Delay optimization system and method based on unmanned aerial vehicle-truck joint emergency communication

Abstract

The application provides a delay optimization system and method based on unmanned aerial vehicle-truck joint emergency communication. The system comprises a coupling modeling module, a scenario generation module, a two-stage robust optimization module and a solving module. The method uses the coupling modeling module to construct a power distribution network fault model, an air-ground mobile communication network model and a communication delay model, uses the scenario generation module to generate a typical scenario set of wind and light output uncertainty, uses the two-stage robust optimization module to establish an optimization model with the minimum whole-cycle communication delay as the target, optimizes node deployment and link pre-configuration in the pre-disaster stage, dynamically schedules truck and unmanned aerial vehicle cooperative communication in the disaster stage, and uses the solving module to decompose and solve the deployment and scheduling scheme. The application couples power failure and communication delay, constructs an air-ground integrated emergency communication network and adopts two-stage robust optimization, thereby reducing end-to-end communication delay under extreme weather, which helps to improve the real-time performance and resilience of power distribution network emergency communication.

Description

Technical Field

[0001] This invention relates to the field of Cyber-Physical System (CPS) and emergency communication network technology, specifically to a delay optimization system and method based on UAV-truck joint emergency communication. Background Technology

[0002] Frequent extreme weather events (such as typhoons, hail, and blizzards) can easily cause large-scale power outages in power distribution networks, while also damaging ground communication base stations, fiber optic cables, and other infrastructure. This results in severe delays or even interruptions in the monitoring, control, and dispatch data transmission within the power information physical system (CPS), seriously threatening the real-time performance and emergency response capabilities of CPS. Traditional emergency communication methods mainly rely on the temporary deployment of communication vehicles after a disaster for single-point deployment. However, when roads are blocked, these vehicles cannot quickly reach blind spots. While drones can fill in gaps in the air, they are mostly deployed temporarily after a disaster, lacking pre-configuration and air-ground coordination mechanisms, leading to fragile communication topologies, unstable links, and high end-to-end latency. Furthermore, drones have limited endurance and are difficult to resupply; deploying them alone can easily result in coverage gaps, making it impossible to form a continuous and stable emergency communication support network.

[0003] Existing research largely focuses on the dynamic scheduling of communication resources after disasters, neglecting the value of preventative deployment before disasters. This leads to a significant lag in communication resource allocation after a disaster, making it difficult to meet the urgent needs of power CPS for low-latency, high-reliability communication in a timely manner. Furthermore, emergency power delivery and communication capability enhancement are often handled separately, failing to unify the planning and resource integration of mobile communication nodes for trucks (as ground mobile communication hubs) and drones (as aerial mobile relays / temporary base stations), resulting in equipment and functional redundancy and low resource utilization efficiency. Although the Flying Sidekick Traveling Salesman Problem (FSTSP) technology has been applied in commercial logistics, its scheduling logic and resource allocation scheme are only suitable for conventional logistics delivery scenarios. It has not been adapted and optimized for power emergency communication scenarios characterized by fragile communication links under extreme weather conditions, dynamic changes in network topology, and sensitivity to data transmission latency, thus failing to meet the stringent requirements of power CPS for real-time and reliable communication.

[0004] At the modeling level, existing research on power systems and communication systems is mostly conducted independently, with insufficient modeling of the coupling relationship between wind and solar power output uncertainties, distribution network line NK faults, and CPS communication delays. Specifically, fluctuations in wind and solar power output can trigger changes in power load, thereby affecting the amount of communication data; distribution network line faults not only cause power outages but also lead to the damage of communication nodes and links attached to power facilities, creating a chain reaction. Existing models are unable to accurately characterize the operational characteristics of power-communication coupled systems under extreme weather conditions, failing to provide effective theoretical support and decision-making basis for low-latency, high-reliability operation of CPS. Furthermore, existing emergency communication network optimization methods often focus solely on node deployment or link establishment, failing to achieve full-process collaborative optimization of communication node site selection, path planning, link configuration, and route scheduling. This easily leads to problems such as overlapping node coverage, link transmission congestion, and unreasonable route planning, further exacerbating communication delays and affecting the efficiency of power emergency dispatch and fault handling.

[0005] In summary, under extreme weather conditions, the emergency communication support of power CPS faces prominent problems such as insufficient coverage, unstable links, high latency, and poor coordination. There is an urgent need for a communication latency optimization method that can integrate pre-disaster pre-configuration and dynamic scheduling during disasters, couple the uncertainties of multiple power and communication systems, and achieve integrated optimization of air and ground mobile communication nodes, so as to improve the resilience and emergency response capabilities of the distribution network. Summary of the Invention

[0006] In view of this, embodiments of the present invention provide a delay optimization system and method based on UAV-truck joint emergency communication to solve the problems of insufficient emergency communication coverage, unstable links and high end-to-end latency caused by damage to ground communication facilities under extreme weather conditions in the prior art; the problem that traditional post-disaster response models are lagging behind and the lack of air-ground coordination mechanisms makes it impossible to achieve pre-disaster pre-configuration and dynamic scheduling of communication resources during disasters; and the problem that existing models fail to couple the uncertainty of wind and solar power output, distribution network NK faults and CPS communication delays and lack the collaborative optimization of the entire process of communication node site selection, path planning and link scheduling.

[0007] This invention proposes a delay optimization system based on UAV-truck joint emergency communication, including a coupled modeling module, a scene generation module, a two-stage robust optimization module, and a solution module; The coupled modeling module is used to construct a power distribution network fault model, an air-to-ground mobile communication network model, and a cyber-physical system communication delay model. In the air-to-ground mobile communication network model, trucks are configured as ground mobile communication hubs, and drones are configured as airborne mobile relay nodes. The trucks and drones work together to form an integrated air-to-ground emergency communication network covering communication blind spots. The cyber-physical system communication delay model uses the sum of access delay, transmission delay, forwarding delay, queue delay, and processing delay to characterize end-to-end communication delay. The scenario generation module is used to generate a set of typical scenarios that characterize the uncertainty of wind power output and photovoltaic power output; The two-stage robust optimization module is used to establish an optimization model with the goal of minimizing the full-cycle communication latency. In the pre-disaster stage, the optimization model optimizes the strategic deployment locations of communication nodes, candidate paths, and the pre-configuration of communication equipment and links. In the disaster stage, in response to network topology damage caused by wind power output fluctuations, photovoltaic output fluctuations, and distribution network line faults, the model dynamically schedules the trucks and drones to conduct collaborative communication in order to minimize the end-to-end communication latency. The distribution network fault model, the uncertainty of wind power output and photovoltaic output, and the cyber-physical system communication latency model are coupled in the optimization model. The solution module is used to decompose and solve the optimization model established by the two-stage robust optimization module, and output the communication node deployment scheme and the collaborative communication scheduling scheme.

[0008] Furthermore, in the air-to-ground mobile communication network model, the truck, as a core ground communication node, has the capabilities of backhaul, switching, relaying, and providing take-off, landing, resupply, and command and control for the UAV; the UAV, as an airborne mobile relay node or airborne temporary base station, is used to extend communication coverage, overcome obstacles, and improve link quality in communication blind spots; the communication links between the truck and the UAV, as well as between the truck and the communication demand points, are established using wireless ad hoc networks, wireless mesh networks, or satellite backhaul methods, and the delays generated by the communication links include access delay, transmission delay, forwarding delay, queue delay, and processing delay.

[0009] Furthermore, the distribution network fault model is a model of a line NK fault occurring in a distribution network under extreme weather conditions. In the distribution network fault model, the load and power of the distribution network nodes fluctuate with the line fault, and the communication demand changes dynamically with the occurrence of the line fault.

[0010] Furthermore, in the cyber-physical system communication delay model, the total end-to-end communication delay is equal to the sum of access delay, transmission delay, forwarding delay, queue delay, and processing delay; the two-stage robust optimization module uses the end-to-end average delay and maximum delay as optimization objectives.

[0011] Furthermore, the scene generation module uses Latin hypercube sampling to generate initial scenes of wind speed, irradiance, and load fluctuations, and then performs backward reduction to obtain the typical scene set. The typical scene set is used to characterize the impact of the uncertainty of wind power output and photovoltaic power output on communication load and power supply reliability.

[0012] A latency optimization method based on UAV-truck joint emergency communication includes: A power distribution network fault model, an air-to-ground mobile communication network model, and a cyber-physical system communication delay model are constructed. Trucks are configured as ground mobile communication hubs and drones are configured as air mobile relay nodes. The trucks and drones work together to form an integrated air-to-ground emergency communication network covering communication blind spots. The end-to-end communication delay is characterized by the sum of access delay, transmission delay, forwarding delay, queue delay, and processing delay. Generate a set of typical scenarios that characterize the uncertainties in wind power output and photovoltaic power output; A two-stage robust optimization model is established with the goal of minimizing the communication latency throughout the entire lifecycle. In the pre-disaster stage, the strategic deployment locations of communication nodes, candidate paths, and the pre-configuration of communication equipment and links are optimized. In the disaster stage, in response to the network topology damage caused by wind power output fluctuations, photovoltaic power output fluctuations, and distribution network line faults, the trucks and drones are dynamically scheduled to conduct collaborative communication to minimize the end-to-end communication latency. The distribution network fault model, the uncertainty of wind power output and photovoltaic power output, and the cyber-physical system communication latency are coupled in the two-stage robust optimization model. The two-stage robust optimization model is decomposed and solved to output the communication node deployment scheme and the cooperative communication scheduling scheme.

[0013] Furthermore, a two-stage robust optimization model is established with the goal of minimizing the entire communication cycle delay. Its objective function is: Where F is the target value of the full-cycle communication delay to be minimized; s represents the uncertainty scenario of wind power and photovoltaic power. Let be the probability of scenario s; i and j are communication nodes, and (i,j) represents the link from node i to node j; The weight of link ij is given by the link with the critical load and the link corresponding to the monitoring point. Let λ be the communication delay of link ij in scenario s; λ is the maximum delay penalty coefficient.

[0014] Furthermore, the distribution network operation constraints of the two-stage robust optimization model include: Constraints on the number of devices that can be configured: in, , , and These are binary decision variables configured at node i during the pre-disaster phase, representing energy storage, photovoltaic power, wind turbines, and emergency power supplies; the value is 1 if configured, and 0 otherwise. Constraints on the number of lines attacked: in, Let K be a binary decision variable for whether to attack line ij in scenario s; it takes 0 if attacking and 1 otherwise. K is the number of attack lines. For distribution network nodes; A collection of uncertain scenarios combining wind and solar power; Constraints on active power balance at nodes: in, Let be the active power of the existing generator at node j in scenario s at time t; The active power of energy storage discharge configured for node j in scenario s at time t; The active power of the emergency power supply configured for node j in scenario s at time t; The actual active power of the wind turbine configured at node j in scenario s at time t; The actual active power of the photovoltaic system configured at node j in scenario s at time t; Let be the actual active power of node j switching loads under scenario s at time t; The active power of energy storage charging configured for node j in scenario s at time t; The active power purchased from the grid by the energy storage configured at node j in scenario s at time t; Let be the active power flowing out of node j in scenario s at time t; Let be the active power flowing into node j in scenario s at time t; Let be the resistance of branch ij; Let be the square of the current in branch ij under scenario s at time t; Constraints on reactive power balance at nodes: in, Let be the reactive power of the existing generator at node j in scenario s at time t; Let t be the reactive power of the energy storage discharge configured for node j in scenario s at time t; The reactive power of the emergency power supply configured for node j in scenario s at time t; The actual reactive power of the wind turbine configured at node j in scenario s at time t; The actual reactive power of the photovoltaic system configured at node j in scenario s at time t; Let t be the actual reactive power of node j switching load under scenario s at time t; The reactive power of the energy storage charging configured for node j in scenario s at time t; Let be the reactive power flowing out of node j in scenario s at time t; Let be the reactive power flowing into node j in scenario s at time t; Let be the reactance value of branch ij; Constraints on the lower bound of node voltage drop: Constraints on the upper bound of node voltage drop: in, , Let be the starting voltage and ending voltage of branch ij under scenario s at time t, respectively; M is a preset constant greater than the maximum allowable deviation range of the voltage amplitude of the distribution network node, used to relax the voltage drop constraint when the branch is disconnected; Branch active power constraints: Branch reactive power constraints: in, This represents the upper limit of active power allowed for branch ij; This represents the upper limit of reactive power allowed for branch ij; Let be the active power on branch ij; The reactive power on branch ij; Traditional generators have limitations in active power output: Constraints of reactive power output of traditional generators: in, , These are the upper limits of active and reactive power of the traditional generator configured at node i, respectively; Constraints on node voltage amplitude: in, , These are the upper and lower limits of the voltage at node i, respectively; Branch current constraints: in, This represents the upper limit of the current in branch ij; Constraints on active power during load shedding: Constraints on reactive power during load shedding: in, Let i be the maximum allowable active power to shed load. The maximum allowable load shedding reactive power for node i; Constraints on second-order cone relaxation in distribution networks: This constraint relaxes the branch power flow equations into a second-order cone form; Constraints on active power of energy storage discharge: Constraints on reactive power during energy storage discharge: in, The active power of discharge for energy stored at node i in scenario s; The reactive power of the energy stored at node i in scenario s; This represents the maximum active power of energy storage discharge. This represents the maximum reactive power of energy storage discharge. Relationship between energy storage charging and discharging power and energy capacity: in, , These are the energy storage charging efficiency and discharging efficiency, respectively. Active power for charging energy storage; The active power of energy storage discharge; Energy storage capacity recursion relationship: in, The energy storage capacity configured for node i in scenario s at time t; For time intervals; Upper and lower limits of energy storage capacity constraints: in, The rated capacity of the energy storage configured for node i; Energy storage charge and discharge states are mutually exclusive: in, , These are the flag variables indicating whether the energy storage at node i is in charging or discharging state under scenario s at time t; Maximum power of energy storage charging: Upper limit of energy storage discharge power: in, The maximum charging power of the energy storage configured for node i in scenario s; The maximum discharge power of the energy storage configured for node i in scenario s; Maximum power capacity for energy storage to purchase electricity from the grid: Electricity purchases are only permitted while the device is charging. Definition of energy storage charge / discharge state change: Energy storage charge / discharge cycle limit: in, The change in the charging and discharging state of the energy storage device configured at node i in scenario s at time t is the change in the charging and discharging state of the energy storage device in adjacent time periods. This represents the maximum permissible number of charge / discharge state switching cycles for energy storage. Wind turbine active power output constraints: Wind turbine reactive power output constraints: in, , These represent the maximum active and reactive power outputs of the wind turbine configured at node i in scenario s, respectively. Solar power output constraints: Solar reactive power output constraints: in, , These represent the maximum values ​​of the active and reactive power outputs of the photovoltaic system configured for node i in scenario s.

[0015] Furthermore, the air-to-ground mobile communication constraints of the two-stage robust optimization model include: Each communication requirement point is covered by at least one of the following methods: truck or drone, represented as: in, For the set of communication demand points; This is a set of drone take-off and landing and relay nodes; The decision variables for deploying the truck communication node at node i; , which is the decision variable for whether the UAV uses node j as its take-off, landing or relay node; The decision variable is whether the drone flies in ijk and acts as a relay. The truck's travel path has no sub-loops and meets the timing requirements for time synchronization and drone takeoff, landing, and recovery, as shown below: in, For the set of truck nodes; The decision variables for deploying the truck communication node at node i; For the decision variable of whether the truck travels between node i and node j and provides link service; For any subset of the set of truck nodes, This represents the number of nodes in the subset. The flight time of a drone shall not exceed its maximum endurance, and the communication coverage distance of a drone shall not exceed its maximum communication coverage radius, as expressed in the following way: in, This refers to the flight duration of the drone; This refers to the maximum flight time of the drone; (i,j,k) represents the communication coverage distance of the UAV; This represents the maximum communication coverage radius of the drone.

[0016] Furthermore, the cyber-physical system communication delay constraints of the two-stage robust optimization model include a single-link delay upper limit constraint and an end-to-end path maximum allowable delay constraint, respectively expressed as: in, Let be the communication delay of link ij in scenario s; This represents the maximum allowable delay for a single link. Let be the number of hops in link ij; A set of communication links; For end-to-end communication path, A set of end-to-end communication paths; This represents the maximum allowable delay for an end-to-end path. This is a set of uncertain scenarios for wind power and photovoltaics; In the process of decomposing and solving the two-stage robust optimization model, the two-stage robust optimization model is a three-layer structure of minimum-maximum-min, and its lower layer includes energy storage charging and discharging and time-series coupling. The nested column and constraint generation algorithm is used for decomposition and solution.

[0017] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention constructs a multi-system joint optimization framework that couples a distribution network NK fault model, a wind and solar power output uncertainty model, and a cyber-physical system communication delay model. It directly maps load fluctuations and dynamic changes in communication demand after a distribution network line fault into end-to-end communication delay calculations. A two-stage robust optimization approach is used to achieve full-process joint optimization of pre-disaster communication node strategic deployment, candidate path and link pre-configuration, and dynamic collaborative scheduling of trucks and drones during a disaster. This overcomes the problems of distorted delay assessment, delayed post-disaster response, and lack of air-ground coordination caused by the separation of power and communication modeling in existing technologies. It reduces end-to-end communication delays in the power cyber-physical system under extreme weather conditions, helping to improve the real-time performance and resilience of distribution network emergency communication. Furthermore, the communication node deployment scheme and collaborative communication scheduling scheme are physically executed by the actual driving and positioning of trucks and the actual take-off and landing of drones, respectively, thereby forming real communication coverage in the disaster area and achieving the technical effect of improving end-to-end communication delays.

[0018] 2. This invention configures trucks as ground mobile communication hubs with backhaul, switching, relay, and UAV take-off and landing resupply capabilities, and configures UAVs as airborne mobile relay nodes or temporary base stations. It establishes air-to-ground mobile communication constraints, including coverage constraints, path loop-free constraints, and endurance and communication coverage constraints. It also introduces single-link delay upper limit constraints and end-to-end path maximum allowable delay constraints, enabling the emergency communication network to be pre-deployed before a disaster and dynamically adjusted to adapt to topology damage during a disaster. This solves the problems of overlapping communication node coverage, link congestion, unreasonable routing planning, and the inability of UAVs to continuously guarantee communication due to limited endurance in existing technologies. While ensuring that the average delay of the entire network is controlled, it suppresses the extreme delay of the most unfavorable link, and realizes reliable and timely transmission of power critical load monitoring data and dispatch instructions. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1This is a block diagram of a delay optimization system based on UAV-truck joint emergency communication according to an embodiment of the present invention; Figure 2 This is a flowchart of a delay optimization method based on UAV-truck joint emergency communication according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the three-layer structure of the two-stage robust optimization model according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the collaborative architecture of the air-ground integrated emergency communication network according to an embodiment of the present invention. Detailed Implementation

[0021] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of the invention. However, those skilled in the art will understand that the invention can be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of the invention with unnecessary detail.

[0022] This invention provides a delay optimization system and method based on UAV-truck joint emergency communication, mainly applied to emergency communication support for power distribution networks under extreme weather conditions, resilience enhancement of power cyber-physical systems, and air-ground cooperative mobile communication. The system integrates a coupled modeling module, a scenario generation module, a two-stage robust optimization module, and a solution module. The method generates a set of typical scenarios characterizing the uncertainty of wind and solar power output by constructing a power distribution network NK fault model, an air-ground mobile communication network model, and a cyber-physical system communication delay model. A two-stage robust optimization model is established with the goal of minimizing the entire lifecycle communication delay.

[0023] In typical application scenarios, the system first pre-configures truck parking locations, drone take-off and landing locations, and communication links in the pre-disaster phase. When extreme weather causes power grid line failures and communication facility damage, the system dynamically schedules trucks to travel along planned routes during the disaster phase and dispatches drones to extend coverage blind spots from relay nodes. Trucks and drones collaborate to form an integrated air-ground emergency communication network through wireless ad hoc networks or satellite backhaul. Traditional methods often rely on temporarily deploying communication vehicles or drones after a disaster, lacking pre-disaster pre-configuration and air-ground coordination mechanisms. This results in fragile communication topologies, large end-to-end latency, and difficulties in refueling. In contrast, this invention reduces end-to-end communication latency under extreme weather conditions by coupling power failure and communication delay models, employing two-stage robust optimization, and introducing coverage constraints, path loop-free constraints, and drone endurance constraints. This helps improve the real-time performance and resilience of power grid emergency communication.

[0024] Example 1 This embodiment provides a latency optimization system based on UAV-truck joint emergency communication. The system includes a coupled modeling module, a scenario generation module, a two-stage robust optimization module, and a solution module. The coupled modeling module constructs a power distribution network fault model, an air-to-ground mobile communication network model, and a cyber-physical system communication latency model. The scenario generation module generates a set of typical scenarios characterizing the uncertainties in wind power output and photovoltaic output. The two-stage robust optimization module establishes an optimization model with the objective of minimizing the entire lifecycle communication latency. The solution module decomposes and solves the optimization model, outputting a communication node deployment scheme and a collaborative communication scheduling scheme. The following section combines... Figure 1 Each module is described in detail.

[0025] In application, the coupled modeling module serves as the data and model foundation for the entire solution, unifying the physical processes on the power side and the information processes on the communication side into a single mathematical model. The distribution network fault model describes the system's operational status after line failures due to extreme weather conditions such as tower collapse and conductor breakage. It considers which lines might fail, how power flow shifts after a failure, and which nodes will lose power. The air-to-ground mobile communication network model configures trucks as ground mobile communication hubs, assigning them the core role of aggregation, backhaul, and switching. UAVs are configured as airborne mobile relay nodes, delivering signals to areas difficult to cover on the ground. Together, they form an integrated air-to-ground emergency communication network capable of covering communication blind spots. The cyber-physical system communication delay model breaks down the entire time of an end-to-end data transmission into five parts: access delay, transmission delay, forwarding delay, queuing delay, and processing delay. The sum of these five parts represents the end-to-end communication delay, allowing for decomposition, localization, and targeted optimization of the delay.

[0026] In the application, the scenario generation module transforms the uncertainties in wind and solar power output into a calculable set of typical scenarios. Wind and solar power output fluctuates randomly due to wind speed and irradiance, altering power supply reliability and the power and load status of communication nodes. The scenario generation module abstracts these random factors into a finite number of representative operating sections, each corresponding to a possible wind-solar power output combination and load level. The entire set of typical scenarios covers various operating conditions, from sufficient to insufficient power output. Subsequent optimizations are then performed on these typical scenarios, enabling the resulting deployment and scheduling schemes to adapt to the diverse situations arising from wind and solar power fluctuations.

[0027] In application, the two-stage robust optimization module establishes an optimization model with the goal of minimizing the entire lifecycle communication latency, dividing the decision-making process into two stages: pre-disaster and during-disaster. The pre-disaster stage is completed before the disaster occurs, and optimization includes the strategic deployment locations of communication nodes (i.e., determining the locations of truck parking points and drone take-off and landing points in advance), candidate paths (i.e., planning the routes that trucks can travel and the flight paths that drones can fly in advance), and the pre-configuration of communication equipment and links (i.e., deploying communication equipment and establishing links in key locations in advance). The during-disaster stage starts after the disaster occurs. Addressing network topology damage caused by fluctuations in wind power output, photovoltaic power output, and distribution network line faults, it dynamically schedules trucks and drones for coordinated communication, minimizing end-to-end communication latency even under the worst-case scenario. The distribution network fault model, the uncertainty of wind and solar power output, and the cyber-physical system communication latency model are coupled in this optimization model, allowing power-side faults and fluctuations to be directly reflected in the latency calculations on the communication side.

[0028] In application, the solution module decomposes and solves the optimization model established by the two-stage robust optimization module. This optimization model includes both pre-disaster deployment decisions and in-disaster scheduling decisions, which are interconnected through scenarios, making direct solution very difficult. The solution module decomposes the model into iterative subproblems based on pre-disaster and in-disaster scenarios. The pre-disaster subproblem provides a set of deployment schemes, while the in-disaster subproblem provides a scheduling scheme for the worst-case scenario under the same deployment and feeds back the delay cost. The two subproblems iterate repeatedly until convergence, ultimately outputting a communication node deployment scheme and a collaborative communication scheduling scheme for emergency command to execute.

[0029] Specifically, in a practical application of emergency communication for power distribution networks, the coupled modeling module first establishes a power distribution network fault model based on the power distribution network topology and equipment parameters, establishes an air-to-ground mobile communication network model based on the capability parameters of trucks and drones, and establishes a cyber-physical system communication delay model based on link characteristics. The scenario generation module then generates a set of typical scenarios covering wind and solar fluctuations. In the pre-disaster stage, the two-stage robust optimization module uses these models and scenarios as inputs to find pre-configuration schemes for truck parking locations, drone take-off and landing locations, and communication equipment and links. In the mid-disaster stage, once line faults and topology damage occur, the module reschedules truck driving and drone flights based on the actual fault situation, so that the communication links in the affected area are quickly replenished. Throughout the process, the solution module iterates the decisions of the pre-disaster and mid-disaster stages until convergence, thereby outputting a complete solution that can both deploy in advance and respond to emergencies.

[0030] The establishment of a distribution network fault model can be characterized by fault enumeration based on line opening and closing state variables to depict line failures, or by fault probability based on historical disaster statistics to depict the probability of line failures. The coordination of the integrated air-ground emergency communication network can cover blind spots by having trucks stop at fixed points and drones relay the signals, or by having trucks move along a path and drones accompany them to dynamically extend coverage.

[0031] This scheme unifies the power grid fault model, wind and solar power output uncertainty, and cyber-physical system (CPS) communication delay model within the same optimization framework. This allows the impact of power faults on communication delays to be directly calculated and specifically mitigated, overcoming the delay assessment distortion caused by separate modeling of power and communication. By configuring trucks and drones as ground mobile communication hubs and airborne mobile relay nodes respectively, and coordinating their networking, communication coverage no longer relies on fixed base stations. Even after ground facilities are damaged, blind spots can be quickly filled, improving the continuity and reliability of emergency communications. The decision-making process is divided into two phases: pre-disaster pre-configuration and in-disaster dynamic scheduling. This ensures that emergency communication resources are deployed before a disaster occurs and can be adjusted as needed afterward, reducing end-to-end communication delays and enhancing the robustness of the communication network.

[0032] In applications, trucks act as core ground communication nodes, undertaking the capabilities of backhauling, switching, relaying, and providing support for UAV takeoffs and landings, resupply, and command and control. Backhauling refers to aggregating monitoring data and control commands collected from the front end and sending them back to the main dispatch station; switching refers to transferring data streams between multiple communication nodes; relaying refers to receiving, amplifying, and forwarding signals to extend transmission distance; providing support for UAV takeoffs and landings means trucks provide platforms for UAVs to take off and land; resupply means trucks replace or recharge batteries for UAVs to extend their operating time; and command and control means trucks uniformly schedule the flight paths and missions of their assigned UAVs. With these capabilities, trucks can become ground-side communication centers, undertaking the core functions of aggregation and forwarding when ground base stations fail. Figure 4 As shown, the truck serves as the core ground communication node, possessing the capabilities of backhaul, switching, relay, and UAV take-off and landing resupply; the UAV serves as the aerial mobile relay node, connecting with the truck through a wireless self-organizing network and extending coverage to communication demand points, forming an integrated air-ground emergency communication network.

[0033] In applications, drones serve as aerial mobile relay nodes or temporary aerial base stations to extend communication coverage, overcome obstacles, and improve link quality in communication blind spots. Extending communication coverage means that after takeoff, the drone, with its higher line-of-sight, can deliver signals to areas that are difficult for ground nodes to reach directly. Overcoming obstacles means that the drone, using its aerial position, can bypass ground obstructions such as mountains and buildings. Improving link quality in communication blind spots means that as the drone approaches the blind spot, it shortens the transmission distance between itself and the terminal in the blind spot, thereby improving signal strength and stability. The aerial maneuverability of drones enables them to establish usable links for disaster-stricken areas even when ground access is blocked.

[0034] In applications, communication links between trucks and drones, as well as between trucks and communication request points, are established using wireless ad hoc networks, wireless mesh networks, or satellite backhaul. Wireless ad hoc networks refer to nodes that can automatically network and forward data to each other without fixed infrastructure. Wireless mesh networks involve nodes forming multipath interconnections to improve link redundancy. Satellite backhaul uses satellites to send data back to a remote master station, eliminating reliance on terrestrial lines. These links generate access delays, transmission delays, forwarding delays, queuing delays, and processing delays during transmission, which constitute the main sources of end-to-end communication latency.

[0035] Specifically, when communication blind spots appear in the disaster area, trucks drive to an accessible location on the edge of the disaster area and stop, then act as ground core communication nodes to establish backhaul and exchange channels. Drones take off from the truck platform and fly over the blind spot as aerial mobile relay nodes. A link is established between the truck and the drone through a wireless ad hoc network. A link is also established between the drone and communication demand points in the blind spot in the same way. Data from the blind spot is relayed to the truck by the drone, and then back to the dispatch master station via satellite from the truck. When the drone's battery is low, it returns to the truck for resupply and continues to perform its mission. Throughout the process, the truck and the drone work together to bring the originally uncovered blind spots into the communication range.

[0036] The link between the truck and the drone can be established using a wireless self-organizing network for rapid and automatic networking, or a wireless mesh network to increase multi-path redundancy. Data can be sent back to the remote master station via satellite to eliminate reliance on terrestrial lines, or via truck relays along routes to maintain the backhaul channel when satellite access is limited.

[0037] The trucks possess backhaul, switching, relay, and command and control capabilities for UAV takeoff and landing resupply, ensuring a fully functional communication center remains on the ground side even after fixed base stations fail, thus guaranteeing the continuity of aggregation and forwarding functions. UAVs, with their aerial mobility, extend coverage and overcome obstacles, allowing network access to blind spots even when ground access is blocked, thereby expanding the coverage of emergency communications. Links are established using various methods such as self-organizing networks, mesh networks, and satellite backhaul, enabling the communication network to maintain connectivity through remaining paths even when some links fail, thus improving link redundancy and resilience.

[0038] In application, the distribution network fault model is a model of line NK faults occurring in the distribution network under extreme weather conditions. A line NK fault refers to the simultaneous failure of several lines in the entire distribution network due to extreme weather. Here, N represents the total number of lines in the system, and K represents the number of lines that may fail simultaneously. An NK fault indicates that any K lines selected from all the lines simultaneously become out of service. Extreme weather includes typhoons, snowstorms, and heavy rains, which can easily cause tower collapses and conductor breaks. The distribution network fault model takes into account the simultaneous failure of multiple lines caused by these weather conditions, thus depicting a more severe damage condition than a single line fault. The number of lines failing simultaneously is set to an adjustable number, allowing the model to describe both minor disasters with a few damaged lines and severe disasters with a large number of lines simultaneously out of service. In the two-stage robust optimization, this model is used to search for the most unfavorable failure combination that maximizes communication latency in the intermediate layer, enabling pre-disaster deployment to prepare for the worst-case scenario, thereby ensuring that the solution is capable of coping with various possible large-scale damage scenarios.

[0039] In applications, the load and power of distribution network nodes fluctuate with line faults, and communication demand changes dynamically with the occurrence of line faults. After a line failure, loads originally powered by that line need to be powered by other lines or are forced to disconnect, thus changing the injected power and power flow distribution of the nodes. This is the meaning of load and power fluctuations with line faults. Simultaneously, line failures change the scope of objects that need to be monitored and controlled. Affected areas need to report more status data and receive more control commands, increasing the amount of communication data in that area. This is the meaning of communication demand changing dynamically with the occurrence of line faults. The distribution network fault model links power-side fluctuations with communication-side demand changes, providing fault-dependent inputs for subsequent delay optimization.

[0040] Specifically, when extreme weather strikes and causes several lines in the distribution network to fail simultaneously, the distribution network fault model first determines the set of lines that have failed. Then, it recalculates the power supply status and power flow distribution of each node to determine which nodes are supplying power normally, which nodes are interrupted, and which nodes need to disconnect some loads. Subsequently, based on the monitoring and control needs of the affected nodes, it calculates the amount of communication data in each area and provides these load power and communication needs that change with the fault to the two-stage robust optimization model, so that the disaster dispatch can arrange communication support for trucks and drones based on the actual consequences of the fault.

[0041] The characterization of line NK faults can be achieved by setting an upper limit on the number of failed lines to limit the fault scale, or by dividing fault sets according to the intensity of extreme weather to better reflect the actual disaster situation. The redistribution of load and power after a fault can be determined by recalculating power flow to ascertain the power supply status of each node, or by identifying power-loss nodes based on line connectivity.

[0042] The distribution network fault model uses line NK faults to depict severe conditions where multiple lines fail simultaneously under extreme weather conditions. This allows the model to address widespread damage in real disasters rather than just single-point faults, thus improving its adaptability to extreme scenarios. The model incorporates fluctuations in node load power and dynamic changes in communication demand, directly translating the extent of damage on the power side into communication demand input. This ensures that communication support arrangements during disasters align with actual fault consequences, enhancing the targeted nature of emergency response. The model sets the number of simultaneously failing lines as an adjustable parameter, allowing the same modeling method to adapt to disasters of varying severity, thereby enhancing the versatility and portability of the solution across different disaster levels.

[0043] In applications, the cyber-physical system (CPS) communication latency model defines the total latency of end-to-end communication as the sum of access latency, transmission latency, forwarding latency, queuing latency, and processing latency. Access latency refers to the time it takes for a terminal to successfully access the communication network after initiating an access request. Transmission latency refers to the time it takes for data to travel from the sender to the receiver on the link. Forwarding latency refers to the time it takes for data to be received by intermediate nodes and then forwarded. Queuing latency refers to the time it takes for data to queue in the node's buffer queue for processing. Processing latency refers to the time it takes for the node to parse and process the data. Adding these five components together yields the total latency of a single end-to-end data transmission. This decomposition clearly identifies the sources of latency, facilitating optimization at different stages. Under this decomposition, access latency is mainly affected by network access mechanisms and channel contention; transmission latency is mainly affected by link bandwidth and data volume; forwarding latency is mainly affected by the number of intermediate nodes and their forwarding capacity; queuing latency is mainly affected by node load and buffer status; and processing latency is mainly affected by node computing power. Therefore, by examining these five components separately, the main sources of latency can be identified and targeted improvements can be made.

[0044] As a quantifiable implementation method, the above five delay components can be quantitatively calculated from communication physical parameters as follows: For link (i,j), the transmission delay is: Where L(i,j,s) is the amount of data transmitted via link (i,j) in scenario s, and B(i,j) is the bandwidth of the link; Forwarding delay: Where H(i,j) is the number of hops traversed by the end-to-end path. This refers to the single-hop forwarding processing time. Queue delay is approximated using M / M / 1 queuing: Where μ is the node service rate, λ is the data arrival rate, and ρ=λ / μ is the node load rate; Processing delay: in This refers to the node's computing and processing capabilities. Access latency: Where n is the number of terminals simultaneously competing for access, and β is the channel contention coefficient. This represents the base access time under contention-free conditions. The latency of link (i,j) in scenario s is: The end-to-end path delay is the sum of the delays of each link on the path.

[0045] Furthermore, the coupling between distribution network line faults and communication delays can be quantitatively characterized by the following mapping: Let V_aff(s) be the set of nodes affected by NK faults (power outage, power transfer, or need for encrypted monitoring) in scenario s, then the amount of communication data of node j is: in For the basic data volume under normal working conditions, The data volume of status reports and control commands added due to the fault of this node; I[·] is the indicator function; the data volume passing through link (i,j) is L(i,j,s)=∑(j∈R(i,j)). Let R(i,j) be the set of nodes whose data is carried by link (i,j). Substituting L(i,j,s) into the above expressions for transmission delay and queue delay, we obtain the set of nodes affected by a line failure. → The increase in node communication data volume L_j(s) → The increase in link data volume L(i,j,s) → The quantitative transmission relationship between the increase in link transmission delay and queue delay is realized, thereby realizing the mutual coupling of the distribution network fault model, the uncertainty of wind and solar power output and the cyber-physical system communication delay model in the optimization model.

[0046] For example, suppose a link bandwidth B = 10 Mbps and a node service rate μ = 50 packets / second: under normal operating conditions, the amount of data passing through this link L = 2 Mbit and the node load ρ = 0.3, then the transmission delay... =2 / 10=0.2 seconds, queue delay =0.3 / [50×(1-0.3)]≈0.0086 seconds; when a fault occurs on an adjacent line, causing an increase in the amount of data reported by the affected node, the amount of data passing through this link to rise to L′=5Mbit, and the node load to rise to ρ′=0.6, the transmission delay increases to =5 / 10 = 0.5 seconds, queue delay increases to =0.6 / [50×(1-0.6)]=0.03 seconds, indicating that the total transmission and queuing delay of a single link increases by approximately 0.32 seconds due to the fault. The two-stage robust optimization involves searching for the most unfavorable NK fault combination that maximizes the above delay in the intermediate layer, and suppressing it through pre-disaster deployment and in-disaster scheduling.

[0047] In application, the two-stage robust optimization module uses end-to-end average latency and maximum latency as optimization objectives. End-to-end average latency reflects the overall transmission speed of the network, while end-to-end maximum latency reflects the transmission performance of the slowest link in the network. Optimizing only the average latency may lead to excessively high latency on individual critical links, while optimizing only the maximum latency may sacrifice overall efficiency. Therefore, both average latency and maximum latency are included in the optimization objectives, so that the solution can reduce the overall latency while suppressing the latency of the most unfavorable link, thus balancing the overall performance of the communication network and its performance under worst-case conditions.

[0048] Specifically, when evaluating a communication deployment and scheduling scheme, the cyber-physical system communication delay model first calculates the access delay, transmission delay, forwarding delay, queue delay, and processing delay for each end-to-end path and sums them to obtain the total delay of that path. Then, it calculates the weighted average of the total delay of all paths in the entire network to obtain the end-to-end average delay. At the same time, it finds the maximum value among the total delays of all paths in the entire network to obtain the end-to-end maximum delay. The two-stage robust optimization module uses both the end-to-end average delay and the end-to-end maximum delay as the basis for evaluating the merits of the scheme, thereby guiding the optimization towards convergence in the direction of both reducing overall delay and suppressing worst-case link delay.

[0049] The latency of each link can be quantified by estimating transmission latency based on link speed and data volume, or by estimating queue latency based on node queue length. The balance between overall performance and worst-case performance can be achieved by constructing a target using a weighted sum of average and maximum latency, or by setting a penalty coefficient on the maximum latency to emphasize suppression of worst-case links.

[0050] The cyber-physical system (CPS) communication latency model decomposes total latency into five parts: access, transmission, forwarding, queuing, and processing. This allows for the identification of latency sources one by one, facilitating optimization of the most critical latency components. The optimization objective incorporates both end-to-end average latency and maximum latency, enabling the solution to reduce overall network latency while suppressing latency on the most unfavorable links. This meets the latency requirements of CPS for real-time control and emergency dispatch, ensuring timely delivery of critical data. Characterizing latency as the sum of these five calculable components allows for direct comparison of the merits of different deployment and scheduling schemes based on latency values. This provides a clear and unified metric for two-stage robust optimization, enhancing the interpretability and credibility of the optimization results.

[0051] In the application, the scene generation module uses Latin hypercube sampling to generate initial scenes for wind speed, irradiance, and load fluctuation. Latin hypercube sampling is a sampling method that divides the range of values ​​for each random variable into several equally probable intervals and takes one sample from each interval. This method can cover the entire range of values ​​for random variables relatively evenly with a smaller number of samples. The scene generation module samples the three types of random quantities—wind speed, irradiance, and load fluctuation—in the above manner, then combines the values ​​from the same sampling into an initial scene. Multiple samplings yield a large number of initial scenes, which collectively reflect the various possible combinations of wind power output, solar power output, and load.

[0052] In the application, the scene generation module further reduces the number of scenes to obtain a typical scene set. Backward reduction is a process that gradually eliminates scenes most similar to the remaining scenes from a large number of initial scenes and merges their probabilities into those similar scenes. Each scene eliminated reduces the number of remaining scenes by one, and this process is repeated until the number of remaining scenes meets the requirements. The typical scene set obtained after backward reduction retains the overall distribution characteristics of the initial scenes with a smaller number of scenes, reducing the computational burden of subsequent optimization while maintaining the representativeness of wind and solar power output and load fluctuations. This typical scene set is used to characterize the impact of uncertainties in wind and solar power output on communication load and power supply reliability. Each retained typical scene carries a probability value, which is the sum of the probabilities of the merged scenes. This ensures that the typical scene set, even after being compressed, can still approximately represent the original large number of scenes in a probabilistic sense, thus providing a concise and accurate input for subsequent scene-probability-weighted optimization.

[0053] Specifically, when preparing optimization inputs for a certain power distribution network area, the scenario generation module first generates a large number of values ​​for wind speed, irradiance, and load fluctuations using Latin hypercube sampling, and combines them into numerous initial scenarios. Then, backward reduction is performed on these initial scenarios, gradually merging similar scenarios and accumulating probabilities, ultimately retaining a moderate number of representative typical scenarios. Each typical scenario corresponds to a combination of wind and solar power output and load level with a corresponding probability. This set of typical scenarios is then fed into a two-stage robust optimization model, enabling the optimization to maintain an acceptable computational scale while covering wind and solar uncertainties.

[0054] The initial scene generation can employ Latin hypercube sampling to uniformly cover the value range, or it can use sampling based on historical weather and load data to fit actual fluctuations. The reduction in the number of scenes can be achieved by backward reduction to gradually merge similar scenes, or by setting a retention threshold based on probability distance to control the final scene size.

[0055] Latin hypercube sampling is used to generate initial scenes, ensuring that the entire range of wind speed, irradiance, and load fluctuations is covered relatively evenly with fewer samples. This avoids the value concentration problem that may occur with random sampling and improves the representativeness of the scenes. A backward reduction process yields a set of typical scenes, effectively compressing the number of scenes while preserving the overall distribution characteristics. This reduces the computational burden of subsequent optimizations while covering wind and solar uncertainties, ensuring the computability of the solution. By combining sampling and reduction, the set of typical scenes is both quantitatively suitable for the solution capability and distributionally close to real fluctuations, achieving a balance between computational efficiency and characterization accuracy. This lays a reliable foundation for uncertainty input in two-stage robust optimization.

[0056] Example 2 This embodiment provides a latency optimization method based on UAV-truck joint emergency communication. The method includes: constructing a power distribution network fault model, an air-to-ground mobile communication network model, and a cyber-physical system communication latency model; generating a set of typical scenarios characterizing the uncertainties in wind power output and photovoltaic output; establishing a two-stage robust optimization model with the goal of minimizing the entire lifecycle communication latency; optimizing the strategic deployment locations of communication nodes, candidate paths, and the pre-configuration of communication equipment and links in the pre-disaster stage; and dynamically scheduling trucks and UAVs for collaborative communication in the mid-disaster stage to minimize end-to-end communication latency, addressing network topology damage caused by wind power output fluctuations, photovoltaic output fluctuations, and power distribution network line faults; and decomposing and solving the two-stage robust optimization model to output a communication node deployment scheme and a collaborative communication scheduling scheme. (Refer to...) Figure 2 The delay optimization method provided in this embodiment includes the following steps S101 to S106, which will be described in detail below with reference to the specific steps.

[0057] S101, construct a power distribution network fault model, an air-to-ground mobile communication network model, and a cyber-physical system communication delay model.

[0058] In application, constructing a distribution network fault model refers to expressing potential line failures and their consequences under extreme weather conditions as mathematical constraints based on the distribution network's topology and equipment parameters. Constructing an air-to-ground mobile communication network model involves configuring trucks as ground mobile communication hubs and drones as airborne mobile relay nodes, then expressing the integrated air-to-ground emergency communication network covering communication blind spots as a network topology and coverage relationship. Constructing a cyber-physical system communication delay model involves expressing end-to-end communication delay as the sum of access delay, transmission delay, forwarding delay, queueing delay, and processing delay. This operation provides a unified model foundation for subsequent optimization.

[0059] S102 generates a set of typical scenarios that characterize the uncertainties in wind power output and photovoltaic power output.

[0060] In application, generating a set of typical scenarios characterizing the uncertainties in wind and solar power output is the second operation of this method. This operation transforms the random output of wind and solar power caused by variations in wind speed and irradiance into a finite number of representative operating sections. Each section corresponds to a combination of wind and solar power output and load levels, and the entire set of typical scenarios covers various operating conditions from sufficient to insufficient output. Generating the set of typical scenarios ensures that subsequent optimization remains effective under various wind and solar operating conditions, thereby enabling deployment and scheduling schemes to cope with uncertainties.

[0061] S103 establishes a two-stage robust optimization model with the goal of minimizing the total communication delay.

[0062] In application, establishing a two-stage robust optimization model with the goal of minimizing the entire lifecycle communication latency is the third operation of this method. For example... Figure 3 As shown, the optimization model adopts a three-layer nested structure: outer layer minimization (pre-disaster deployment), middle layer maximization (most unfavorable scenario search), and inner layer minimization (in-disaster scheduling). The lower layer includes the timing coupling of energy storage charging and discharging. The model is decomposed and solved using a nested column and constraint generation algorithm. The two-stage robust optimization divides the decision-making into two stages: pre-disaster and in-disaster. In this model, the distribution network fault model, the uncertainty of wind and solar power output, and the communication delay of the cyber-physical system are coupled with each other, so that the faults and fluctuations on the power side can be directly reflected in the calculation of communication delay.

[0063] S104, in the pre-disaster phase, optimize the strategic deployment locations of communication nodes, candidate paths, and the pre-configuration of communication equipment and links.

[0064] Specifically, the pre-disaster phase is completed before the disaster occurs. The optimization includes the strategic deployment locations of communication nodes, that is, determining the locations of truck parking points and drone take-off and landing points in advance; candidate routes, that is, planning the routes that trucks can travel and the flight paths that drones can fly in advance; and the pre-configuration of communication equipment and communication links, that is, deploying communication equipment and establishing links in key locations in advance.

[0065] S105, during the disaster phase, dynamically schedules trucks and drones to conduct collaborative communication to minimize end-to-end communication delays in response to network topology damage caused by fluctuations in wind power output, fluctuations in photovoltaic power output, and faults in distribution network lines.

[0066] Specifically, the disaster response phase is initiated after a disaster occurs. In response to fluctuations in wind power output, photovoltaic power output, and network topology damage caused by power grid line faults, trucks and drones are dynamically scheduled to conduct collaborative communication, so that end-to-end communication delays are minimized even under the most unfavorable circumstances.

[0067] S106, decompose and solve the two-stage robust optimization model to output the communication node deployment scheme and the cooperative communication scheduling scheme.

[0068] In application, decomposing and solving the two-stage robust optimization model is the fourth operation of this method. Since the model includes both pre-disaster deployment and in-disaster scheduling, and the two are coupled through scenarios, it is very difficult to solve the whole directly. Therefore, the model is decomposed into two sub-problems, pre-disaster and in-disaster, which are iterated alternately. The pre-disaster sub-problem provides a set of deployment schemes, and the in-disaster sub-problem provides a scheduling scheme for the worst-case scenario under the same deployment and feeds back the delay cost. The two are iterated repeatedly until convergence, and finally output the communication node deployment scheme and the cooperative communication scheduling scheme.

[0069] Specifically, in a complete application process for emergency communication in distribution networks, a distribution network fault model, an air-to-ground mobile communication network model, and a cyber-physical system communication delay model are first constructed based on the parameters of the distribution network and communication equipment. Then, a set of typical scenarios covering wind and solar fluctuations is generated. Subsequently, a two-stage robust optimization model is established with the goal of minimizing the full-cycle communication delay. In the pre-disaster stage, the pre-configuration schemes for truck parking locations, drone take-off and landing locations, and communication equipment and links are obtained. After the disaster occurs, in the mid-disaster stage, truck driving and drone flight are rescheduled based on actual line faults and topology damage. Finally, the pre-disaster and mid-disaster two-stage decisions are repeatedly iterated until convergence through the decomposition and solution process, outputting a complete communication deployment and scheduling scheme that can both deploy in advance and respond to emergencies.

[0070] The coupling of the model can be achieved by directly using the fault state of the distribution network as the input for calculating communication delay, or by associating the power supply status of the communication nodes with the power supply results of the distribution network. The decomposition and solution of the model can be achieved by using a hierarchical iterative approach based on pre-disaster and during-disaster conditions to reduce the difficulty of the solution, or by successively adding constraints to the subproblems to approximate the global optimum.

[0071] This method unifies power grid faults, wind and solar power output uncertainties, and end-to-end communication delays on the communication side into a two-stage robust optimization model. This allows the impact of power faults on communication delays to be directly calculated and specifically mitigated, thus avoiding the biases caused by separating power and communication processing. The method divides communication resource allocation into two stages: pre-disaster pre-configuration and in-disaster dynamic scheduling. This ensures that emergency communications are deployed before a disaster occurs and adjusted as needed afterward, thereby reducing end-to-end communication delays. The method employs a decomposition solution for the model, enabling the two-stage robust optimization model, which would otherwise be difficult to solve holistically, to efficiently obtain deployment and scheduling schemes, thus balancing optimization effectiveness and computational efficiency.

[0072] In the application, a two-stage robust optimization model is established with the goal of minimizing the total communication latency. Its objective function is: Where F is the target value of the full-cycle communication delay to be minimized; s represents the uncertainty scenario of wind power and photovoltaic power. Let be the probability of scenario s; i and j are communication nodes, and (i,j) represents the link from node i to node j; The weight of link ij is given by the link with the critical load and the link corresponding to the monitoring point. Let λ be the communication delay of link ij in scenario s; λ is the maximum delay penalty coefficient.

[0073] The weighted average delay term in the objective function multiplies the communication delay of each link in a given scenario by its weight, and then sums these values ​​over all links. The link weight reflects the importance of the link; links carrying critical loads and monitoring data are given higher weights, thus their delays account for a larger proportion of the summation. This structure ensures that optimization prioritizes important links when reducing latency, thereby preventing critical data from failing to arrive on time due to excessive link latency.

[0074] In application, the maximum latency penalty term in the objective function multiplies the maximum latency of all links in a given scenario by a maximum latency penalty coefficient and then includes it in the objective. The maximum latency reflects the latency performance of the slowest link in that scenario, and the maximum latency penalty coefficient is used to adjust the degree of emphasis on the worst-case link. The larger the penalty coefficient, the more the optimization tends to reduce the latency of the slowest link. Introducing this term ensures that the optimization does not only focus on reducing the overall average latency while allowing individual links to have excessively high latency, enabling the solution to improve the overall performance while suppressing the worst-case scenario.

[0075] In application, the objective function sums the weighted average delay and maximum delay penalty for each scenario, multiplying the sum by the probability of that scenario occurring, and then sums the results over all scenarios. Scenario probability reflects the likelihood of a scenario occurring; scenarios with higher probabilities carry greater weight in the objective. By weighting the sum according to scenario probabilities, the objective function integrates the delays of various possible operating conditions under the uncertainty of wind and solar power output into a total delay with a desired meaning, making the optimization result adaptable to various wind and solar power operating conditions.

[0076] Specifically, when solving the two-stage robust optimization model, for each typical scenario, the communication latency of each link in that scenario is first calculated. Then, the latency of each link is weighted and summed according to the link weight to obtain the weighted average latency of that scenario. At the same time, the maximum value of the latency of each link in that scenario is taken and multiplied by the maximum latency penalty coefficient to obtain the maximum latency penalty of that scenario. The two are added together to obtain the latency cost of that scenario. Then, the latency costs of each scenario are summed according to their probabilities to obtain the target value of the full-cycle communication latency. The optimization process continuously adjusts the pre-disaster deployment and in-disaster scheduling to minimize the target value, thereby obtaining the deployment and scheduling scheme that minimizes the full-cycle communication latency.

[0077] The importance of links can be reflected by assigning higher weights to links carrying critical loads and monitoring points, or by assigning weights according to the urgency of the data carried by the link. Suppressing the worst-case links can be achieved by introducing a maximum delay penalty term, or by increasing the maximum delay penalty coefficient to strengthen the suppression.

[0078] The objective function incorporates both a weighted average latency term and a maximum latency penalty term, enabling optimization to reduce overall network latency while suppressing the latency of the most unfavorable links, thus balancing overall performance with worst-case performance. The objective function assigns higher weights to links carrying critical loads and monitoring points, prioritizing the reduction of latency for links corresponding to important data, thereby ensuring the timely transmission of critical control and monitoring data. The objective function uses a weighted summation of latency costs for each scenario based on scenario probability, ensuring the optimization results remain effective under various operating conditions with uncertain wind and solar power output, thus improving the robustness of the solution. By condensing the entire lifecycle communication latency into a single optimizable objective value, pre-disaster deployment and in-disaster scheduling can be uniformly weighed on the same scale, avoiding the trade-offs caused by multiple objectives acting independently and improving the operability of the optimization.

[0079] In this embodiment, the distribution network operation constraints of the two-stage robust optimization model include: Constraints on the number of devices that can be configured: in, , , and These are binary decision variables for configuring energy storage, photovoltaics, wind turbines, and emergency power supplies at node i during the pre-disaster phase; a value of 1 indicates configuration, otherwise 0. This constraint limits the number of various emergency power supply devices that can be deployed on each node before a disaster to no more than a given maximum number. Since each node can only be configured with at most one device of a certain type (binary variable), this constraint also effectively ensures that the total number of devices of all types in the entire network does not exceed the resource limit of the planning phase. It provides a hard boundary for device configuration in the first stage of the two-stage robust optimization decision.

[0080] Constraints on the number of lines attacked: in, Let K be a binary decision variable for whether to attack line ij in scenario s; it takes 0 if attacking and 1 otherwise. K is the number of attack lines. For distribution network nodes; This is a set of uncertain scenarios involving combined wind and solar power; this constraint is used to simulate line damage under the worst-case scenario. An attacker can choose any number of lines, up to K, to disable them. =0). Robust optimization will seek the disruptive combination that maximizes communication latency among all attack scenarios that satisfy this constraint, while decision-makers pre-configure the device to minimize latency in the worst case.

[0081] Constraints on active power balance at nodes: in, Let be the active power of the existing generator at node j in scenario s at time t; The active power of energy storage discharge configured for node j in scenario s at time t; The active power of the emergency power supply configured for node j in scenario s at time t; The actual active power of the wind turbine configured at node j in scenario s at time t; The actual active power of the photovoltaic system configured at node j in scenario s at time t; Let be the actual active power of node j switching loads under scenario s at time t; The active power of energy storage charging configured for node j in scenario s at time t; The active power purchased from the grid by the energy storage configured at node j in scenario s at time t; Let be the active power flowing out of node j in scenario s at time t; Let be the active power flowing into node j in scenario s at time t; Let be the resistance of branch ij; Let be the square of the current in branch ij under scenario s at time t; this constraint is the application of Kirchhoff's current law for active power in the distribution network at the nodes. The left side represents the total power injected into the node (generators, energy storage discharge, new energy sources, emergency power) minus the power flowing out of the node (load shedding, energy storage charging, purchased electricity). The right side represents the sum of the net power outflow from the node and line losses. This equation ensures the power balance of each node under any scenario and at any time, and is a fundamental constraint for the operation of the power system.

[0082] Constraints on reactive power balance at nodes: in, Let be the reactive power of the existing generator at node j in scenario s at time t; Let t be the reactive power of the energy storage discharge configured for node j in scenario s at time t; The reactive power of the emergency power supply configured for node j in scenario s at time t; The actual reactive power of the wind turbine configured at node j in scenario s at time t; The actual reactive power of the photovoltaic system configured at node j in scenario s at time t; Let t be the actual reactive power of node j switching load under scenario s at time t; The reactive power of the energy storage charging configured for node j in scenario s at time t; Let be the reactive power flowing out of node j in scenario s at time t; Let be the reactive power flowing into node j in scenario s at time t; Let be the reactance value of branch ij; this constraint is symmetrical with the active power balance, ensuring the reactive power balance of each node. Reactive power is crucial for voltage support, especially when the line is attacked, the system may experience voltage exceedances. This constraint, together with the node voltage drop constraint, restricts the feasible range of the system voltage.

[0083] Constraints on the lower bound of node voltage drop: Constraints on the upper bound of node voltage drop: in, , Let be the starting and ending voltages of branch ij in scenario s at time t, respectively; M is a sufficiently large number used for linearization constraints; these two constraints together constitute a linearized expression of the branch voltage drop equation, and the Big M method is used to handle the logic of whether the line exists. When the line is not attacked ( When =1), the inequalities on both sides degenerate into equality, i.e., the standard distribution network branch voltage drop formula. When the line is attacked ( When (=0), the right-hand side terms become -M and +M, which is equivalent to loosening the constraint, so that the line does not participate in power transmission. This is a common technique for handling topology reconfiguration.

[0084] Branch active power constraints: Branch reactive power constraints: in, This represents the upper limit of active power allowed for branch ij; This represents the upper limit of reactive power allowed for branch ij; Let be the active power on branch ij; The reactive power on branch ij; when the line is attacked ( When the voltage drop constraint is 0, the active and reactive power of the branch is forcibly limited to 0, i.e., the line is disconnected; when the line is normal, the power is within the thermal limit range. This constraint, together with the voltage drop constraint, accurately characterizes the availability and capacity limitations of the line.

[0085] Traditional generators have limitations in active power output: Constraints of reactive power output of traditional generators: in, , These represent the upper limits of active and reactive power of the conventional generator configured at node i, respectively. The active and reactive power output of the conventional generator set cannot exceed its rated capacity, and the output is non-negative. This constraint limits the generator's regulation capability in post-disaster scenarios and is the physical boundary for the safe operation of the system.

[0086] Constraints on node voltage amplitude: in, , These represent the upper and lower limits of the voltage at node i, respectively. National standards and electrical equipment requirements stipulate that the node voltage must be within a certain range (e.g., 0.95~1.05 pu). This constraint ensures that the system voltage does not exceed the limits regardless of whether the line is damaged, thus guaranteeing power supply quality.

[0087] Branch current constraints: in, This is the upper limit of the current on branch ij; the square of the branch current must not exceed the thermal stability limit to prevent line overload and burnout. This constraint is complementary to the active / reactive power limits, since the current limit is related to apparent power.

[0088] Constraints on active power during load shedding: Constraints on reactive power during load shedding: in, Let i be the maximum allowable active power to shed load. This represents the maximum reactive power allowed for load shedding at node i. When generation capacity is insufficient or the network is congested, partial load shedding is permitted, but cannot exceed the node's total load. Load shedding is selective; typically, lower-priority loads are shedding first. This constraint provides a physical upper limit for load shedding.

[0089] Constraints on second-order cone relaxation in distribution networks: This constraint relaxes the branch power flow equations into a second-order cone form; it relaxes the original non-convex AC power flow constraint into a convex second-order cone constraint, making the optimization problem solvable efficiently. When the relaxation is tight, the solution obtained is the exact AC power flow solution. This relaxation usually holds strictly in radial distribution networks and is therefore widely used in distribution network optimization.

[0090] Constraints on active power of energy storage discharge: Constraints on reactive power during energy storage discharge: in, The active power of discharge for energy stored at node i in scenario s; The reactive power of the energy stored at node i in scenario s; This represents the maximum active power of energy storage discharge. This represents the maximum reactive power of the energy storage system; the energy storage inverter has a maximum active and reactive power discharge capacity, typically limited by its rated power. This constraint limits the maximum support power that the energy storage system can provide after a disaster.

[0091] Relationship between energy storage charging and discharging power and energy capacity: in, , These are the energy storage charging efficiency and discharging efficiency, respectively. Active power for charging energy storage; This refers to the active power during energy storage discharge. The active power absorbed during energy storage charging, after efficiency conversion, satisfies the energy conservation principle with the active power released during discharge. More precisely, charging power and discharging power cannot be positive simultaneously, and their energy conversion must satisfy efficiency requirements.

[0092] Energy storage capacity recursion relationship: in, The energy storage capacity configured for node i in scenario s at time t; The time interval; this constraint describes the change of the energy storage state of charge (SOC) over time: the current energy level equals the energy level at the previous time level plus the charging energy (efficiency). Subtract the discharge energy (the reciprocal of efficiency) from the total energy storage capacity. This recursive relationship couples the energy storage behavior at different time periods and is the core of energy storage modeling.

[0093] Upper and lower limits of energy storage capacity constraints: in, The rated capacity of the energy storage configured for node i; to prevent damage from overcharging and over-discharging, 10% to 90% of the capacity is typically reserved. Configuration variables. This constraint ensures that nodes without energy storage always have zero charge. This extends the lifespan of energy storage and guarantees the feasibility of scheduling.

[0094] Energy storage charge and discharge states are mutually exclusive: in, , Let $\mathbf$ and $\mathbf$ be the flag variables indicating whether node $i$ is in a charging or discharging state under scenario $s$ at time $t$. The energy storage cannot charge and discharge simultaneously; this constraint mandates that charging and discharging states are mutually exclusive. If they are not mutually exclusive, the model might simultaneously buy and sell electrical energy, creating a circular flow, which violates physical reality.

[0095] Maximum power of energy storage charging: Upper limit of energy storage discharge power: in, The maximum charging power of the energy storage configured for node i in scenario s; This constraint defines the maximum discharge power of the energy storage configured for node i in scenario s; when the configuration flag is 0 or the status flag is 0, the charging / discharging power is forced to 0. This constraint unifies device existence, operating status, and power limits, preventing the model from generating non-zero power when no device is configured or charging / discharging is not permitted.

[0096] Maximum power capacity for energy storage to purchase electricity from the grid: Electricity purchases are only permitted while the device is charging; energy storage can only purchase electricity from the grid while charging and the device is configured, and the purchased power cannot exceed the charging power limit. This constraint restricts the ability of energy storage to purchase electricity from the main grid after a disaster, taking into account scenarios where the grid may partially recover.

[0097] Definition of energy storage charge / discharge state change: Energy storage charge / discharge cycle limit: in, The change in the charging and discharging state of the energy storage device configured at node i in scenario s at time t is the change in the charging and discharging state of the energy storage device in adjacent time periods. This represents the maximum permissible number of charge / discharge state switching cycles for energy storage. Frequent switching between charge and discharge states accelerates energy storage aging. By statistically analyzing the number of times the charging state changes from 0 to 1, the maximum number of switching cycles allowed within a single scheduling cycle is limited. This constraint effectively extends the actual lifespan of the energy storage.

[0098] Wind turbine active power output constraints: Wind turbine reactive power output constraints: in, , These represent the maximum active and reactive power outputs of the wind turbine configured at node i in scenario s, respectively. The actual output of the wind turbine is constrained by the equipment configuration flags and the maximum available output in the current scenario (e.g., different power outputs corresponding to different wind speeds). This constraint links the upper limit of wind turbine output in uncertain scenarios with the configuration decision.

[0099] Solar power output constraints: Solar reactive power output constraints: in, , These represent the maximum active and reactive power outputs of the photovoltaic system configured for node i in scenario s, respectively. Similar to wind turbines, the actual active and reactive power outputs of photovoltaic systems are limited by configuration flags and the maximum output in the scenario (e.g., solar irradiance). This constraint, together with the constraint on wind turbines, models the randomness and controllability of distributed renewable energy.

[0100] In application, the constraints on the number of devices configured and the number of lines attacked in the distribution network operation constraints are used to limit the scale of configurable resources before a disaster and the scale of faults considered during a disaster. The constraint on the number of devices configured requires that the number of energy storage, photovoltaic, wind turbines, and emergency power supplies each be limited to a given upper limit, to avoid exceeding the actual available resources before a disaster. The constraint on the number of lines attacked requires that the number of lines that fail simultaneously does not exceed a given number of attacked lines, to characterize the worst-case scenario of multiple lines being damaged simultaneously under extreme weather conditions. These two types of constraints together determine the boundaries of optimization in terms of both resources and faults.

[0101] In applications, the active and reactive power balance constraint at each node requires that the power flowing into and out of each distribution network node remain balanced. This constraint links the existing generator output, energy storage charging and discharging, emergency power output, wind turbine output, photovoltaic output, load shedding, and power purchased from the grid at the node with the branch power flowing into and out of that node, ensuring that each node satisfies power conservation at any time and under any scenario. The reactive power balance constraint is similar, requiring that the reactive power at each node also remain balanced. The power balance constraint guarantees that the operating state of the distribution network under faults and fluctuations is physically valid.

[0102] In applications, node voltage drop constraints, branch power constraints, node voltage magnitude constraints, branch current constraints, and second-order cone relaxation constraints of the distribution network jointly characterize the power flow relationships and operational limits of the distribution network. Node voltage drop constraints link the voltage difference between adjacent nodes to the power flowing through the branch and the line impedance. Branch power constraints limit the active and reactive power transmitted on the branch to a range corresponding to the line connectivity state. Node voltage magnitude constraints and branch current constraints limit node voltage and branch current to safe ranges, respectively. Second-order cone relaxation constraints of the distribution network relax the non-convex parts of the power flow equations into an efficiently solvable second-order cone form. These constraints collectively ensure that the power flow calculations are both consistent with physical laws and easy to solve.

[0103] In applications, traditional generator output constraints, load shedding output constraints, wind turbine output constraints, and photovoltaic output constraints are used to limit various power sources and load regulation methods within their respective feasible ranges. Traditional generator output constraints limit the active and reactive power output of existing generators to their upper limits; load shedding output constraints limit the active and reactive power output of loads that can be shelved to within allowable ranges; and wind turbine output constraints and photovoltaic output constraints respectively limit the actual active and reactive power output of wind turbines and photovoltaics to their maximum output capacity in that scenario, and are related to whether a corresponding power source is configured at that node. These constraints ensure that the regulation of various power sources and loads does not exceed actual capabilities.

[0104] In applications, energy storage charge / discharge constraints, including grid-purchased power constraints and constraints on the number of charge / discharge cycles, are used to characterize the operating patterns of energy storage devices. The stored capacity varies with charging and discharging; that is, the current stored capacity equals the previous stored capacity plus the charging amount calculated based on charging efficiency, minus the discharging amount calculated based on discharging efficiency. Energy storage charge / discharge constraints also require that the energy storage cannot be charged and discharged simultaneously at any given time, and that the charging and discharging power be limited to maximum power. Grid-purchased power constraints limit the power purchased from the grid for energy storage, and constraints on the number of charge / discharge cycles limit the number of times the energy storage switches between charge and discharge states within a day to protect the energy storage's lifespan. These constraints collectively ensure that energy storage operation meets its physical characteristics and lifespan requirements.

[0105] Specifically, when the two-stage robust optimization model solves a typical scenario, the constraints on the number of equipment configurations and the number of lines attacked first determine the range of configurable resources and damaged lines. Then, the constraints on the balance of active and reactive power at nodes determine the power conservation relationship of each node. Subsequently, the constraints on node voltage drop, branch power, node voltage amplitude, branch current, and second-order cone relaxation determine the power flow distribution that conforms to physical laws. Next, the constraints on traditional generators, load shedding, wind turbines, and photovoltaic output limit the regulation of various power sources and loads to a feasible range. Finally, the constraints on energy storage charging and discharging, purchased electricity, and charging and discharging times determine the operating status of energy storage at each time. The above constraints together constitute the feasible operating domain of the distribution network under faults and fluctuations, making the optimized deployment and scheduling scheme truly feasible on the power side.

[0106] In the power flow equations, the non-convex parts can be transformed into an efficient solution using a second-order cone relaxation method, or approximated using piecewise linearization. Energy storage lifetime protection can be achieved by limiting the number of charge / discharge cycles per day, or by limiting the upper and lower limits of the stored capacity to prevent overcharging and over-discharging.

[0107] The distribution network operation constraints comprehensively incorporate various aspects such as equipment configuration, line faults, power balance, power flow limits, power output, and energy storage operation, ensuring the feasibility of the optimized solution on the power side and thus guaranteeing a stable and reliable power supply foundation for communication nodes. Second-order cone relaxation is used in the constraints to handle the non-convex portion of the power flow, making the distribution network power flow constraints easier to solve efficiently while maintaining physical meaning, thereby improving the overall model's computability. The constraints limit the energy storage capacity, charging / discharging power, and number of charge / discharge cycles, ensuring that energy storage operates within a safe and reasonable range when supplying power to communication nodes, thereby extending energy storage life and ensuring power supply continuity.

[0108] In the application, each communication requirement point is covered by at least one of the following methods: truck or drone, as shown below: The truck's travel path has no sub-loops and meets the timing requirements for time synchronization and drone takeoff, landing, and recovery, as shown below: The flight time of a drone shall not exceed its maximum endurance, and the communication coverage distance of a drone shall not exceed its maximum communication coverage radius, as expressed in the following way: in, For the set of communication demand points; This is a set of drone take-off and landing and relay nodes; For the set of truck nodes; The decision variable for deploying the truck communication node at node i is set to 1 if configured, and 0 otherwise. The decision variable is whether the UAV uses node j as its take-off, landing, or relay node; if yes, it takes the value 1, otherwise it takes the value 0. The decision variable is set to 1 if the truck travels between node i and node j and provides link services, and 0 otherwise. Let $\frac{1}{2}$ be the decision variable for whether the drone flies along nodes $i$, $j$, and $k$ and acts as a relay. If it does, $\frac{1}{2}$ is set to $1$, otherwise $\frac{0}{2}$. This refers to the flight duration of the drone; This refers to the maximum flight time of the drone; (i,j,k) represents the communication coverage distance of the UAV; This represents the maximum communication coverage radius of the drone. For any subset of the set of truck nodes, This represents the number of nodes in the subset.

[0109] Communication demand points refer to locations in the disaster area that require access to the communication network, and coverage means that these locations can access the communication network directly via trucks or via drone relays. This constraint ensures that no communication demand points are overlooked, enabling every location in the disaster area that needs communication to be included in the integrated air-ground emergency communication network, thereby avoiding communication blind spots.

[0110] In this application, the truck's travel path must be free of sub-loops and must satisfy the timing requirements for time synchronization and the takeoff, landing, and recovery of the drone. A sub-loop refers to an isolated closed loop that deviates from the main path within the truck's route. The absence of sub-loops requires that the truck's travel route be continuous and free of such isolated loops. Time synchronization requires that the truck and drone's data exchange and takeoff / landing times correspond. The timing of drone takeoff, landing, and recovery requires that the drone's takeoff, relay, and return to the truck be properly scheduled so that the drone can return to the truck before its battery runs out. This constraint ensures that the truck and drone coordinate their collaborative communication in time and space.

[0111] In application, maximum flight time refers to the longest period of continuous flight a drone can sustain on its own power after a single takeoff. Flying time not exceeding the maximum flight time ensures the drone will not lose control due to depleted battery. Maximum communication coverage radius refers to the farthest distance that the drone's onboard communication equipment can effectively cover. Communication coverage distance not exceeding the maximum communication coverage radius ensures the demand points served by the drone are indeed within its effective coverage area. This constraint ensures that the drone's mission scheduling aligns with its own flight time and communication capabilities.

[0112] Specifically, when planning air-ground coordinated communication for disaster-stricken areas, coverage constraints first confirm that each communication demand point is directly covered by a truck or relayed by a drone. Then, truck route constraints arrange for trucks to travel along a continuous route without isolated loops and to keep synchronized with the drones at the handover time. Subsequently, the drone take-off, landing, and recovery sequence arranges for drones to take off from the trucks, fly to the blind spot to act as relays, and return to the trucks for resupply before their power is exhausted. At the same time, endurance and coverage constraints ensure that the flight time and service distance of each drone are within its capabilities. The above constraints together ensure that the coordinated deployment of trucks and drones is feasible in terms of time, space, and capability.

[0113] The coverage of communication needs can be achieved through direct truck access or through drone relay access. Ensuring that drones return before running out of power can be achieved by limiting flight time to their maximum endurance, or by having drones return to trucks for resupply before taking off again.

[0114] Coverage constraints require that each communication demand point be covered by at least one truck or drone, ensuring no communication blind spots in the disaster area and guaranteeing the integrity of emergency communication coverage. Truck route loop-free and timing constraints ensure that trucks and drones are coordinated in time and space, avoiding route waste and handover misalignment, and improving coordination efficiency. Drone endurance and coverage constraints limit drone mission assignments to their endurance and communication capabilities, enabling drones to reliably complete relay missions and ensuring the continuity of air-to-ground collaborative communication.

[0115] In applications, the single-link delay upper limit constraint in cyber-physical system communication delay constraints requires that the communication delay of each communication link in each scenario does not exceed the given maximum permissible delay of a single link, and the end-to-end path maximum permissible delay constraint requires that the cumulative delay of each segment of the end-to-end communication path and the number of hops in each scenario do not exceed the given maximum permissible delay of the end-to-end path, respectively expressed as: in, Let be the communication delay of link ij in scenario s; This represents the maximum allowable delay for a single link. Let be the number of hops in link ij; A set of communication links; For end-to-end communication path, A set of end-to-end communication paths; This represents the maximum allowable delay for an end-to-end path. This is a set of uncertain scenarios for wind power and photovoltaics.

[0116] A single link refers to a direct link between two adjacent nodes in a communication network. The maximum allowable delay of a single link is the upper limit set on the delay of a single link to ensure timely data transmission. This constraint ensures that there are no single links with excessively high delays, so that each link meets the basic latency requirements, thus laying the foundation for timely end-to-end transmission.

[0117] In applications, an end-to-end communication path refers to the complete link sequence that data traverses from the source node through several intermediate nodes to finally reach the destination node. The hop count refers to the number of link segments the data passes through on this path, and the maximum allowable delay for the end-to-end path is the upper limit set on the cumulative delay of the entire path to meet emergency dispatch delay requirements. This constraint ensures that the cumulative delay of the entire transmission path is controlled, enabling critical data to be delivered within the specified time limit.

[0118] In application, the two-stage robust optimization model is a three-layer structure of min-max-min, where the lower layer includes energy storage charging and discharging coupled with time-series coupling, and is decomposed and solved using a nested column and constraint generation algorithm. The min-max-min three-layer structure means that the outermost layer selects a deployment scheme before a disaster with the goal of minimizing latency; the middle layer maximizes latency under the given deployment and worst-case failure scenario; and the innermost layer arranges disaster-prone scheduling with the goal of minimizing latency under the worst-case scenario. Since the lower layer contains time-series coupling of energy storage charging and discharging, which is difficult to handle directly, a nested column and constraint generation algorithm is used to decompose the three-layer structure into a main problem and subproblems that can be solved iteratively. The main problem provides the deployment and scheduling schemes, while the subproblems identify the worst-case scenario and supplement the main problem with corresponding constraints. The two iterate repeatedly until convergence.

[0119] Specifically, when solving the two-stage robust optimization model, the single-link delay upper limit constraint is used to check whether the delay of each link in each scenario does not exceed the maximum allowable delay of the single link. Then, the maximum allowable delay constraint of the end-to-end path is used to check whether the cumulative delay of each end-to-end path in each scenario does not exceed the maximum allowable delay of the end-to-end path. Subsequently, the nested column and constraint generation algorithm selects a set of deployment schemes at the outermost layer, searches for the most unfavorable failure scenario that maximizes the delay in the middle layer, and arranges disaster relief scheduling of trucks and drones for this scenario in the innermost layer. The constraints corresponding to the most unfavorable scenario are added to the main problem and solved again. This process is repeated iteratively until the deployment and scheduling scheme still satisfies all delay constraints and minimizes the total lifecycle delay in the most unfavorable scenario. Finally, the deployment and scheduling scheme that meets the latency requirements is output.

[0120] The control of single-link latency can be achieved by setting a maximum allowable latency limit for a single link, or by checking the link latency based on the link rate and data volume. The efficient solution of the three-layer structure can be achieved through a layered iterative approach using nested column and constraint generation algorithms, or by successively supplementing the main problem with the most unfavorable scenario constraints to approximate the global optimum.

[0121] Single-link delay upper limit constraints and end-to-end path maximum allowable delay constraints control delay at both the single-link and entire-path levels, ensuring that the communication network has neither excessively high-latency individual links nor entire paths with accumulated delay exceeding limits, thus effectively meeting the real-time requirements of cyber-physical systems. The model employs a min-max-min three-layer structure, ensuring that deployment and scheduling schemes maintain delay control even under the most unfavorable failure scenarios, thereby enhancing the robustness of the communication network to extreme failures. Nested column and constraint generation algorithms are used to decompose and solve the three-layer structure, enabling the efficient acquisition of solutions that satisfy delay constraints for complex models involving energy storage time-series coupling, thus balancing global optimization with computational efficiency.

[0122] In one specific embodiment, to further verify the feasibility of the two-stage robust optimization model of the present invention on the distribution network side and the reliability of the power supply foundation of the communication nodes obtained therefrom, a radial distribution network with 33 nodes is used as a case study to perform power flow calculation and network loss minimization optimization on the distribution network operation constraints of the present invention. The reference voltage of the distribution network in this case study is 12.66kV, the reference capacity is 100MVA, and the corresponding reference impedance is approximately 1.6028Ω; the upper and lower limits of the node voltage of the entire network are 1.1pu and 0.9pu, respectively; the total active load of the entire network is 3715kW, and the total reactive load is 2300kVar. This case study does not connect to distributed power sources, and only the first node supplies power to the entire network through an external power source. The active and reactive power injections from the external power source are both approximately 0.0005pu. The node load parameters of this case study are shown in Table 1, and the resistance and reactance parameters (per-unit values) of each branch are shown in Table 2.

[0123] Table 1 Distribution Network Node Load Parameters Table 2. Distribution Network Branch Impedance Parameters Based on the above system parameters, and in accordance with the node active and reactive power balance constraints, node voltage drop constraints, branch power constraints, node voltage amplitude constraints, branch current constraints, and second-order cone relaxation constraints of the distribution network operation constraints in this invention, power flow optimization is performed on this example with the objective of minimizing the overall network active power loss. The measured results of the optimized node voltage amplitudes are shown in Table 3, the measured results of the active and reactive power flows of each branch are shown in Table 4, and the summary indices of the power flow optimization solution are shown in Table 5.

[0124] Table 3. Optimized voltage amplitudes at each node Table 4 Optimized power flow of each branch Table 5 Summary Indicators of Power Flow Optimization Solution As shown in Table 3, after optimizing the power flow with the goal of minimizing network loss, the voltage amplitude of all nodes in the entire network falls within the allowable range of [0.9, 1.1] pu: the voltage of the first node is 1.0 pu, and the lowest voltage point occurs at node 18, with an amplitude of 0.9131 pu, which is still higher than the lower limit of 0.9 pu. This indicates that the node voltage amplitude constraint and node voltage drop constraint in the distribution network operation constraints of this invention are both satisfied in this example, and the obtained power flow distribution conforms to the physical operation law of the distribution network.

[0125] As shown in Tables 4 and 5, the total active power loss of the entire network after optimization is 202.73 kW, corresponding to an objective function value of approximately 0.002027 in per-unit terms. The total active power injected into the network by external power sources is 3917.72 kW, which is approximately equal to the sum of the total active load of 3715 kW and the total network loss of 202.73 kW. The total reactive power injected is 2435.21 kVar. The power flowing into and out of each node strictly satisfies the power conservation principle, indicating that the active and reactive power balance constraints at each node are valid under this example. The power flow of each branch decreases stepwise from the head node along the feeder, which conforms to the power flow characteristics of a radial distribution network supplying power from the source end to the end. This also indicates that the branch power constraints, branch current constraints, and the second-order cone relaxation constraints of the distribution network are all satisfied.

[0126] In the above content, there is a 0.01 kW deviation between the external power injection power (3917.72 kW) and the total load + network loss (3917.73 kW) in Table 5. This deviation is caused by the rounding error in the numerical solution during the power flow iteration calculation (the solver convergence accuracy is taken as 10). -6 The difference (pu) is much smaller than the allowable error range in engineering and does not affect the power balance analysis results.

[0127] The above measured data show that the distribution network operation constraints and their second-order cone relaxation form established in this invention can be stably solved and converged on the 33-node distribution network example. The resulting power flow distribution is physically feasible, the voltage quality meets the requirements, and the network loss is effectively reduced. Since this invention establishes the power supply foundation for communication nodes such as truck ground communication hubs, UAV take-off and landing and resupply points on this distribution network, the feasibility of the power flow and the stability of the voltage indicate that the above-mentioned communication nodes can obtain stable and reliable power supply support, thus providing a solid power foundation for pre-disaster pre-configuration and dynamic scheduling of air-ground collaborative communication during disasters. This example verifies the feasibility of the technical solution of this invention from the distribution network side and further supports the realization of the optimization goal of minimizing end-to-end communication delay.

[0128] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A latency optimization system based on UAV-truck joint emergency communication, characterized in that, It includes a coupled modeling module, a scene generation module, a two-stage robust optimization module, and a solution module; The coupled modeling module is used to construct a power distribution network fault model, an air-to-ground mobile communication network model, and a cyber-physical system communication delay model. In the air-to-ground mobile communication network model, trucks are configured as ground mobile communication hubs, and drones are configured as airborne mobile relay nodes. The trucks and drones work together to form an integrated air-to-ground emergency communication network covering communication blind spots. The cyber-physical system communication delay model uses the sum of access delay, transmission delay, forwarding delay, queue delay, and processing delay to characterize end-to-end communication delay. The scenario generation module is used to generate a set of typical scenarios that characterize the uncertainty of wind power output and photovoltaic power output; The two-stage robust optimization module is used to establish an optimization model with the goal of minimizing the full-cycle communication latency. In the pre-disaster stage, the optimization model optimizes the strategic deployment locations of communication nodes, candidate paths, and the pre-configuration of communication equipment and links. In the disaster stage, in response to network topology damage caused by wind power output fluctuations, photovoltaic output fluctuations, and distribution network line faults, the model dynamically schedules the trucks and drones to conduct collaborative communication in order to minimize the end-to-end communication latency. The distribution network fault model, the uncertainty of wind power output and photovoltaic output, and the cyber-physical system communication latency model are coupled in the optimization model. The solution module is used to decompose and solve the optimization model established by the two-stage robust optimization module, and output the communication node deployment scheme and the collaborative communication scheduling scheme.

2. The delay optimization system based on UAV-truck joint emergency communication according to claim 1, characterized in that, In the air-to-ground mobile communication network model, the truck, as a core ground communication node, has the capabilities of backhaul, switching, relaying, and providing take-off, landing, resupply, and command and control for the UAV; the UAV, as an airborne mobile relay node or airborne temporary base station, is used to extend communication coverage, overcome obstacles, and improve link quality in communication blind spots; the communication links between the truck and the UAV, as well as between the truck and the communication demand points, are established using wireless ad hoc networks, wireless mesh networks, or satellite backhaul methods, and the delays generated by the communication links include access delay, transmission delay, forwarding delay, queuing delay, and processing delay.

3. The delay optimization system based on UAV-truck joint emergency communication according to claim 1, characterized in that, The distribution network fault model is a model of a line NK fault occurring in a distribution network under extreme weather conditions. In the distribution network fault model, the load and power of the distribution network nodes fluctuate with the line fault, and the communication demand changes dynamically with the occurrence of the line fault.

4. The delay optimization system based on UAV-truck joint emergency communication according to claim 1, characterized in that, In the cyber-physical system communication delay model, the total end-to-end communication delay is equal to the sum of access delay, transmission delay, forwarding delay, queue delay, and processing delay; the two-stage robust optimization module uses the end-to-end average delay and maximum delay as optimization objectives.

5. The delay optimization system based on UAV-truck joint emergency communication according to claim 1, characterized in that, The scene generation module uses Latin hypercube sampling to generate initial scenes of wind speed, irradiance, and load fluctuations, and then performs backward reduction to obtain the typical scene set. The typical scene set is used to characterize the impact of the uncertainty of wind power output and photovoltaic power output on communication load and power supply reliability.

6. A delay optimization method based on UAV-truck joint emergency communication, characterized in that, include: A power distribution network fault model, an air-to-ground mobile communication network model, and a cyber-physical system communication delay model are constructed. Trucks are configured as ground mobile communication hubs and drones are configured as air mobile relay nodes. The trucks and drones work together to form an integrated air-to-ground emergency communication network covering communication blind spots. The end-to-end communication delay is characterized by the sum of access delay, transmission delay, forwarding delay, queue delay, and processing delay. Generate a set of typical scenarios that characterize the uncertainties in wind power output and photovoltaic power output; A two-stage robust optimization model is established with the goal of minimizing the communication latency throughout the entire lifecycle. In the pre-disaster stage, the strategic deployment locations of communication nodes, candidate paths, and the pre-configuration of communication equipment and links are optimized. In the disaster stage, in response to the network topology damage caused by wind power output fluctuations, photovoltaic power output fluctuations, and distribution network line faults, the trucks and drones are dynamically scheduled to conduct collaborative communication to minimize the end-to-end communication latency. The distribution network fault model, the uncertainty of wind power output and photovoltaic power output, and the cyber-physical system communication latency are coupled in the two-stage robust optimization model. The two-stage robust optimization model is decomposed and solved to output the communication node deployment scheme and the cooperative communication scheduling scheme.

7. The delay optimization method based on UAV-truck joint emergency communication according to claim 6, characterized in that, The two-stage robust optimization model established with the goal of minimizing the entire communication cycle delay has the following objective function: Where F is the target value of the full-cycle communication delay to be minimized; s represents the uncertainty scenario of wind power and photovoltaic power. Let be the probability of scenario s; i and j are communication nodes, and (i,j) represents the link from node i to node j; The weight of link ij is given by the link with the critical load and the link corresponding to the monitoring point. Let λ be the communication delay of link ij in scenario s; λ is the maximum delay penalty coefficient.

8. The delay optimization method based on UAV-truck joint emergency communication according to claim 6, characterized in that, The power distribution network operation constraints of the two-stage robust optimization model include: Constraints on the number of devices that can be configured: in, , , and These are binary decision variables for configuring energy storage, photovoltaics, wind turbines, and emergency power supplies at node i during the pre-disaster phase. Constraints on the number of lines attacked: in, Let K be the binary decision variable for whether to attack line ij in scenario s; K is the number of attack lines. For distribution network nodes; A collection of uncertain scenarios combining wind and solar power; Constraints on active power balance at nodes: in, Let be the active power of the existing generator at node j in scenario s at time t; The active power of energy storage discharge configured for node j in scenario s at time t; The active power of the emergency power supply configured for node j in scenario s at time t; The actual active power of the wind turbine configured at node j in scenario s at time t; The actual active power of the photovoltaic system configured at node j in scenario s at time t; Let be the actual active power of node j switching loads under scenario s at time t; The active power of energy storage charging configured for node j in scenario s at time t; The active power purchased from the grid by the energy storage configured at node j in scenario s at time t; Let be the active power flowing out of node j in scenario s at time t; Let be the active power flowing into node j in scenario s at time t; Let be the resistance of branch ij; Let be the square of the current in branch ij under scenario s at time t; Constraints on reactive power balance at nodes: in, Let be the reactive power of the existing generator at node j in scenario s at time t; Let t be the reactive power of the energy storage discharge configured for node j in scenario s at time t; The reactive power of the emergency power supply configured for node j in scenario s at time t; The actual reactive power of the wind turbine configured at node j in scenario s at time t; The actual reactive power of the photovoltaic system configured at node j in scenario s at time t; Let t be the actual reactive power of node j switching load under scenario s at time t; The reactive power of the energy storage charging configured for node j in scenario s at time t; Let be the reactive power flowing out of node j in scenario s at time t; Let be the reactive power flowing into node j in scenario s at time t; Let be the reactance value of branch ij; Constraints on the lower bound of node voltage drop: Constraints on the upper bound of node voltage drop: in, , Let be the starting voltage and ending voltage of branch ij under scenario s at time t, respectively; M is a preset constant greater than the maximum allowable deviation range of the voltage amplitude of the distribution network node, used to relax the voltage drop constraint when the branch is disconnected; Branch active power constraints: Branch reactive power constraints: in, This represents the upper limit of active power allowed for branch ij; This represents the upper limit of reactive power allowed for branch ij; Let be the active power on branch ij; The reactive power on branch ij; Traditional generators have limitations in active power output: Constraints of reactive power output of traditional generators: in, , These are the upper limits of active and reactive power of the traditional generator configured at node i, respectively; Constraints on node voltage amplitude: in, , These are the upper and lower limits of the voltage at node i, respectively; Branch current constraints: in, This represents the upper limit of the current in branch ij; Constraints on active power during load shedding: Constraints on reactive power during load shedding: in, Let i be the maximum allowable active power to shed load. The maximum allowable load shedding reactive power for node i; Constraints on second-order cone relaxation in distribution networks: This constraint relaxes the branch power flow equations into a second-order cone form; Constraints on active power of energy storage discharge: Constraints on reactive power during energy storage discharge: in, The active power of discharge for energy stored at node i in scenario s; The reactive power of the energy stored at node i in scenario s; This represents the maximum active power of energy storage discharge. This represents the maximum reactive power of energy storage discharge. Relationship between energy storage charging and discharging power and energy capacity: in, , These are the energy storage charging efficiency and discharging efficiency, respectively. Active power for charging energy storage; The active power of energy storage discharge; Energy storage capacity recursion relationship: in, The energy storage capacity configured for node i in scenario s at time t; For time intervals; Upper and lower limits of energy storage capacity constraints: in, The rated capacity of the energy storage configured for node i; Energy storage charge and discharge states are mutually exclusive: in, , These are the flag variables indicating whether the energy storage at node i is in charging or discharging state under scenario s at time t; Maximum power of energy storage charging: Upper limit of energy storage discharge power: in, The maximum charging power of the energy storage configured for node i in scenario s; The maximum discharge power of the energy storage configured for node i in scenario s; Maximum power capacity for energy storage to purchase electricity from the grid: Electricity purchases are only permitted while the device is charging. Definition of energy storage charge / discharge state change: Energy storage charge / discharge cycle limit: in, The change in the charging and discharging state of the energy storage device configured at node i in scenario s at time t is the change in the charging and discharging state of the energy storage device in adjacent time periods. This represents the maximum permissible number of charge / discharge state switching cycles for energy storage. Wind turbine active power output constraints: Wind turbine reactive power output constraints: in, , These represent the maximum active and reactive power outputs of the wind turbine configured at node i in scenario s, respectively. Solar power output constraints: Solar reactive power output constraints: in, , These represent the maximum values ​​of the active and reactive power outputs of the photovoltaic system configured for node i in scenario s.

9. The delay optimization method based on UAV-truck joint emergency communication according to claim 6, characterized in that, The air-to-ground mobile communication constraints of the two-stage robust optimization model include: Each communication requirement point is covered by at least one of the following methods: truck or drone, represented as: in, For the set of communication demand points; This is a set of drone take-off and landing and relay nodes; The decision variables for deploying the truck communication node at node i; , which is the decision variable for whether the UAV uses node j as its take-off, landing or relay node; The decision variable is whether the drone flies in ijk and acts as a relay. The truck's travel path has no sub-loops and meets the timing requirements for time synchronization and drone takeoff, landing, and recovery, as shown below: in, For the set of truck nodes; The decision variables for deploying the truck communication node at node i; For the decision variable of whether the truck travels between node i and node j and provides link service; For any subset of the set of truck nodes, This represents the number of nodes in the subset. The flight time of a drone shall not exceed its maximum endurance, and the communication coverage distance of a drone shall not exceed its maximum communication coverage radius, as expressed in the following way: in, This refers to the flight duration of the drone; This refers to the maximum flight time of the drone; (i,j,k) represents the communication coverage distance of the UAV; This represents the maximum communication coverage radius of the drone.

10. The delay optimization method based on UAV-truck joint emergency communication according to claim 6, characterized in that, The cyber-physical system communication delay constraints of the two-stage robust optimization model include a single-link delay upper limit constraint and an end-to-end path maximum allowable delay constraint, respectively expressed as: in, Let be the communication delay of link ij in scenario s; This represents the maximum allowable delay for a single link. Let be the number of hops in link ij; A set of communication links; For end-to-end communication path, A set of end-to-end communication paths; This represents the maximum allowable delay for an end-to-end path. This is a set of uncertain scenarios for wind power and photovoltaics; In the process of decomposing and solving the two-stage robust optimization model, the two-stage robust optimization model is a three-layer structure of minimum-maximum-min, and its lower layer includes energy storage charging and discharging and time-series coupling. The nested column and constraint generation algorithm is used for decomposition and solution.

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