Power distribution network air-ground collaborative emergency communication recovery method considering information-physical coupling

Abstract

This invention discloses a method for emergency communication recovery of distribution networks using air-ground coordination, considering cyber-physical coupling, belonging to the field of distribution network resilience technology. This invention aims to solve the technical problem of load recovery difficulties caused by combined faults in distribution and communication networks under extreme disasters. The method constructs a communication network data flow model, a UAV and mobile communication vehicle channel model, an emergency resource working model, and a traffic network model, and combines cyber-physical coupling and distribution network operation constraints to establish an optimization model with the goal of minimizing distribution network load loss. This invention, by jointly optimizing the deployment and trajectory of air-ground emergency communication resources, prioritizes the restoration of communication at key nodes that significantly support the power grid, while meeting communication quality constraints, achieving efficient distribution network load recovery. It is mainly used for emergency repair and power restoration of distribution networks after disasters.

Description

Technical Field

[0001] This invention relates to the field of power distribution network resilience and emergency communication technology, and in particular to a power distribution network air-ground coordinated emergency communication recovery method that considers cyber-physical coupling. Background Technology

[0002] With the deep integration of information and communication technologies and smart grids, traditional distribution networks are gradually evolving into highly integrated cyber-physical systems. Communication networks undertake key functions such as distribution network status awareness, data feedback, and dispatch command issuance, significantly improving the system's observability and controllability. However, under extreme natural disasters, power facilities and communication infrastructure often suffer simultaneous damage, resulting in complex cyber-physical system failures. Communication node failures trigger significant chain reactions: dispatch centers struggle to grasp system operating status due to missing measurement data, and distributed power sources and load demands cannot be effectively perceived; simultaneously, distribution automation terminals fail to operate due to communication interruptions, rendering critical operations such as remote fault isolation, network reconfiguration, and black start ineffective, causing isolated microgrids with power supply capabilities to be unable to operate, further expanding the scope and extent of power outages.

[0003] Existing research on disaster recovery of power distribution networks largely focuses on physical layer repairs, such as the dispatch of emergency power vehicles or repair teams. It typically assumes that communication networks are available, neglecting the fundamental constraints that communication interruptions impose on power control and recovery logic. The few studies involving communication recovery also often employ a decoupling approach, prioritizing communication coverage or relying solely on drones. This approach suffers from problems such as target bias, resource constraints, and insufficient characterization of the coupling relationship between communication, power, and physical constraints, making it difficult to guarantee the engineering feasibility and overall efficiency of the recovery plan. Summary of the Invention

[0004] This invention provides a method for emergency communication restoration of power distribution networks that considers cyber-physical coupling. Its core objective is to optimize the deployment of emergency communication resources and prioritize the restoration of communication at key power nodes in the event of simultaneous damage to communication and power facilities after a disaster, thereby maximizing the load recovery of the power distribution network.

[0005] As a preferred embodiment of the present invention, the method includes constructing a communication network data flow model. In the model, a terminal node is configured to only be able to select wired communication mode, wireless communication mode, or be in a packet loss state at any given time. Data packets must meet traffic balancing conditions during transmission, meaning that generated data packets are either successfully transmitted or confirmed as lost. Simultaneously, the model strictly limits transmission latency, requiring that the transmission latency of wired paths or wireless links not exceed the maximum latency threshold allowed by the service. Furthermore, the total amount of data flowing through all physical links must not exceed the bandwidth capacity limit of that link, and link failure states must be considered.

[0006] As a preferred embodiment of the present invention, the method includes constructing a UAV channel model. This model calculates the spatial distance and ground elevation angle based on the three-dimensional position of the UAV and the two-dimensional position of the terminal. The line-of-sight (LAS) propagation probability and non-LAS propagation probability are calculated based on the elevation angle, and path loss is calculated by combining the path loss exponent and the non-LAS additional attenuation coefficient. The model also introduces a shadowing fading factor that follows a log-normal distribution to calculate the desired channel gain, signal-to-noise ratio (SNR), and upper bound of the link capacity.

[0007] As a preferred embodiment of the present invention, the method includes constructing a mobile communication vehicle channel model. Since both the mobile communication vehicle and the terminal are located on the ground, the model ignores height differences and calculates the line-of-sight propagation probability using an exponential attenuation model based on horizontal distance. Path loss is described using a logarithmic distance model, calculating the losses for line-of-sight and non-line-of-sight paths separately, and combining the probabilities to obtain the expected path loss. The link capacity between the mobile communication vehicle and the terminal is also calculated, considering the impact of shadow fading.

[0008] As a preferred embodiment of the present invention, the method includes constructing an emergency communication resource working model. This model stipulates that a terminal can only access wireless resources if the signal-to-noise ratio is not lower than a minimum threshold. To avoid interference, a terminal is limited to being served by only one drone or one mobile communication vehicle at a time. Simultaneously, a maximum number of terminals that a single emergency communication resource can serve simultaneously is set.

[0009] As a preferred embodiment of the present invention, the method includes constructing a traffic network model for mobile communication vehicles. This model constrains the mobile communication vehicles to be located at nodes or roads within the traffic network, their movement speed to be limited by a maximum speed, and their position changes at adjacent times to satisfy the requirements of network topology and flow conservation continuity.

[0010] As a preferred embodiment of the present invention, the method includes constructing a cyber-physical system coupling and distribution network operation constraint model. This is the core part of the present invention, establishing the coupling relationship between successful communication and load recovery. A communication success identifier variable is defined; only when a terminal successfully establishes a communication connection can the corresponding load node meet the recovery conditions, and the corresponding distributed power source receive the start command. Regarding distribution network operation constraints, a virtual flow method is used to ensure that the restored network maintains a radial topology while satisfying electrical constraints such as node power balance, line capacity limitations, and node voltage deviation.

[0011] As a preferred embodiment of the present invention, the method ultimately establishes and solves an objective function for minimizing load loss in the distribution network. This objective function aims to minimize the weighted sum of the differences between the demand and actual recovery of each load node at each time point, where the weighting coefficients reflect the importance of the loads. By solving this mixed-integer linear programming model, the optimal scheduling scheme for unmanned aerial vehicles (UAVs) and mobile communication vehicles is obtained.

[0012] The present invention proposes a method for restoring emergency communication in a power distribution network that considers cyber-physical coupling, which has the following beneficial effects:

[0013] 1. This invention departs from the traditional approach of simply maximizing communication coverage, treating communication restoration as a means and power load restoration as the ultimate goal. By establishing a cyber-physical coupling constraint model, it clarifies the decisive role of communication connectivity on the controllability of power load, ensuring that emergency resources prioritize serving the key nodes that contribute the most to power grid restoration, thereby maximizing the restoration efficiency of distribution network load with limited resources.

[0014] 2. This invention comprehensively utilizes the advantages of UAVs (unrestricted by terrain) and their excellent line-of-sight transmission performance, as well as the characteristics of mobile communication vehicles (MOVs) with long battery life and large bandwidth, but limited by road networks. By constructing separate air-to-ground and ground-to-ground channel models and introducing traffic network constraints, it achieves complementary advantages and coordinated scheduling of air and ground resources, significantly improving the practical feasibility of the recovery scheme in complex geographical environments.

[0015] 3. This invention takes into account service delay constraints, link bandwidth limitations, signal-to-noise ratio thresholds, and multi-hop routing in the model to ensure that the restored communication network can not only be connected, but also meet the strict requirements of power distribution automation services for communication quality, effectively avoiding the problem of control command failure due to substandard communication quality. Attached Figure Description

[0016] Figure 1 This is a flowchart of the method steps of the present invention;

[0017] Figure 2 This is a schematic diagram of the cyber-physical system-transportation network coupling of the present invention;

[0018] Figure 3 This is a schematic diagram of a cyber-physical system-transportation network fault in an embodiment of the present invention;

[0019] Figure 4 This is a schematic diagram comparing the load recovery of different recovery strategies of the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0021] like Figure 1As shown, the present invention provides a distribution network air-ground coordinated emergency communication recovery method considering cyber-physical coupling. The overall technical framework, from top to bottom, includes the construction of a communication network data flow model, the parallel establishment of UAV and communication vehicle channel models, the construction of an emergency communication resource working model and a communication vehicle transportation network coupling model, the establishment of a cyber-physical system coupling model, and the formation of a distribution network operation constraint model. Ultimately, it boils down to solving the objective function model for minimizing distribution network load loss. The technical idea behind this method is that when extreme natural disasters cause simultaneous damage to the distribution network and communication network, the failure of communication nodes will trigger a chain reaction. The dispatch center will be unable to grasp the system's operating status due to missing measurement data, and distribution automation terminals will refuse to operate due to communication interruptions. Remote fault isolation, network reconstruction, and black start operations will all be impossible to execute. This invention achieves coordinated scheduling of emergency communication resources by jointly optimizing the deployment positions and movement trajectories of UAVs and mobile communication vehicles, while meeting communication quality constraints, with the ultimate goal of distribution network load recovery.

[0022] like Figure 2 As shown, the cyber-physical system involved in this invention presents a three-layer coupled structure with the transportation network. The top layer is the communication network, which includes communication facilities such as dispatch centers, communication base stations, and drones, responsible for data transmission and command issuance. The middle layer is the distribution network, which includes electrical equipment such as transformers, distributed power sources, load nodes, and line switches, serving as the physical carrier for power transmission and distribution. The bottom layer is the transportation network, composed of road nodes and roadside structures, with the mobile communication vehicle depot located within the transportation network, and the travel path of the mobile communication vehicle constrained by the transportation network topology. There is a tight coupling relationship between the three layers: the communication network and the distribution network are cyber-physically coupled through terminal nodes, and the communication status of the terminal nodes directly determines the controllability of the corresponding electrical nodes; the transportation network and the communication network are coupled through mobile communication vehicles, the location of which is constrained by the transportation network, and their communication coverage affects the wireless access of the terminal nodes.

[0023] The method of the present invention includes the following steps:

[0024] Step 1: Construct a data flow model for the communication network.

[0025] In a distribution network cyber-physical system, terminal nodes need to transmit collected status data back to the dispatch center and receive dispatch instructions. The communication network carries the transmission of these data streams, and its availability directly determines the observability and controllability of the distribution network. This invention first models the data stream transmission process of the communication network to characterize the data transmission constraints under both wired and wireless communication modes.

[0026] For any information node At any given moment This node can only choose either wired or wireless communication mode for data transmission, or it may lose packets due to the lack of an available communication path. This constraint is expressed as:

[0027]

[0028] In the above formula, Represents a node A pre-calculated set of alternative wired paths, which is generated in advance based on the communication network topology before the disaster. This refers to a set of wireless resources, including a set of drones. Mobile communication vehicle collection and fixed base station set ,Right now ; Select variables for wired paths, when nodes At any moment Select wired path The value is 1 when transmitting data, and 0 otherwise. For wireless access variables, when node At any moment Access to wireless resources The value is 1 if it is true, and 0 otherwise.

[0029] Data packets must meet traffic balancing conditions during transmission. For nodes... At any moment generated data packets The data packet must either be successfully transmitted via wired or wireless means, or it will be lost. This constraint is expressed as:

[0030]

[0031] In the formula Represents a node At any moment The amount of lost data packets. When a node successfully establishes a communication connection, all of its generated data packets are transmitted; when a node is in a communication dead zone, all data packets are lost.

[0032] Power distribution automation operations have strict requirements on communication latency; excessive latency will cause control commands to fail. In wired communication, selecting a specific path... This is contingent on the transmission delay of the path not exceeding the maximum allowed delay threshold of the service. This constraint is expressed as:

[0033]

[0034] In the formula Indicates a wired path Fixed transmission delay, Represents a node The maximum allowable latency threshold for the business. This constraint ensures that a path can only be selected if its latency meets the business requirements.

[0035] Similarly, the time delay constraint under wireless communication is expressed as:

[0036]

[0037] In the formula Represents a node Connect to wireless resources The wireless transmission latency is related to the channel quality and transmission distance of the wireless link.

[0038] Physical link bandwidth resources are limited; the total amount of data flow passing through the same link cannot exceed the link's bandwidth capacity. Simultaneously, the link's failure state during a disaster must be considered, as a failed link cannot carry data flow. The aggregation constraint for wired links is expressed as:

[0039]

[0040] In the formula Represents a set of terminal nodes; Let be the path topology matrix, when the path via link The value is 1 if the condition is met, and 0 otherwise. Indicates a wired link The maximum bandwidth limit; Indicates a wired link At any moment The value is 1 if the link is normal, and 0 if the link fails due to a disaster.

[0041] Wireless resources also have bandwidth limitations; the total data flow from all terminals accessing the same wireless resource cannot exceed the bandwidth capacity of that resource. The aggregation constraint of wireless resources is expressed as:

[0042]

[0043] In the formula Indicates wireless resources Total bandwidth limit; Indicates wireless resources At any moment The state.

[0044] Whether a terminal node can access a certain wireless resource depends on whether the terminal is within the signal coverage area of ​​the wireless resource. Coverage constraints are expressed as:

[0045]

[0046] In the formula To cover the matrix, when the node Located in wireless resources The value is 1 when the signal-to-noise ratio is within the coverage area, and 0 otherwise. The coverage area is determined based on whether the signal-to-noise ratio calculated by the wireless channel model meets the threshold requirement.

[0047] Step 2: Construct the UAV channel model.

[0048] As an aerial emergency communication platform, unmanned aerial vehicles (UAVs) have the advantages of being unrestricted by terrain and highly maneuverable. Their communication with ground terminals is primarily line-of-sight (LAS) transmission, offering superior channel characteristics compared to terrestrial mobile communication. This invention models the air-to-ground channel between UAVs and ground terminals to accurately characterize communication coverage and link capacity.

[0049] The spatial distance between the UAV and the ground terminal is determined by the three-dimensional position of the UAV and the two-dimensional position of the terminal. Let the terminal... The position coordinates are drones The position coordinates are ,in This refers to the drone's flight altitude. (Drone) With terminal The distance between them is defined as:

[0050]

[0051] In the formula Indicates drone With terminal The horizontal distance between them Indicates drone Compared to the terminal The ground elevation angle. The horizontal distance is calculated as follows:

[0052]

[0053] Signal propagation between the UAV and the terminal can occur via two paths: line-of-sight (LAS) and non-LAS, each with different path loss characteristics. The path loss model is expressed as:

[0054]

[0055] In the formula Channel gain at the reference distance; This is the path loss exponent, a parameter that is related to the propagation environment; the larger the value, the faster the signal attenuates. This is the additional attenuation factor for non-line-of-sight propagation, with a value range of [value missing]. This reflects the additional loss of non-line-of-sight paths compared to line-of-sight paths.

[0056] In real-world propagation environments, line-of-sight (LAS) propagation and non-LAS propagation occur with a certain probability, which is closely related to the drone's elevation angle. A larger elevation angle reduces the probability of the signal being blocked by obstacles such as buildings, thus increasing the probability of LAS propagation. The LAS probability model is expressed as:

[0057]

[0058]

[0059] In the formula Indicates the probability of line-of-sight propagation. Indicates the probability of non-line-of-sight propagation; , These are empirical parameters related to the transmission environment and can be set based on factors such as urban building density.

[0060] Wireless channels also suffer from shadowing fading, an effect caused by large-scale obstacles, which typically follows a log-normal distribution. To ensure communication reliability, a shadowing margin needs to be factored into the channel model. In the linear domain, the reliability is... The shadow fading factor is expressed as:

[0061]

[0062] In the formula This is the mean parameter for shadow fading, in dB; This is the standard deviation parameter for shadow fading, in dB. For reliability The corresponding standard normal distribution quantiles, for example, when 95% reliability is required. The value is approximately 1.645.

[0063] Taking into account both line-of-sight and non-line-of-sight propagation probabilities, as well as shadow fading, UAVs With terminal The expected channel gain between them is expressed as:

[0064]

[0065] The terminal received data from the drone. The signal power is:

[0066]

[0067] In the formula For drones The transmission power.

[0068] Considering the impact of noise and interference, drones With terminal The signal-to-noise ratio between them is expressed as:

[0069]

[0070] In the formula The noise power is calculated as follows: , For noise power spectral density, For system bandwidth; Interference power is considered when multiple wireless resources are operating simultaneously, and mutual interference must be taken into account.

[0071] According to Shannon's formula, drones With terminal The upper bound of the link capacity between them is:

[0072]

[0073] This capacity limits the maximum data traffic that a single wireless link can carry.

[0074] Step 3: Construct a mobile communication vehicle channel model.

[0075] Mobile communication vehicles, as ground-based emergency communication platforms, have advantages such as long endurance and large communication bandwidth, but their mobility is limited by road traffic networks. Unlike the air-to-ground channel of UAVs, the communication between mobile communication vehicles and terminals is a ground-to-ground channel, resulting in a more complex propagation environment and a higher probability of non-line-of-sight propagation. This invention models the channel characteristics of mobile communication vehicles separately.

[0076] Both the mobile communication vehicle and the terminal are located on the ground. Ignoring height differences, the distance between them is simplified to a horizontal distance. Let the mobile communication vehicle... At any moment The position coordinates are Then mobile communication vehicle With terminal At any moment The distance is:

[0077]

[0078] In ground-based propagation environments, the probability of line-of-sight propagation decreases with increasing distance; this characteristic can be described using an exponential decay model.

[0079]

[0080]

[0081] In the formula This is the line-of-sight probability attenuation distance parameter. This parameter is related to the urban built environment, and its value is smaller in densely built-up areas.

[0082] The path loss of the mobile communication vehicle channel is described using a logarithmic distance model. The losses for line-of-sight (LAS) and non-LAS paths are expressed as follows:

[0083]

[0084]

[0085] In the formula For reference distance Path loss at the location; The line-of-sight path loss index; The non-line-of-sight path loss exponent is typically greater than [value missing]. ; This is an additional fixed attenuation for non-line-of-sight propagation, reflecting the additional losses caused by penetrating obstacles such as buildings.

[0086] Combining line-of-sight and non-line-of-sight propagation probabilities, the expected path loss is:

[0087]

[0088] The mobile communication vehicle channel also suffers from shadowing fading, with a reliability of [missing information]. The shading factor is represented as:

[0089]

[0090] In the formula This is the standard deviation parameter for shadow fading.

[0091] Mobile communication vehicle With terminal At any moment The channel gain is:

[0092]

[0093] The terminal received the data from the mobile communication vehicle. The signal power and signal-to-noise ratio are as follows:

[0094]

[0095]

[0096] In the formula For mobile communication vehicles The transmission power.

[0097] Mobile communication vehicle With terminal At any moment The upper bound of the link capacity is:

[0098]

[0099] Step 4: Construct an emergency communication resource working model.

[0100] As emergency communication resources, drones and mobile communication vehicles must meet certain technical and resource constraints when providing communication services to terminals. This step models these constraints to ensure the engineering feasibility of the recovery plan.

[0101] For a terminal to connect to a drone or mobile communication vehicle, the signal-to-noise ratio (SNR) between the two must be no less than a minimum threshold. This constraint is expressed as:

[0102]

[0103] In the formula This is the minimum signal-to-noise ratio (SNR) threshold for the wireless channel, determined based on the service's bit error rate (BER) requirements. When a terminal is not connected to a certain wireless resource, the corresponding... If the value is 0, the above constraints are automatically satisfied; when a terminal accesses a certain wireless resource, it must ensure that the signal-to-noise ratio is not lower than the threshold value.

[0104] Considering the signal interference issue of wireless resources, a terminal can only be served by one drone or one mobile communication vehicle at a time, and cannot access multiple similar resources simultaneously. This constraint is expressed as:

[0105]

[0106]

[0107] Each emergency communication resource has a maximum number of terminals it can serve simultaneously, determined by the processing capacity and spectrum resources of the wireless resource. The maximum load constraint is expressed as:

[0108]

[0109] In the formula This refers to the maximum number of terminals that a single emergency communication resource can serve simultaneously.

[0110] Step 5: Construct a traffic network model for mobile communication vehicles.

[0111] See Figure 2 The movement of mobile communication vehicles is constrained by the road traffic network; they can only travel along roads and cannot fly arbitrarily like drones. This step models the movement process of mobile communication vehicles on the traffic network.

[0112] The location of a mobile communication vehicle at any given time must be within the traffic network, that is, at a specific traffic node or on a specific road. This constraint is expressed as:

[0113]

[0114] In the formula Represents the set of nodes in the transportation network. This represents the set of directed edges of the transportation network. Indicates mobile communication vehicle At any moment The location.

[0115] The displacement of the mobile communication vehicle between adjacent moments is limited by its maximum speed. This constraint is expressed as:

[0116]

[0117] In the formula Indicates the mobile communication vehicle from location Arrive at the location The shortest path distance on the road network; This refers to the maximum speed of the mobile communication vehicle. For time step.

[0118] At any given time, the mobile communication vehicle can either be traveling on the side of a road or be stationary. This constraint is expressed as:

[0119]

[0120] In the formula As a binary variable, when the mobile communication vehicle At any moment Driving along the side of the road network The value is 1 when it is above, and 0 otherwise.

[0121] The location changes of a mobile communication vehicle must meet the continuity requirement, meaning that adjacent locations must be connected through a valid path. The location continuity constraint is expressed in the form of flow conservation:

[0122]

[0123] This constraint ensures that the mobile communication vehicle moves continuously along the road network without any position jumps.

[0124] Step 6: Construct a model of cyber-physical system coupling and distribution network operation constraints.

[0125] The core of this invention lies in characterizing the cyber-physical coupling relationship between the communication network and the distribution network. The fundamental purpose of communication restoration is to restore the controllability of the distribution automation terminal, thereby achieving load restoration. This step establishes the coupling constraints between successful communication and load restoration, as well as the electrical constraints during the operation of the distribution network.

[0126] The actual amount of data transmitted by the terminal cannot exceed the capacity of the wireless link it is connected to. This constraint is expressed as:

[0127]

[0128] In the formula This represents the upper limit of the wireless link capacity, calculated using the aforementioned channel model.

[0129] The communication state of the terminal node is represented by a binary variable. This is an identifier used when a terminal successfully establishes a communication connection via wired or wireless means. ;otherwise The communication success flag constraint is represented as follows:

[0130]

[0131] For a terminal at a corresponding load node, whether its load can be restored depends on whether communication is successful. Only when the terminal successfully communicates can the dispatch center obtain the status information of the load and issue a recovery command. The coupling constraint between load restoration and successful communication is expressed as:

[0132]

[0133]

[0134] In the formula The actual active power load restored; The actual reactive load restored; For active power load demand; For reactive load demand; For the set of load terminals. When At that time, the actual restored load is forced to be 0, meaning that the load of the communication disconnection cannot be restored.

[0135] Similarly, the output of the corresponding distributed power node's terminal is also constrained by the communication status. Only when the terminal successfully communicates can the distributed power source receive the black-start command and begin operation. This constraint is expressed as:

[0136]

[0137] In the formula For the actual output of distributed power sources; This refers to the rated maximum output of the distributed power source. It is a collection of distributed power supply terminals.

[0138] During the restoration process, the distribution network needs to maintain a radial topology to meet the basic requirements for distribution network operation. This invention uses a virtual flow method to model topological constraints. A forward virtual connection flow is defined. and reverse virtual connection stream The sum of the two equals the actual physical state of the line:

[0139]

[0140] In the formula Indicates the line - At any moment The physical state of the object is 1 when it is connected and 0 when it is disconnected. This represents a set of distribution network lines.

[0141] To maintain the tree-like topology, the inflow degree of each load node cannot exceed 1. This constraint is achieved through the following inequality:

[0142]

[0143] In the formula Represents the set of all nodes in the distribution network; Represents the set of power nodes; This represents the set of non-power nodes.

[0144] The outflow constraint of a power node is expressed as:

[0145]

[0146] Virtual stream variables are continuous non-negative variables:

[0147]

[0148] Distribution network nodes must meet active and reactive power balance constraints:

[0149]

[0150]

[0151] In the formula For the line - At any moment The meritorious trend; For the line - At any moment The unproductive current; For nodes At any moment Active power generation; For nodes At any moment The reactive power generation capacity; The power factor of the load node.

[0152] The power flow of a distribution network line must not exceed the line's transmission capacity. Simultaneously, the fault state of the line during a disaster must be considered; a faulty line cannot transmit power. The line capacity constraint is expressed as:

[0153]

[0154]

[0155] In the formula For the line - Maximum transmission capacity; This represents the line status. If the line is disconnected during a disaster, the value is 0; otherwise, the value is 1.

[0156] The voltage at distribution network nodes must be kept within the allowable deviation range. Using a linearized power flow model, the voltage relationship between nodes is expressed as:

[0157]

[0158]

[0159]

[0160] In the formula For nodes At any moment The square of the voltage amplitude; and The lines are respectively - Resistance and reactance; and These are the lower and upper limits of the node voltage, respectively.

[0161] Step 7: Establish and solve the objective function for minimizing the load loss of the distribution network.

[0162] This invention aims to restore the load of the power distribution network by minimizing load loss through optimizing the deployment locations and movement trajectories of drones and mobile communication vehicles. The objective function is expressed as:

[0163]

[0164] In the formula For load nodes The weighting coefficients are used to distinguish the importance of different loads, with important loads such as hospitals and emergency command centers assigned higher weights. The physical meaning of the objective function is to minimize the weighted sum of the differences between the demand and actual recovery of each load node at each time point, thereby minimizing load losses caused by disasters.

[0165] By integrating the communication network data flow model, UAV channel model, mobile communication vehicle channel model, emergency communication resource working model, transportation network model, and cyber-physical system coupling and distribution network operation constraint model established in the above steps, a complete mixed-integer linear programming model is formed. The decision variables of this model include wired path selection variables. Wireless access variables Communication success flag variable drone location Location of mobile communication vehicle Mobile communication vehicle path variables Actual restored load and Line flow and Node voltage and virtual stream variables and wait.

[0166] This optimization model can be solved using commercial solvers such as CPLEX in the MATLAB environment. The CPLEX solver uses a branch and bound algorithm to handle integer variables and combines linear programming relaxation to provide optimal bounds, enabling it to obtain high-quality solutions or prove optimality in a reasonable time.

[0167] The application process and effects of the method of the present invention are illustrated below with a specific embodiment.

[0168] like Figure 3As shown, the method of this invention is verified using an improved IEEE 33-node distribution network and communication network coupling system. The figure illustrates the distribution network topology, including transformers, three distributed power sources (marked as G), load nodes (black solid circles), the connection and disconnection status of terminal nodes (indicated by different boxes), fault locations (lightning bolt symbols), power lines, line switches, and the traffic network at the bottom. The traffic network consists of traffic nodes (yellow dots) and roads (yellow line segments), with the communication vehicle depot (red solid circle) located within it. Under normal operating conditions, the distribution network supplies power to the loads through the main grid power supply and distributed power sources located in different locations, while the communication network provides a data transmission channel for the distribution automation system. After the system encounters an extreme disaster, all sectional switches in the distribution network automatically trip to prevent the accident from escalating, and three line disconnection faults occur simultaneously: branch lines 3-4, 23-24, and 26-27 are disconnected. Regarding the communication network, some communication base stations and links are also damaged due to the disaster; the terminal nodes marked with red boxes in the figure represent communication disconnection states. After the disaster, only the main grid power supply and the distributed power supply DG1 at node 20 have the ability to provide immediate power. DG2 at node 15 and DG3 at node 30 are in a communication blind spot, and the dispatch center cannot establish communication with them, so it is impossible to issue a black start command to put them into operation.

[0169] Assume available emergency communication resources include two drones and one mobile communication vehicle, all initially located in the vehicle's warehouse. The recovery process is divided into three phases:

[0170] The first phase involves power supply and islanding status identification. Based on fault branch information, the system determines the islanding situation of the distribution network, identifying nodes 6 to 18 as one island, which can be powered by distributed generation source DG2 at node 15; and nodes 27 to 33 as another island, which can be powered by distributed generation source DG3 at node 30. After clarifying the power supply relationships for each island, the priority targets for communication restoration are determined.

[0171] The second phase involves coordinated air-to-ground recovery. For the area where the road network is inaccessible (e.g., Node 30), a UAV1 is dispatched to fly directly over Node 30, establish a wireless connection with the communication terminal there, and issue a black-start command to activate DG3. After DG3 is activated, the UAV1 continues to hover or move, gradually expanding the communication coverage area so that communication terminals at adjacent nodes can also access it, thereby sequentially closing the corresponding switches and constructing a micronetwork centered on DG3, gradually restoring the load in the area from Nodes 27 to Node 33. Simultaneously, for the chained area from Nodes 6 to Node 18, a mobile communication vehicle is dispatched along the road network from the vehicle depot to the vicinity of Node 15, establishes a connection with the communication terminal there, and issues a black-start command to activate DG2. After DG2 is activated, the mobile communication vehicle moves along the route, restoring communication to nodes along the way and closing the corresponding switches, achieving orderly load recovery in this area.

[0172] The third phase involves extending and restoring the main network. Based on the stable operation of the isolated system, existing communication facilities or the auxiliary communication capabilities of UAV1 are utilized to close critical line switches, gradually extending the main network power supply range towards nodes 4 to 5, thereby achieving orderly reconstruction and overall restoration of the system.

[0173] like Figure 4 As shown, the method of this invention is compared with other recovery strategies. The figure displays the distribution network load recovery rate (red bars) and the number of restored communication nodes (blue bars) of the four methods in bar chart form, while the number of successfully started distributed power sources is indicated by a star. The method of this invention (air-ground coordination + CPS coupling) achieved a 94% distribution network load recovery rate, restored 29 communication nodes, and successfully started 2 distributed power sources. Comparison Method 1 is a communication density-priority strategy, which aims to maximize the number of communication coverage nodes, ignoring the actual contribution of nodes to power recovery. Although 30 communication nodes were restored, the distribution network load recovery rate was only 20%, and the number of successfully started distributed power sources was also relatively small. Comparison Method 2 is a strategy relying solely on drones, without considering the collaborative effect of mobile communication vehicles. Due to the limitations of drone endurance and bandwidth, the distribution network load recovery rate was 70%, and 22 communication nodes were restored. Comparison Method 3 is a strategy focusing solely on restoring main road communication, prioritizing the restoration of main line communication and ignoring the restoration value of branches where distributed power sources are located. The distribution network load recovery rate was only 40%, and 18 communication nodes were restored.

[0174] The comparative results show that the method of this invention significantly outperforms the aforementioned comparative strategies in terms of distribution network load recovery rate. Under the condition of complete power outage, the method of this invention can prioritize the restoration of communication at key nodes that contribute the most to the power system by coordinating the dispatch of drones and mobile communication vehicles, enabling distributed power sources to be put into operation as soon as possible, thereby achieving a higher load recovery rate. Compared with the strategy that only prioritizes communication density, the load recovery rate of the method of this invention is improved by 74 percentage points; compared with the drone-only strategy, it is improved by 24 percentage points; and compared with the backbone-only strategy, it is improved by 54 percentage points.

[0175] The core advantage of this invention lies in using communication network restoration as an enabling means of power load restoration, rather than solely pursuing the maximization of communication coverage. Mathematical modeling clarifies the decisive constraint relationship between communication connectivity and power load controllability, ensuring that emergency communication resources prioritize nodes that contribute most to distribution network restoration. Simultaneously, this invention fully leverages the advantages of UAVs (unrestricted by terrain and with excellent line-of-sight transmission) and mobile communication vehicles (vehicles) with long endurance and high bandwidth. By meticulously characterizing the differences in air-to-ground channel models and motion constraints within the model, the practical feasibility of the scheduling scheme is improved.

[0176] The mixed-integer linear programming model established in this invention not only considers the establishment of communication connections but also deeply considers communication quality requirements such as service delay constraints, link bandwidth limitations, signal-to-noise ratio thresholds, and multi-hop routing selection, ensuring that the restored communication network can meet the actual needs of distribution automation services. By abstracting the complex cyber-physical coupling problem into a solvable mathematical optimization model, it can calculate the optimal resource deployment scheme under extremely limited resource conditions after a disaster, minimizing load losses caused by disasters and improving the resilience of the distribution network under extreme events.

[0177] It should be noted that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A power distribution network air-ground collaborative emergency communication recovery method considering information-physical coupling, characterized in that, Includes the following steps: Step 1: Construct a data flow model for the communication network and determine the data transmission mode and traffic balancing conditions of the terminal nodes; Step 2: Construct a UAV channel model and calculate the line-of-sight and non-line-of-sight propagation probabilities and channel gain between the UAV and the ground terminal; Step 3: Construct a mobile communication vehicle channel model and calculate the path loss and channel capacity between the mobile communication vehicle and the ground terminal; Step 4: Combining the UAV channel model and the mobile communication vehicle channel model, construct an emergency communication resource working model, and set resource access constraints and load limits; Step 5: Construct a traffic network model for mobile communication vehicles, and constrain the driving path and location continuity of the mobile communication vehicles; Step 6: Construct a cyber-physical system coupling and distribution network operation constraint model to establish the coupling relationship between communication status and the controllability of distribution network equipment; Step 7: Based on the communication network data flow, and combined with the UAV channel model, mobile communication vehicle channel model, emergency communication resource working model, communication vehicle traffic network coupling model, cyber-physical system coupling and distribution network operation constraint model, establish an optimization function with the goal of minimizing distribution network load loss, and solve it to obtain the deployment location and movement trajectory of emergency communication resources. 2.The power grid air-ground collaborative emergency communication recovery method considering information-physical coupling according to claim 1, wherein, In step 1, the communication network data flow model includes: The constraints include: mutual exclusion constraints for terminal nodes to select wired communication mode, wireless communication mode, or packet loss state; traffic balance constraints for data packets during transmission; transmission delay constraints for wired paths and wireless links to ensure that the transmission delay does not exceed the maximum delay threshold allowed by the service; and bandwidth capacity constraints for wired links and wireless resources. 3.The power grid air-ground collaborative emergency communication recovery method considering information-physical coupling according to claim 1, wherein, In step 2, the UAV channel model specifically includes: The spatial distance between the UAV and the terminal and the ground elevation angle are calculated based on the UAV's flight altitude and horizontal distance. The line-of-sight propagation probability and non-line-of-sight propagation probability are calculated based on the ground elevation angle. The expected channel gain between the UAV and the terminal is calculated by comprehensively considering the path loss index, the non-line-of-sight additional attenuation coefficient, and the shadow fading factor. The signal-to-noise ratio and the upper limit of the link capacity are calculated based on the transmit power, interference power, and noise power.

4. The power grid air-ground collaborative emergency communication recovery method considering information-physical coupling according to claim 1, wherein, In step 3, the mobile communication vehicle channel model specifically includes: Based on the horizontal distance between the mobile communication vehicle and the terminal, the line-of-sight propagation probability is calculated using an exponential attenuation model; the loss of the line-of-sight path and the non-line-of-sight path are calculated using a logarithmic distance model, and the expected path loss is calculated in combination with the propagation probability; the shadow fading standard deviation parameter is introduced to calculate the channel gain and link capacity of the mobile communication vehicle and the terminal.

5. The power grid air-ground collaborative emergency communication recovery method considering information-physical coupling according to claim 1, wherein, In step 4, the emergency communication resource working model satisfies the following constraints: When a terminal accesses a wireless resource, the signal-to-noise ratio shall not be lower than the set minimum threshold; any terminal may access at most one drone or one mobile communication vehicle at any given time; the number of terminals served by a single emergency communication resource shall not exceed its maximum load limit.

6. The power grid air-ground collaborative emergency communication recovery method considering information-physical coupling according to claim 1, wherein, In step 5, the mobile communication vehicle traffic network model satisfies the following constraints: The mobile communication vehicle must be located at a node or edge of the traffic network at any given time; the displacement distance of the mobile communication vehicle at adjacent times is limited by the maximum driving speed and time step; the movement of the mobile communication vehicle on the road network satisfies the positional continuity constraint in the form of flow conservation.

7. The power grid air-ground collaborative emergency communication recovery method considering information-physical coupling according to claim 1, wherein, In step 6, the cyber-physical system coupling and distribution network operation constraint model includes coupling constraints between communication and load recovery: Define a communication success flag variable. This variable is set to 1 when a terminal establishes a valid communication connection, and 0 otherwise. The actual recovery amount of the load node is constrained by the communication success flag variable. When communication is interrupted, the actual recovered load is forced to be 0. The actual output of the distributed power source is constrained by the communication success flag variable. When communication is interrupted, the distributed power source cannot receive the start command and its output is 0.

8. The power distribution network air-ground collaborative emergency communication recovery method considering information-physical coupling according to claim 7, wherein, Step 6 also includes distribution network topology constraints: The virtual flow method is used to describe the distribution network topology, defining forward virtual connection flow and reverse virtual connection flow; the in-degree of non-power nodes is constrained to not exceed 1, and the out-degree of power nodes satisfies the requirements of radial topology. Virtual flow variables are kept consistent with line physical state variables.

9. The power distribution network air-ground collaborative emergency communication recovery method considering information-physical coupling according to claim 8, wherein, Step 6 also includes electrical constraints of the distribution network: Constraints on the balance of active and reactive power at each node; constraints on the line power flow not exceeding the maximum transmission capacity of the line and the physical state of the line; and node voltage deviation constraints based on the linearized power flow model.

10. The power distribution network air-ground collaborative emergency communication recovery method considering information-physical coupling according to claim 1, wherein, In step 7, the objective function for minimizing the load loss of the distribution network is: Minimize the weighted sum of the differences between the demand and actual recovery of all load nodes at each time point; where the weighting coefficient is set according to the importance of the load nodes.

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