fluid variables of grid point i at time t to time t+Δt using the time-progression formula, thereby simulating the spatiotemporal distribution of flood disasters, as shown in (18): In the formula, This represents the fluid variables in the nth time period of grid i.

3. The dynamic damage perception and collaborative recovery method for power distribution networks in response to flood disasters as described in claim 2, characterized in that: s1, s2, and s3 are calculated using the following formulas: Among them, h * and u ⊥,* This represents the average quantity of Roy.

4. The dynamic damage perception and collaborative recovery method for power distribution networks in response to flood disasters as described in claim 3, characterized in that: The process of building a search and fault perception model includes: The communication network PN and the physical network CN are modeled as undirected graphs G(N). d ,L d ) and G(N c ,L c Each electrical node is mapped to a network node; The affected lines are defined as network blind zone lines CBL, forming a blind zone line set ε. cb ;ε cb The lines in the system are isolated from the substation and communication is interrupted, meeting the following conditions: f ij,ui =(1-c i )∧(1-d j ) (19) Wherein, binary variable f ij,cb The line (i,j) belongs to ε cb The flag bit, when set to 1, indicates that it belongs to ε. cb binary variable c j and d j These represent the communication state of network node j and the isolation state of the corresponding electrical node j, respectively. If communication is connected or there is no isolation, the value is 1; the binary constant u ij,c u ij,d This represents the communication / power distribution line status between i and j, with a fault value of 0; it is assumed that the communication system between the substation and the command center is well protected and does not experience faults, satisfying c. cen,k =1; Based on time-varying failure probabilities, multiple random failure scenarios s∈S are generated using the Monte Carlo method. dam This indicates the possible fault conditions and degree of damage; when the rainfall intensity exceeds the threshold, flashover of the insulator leads to insulation damage, while the mud and sand carried by the flood impacting the tower causes collapse; the fault probability is calculated as follows: in, This represents the probability that the k-th insulator / tower of line (i,j) will experience a flashover / collapse fault during time period t. and V represents the mean and standard deviation of the critical rainfall intensity; ij,k,t The flow velocity is represented by f(·), which is the flood capacity threshold curve, indicating the relationship between the flow velocity leading to tower collapse and the flood depth; R ij,k,t dR represents the rainfall intensity experienced by the k-th insulator of line (i,j) during time period t; dR is the differential symbol for the rainfall intensity; h ij,k,t The flood depth is indicated at the location of the k-th tower of line (i,j); The random damage scenario s generated by the Monte Carlo method divides the network blind zone lines (CBLs) into two sets: and These represent faulty lines in the network blind zone and potentially faulty lines, respectively; the simulated damage state of the k-th insulator / tower on line (i,j) is defined as... The subscripts ij, s, and k represent the line (i,j), the random damage scenario s, and the k-th recovery event, respectively.

5. The dynamic damage perception and collaborative recovery method for power distribution networks in response to flood disasters as described in claim 4, characterized in that: The process of constructing a stochastic maintenance time model includes: Two approximations, a coarse approximation and a precise approximation, are constructed to estimate maintenance time. The coarse approximation uses a statistical method, based on the mean value of s. and variance To describe repair time; an accurate approximation is based on accurate FI processing, providing an accurate approximation of repair time by truncating the normal distribution, including the mean. variance Upper limit of exact approximation and lower limit Repair time estimates are used for both pessimistic and optimistic scenarios; based on these, the average of two approximate estimates is calculated as follows: in, This represents the average repair time per unit for damaged insulators / towers, derived from historical maintenance team data; These represent the number of insulators and towers on line (i,j), respectively. These represent the status of the insulator and the tower, respectively; a value of 1 indicates a fault. Random repair time This is represented as having an ideal probability level. Opportunity constraints: Where F(·) is the cumulative distribution function CDF; maintenance time The formulas for the rough approximation and the exact approximation are (26) and (27), respectively: Where Φ(·) and Φ -1 (·) represents the CDF and inverse CDF of the standard normal distribution; κ, α 1 / 2 These are the introduced parameters; An additional chance constraint is introduced to limit robustness, minimizing the probability of adverse situations; Where ∈ represents the probability of an unfavorable situation; Used to calculate the probability of random event E; The sample mean approximation SAA is applied by sampling |S| scenarios and using the frequency of scenarios that satisfy the constraints to approximate the probability of the constraints being satisfied; the SAA of formula (29) is written as (30): Among them, z s ∈{0,1}; M1 is a number greater than a preset value; when z s When z = 0, constraint (26) is satisfied in scenario s; when z = 0, constraint (26) is satisfied in scenario s; s When =1, the constraint is relaxed by making the first formula in (30) redundant; the second formula in (30) limits the number of cases that violate the rough approximation to no more than ∈*|S|.

6. The dynamic damage perception and collaborative recovery method for power distribution networks in response to flood disasters as described in claim 5, characterized in that: The construction process of the drone-maintenance team collaborative scheduling model includes: (1) Scheduling problem; using This refers to the coordination and scheduling problem between the maintenance team and the drones. If the first... If the k-th recovery event in the step corresponds to maintenance team c or drone d at work point q, then the value is 1; the superscripts c and d represent maintenance team and drone respectively; the subscripts q and k represent work point q and the k-th recovery event respectively. The scheduling model is constructed as follows: Where C and D represent the sets of repair teams and drones; K represents the set of recovery events; N R and N A These represent the work sites of the maintenance team and the drones, respectively. N A ={ε cb ,ε com };ε F and ε com Let ε represent the sets of observable faulty lines and network blind spots, respectively; cb This represents the set of network blind spots, faulty lines, and potentially faulty lines. This represents a set of faulty lines in network dead zones. (2) Target path problem; defined The path relationship between work points p and q is represented, and the target path problem is modeled as follows: Where the subscript 0 indicates the starting point; the first equation of constraint (32) represents and The second equation prevents paths from being at the same work point; constraint (33) means that the path will only be valid if the maintenance team or the drone reaches work point q after reaching p. Talent is 1; (3) Time schedule problem; First, determine the completion time of step k. The model is as follows: in, and The event completion times for the repair team and the drone, respectively; t start Indicates the start time of the step; The maintenance time is given by formulas (27) and (30). It consists of three terms in formula (36): 1) the past time before reaching q. 2) Maintenance time; 3) Time required for inspection q in, t represents the travel time required for the maintenance team to travel from work point p to work point q; ass Indicates the time for line inspection; Drone line inspection completion time and the time required to restore communication functionality as follows: in, Indicates the dwell time of the drone; Indicates the travel time for the drone; (4) Traffic time problem; model the traffic network TN as an undirected graph G = (N T ,L T ), where N T and L T Represent traffic nodes and edge sets, respectively; A dynamic adjacency traffic time matrix is ​​proposed. To reflect N T Dynamic changes in indirect connectivity and corresponding travel time As shown in formula (40); this matrix is ​​used to improve the performance of the Floyd algorithm in calculating traffic time in the Honglai scenario; in, This represents the minimum travel time through edge (i,j); Modeling is performed considering expressways, arterial roads, and secondary roads; the depth destruction function in formula (43) models the speed limit in grid m for each road type. With the depth of waterlogging h m The relationship; accordingly, The calculation is as shown in formula (42): Where a, b, and c are parameters related to road type; l m,ij This represents the length of edge (i,j) in grid m; Then, the minimum travel time between any two work points is determined using the Floyd algorithm. And the corresponding route, where the unreachable fault point j satisfies Ignoring factors such as flight altitude and energy consumption, we assume that the drone's flight speed is a constant V. d The flight time of the UAV is determined by the nearest neighbor path selection principle. The Euclidean distance between any two working points divided by V d .

7. The dynamic damage perception and collaborative recovery method for power distribution networks in response to flood disasters as described in claim 6, characterized in that: The process of constructing the communication recovery and switching control model includes: The worst-case scenario is defined as communication recovery relying entirely on EC provided by the UAV, as shown in Equation (47). All maintenance resources are allocated to PN fault repair to improve load recovery efficiency. The communication recovery constraints are as follows: in, Indicates whether the communication function of node i has been restored by drone d; This represents the straight-line distance from node i to the center of EC; The coordinates of the EC center; v i,k This indicates the communication status of node i; r represents the preset distance threshold. The preset network node threshold; In CPDS, both communication status and physical faults affect switching control; observable and controllable distributed generation (DGs) restores critical loads in fault-free areas through unplanned islanding, while DGs with communication interruptions rely on planned islanding operation by the local controller; planned islanding of DGs divides the PN into internal lines. Boundary Line and external lines The control service model is as follows: Among them, s ij,k ∈{0,1} represents the switching state of line (i,j); v g,k Indicates the network state of DGg; ε I A collection representing intact lines; This represents the set of potentially faulty lines.

8. The dynamic damage perception and collaborative recovery method for power distribution networks in response to flood disasters as described in claim 7, characterized in that: The process of constructing an urban flooding development model includes: Based on the principle of water balance, the dynamic process of flood dynamics in time and space is represented by mathematical formula (51), where the total drainage volume is the sum of pump drainage volume, infiltration volume, and evaporation volume; the waterlogged area Net infiltration rate Evaporation rate Calculated using formula (52); Where, ζ zn and N zn These represent the sets of water pumps and grids in the flooded area zn, respectively; Δh zn,k This represents the average decrease in water depth; Δt is the time interval between events. Let n be the drainage rate of pump n; Indicates the wet / dry state of grid i; C is the drainage rate of underground pipelines; C is an empirical coefficient. and These represent the saturated vapor pressure and the actual vapor pressure, respectively. Wind speed; T em Represents thermodynamic temperature; Water pump power With drainage rate The relationship is shown in (53); Where ρ is the density of water; For still water lift; For pump efficiency; ω n,k ∈{0,1} represents the power state; and These represent the upper and lower limits of the water pump power, respectively.

9. The dynamic damage perception and collaborative recovery method for power distribution networks in response to flood disasters as described in claim 8, characterized in that: The process of building a constraint model includes: Define the coefficient of recovery The proportion of recoverable load in quantized zn is determined by the average unit load density Ld of grid m or region zn. m / zn and security depth threshold Control measures are implemented to ensure that areas with water depths below this threshold can be restored; recovery coefficient. The calculation formula is: For each recovery event, possible system state transitions are controlled by formulas (56)-(58); in, and Let p represent the active and reactive loads at node i or region zn∈i, respectively; ij,k and q ij,k Let i and j represent the active and reactive power flows on line (i,j), respectively; in formula (56), node o and node j represent the upstream and downstream nodes of i, respectively. and These represent the active power generation and reactive power generation of the DG or substation at point i, respectively. R represents the square of the voltage at point i; ij and X ij The resistance and reactance of (i,j) are respectively; F ij,max The maximum apparent power allowed through (i,j); and These represent the upper and lower limits of the square node voltage amplitude, respectively; During the recovery process, the faulty line and PFLs are isolated, the command center reconstructs the PN, and the load in the fault-free area is restored. To maintain the radial topology, a single-commodity flow method is used, as shown below: Among them, κ i,k ∈{0,1} represents the root node; Indicates the connectivity state of line (i,j); f ij,k This represents the flow of virtual goods; M2 is a number greater than a preset large value.

10. The dynamic damage perception and collaborative recovery method for power distribution networks in response to flood disasters as described in claim 9, characterized in that: In S3, the objective function is: Where, λ i T represents the weight coefficient of node i; end This is a conservative estimate of the recovery time; c is the energy cost per drainage pump; r is the reward factor for FI perception. This represents the time interval between the completion of perception and the termination of the model predictive control step. N represents the completion time of event k; D This represents the set of distribution network nodes.

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