AC / DC power distribution network post-disaster recovery method considering multi-type maintenance resource scheduling

Abstract

The invention relates to the technical field of post-disaster recovery of an AC / DC power distribution network, in particular to a post-disaster recovery method of the AC / DC power distribution network considering multi-type maintenance resource scheduling, which comprises the following steps: S1, defining a control mode of a voltage source converter (VSC); s2, constructing a VSC operation equivalent model; s3, constructing a scheduling model of multiple types of maintenance resources; s4, constructing a communication fault analysis system for identifying a communication blind area range, and judging whether the control function of each device can be recovered after the maintenance resource arrives; s5, constructing a joint optimization framework including a network reconstruction constraint, a power distribution system operation constraint and an equipment control time sequence constraint; s6, on the basis of the joint optimization framework constructed in the S5, constructing a collaborative optimization model for post-disaster system recovery; and S7, solving the collaborative optimization model in the S5 based on actual data to obtain a post-disaster recovery scheme. According to the method, information physical coupling characteristics can be considered, and rapid, ordered and efficient recovery of the load is realized.

Description

Technical Field

[0001] This invention belongs to the field of power system post-disaster recovery technology, and particularly relates to a post-disaster recovery method for AC / DC distribution networks that considers the scheduling of multiple types of maintenance resources. Background Technology

[0002] With the deepening of energy structure transformation, hybrid AC / DC distribution systems (HDS) have become an important direction for the development of future smart distribution networks. This system achieves flexible interconnection between AC and DC subsystems through voltage source converters (VSCs), enabling efficient access to distributed renewable energy, energy storage devices, and DC loads, while significantly improving system operational flexibility and power supply reliability. However, the stable operation of HDS highly depends on advanced communication and control technologies; it is essentially a typical cyber-physical distribution system (CPDS). In this deeply integrated architecture, the energy flow of the physical system and the data interaction of the information system are tightly coupled. In the event of a natural disaster or major fault, communication interruptions at the information layer may directly prevent control commands from being issued, leading to voltage instability, islanding failure, or even recovery interruptions at the physical layer, severely restricting the system's post-disaster recovery capabilities.

[0003] Following a disaster, the recovery process of a distribution network typically involves two key phases: emergency power supply and service restoration. In the first phase, the system needs to quickly isolate the faulty area and reconfigure the network to create controllable islands supported by distributed generation (DG) or virtual stationary controllers (VSCs) to restore power to critical loads. During this phase, VSCs can provide voltage and frequency support to the islands by switching control modes (e.g., from PQ control to UAC-f or UDC-Q control) to maintain system stability. In the second phase, as maintenance resources gradually repair damaged equipment, the system topology dynamically changes. VSCs must continuously provide voltage support and cooperate with network reconfiguration to achieve orderly load restoration. Although VSCs possess the potential for multi-mode operation, existing research has largely focused on applying them only to a single recovery phase, and has not adequately explored the dynamic support capabilities brought about by control mode switching, failing to fully leverage their flexibility advantages throughout the entire recovery process.

[0004] More critically, existing HDS post-disaster recovery research generally neglects the strong coupling characteristics of cyber-physical systems. Communication system failures can disrupt the information link between the dispatch center and field equipment, creating a "communication blind spot." This prevents remote control and status monitoring even after physical equipment has been repaired, thus delaying the recovery process. For example, even if VSCs or switching equipment are powered on, the inability to execute control commands due to communication failure can lead to voltage support failure or network reconfiguration obstruction. Furthermore, maintenance resources are diverse: Power Fault Repair Personnel (PMCs) repair power equipment, while Communication Fault Repair Personnel (CMCs) and Emergency Communication Vehicles (ECVs) handle communication link repairs. Different types of maintenance resources differ in spatial distribution, response speed, and function, and their coordinated scheduling directly impacts the efficiency of synchronous recovery of cyber-physical systems. However, most current recovery models simplify maintenance resources to a homogenized approach, lacking refined modeling of multi-type resource path planning, operation timing, and their impact on control function recovery.

[0005] The root cause of the above problems lies in two aspects: firstly, the VSC's multi-mode control capabilities lack a collaborative optimization mechanism with the dynamic requirements of the system recovery process; secondly, the communication state of the information layer and the equipment operation state of the physical layer are treated separately in the recovery model, causing the recovery scheme to fail in actual execution due to "power without control" or "control without communication." The complexity of this cross-domain coupling relationship makes joint optimization modeling extremely challenging. It requires consideration of physical laws such as nonlinear power flow and radial constraints of network topology, as well as the integration of information logic such as communication reachability, control timing dependence, and multi-resource path dynamics, placing extremely high demands on the model's expressive power and solution efficiency.

[0006] Therefore, how to balance the cyber-physical coupling characteristics and achieve rapid, orderly, and efficient load recovery has become an urgent problem to be solved. Summary of the Invention

[0007] To address the shortcomings of the existing technologies, this invention provides a post-disaster recovery method for AC / DC distribution networks that considers the scheduling of multiple types of maintenance resources. This method can take into account the cyber-physical coupling characteristics and achieve rapid, orderly, and efficient load recovery.

[0008] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0009] A post-disaster recovery method for AC / DC distribution networks considering the scheduling of multiple types of maintenance resources includes the following steps:

[0010] S1. Define the control mode of the voltage source converter VSC, wherein the control mode includes DC voltage and reactive power control U. DC -Q, Active and reactive power control PQ, AC voltage and frequency control UAC -f;

[0011] S2. Construct an equivalent model of VSC operation to analyze the ability of VSC to support voltage in non-fault areas through control mode switching during fault isolation and recovery.

[0012] S3. Construct a scheduling model for multiple types of maintenance resources to optimize the path and time of each type of maintenance resource; among which, the types of maintenance resources include power fault repair personnel (PMC), communication fault repair personnel (CMC), and emergency communication vehicles (ECV);

[0013] S4. Construct a communication fault analysis system to identify the range of communication blind spots and determine whether each device can restore its control function after maintenance resources arrive.

[0014] S5. Taking into account the coupling characteristics of information and physical systems in the power distribution system, a joint optimization framework is constructed that includes network reconfiguration constraints, power distribution system operation constraints, and equipment control timing constraints.

[0015] Among them, the network reconfiguration constraint is constructed based on the spanning tree theory method, which treats the distribution network as a graph, where nodes represent buses and edges represent lines or switches. A radially connected network is equivalent to a spanning tree of this graph. The network reconfiguration constraint is used to ensure that at any time during the post-disaster recovery process, the topology of the AC distribution network always remains radial and connected, avoiding the formation of loops, and only allowing the formation of controllable islands with the support of VSC or DG.

[0016] The power distribution system operation constraints are constructed using the DistFlow model for AC power grids and a simplified DC power flow model for DC power grids to ensure that at each recovery time point, the electrical operating state of the system meets physical laws and safety specifications, thus guaranteeing power supply quality and equipment safety.

[0017] Equipment control timing constraints are constructed by introducing time variables and logical constraints to characterize the logical dependencies and temporal sequence of various operations during the recovery process, ensuring that the recovery process proceeds in an orderly and safe manner.

[0018] S6. Based on the joint optimization framework constructed in S5, the VSC operation equivalent model of S2, the multi-type maintenance resource scheduling model of S3, and the communication fault analysis results of S4 are embedded into the joint optimization framework as specific constraints or parameters. The objective function is to maximize the load recovery amount, minimize the total load reduction amount, and prioritize the recovery of high-priority loads. A collaborative optimization model for post-disaster system recovery is constructed.

[0019] S7. When a disaster occurs, solve the collaborative optimization model in S5 based on actual data to obtain a post-disaster recovery plan.

[0020] Compared with the prior art, the present invention has the following beneficial effects:

[0021] 1. Achieve dynamic switching and full-process support for VSC control modes, enhancing system flexibility. Unlike existing technologies that often limit VSC to a specific recovery phase (e.g., only for islanded power supply) or a fixed control mode, this solution defines and models multiple control modes of VSC (PQ, UAC-f, UDC-Q) and constructs their equivalent operational models. This allows for flexible switching of control strategies at different stages, such as fault isolation, islanding formation, and network reconfiguration. For example, in the initial recovery phase, it can switch to UAC-f mode to provide voltage and frequency support to the power-loss area, ensuring power supply to critical loads; as the system gradually recovers, it switches back to PQ mode to participate in power regulation. This mechanism fully leverages the multi-functionality of VSC, significantly enhancing the voltage stability and operational flexibility of the system during dynamic recovery.

[0022] 2. Achieve differentiated scheduling and collaborative optimization of multiple types of maintenance resources. Existing methods typically treat maintenance resources as a single type, failing to reflect the differences between power and communication repair tasks. This solution clearly distinguishes between multiple resource types, such as power fault repair personnel (PMC), communication fault repair personnel (CMC), and emergency communication vehicles (ECV), and constructs path planning and job time scheduling models for them. By optimizing the dispatch order and spatial paths of different types of resources, the problem of "power equipment has been repaired but cannot be remotely controlled" caused by communication repair delays is avoided, improving the overall coordination and execution efficiency of resource scheduling.

[0023] 3. Effectively address communication blind spots, enhancing the feasibility and security of recovery strategies. Addressing the common oversight in existing research of "powered but uncontrolled" situations caused by communication failures, this solution constructs a communication failure analysis system capable of dynamically identifying the extent of communication blind spots after a disaster and determining whether key equipment (such as VSCs and tie switches) possess the capability to restore communication and control functions once maintenance resources arrive. This mechanism uses communication status as a prerequisite for recovery operations, ensuring that critical operations such as network reconstruction or control mode switching are only permitted when communication is available. Compared to the simplified approach of traditional methods that assume complete reliability or independent handling of communication repair, this solution significantly improves the feasibility and security of recovery strategies in real-world environments.

[0024] 4. Constructing a deep cyber-physical integration joint optimization framework to achieve global collaborative decision-making. This scheme innovatively integrates network reconfiguration constraints (based on spanning tree theory), power distribution system operation constraints (DistFlow and DC power flow models), and equipment control timing constraints into a unified joint optimization framework, embedding the VSC equivalent model, multi-resource scheduling model, and communication state analysis results as key parameters. This framework can simultaneously consider multiple constraints such as electrical safety, topology radiation, control logic timing, and communication reachability, generating physically feasible, informationally executable, and timing-reasonable recovery schemes. Compared to the phased and fragmented optimization strategies in existing research, this method achieves cross-domain, full-chain collaborative decision-making, significantly improving the overall performance of post-disaster recovery.

[0025] In summary, this method can take into account the cyber-physical coupling characteristics and achieve rapid, orderly, and efficient load recovery.

[0026] Preferably, in S2, if the VSC running equivalent model adopts U DC If -Q or Uac-f control is applied, the voltage on the fault side should meet the following constraints:

[0027]

[0028] In the formula, U is the voltage at faulty node i, and U0 is the preset voltage.

[0029] Preferably, in S2, when constructing the VSC operation equivalent model, an equivalent circuit diagram of the VSC consisting of equivalent impedance and ideal VSC is constructed. The VSC is connected to the AC side bus ka and the DC side bus kd through a circuit breaker for isolation, and it is assumed that the circuit breaker and the buses connected on both sides are included in the VSC station; the constraints of the VSC operation equivalent model include (2)-(5):

[0030]

[0031] In the formula, Ω VSC For VSC site collection; U represents the capacity of the k-th VSC. i,t U represents the voltage magnitude of node i at time t. j,t P represents the voltage magnitude of node j at time t. dk,t P represents the active power of dk connected to the VSC branch at time t. i,ka,t Q i,ka,t P represents the active power and reactive power of AC node i at time t, respectively; kd,j,t Let I be the active power at DC node j at time t; i,ka,t I kd,j,t Ri represents the current at AC node i and DC node j at time t, respectively;ka R kd These are the resistances of the AC and DC circuits, respectively; X k Reactance of AC lines; Let VSC k be the active power and reactive power at time t; These are the upper and lower limits of reactive power output for VSC k, respectively; U ka,t U kd,t Let be the AC bus voltage and DC bus voltage at time t; R represents the resistance and reactance of AC line i; kd，j Let be the resistance of DC line j.

[0032] This approach offers several advantages. First, unlike existing studies that often employ simplified or black-box models to handle VSCs, this scheme constructs a detailed equivalent circuit diagram that includes equivalent impedance and an ideal VSC. This allows for a more realistic reflection of the power flow and voltage coupling relationship of the VSC during actual operation. Second, this equivalent model can flexibly adapt to different control modes of the VSC (such as PQ, UAC-f, UDC-Q). By adjusting the target variables and constraints, it achieves unified modeling of the VSC in scenarios such as islanded operation, voltage support, and power regulation. This flexibility overcomes the limitation of traditional models that are only applicable to a single operating mode.

[0033] 2. Embedding the equivalent VSC model into the joint optimization framework allows the recovery plan to fully consider the actual operational capabilities and constraints of the VSC during the planning stage. Compared to simplified models that ignore the internal characteristics of the VSC, this method can more accurately assess its ability to support load power supply at different time points, avoiding the problem of infeasible recovery plans due to overestimating VSC performance, and significantly improving the engineering applicability of the optimization results.

[0034] 3. In cyber-physical coupling recovery scenarios, the VSC is not only a power support node but also a critical control device upon which communication depends. This equivalent model, by clarifying its electrical parameters and topological connections, provides a foundation for subsequently determining whether it possesses control functions. For example, if communication is not restored, even if the VSC is in a normal state, it cannot execute control commands; and this model can serve as one of the physical bases for determining whether it "can be controlled," thereby achieving a linked analysis between "communication status—control capability—electrical operation."

[0035] Preferably, in S3, the constraints of the scheduling model include routing problem constraints and time problem constraints;

[0036] The constraints of the routing problem include (6)-(11):

[0037]

[0038] In the formula, x dp(γ),T(γ),γ Indicates whether maintenance resource γ is moved from warehouse dp(γ) to work point T(γ); x O(γ),dp(γ),γ This indicates whether maintenance resource γ travels from work point O(γ) to work point dp(γ); dp(γ) represents the warehouse to which the maintenance resource belongs; T(γ) represents the work point that maintenance resource γ arrives at; O(γ) represents the work point from which maintenance resource γ departs; γ represents a certain type of maintenance resource.

[0039] In the formula, x dp,T(γ),γ Indicates whether maintenance resource γ is moved from warehouse dp to work point T(γ); x O(γ),dp,γ This indicates whether maintenance resource γ travels from work point O(γ) to warehouse dp; DP / {dp(γ)} represents a warehouse that is not a maintenance resource.

[0040]

[0041] In the formula, x O(γ),T(γ),γ Indicates whether maintenance resource γ moves from work point O(γ) to work point T(γ); V MC DP represents the set of work points for maintenance personnel; DP represents the set of all maintenance resource repositories; k represents the index of the work point.

[0042]

[0043] In the formula, x m,n,pmc This indicates whether power fault repair personnel have traveled from work point m to work point n; D represents the set of power failure points; D represents the set of warehouses.

[0044]

[0045] In the formula, x p,q,cmc Indicates whether the communication fault repair personnel have traveled from work point m to work point n; This represents the set of work locations for communication fault repair personnel; cmc represents the index of the communication fault repair personnel.

[0046]

[0047] In the formula, x a,b,ecv Indicate whether the emergency communication vehicle is traveling from work point a to work point b; This represents the set of emergency communication vehicle work points; ecv represents the index of the emergency communication vehicle.

[0048] This setup enables differentiated path planning for various types of maintenance resources. Unlike existing studies that often treat maintenance resources as homogeneous individuals and schedule them uniformly, this scheme clearly distinguishes between three types of resources: power maintenance personnel (PMC), communication maintenance personnel (CMC), and emergency communication vehicles (ECV), and defines independent sets of work points and movement constraints for each of them (as shown in equations (9), (10), and (11)). This allows the scheduling model to accurately reflect the task attributes, mobility, and operational scope of different types of resources, avoiding scheduling conflicts or inefficiencies caused by resource confusion.

[0049] 2. By using routing constraints such as equations (6)–(8), we ensure that the movement path of each type of maintenance resource has a clear starting point (warehouse or previous work point) and ending point, and that there are no unreasonable "jumping" or "circular" paths. For example, equation (6) ensures that a resource must enter the next work point after starting from a certain location, and equation (7) prevents resources from making ineffective round trips between warehouses that are not their own, thereby improving the physical feasibility and actual executability of the path planning.

[0050] 3. By introducing binary variables, the movement process of maintenance resources is transformed into a quantifiable time-series decision problem. These variables can serve as input parameters in the subsequent joint optimization framework to calculate the repair completion time of each device, thereby affecting key operations such as VSC control mode switching and network reconfiguration timing. Compared with traditional static or heuristic scheduling methods, this model has stronger temporal coupling capabilities, which helps to achieve dynamic coordination of the entire process of "power repair - communication - power control".

[0051] Preferably, the time problem constraints include (12)-(18):

[0052]

[0053] In the formula, This indicates that maintenance resources γ have arrived at the work point. T(γ) Time; This indicates that maintenance resources γ have arrived at the work point. O(γ) Time; This indicates that maintenance resource γ is at the working point. O(γ) Required working hours; Indicates that maintenance resources γ originate from the work point O(γ) Heading to work T(γ) Required travel time; M represents an integer greater than the preset value;

[0054]

[0055]

[0056] In the formula, This indicates that maintenance resource γ has left the work point. T(γ) Time; This indicates that maintenance resource γ is at the working point. T(γ) Required working hours;

[0057]

[0058] In the formula, This indicates the time when the emergency communication vehicle arrived at work point b; This indicates the time when the emergency communication vehicle arrived at work point a; This indicates the working time required for the emergency communication vehicle to reach work point a; This indicates the travel time required for the emergency communication vehicle to travel from work point A to work point B;

[0059]

[0060] In the formula, Indicates the time when the emergency communication vehicle left work point b;

[0061]

[0062] In the formula, This indicates the working time required for the emergency communication vehicle to reach work point b;

[0063]

[0064] In the formula, x b,a,ecv This indicates whether the emergency communication vehicle is traveling from work point a to work point b; 1 indicates that it is traveling, and 0 indicates that it is not traveling. This indicates the required operation time for the equipment located at work point a; This indicates the operation time required for the emergency communication vehicle.

[0065] This setup, unlike the static or heuristic time estimation commonly used in existing studies, achieves a dynamic temporal characterization of the entire process of maintenance resource movement and operation by defining continuous variables such as arrival time and departure time, and combining path variables with the Big M method (as shown in Equation (15)). For example, Equation (12) ensures that the arrival time of a resource from its starting point to its destination is no less than the departure time of its previous node plus the travel time, thereby avoiding time inversion or logical conflicts and improving the physical rationality of the scheduling scheme.

[0066] 2. This time constraint system is applicable to three types of resources: PMC, CMC, and ECV, and can handle their different operational characteristics respectively. For example, for the Emergency Communication Vehicle (ECV), equations (16)–(18) specifically consider the time dependency of its movement between different work points and include the equipment operation time. With the vehicle's own operating time This differentiation reflects the unique nature of communication restoration tasks. This differentiated modeling allows for independent planning and coordination of the operation times of different resources, preventing delays in communication restoration from affecting the restoration of power system control functions.

[0067] 3. Improve the scheduling model's adaptability to actual operating conditions. This is achieved by introducing T... stay The actual working time at the work point is represented and associated with the path variable (as shown in Equation (14)). The model can reflect the dwell time of resources at different locations, which in turn affects the start time of subsequent tasks. At the same time, the Big M method is used to process logical branches (such as "whether it passes through a certain point"), so that the model can automatically eliminate invalid paths or unreasonable timing during the optimization process, which enhances the robustness of the model in the face of real challenges such as complex terrain, traffic congestion or resource shortage.

[0068] 4. In post-disaster recovery, communication restoration time directly impacts the timely response of critical equipment such as VSCs to control commands. This solution provides a time-based basis for determining "when communication will be restored" by accurately modeling the arrival and operation times of communication resources such as ECVs. This time-driven modeling approach effectively connects the "electricity-communication-control" chain of the entire recovery process in the time dimension, significantly improving the accuracy and practicality of the joint optimization framework.

[0069] Preferably, in S4, when constructing the communication fault analysis system, it is assumed that the power grid and communication network in the Cyber-Physical System (CPDS) have geographical isomorphism, and the communication network adopts a radial topology, corresponding one-to-one with the power nodes. When a communication link is damaged, the downstream communication nodes form a communication blind zone because they cannot communicate with the command center. Within the communication blind zone, the remote control switches RCS and VSC lose their remote control capabilities, affecting system reconstruction and recovery operations. The range of the communication blind zone is identified by the shortest path method, and constraints are established to determine whether each device can restore its control function after maintenance resources arrive.

[0070] This setup, by establishing a communication blind spot identification and control function recovery judgment mechanism, achieves a deep characterization of the information-physical coupling characteristics, providing high-precision and strongly coupled communication status analysis support for the post-disaster recovery of AC / DC distribution networks.

[0071] Preferably, the constraints (19)-(23) of the communication fault analysis system include:

[0072]

[0073] In the formula, c is the communication blind zone, C is the set of communication blind zones; e(c) represents the set of all damaged communication lines located at vertex e that cause the formation of the communication blind zone c; The time required to complete repairs of the i-communication function in the communication blind zone; The time required to complete repairs for communication fault e(c); x is the time required to complete repairs for all communication faults within the communication dead zone c; f,e(c),cmc Whether communication maintenance personnel should go to the communication fault e(c); N c A collection of communication blind spots;

[0074]

[0075] In the formula, binary variables A value of 1 indicates that the communication function of vertex a is restored by ECV; binary variable. A value of 1 indicates that the communication function of vertex a is restored by the CMC; Ω VSC For the VSC set; Ω RCS For RCS set;

[0076]

[0077] In the formula, The time it takes for equipment a to be repaired by ECV; Let ecv be the dwell time at device a; The time it takes for CMC to complete the maintenance of equipment a; The time required for node j to restore its communication function;

[0078]

[0079] In the formula, This is the final recovery time for device a.

[0080] This setup enables: 1. Fine-grained timing modeling of communication function recovery within communication dead zones. Unlike existing studies that often treat communication recovery as a single event or ignore its internal timing differences, this scheme defines... This represents the time required for the communication function to be fully restored in communication blind zone i, and is compared with the repair time for all communication failures within the area. The correlation (Equation (19)) enables a dynamic characterization of the local recovery process of the communication network. This modeling method can accurately reflect the "segment-by-segment repair" characteristic of the communication system and avoid failure due to premature execution of subsequent control operations caused by overestimating the communication recovery speed.

[0081] 2. Improve the coupling accuracy between communication recovery and physical control operations. This model will reduce the communication function recovery time. As a key output variable, it is ensured by equation (23) that it is not earlier than the completion time of either ECV or CMC. This mechanism guarantees that the relevant devices (such as VSC and RCS) will only have remote control capabilities after communication is truly restored, thereby effectively preventing the erroneous operation of "attempting control when communication is not established" and significantly improving the security and reliability of cyber-physical system collaborative recovery.

[0082] 3. Traditional methods often simplify communication status to a binary "present / absent" variable, failing to reflect its dynamic changes. This solution, by constructing continuous-time variables and logical constraints, generates a precise time series for communication function recovery. This data can be directly used as parameters or constraints in a joint optimization model to determine when to allow communication-dependent operations such as network reconfiguration and VSC control switching. This embeddability transforms communication repair from an independent task into a key driving factor in the entire post-disaster recovery process.

[0083] Preferably, in S5, the network reconstruction constraints include (24)-(27):

[0084]

[0085] In the formula, This indicates the connection relationship of AC lines ij at time t; This indicates the connection relationship of AC line ji at time t; B represents the on / off state of AC line ij at time t; AC Indicates a set of communication lines; This indicates the connection relationship of DC lines ij at time t; This indicates the connection relationship of the DC line ji at time t; B represents the on / off state of DC line ij at time t; DC Represents a set of DC lines;

[0086]

[0087] In the formula, the binary variable r i,t When N is 1, it indicates that node i is the root node at time t; AC N represents the set of communication nodes; DC Represents the set of DC nodes;

[0088]

[0089] In the formula, s i,t This represents the state of node i at time t; This represents the set of VSC communication-side nodes; Let N represent the set of DC-side nodes of the VSC; N represents the set of all nodes; N subThis represents the set of nodes where the substation is located;

[0090]

[0091] In the formula, This indicates the connection state of line ij at time t. If node i is the parent node of node j, then... otherwise This indicates the energized state of node i at time t; This indicates the connection relationship of the DC-side line ik at time t; This indicates the connection relationship of AC side line ki at time t; This indicates the connection relationship of DC-side line jk at time t; B represents the on / off state of AC line kj at time t; VSC This represents the set of lines where VSC is located.

[0092] This setup, unlike existing studies that often use heuristics or empirical rules for network reconstruction, strictly adheres to the spanning tree theory through the constraint in equation (25) that "each non-root node has only one parent node," ensuring that at any recovery time point, the topology of the AC distribution network is a loop-free, connected spanning tree. This effectively avoids problems such as the formation of ring networks or incomplete island isolation caused by misoperation, significantly improving the safety and stability of system operation.

[0093] 2. Considering the characteristics of VSC as a key interconnection node in AC / DC hybrid distribution networks, this scheme establishes consistency constraints on the connection status of the lines on both sides (AC side and DC side) of VSC through equations (26) and (27). For example, if the AC side line of VSC is closed, its DC side must also be in the corresponding state, thereby ensuring that VSC can operate normally and provide voltage support. This cross-domain coupling constraint makes up for the shortcomings of traditional single grid reconfiguration models in handling AC / DC coupling characteristics, and realizes the unified planning of the entire system topology.

[0094] 3. Achieve topological continuity and traceability in the dynamic recovery process. This is achieved by introducing time variable t and state variable. This model can dynamically track the changes in the open / closed state of the line during multiple recovery phases. Combined with the mandatory consistency of the bidirectional connection of the line by Equation (24), it ensures that each switching action conforms to electrical logic and prevents invalid operations such as "one end closed, the other end open". This time-sequential modeling method makes the network reconstruction process highly controllable and predictable, which is convenient for the verification and adjustment of subsequent recovery strategies.

[0095] Preferably, in S5, the operating constraints of the power distribution system include (29)-(36):

[0096] Power flow constraints in AC power grids:

[0097]

[0098] In the formula, ds(i) represents the set of downstream nodes connected to node i; us(i) represents the set of upstream nodes; P i,j,t P represents the active power of line ij at time t; j,i,t This represents the active power of line ji at time t; This represents the active power of the generator at node i at time t; Q represents the active load at node i; i,j,t Q represents the reactive power of ij at time t; j,i,t This represents the reactive power of ji at time t; This represents the reactive power of the generator at node i at time t; N represents the reactive load at node i; AC T represents the set of communication nodes; T represents the time set.

[0099]

[0100] In the formula, U i,t U represents the voltage magnitude of node i at time t; j,t R represents the voltage magnitude of node j at time t; i,j X represents the resistance of line ij; i,j Q represents the reactance of line ij; i,j,t This represents the reactive power of line ij at time t; s ij,t This indicates the on / off state of line ij at time t;

[0101] Power flow constraints in DC power grids:

[0102]

[0103] Safety constraints:

[0104]

[0105] In the formula, This represents the maximum active power of line ij; s i,j,t B represents the state of line ij at time t; B represents the set of branches.

[0106]

[0107] In the formula, This represents the upper limit of active power of node i; N represents the upper limit of reactive power of node i; GRepresents the set of nodes where the generator is located;

[0108]

[0109] In the formula, These represent the upper and lower limits of the voltage amplitude at node i, respectively.

[0110]

[0111] This approach, unlike existing studies which often simplify or ignore the DC component, employs the DistFlow model (Equations (29) and (30)) for AC power grids and a simplified DC power flow model (Equations (31) and (32)) for DC power grids, thus achieving an accurate description of the power flow and voltage distribution of both types of networks. For example, Equation (30) captures the voltage drop characteristics of AC lines through nonlinear voltage relationships, while Equation (32) uses linear voltage difference constraints to reflect the resistance loss of DC lines, significantly improving the model's ability to fit the actual system behavior.

[0112] 2. By introducing safety constraints such as power limit constraints (Equation (33)), generator output upper limit (Equation (34)), and voltage upper and lower limits (Equation (35)), this model ensures that the system will not experience overload, voltage exceeding limits, or equipment overheating at any recovery time point. This time-by-time safety verification mechanism effectively prevents secondary faults caused by blindly restoring the load, and significantly improves the safety margin and reliability of the post-disaster recovery process.

[0113] 3. Supports continuous operation analysis under dynamic topology changes. All constraints are indexed by the time variable t and linked to the line state variable s. i,j,t Coupling allows the model to adapt to topological changes brought about by network reconstruction. For example, when a line is disconnected (s i,j,t When t=0), equations (29) and (31) automatically exclude power flow, avoiding invalid calculations; meanwhile, equations (30) and (32) only take effect when connected. This dynamic response capability makes the model applicable to the entire recovery scenario from islanded operation to gradual networking, enhancing its applicability and robustness.

[0114] Preferably, in S6, the objective function of the collaborative optimization model for post-disaster system recovery includes:

[0115]

[0116] In the formula, ω i This represents the priority weight coefficient of node i; This represents the active load of node i.

[0117] This setup, by constructing a load recovery objective function based on priority weights, enables intelligent guidance of the post-disaster recovery process, providing a scientific basis for decision-making to achieve efficient, orderly, and differentiated recovery of AC / DC distribution networks in complex disaster scenarios. Attached Figure Description

[0118] To make the objectives, technical solutions, and advantages of the invention clearer, the invention will now be described in further detail with reference to the accompanying drawings, wherein:

[0119] Figure 1 This is a flowchart of the method;

[0120] Figure 2 The equivalent circuit diagram of VSC in Example 1;

[0121] Figure 3 This is a schematic diagram of the PMC scheduling path results in Example 2;

[0122] Figure 4 This is a schematic diagram of the scheduling path results for CMC and ECV in Example 2. Detailed Implementation

[0123] The following detailed explanation illustrates the specific implementation methods:

[0124] Example 1

[0125] To address the technical problems of existing technologies, this invention proposes a novel DSR framework. First, this invention introduces an operational model that provides voltage support for VSC (Vehicle Service Controller). Based on real-time emergency repair conditions and system recovery status, the voltage support and power dispatch functions are optimized. Second, this invention considers cyber-physical systems, explores the impact mechanism of communication failures, and quantifies their consequences. Then, it establishes scheduling models for three types of emergency repair resources and a system service recovery model. Finally, a new optimization framework is constructed, which, under the premise of voltage support provided by VSC, collaboratively optimizes power and communication fault repair strategies as well as system power supply recovery strategies, solving the problems of traditional DSR research failing to efficiently utilize various types of dispatch resources and focusing only on power-side faults and maintenance.

[0126] like Figure 1 As shown, the AC / DC distribution network post-disaster recovery method of the present invention, which considers the scheduling of multiple types of maintenance resources, includes the following steps:

[0127] S1. Define the control mode of the voltage source converter VSC, wherein the control mode includes DC voltage and reactive power control U. DC -Q, Active and reactive power control PQ, AC voltage and frequency control U AC -f.

[0128] A hybrid distribution system (HDS) consists of an AC distribution network, a DC distribution network, a voltage source converter (VSC) station, and other protection and control equipment.

[0129] For AC / DC hybrid power distribution systems, the VSC can be controlled by selecting two variables: active / reactive power and AC / DC voltage. Therefore, the VSC has the following main control modes:

[0130] (1) DC voltage and reactive power control (U DC -Q); Used to maintain DC-side voltage stability, suitable for islanded operation or voltage support;

[0131] (2) Active and reactive power control (PQ); used for normal power flow regulation;

[0132] (3) AC voltage and frequency control (U AC -f); used to provide voltage and frequency support for AC-side islanding.

[0133] During normal operation, the VSCs in the DC network can be coordinated through master-slave control, with one VSC acting as the master controller (U). DC -Q control regulates the DC voltage, while other VSCs act as slave controllers (PQ control) to improve the power flow distribution of the system and balance the feeder load.

[0134] When a fault occurs, the inverter control system will coordinate with the distribution automation system to restore operation. Upon fault detection, the DC fault protection system will quickly detect the fault and initiate a low-voltage ride-through process. Then, the relays will identify and locate the fault. After the fault is cleared, the low-voltage ride-through process ends. Once the circuit breaker successfully recloses, VSC will quickly adjust from U... DC -Q or Uac-f control provides voltage support for non-faulty areas, enabling uninterrupted power supply.

[0135] S2. Construct an equivalent model of VSC operation to analyze the ability of VSC to support voltage in non-fault areas through control mode switching during fault isolation and recovery.

[0136] Among them, if the VSC running equivalent model adopts U DC If -Q or Uac-f control is applied, the voltage on the fault side should meet the following constraints:

[0137]

[0138] In the formula, U is the voltage at faulty node i, and U0 is the preset voltage.

[0139] The equivalent circuit diagram of VSC is as follows: Figure 2 As shown, it consists of equivalent impedance and an ideal VSC. The VSC is connected to the AC side bus ka and the DC side bus kd via circuit breakers for isolation. This method assumes that these circuit breakers and the buses connected on both sides are included in the VSC station.

[0140] In the diagram, P ka,t Q ka,t and P kd,t Let Q be the active and reactive power of AC node i at time t, and Q be the active power of DC node j. k,t The reactive power of VSC k; represents the magnitude of the AC bus voltage; represents the magnitude of the VSC equivalent internal potential. R represents the magnitude of the DC bus voltage. k X k For AC line resistance and reactance.

[0141] When constructing the VSC operation equivalent model, an equivalent circuit diagram of the VSC consisting of equivalent impedance and ideal VSC is constructed. The VSC is connected to the AC side bus ka and the DC side bus kd through a circuit breaker for isolation, and it is assumed that the circuit breaker and the buses connected on both sides are included in the VSC station. The constraints of the VSC operation equivalent model include (2)-(5):

[0142]

[0143] In the formula, Ω VSC For VSC site collection; U represents the capacity of the k-th VSC. i,t U represents the voltage magnitude of node i at time t. j,t P represents the voltage magnitude of node j at time t. dk,t P represents the active power of dk connected to the VSC branch at time t. i,ka,t Q i,ka,t P represents the active power and reactive power of AC node i at time t, respectively; kd,j,t Let I be the active power at DC node j at time t; i,ka,t I kd,j,t Ri represents the current at AC node i and DC node j at time t, respectively; ka R kd These are the resistances of the AC and DC circuits, respectively; X k Reactance of AC lines; Let VSC k be the active power and reactive power at time t; These are the upper and lower limits of the reactive power output of VSC k, respectively; U kd,tLet be the AC bus voltage and DC bus voltage at time t; Let i be the resistance and reactance of AC line i; Let be the resistance of DC line j.

[0144] Unlike existing studies that often use simplified or black-box models to handle VSCs, this approach constructs a detailed equivalent circuit diagram that includes equivalent impedance and an ideal VSC, thus more realistically reflecting the power flow and voltage coupling relationship of VSCs in actual operation. Furthermore, this equivalent model can flexibly adapt to different VSC control modes (such as PQ, UAC-f, UDC-Q), achieving unified modeling of VSCs in islanded operation, voltage support, and power regulation scenarios by adjusting objective variables and constraints. This flexibility overcomes the limitation of traditional models that are only applicable to a single operating mode. In addition, embedding this VSC equivalent model into a joint optimization framework allows the recovery scheme to fully consider the actual operating capabilities and constraints of the VSC during the planning stage. Compared to simplified models that ignore the internal characteristics of the VSC, this method can more accurately assess its ability to support load power supply at different time points, avoiding the problem of infeasible recovery plans due to overestimating VSC performance, and significantly improving the engineering applicability of the optimization results. Moreover, in cyber-physical coupling recovery scenarios, the VSC is not only a power support node but also a key control device dependent on communication. This equivalent model, by clarifying the relationship between its electrical parameters and topological connections, provides a foundation for subsequent judgments on whether it possesses control functions. For example, if communication is not restored, even if the VSC is in a normal state, it cannot execute control commands; and this model can serve as one of the physical bases for judging whether it "can be controlled," thereby realizing the linkage analysis between "communication status—control capability—electrical operation."

[0145] S3. Construct a scheduling model for multiple types of maintenance resources to optimize the path and time of each type of maintenance resource; among which, the types of maintenance resources include power fault repair personnel (PMC), communication fault repair personnel (CMC), and emergency communication vehicles (ECV).

[0146] Power line maintenance (PMC) personnel and communication fault maintenance (CMC) personnel are two types of maintenance workers, responsible for repairing damaged power lines and communication links, respectively. In addition, emergency communication vehicles (ECVs) can restore communication functionality between the power line control system (VCS) and the remote control switch (RCS) by establishing wireless communication. Their scheduling models are designed to determine routes and timelines to complete the repair work.

[0147] In practice, the constraints of the scheduling model include routing constraints and time constraints.

[0148] The constraints of the routing problem include (6)-(11):

[0149]

[0150] In the formula, x dp(γ),T(γ),γ Indicates whether maintenance resource γ is moved from warehouse dp(γ) to work point T(γ); x O(γ),dp(γ),γ This indicates whether maintenance resource γ travels from work point O(γ) to work point dp(γ); dp(γ) represents the warehouse to which the maintenance resource belongs; T(γ) represents the work point that maintenance resource γ arrives at; O(γ) represents the work point from which maintenance resource γ departs; γ represents a certain type of maintenance resource.

[0151] In the formula, x dp,T(γ),γ Indicates whether maintenance resource γ is moved from warehouse dp to work point T(γ); x O(γ),dp,γ This indicates whether maintenance resource γ travels from work point O(γ) to warehouse dp; DP / {dp(γ)} represents a warehouse that is not a maintenance resource.

[0152]

[0153] In the formula, x O(γ),T(γ),γ Indicates whether maintenance resource γ moves from work point O(γ) to work point T(γ); V MC DP represents the set of work points for maintenance personnel; DP represents the set of all maintenance resource repositories; k represents the index of the work point.

[0154] Constraints (6) and (7) indicate that during the maintenance task from start to finish, schedulable resources can leave and return to their respective maintenance stations without passing through other maintenance stations.

[0155] Constraint (8) indicates the continuity of the maintenance process. Schedulable resources can reach a non-warehouse node, complete the maintenance task at the node, and then leave the node to move to the next node.

[0156]

[0157] In the formula, x m,n,pmc This indicates whether power fault repair personnel have traveled from work point m to work point n; D represents the set of power failure points; D represents the set of warehouses.

[0158]

[0159] In the formula, x p,q,cmc Indicates whether the communication fault repair personnel have traveled from work point m to work point n; This represents the set of work locations for communication fault repair personnel; cmc represents the index of the communication fault repair personnel.

[0160]

[0161] In the formula, x a,b,ecv Indicate whether the emergency communication vehicle is traveling from work point a to work point b; This represents the set of emergency communication vehicle work points; ecv represents the index of the emergency communication vehicle.

[0162] Constraint (9) indicates that each power failure requires repair, but can only be repaired by a single PMC.

[0163] Constraint (10) differs from (9) in two ways. First, not all RCSs need to be shut down. Second, the ultimate goal of the CMC and ECV is to restore the communication functionality of the RCSs and VSCs to ensure they can be controlled when needed, and there are two ways to restore communication functionality: 1) the CMC repairs the relevant damaged communication links; 2) the ECV goes to the site to provide emergency communication.

[0164] Unlike existing studies that often treat maintenance resources as homogeneous individuals and schedule them uniformly, this scheme clearly distinguishes three types of resources: power maintenance personnel (PMC), communication maintenance personnel (CMC), and emergency communication vehicles (ECV), and defines independent sets of work points and movement constraints for each of them (equations (9), (10), and (11)). This allows the scheduling model to accurately reflect the task attributes, mobility, and operational scope of different types of resources, avoiding scheduling conflicts or inefficiencies caused by resource confusion. In addition, through routing constraints such as equations (6)–(8), it is ensured that the movement path of each type of maintenance resource has a clear starting point (warehouse or previous work point) and ending point, and there will be no unreasonable "jumping" or "circular" paths. For example, equation (6) ensures that a resource must enter the next work point after departing from a certain location, and equation (7) prevents resources from making ineffective round trips between warehouses that are not their respective belongings, thereby improving the physical feasibility and actual executability of path planning. Furthermore, by introducing binary variables, the movement process of maintenance resources is transformed into a quantifiable time series decision problem. These variables can serve as input parameters in the subsequent joint optimization framework to calculate the repair completion time of each device, thereby affecting key operations such as VSC control mode switching and network reconfiguration timing. Compared with traditional static or heuristic scheduling methods, this model has stronger temporal coupling capabilities, which helps to achieve dynamic coordination of the entire process of "power repair - communication - power control".

[0165] The model for the scheduling problem is designed to represent the temporal relationship between the three schedulable resources in the DSR.

[0166] The time constraints include (12)-(18):

[0167]

[0168] In the formula, This indicates that maintenance resources γ have arrived at the work point. T(γ) Time; This indicates that maintenance resources γ have arrived at the work point. O(γ) Time; This indicates that maintenance resource γ is at the working point. O(γ) Required working hours; Indicates that maintenance resources γ originate from the work point O(γ) Heading to work T(γ) Required travel time; M represents an integer greater than the preset value;

[0169]

[0170] In the formula, This indicates that maintenance resource γ has left the work point. T(γ) Time; This indicates that maintenance resource γ is at the working point. T(γ) Required working hours;

[0171] Constraint (12) describes the temporal relationship of maintenance resources moving between O(γ) and T(γ) to perform maintenance tasks. Specifically, if γ moves from O(γ) to T(γ), i.e. x O(γ),T(γ),γ =1, then Arrival. However, if γ is not dispatched to T(γ) to perform maintenance work, i.e. ∑ O(γ) x O(γ),T(γ),γ =0, then The constraint (13) is set to 0.

[0172] Constraint (14) indicates that if γ arrives and repairs the corresponding fault, i.e., ∑ O(γ) x O(γ),T(γ),γ =1, then the departure time satisfies For example, if γ = pmc and ∑ m x m,n,pmc =1, then the time relationship is

[0173] In the formula, This indicates the time when the emergency communication vehicle arrived at work point b; This indicates the time when the emergency communication vehicle arrived at work point a; This indicates the working time required for the emergency communication vehicle to reach work point a; This indicates the travel time required for the emergency communication vehicle to travel from work point A to work point B;

[0174]

[0175] In the formula, Indicates the time when the emergency communication vehicle left work point b;

[0176]

[0177] In the formula, This indicates the working time required for the emergency communication vehicle to reach work point b;

[0178]

[0179] In the formula, x b,a,ecv This indicates whether the emergency communication vehicle is traveling from work point a to work point b; 1 indicates that it is traveling, and 0 indicates that it is not traveling. This indicates the required operation time for the equipment located at work point a; This indicates the operation time required for the emergency communication vehicle.

[0180] Constraint (15) indicates that if ecv starts from vertex a and travels to b (i.e., x), a,b,ecv =1), then the arrival time of ECV is However, if ecv is not assigned to vertex b, i.e. Arrival time of vertex b and departure time All are 0, as set by constraint (16).

[0181] Unlike the PMC, which leaves the vertex immediately after repairing the damaged line, the ECV requires a certain amount of time to deploy its work and restore communication functionality after arriving at the vertex, thus ensuring the operation of the RCS and the switching of the VSC. Therefore, constraint (17) ensures that if the ECV arrives at vertex a, it leaves vertex a after restoring communication functionality and waiting for the device operation to complete. Furthermore, As defined by constraint (18).

[0182] S4. Construct a communication fault analysis system to identify the range of communication blind spots and determine whether each device can restore its control function after maintenance resources arrive.

[0183] In this invention, the power grid and communication network are considered to have geographical similarity in the CPDS. Therefore, the communication system has the same topology as the power system (i.e., each power node is coupled to a communication node located in the same location). This invention divides communication nodes connected to the command center via the same communication feeder into a communication node block. Based on the above assumptions, the communication system also has a radial topology. Then, the concept of a communication dead zone is defined to explain the range of communication nodes that lose communication functionality due to communication failures in the communication system.

[0184] Specifically, when extreme events cause communication link damage, the connected downstream communication nodes will lose contact with the command center, causing some power nodes to lose monitoring and control. Within the communication blind zone, RCS and VSC will malfunction, affecting system recovery. This invention assumes that some specific communication nodes controlled by the same command center are divided into a communication node block. The communication blind zone set C and the communication nodes contained in each blind zone can be obtained using the shortest path method.

[0185] In practical implementation, when constructing the communication fault analysis system, it is assumed that the power grid and communication network in the Cyber-Physical System (CPDS) are geographically isomorphic, and the communication network adopts a radial topology, corresponding one-to-one with the power nodes. When a communication link is damaged, the downstream communication nodes cannot communicate with the command center, forming a communication blind zone. Within the communication blind zone, the remote control switches RCS and VSC lose their remote control capabilities, affecting system reconstruction and recovery operations. The range of the communication blind zone is identified by the shortest path method, and constraints are established to determine whether each device can restore its control function after maintenance resources arrive.

[0186] In this way, by establishing a communication blind spot identification and control function recovery judgment mechanism, a deep characterization of the information physical coupling characteristics is achieved, providing high-precision and strongly coupled communication status analysis support for the post-disaster recovery of AC / DC distribution networks.

[0187] In specific implementation, the constraints (19)-(23) of the communication fault analysis system include:

[0188]

[0189] In the formula, c is the communication blind zone, C is the set of communication blind zones; e(c) represents the set of all damaged communication lines located at vertex e that cause the formation of the communication blind zone c; The time required to complete repairs of the i-communication function in the communication blind zone; The time required to complete repairs for communication fault e(c); x is the time required to complete repairs for all communication faults within the communication dead zone c; f,e(c),cmc Whether communication maintenance personnel should go to the communication fault e(c); N c A collection of communication blind spots;

[0190] In (19), it is assumed that the formation of a communication dead zone c may be related to multiple communication failures e(c). For a communication node i in such a communication dead zone c, communication function will be restored if and only if all communication failures that caused c have been repaired, i.e. therefore equal This indicates the maximum repair completion time for a damaged communication line upstream of the same feeder. Otherwise, therefore This will be set to a larger value. Furthermore, if communication node i is not in the communication dead zone, then... Set to 0. e(c) represents a damaged communication line in vertex e that causes a communication dead zone c.

[0191] Only when the communication function between the two nodes is intact can the RCS successfully receive action commands, and the VSC successfully receive commands to select the corresponding control variables. The time it takes for the two nodes of the RC and VSC to restore communication function is related to ECV and CMC. Binary variables and This indicates whether the communication function between RC and VSC is restored by ECV or CMC.

[0192]

[0193] In the formula, binary variables A value of 1 indicates that the communication function of vertex a is restored by ECV; binary variable. A value of 1 indicates that the communication function of vertex a is restored by the CMC; Ω VSC For the VSC set; Ω RCS For RCS set;

[0194]

[0195] In the formula, The time it takes for equipment a to be repaired by ECV; Let ecv be the dwell time at device a; The time it takes for CMC to complete the maintenance of equipment a; The time required for node j to restore its communication function;

[0196] If the communication functionality of the component at vertex a is repaired by ECV, that is... According to constraint (21), the time during which the component at point a can be controlled is set to... Accordingly, since the component at vertex a was not repaired by CMC, therefore According to constraint (22), Set it to 0.

[0197] If the communication function on both sides of component a is repaired by CMC, that is According to constraint (22), the time during which this component can be controlled is set to... That is, the maximum value of the communication function recovery time between the two nodes. Therefore, since the component at vertex a was not repaired by ECV, according to constraint (21), Set it to 0.

[0198] Finally, the constraint (23) is used to determine the time when component a can be successfully controlled.

[0199]

[0200] In the formula, This is the final recovery time for device a.

[0201] S5. Taking into account the coupling characteristics of information and physical systems in the power distribution system, a joint optimization framework is constructed that includes network reconfiguration constraints, power distribution system operation constraints, and equipment control timing constraints.

[0202] Among them, the network reconfiguration constraint is constructed based on the spanning tree theory method, which treats the distribution network as a graph, where nodes represent buses and edges represent lines or switches. A radially connected network is equivalent to a spanning tree of this graph. The network reconfiguration constraint is used to ensure that at any time during the post-disaster recovery process, the topology of the AC distribution network always remains radial and connected, avoiding the formation of loops, and only allowing the formation of controllable islands with the support of VSC or DG.

[0203] The power distribution system operation constraints are constructed using the DistFlow model for AC power grids and a simplified DC power flow model for DC power grids to ensure that at each recovery time point, the electrical operating state of the system meets physical laws and safety specifications, thus guaranteeing power supply quality and equipment safety.

[0204] Equipment control timing constraints are constructed by introducing time variables and logical constraints to characterize the logical dependencies and temporal order of various operations during the recovery process, ensuring that the recovery process proceeds in an orderly and safe manner.

[0205] Considering the coupling of information and physical systems, this invention addresses the DSR problem by jointly optimizing the scheduling of PMC, CMC, ECV, and DG, the RCS sequential action strategy, and the VSC control mode switching strategy, thereby achieving gradual restoration of power supply after a disaster. The DSR model can be divided into two parts: network reconfiguration constraints and distribution system operation constraints.

[0206] Network Reconfiguration Constraints

[0207] Constraints are established based on spanning tree theory to ensure the radial configuration of the AC power distribution system.

[0208] For example, if a bus controls the voltage, then that bus is the root bus and has no parent bus; if a bus does not control the voltage, then that bus has at most one parent bus. Based on spanning tree theory, a method is proposed to realize VSC as the root node to fully utilize its voltage support function.

[0209] In practice, network reconstruction constraints include (24)-(27):

[0210]

[0211] In the formula, This indicates the connection relationship of AC lines ij at time t; This indicates the connection relationship of AC line ji at time t; B represents the on / off state of AC line ij at time t; AC Indicates a set of communication lines; This indicates the connection relationship of DC lines ij at time t; This indicates the connection relationship of the DC line ji at time t; B represents the on / off state of DC line ij at time t; DC Represents a set of DC lines;

[0212]

[0213] In the formula, the binary variable r i,t When N is 1, it indicates that node i is the root node at time t; AC N represents the set of communication nodes; DC Represents the set of DC nodes;

[0214]

[0215] In the formula, s i,t This represents the state of node i at time t; This represents the set of VSC communication-side nodes; Let N represent the set of DC-side nodes of the VSC; N represents the set of all nodes; N sub This represents the set of nodes where the substation is located;

[0216]

[0217] In the formula, This indicates the connection state of line ij at time t. If node i is the parent node of node j, then... otherwise This indicates the energized state of node i at time t; This indicates the connection relationship of the DC-side line ik at time t; This indicates the connection relationship of AC side line ki at time t; This indicates the connection relationship of DC-side line jk at time t; B represents the on / off state of AC line kj at time t; VSC This represents the set of lines where VSC is located.

[0218] in, This represents the connection state of line ij at time t. If node i is the parent node of node j, then... otherwise This indicates the energized state of node i at time t. (24) indicates the connection state. With spanning tree variables The relationship between r, (25) represents r i,t and The relationship between them. For any node i, if... Then node i will be the root node, with no parent node; if Then node i will have a parent node, i.e., r. i,t =1. (26) indicates s i,t and r i,t The relationship between nodes is as follows: Node i can only have a parent node or become the root node when it is energized. Therefore, for a normal bus, r... i,t =s i,t For the buses on both sides of VSC, r i,t ≤s i,t (27) indicates that the AC and DC lines connected to the VSC have the same connection status, and the two lines have the same parent node, in order to prevent the buses on both sides of the VSC from becoming root buses at the same time, that is:

[0219] r i,t =r j,t =0 (28)

[0220] This is technically impossible.

[0221] Power distribution system operation constraints

[0222] The power flow constraint of AC power grids is based on the Dist-flow model, which has been widely used and validated.

[0223] The operating constraints of the power distribution system include (29)-(36):

[0224] Power flow constraints in AC power grids:

[0225]

[0226] In the formula, ds(i) represents the set of downstream nodes connected to node i; us(i) represents the set of upstream nodes; P i,j,t P represents the active power of line ij at time t; j,i,t This represents the active power of line ji at time t; This represents the active power of the generator at node i at time t; Q represents the active load at node i; i,j,t Q represents the reactive power of ij at time t; j,i,t This represents the reactive power of ji at time t; This represents the reactive power of the generator at node i at time t; N represents the reactive load at node i; AC T represents the set of communication nodes; T represents the time set.

[0227]

[0228] In the formula, U i,t U represents the voltage magnitude of node i at time t; j,t R represents the voltage magnitude of node j at time t; i,j X represents the resistance of line ij; i,j Q represents the reactance of line ij; i,j,t This represents the reactive power of line ij at time t; s ij,t This indicates the on / off state of line ij at time t;

[0229] Constraint (29) represents the active and reactive power balance of the power node, ds(i) represents the set of downstream nodes connected to node i, and us(i) represents the set of upstream nodes. Constraint (30) limits the voltage drop of line ij.

[0230] By simplifying the power flow constraints of the AC power grid, the power flow constraints of the DC power grid can be established as follows.

[0231] Power flow constraints in DC power grids:

[0232]

[0233] Safety constraints:

[0234]

[0235] In the formula, This represents the maximum active power of line ij; s i,j,t B represents the state of line ij at time t; B represents the set of branches.

[0236]

[0237] In the formula, This represents the upper limit of active power of node i; N represents the upper limit of reactive power of node i; G Represents the set of nodes where the generator is located;

[0238]

[0239] In the formula, These represent the upper and lower limits of the voltage amplitude at node i, respectively.

[0240]

[0241] In addition, to ensure stable system operation, some safety constraints need to be added. For example, constraint (33) specifies the maximum limits of active and reactive power of the line, (34) specifies the node generation capacity, and (35) specifies the maximum and minimum limits of node voltage. (36) Ensure that all loads are restored.

[0242] Unlike existing studies that often simplify or ignore the DC component, this scheme uses the DistFlow model (Equations (29) and (30)) for AC grids and a simplified DC power flow model (Equations (31) and (32)) for DC grids, achieving accurate descriptions of power flow and voltage distribution in both types of networks. For example, Equation (30) captures the voltage drop characteristics of AC lines through nonlinear voltage relationships, while Equation (32) uses linear voltage difference constraints to reflect the resistance loss of DC lines, significantly improving the model's ability to fit the actual system behavior. In addition, by introducing safety constraints such as power limit constraints (Equation (33)), generator output upper limit (Equation (34)), and voltage upper and lower limits (Equation (35)), the model ensures that the system will not experience overload, voltage exceedance, or equipment overheating at each recovery time point. This time-by-time safety verification mechanism effectively prevents secondary faults caused by blindly restoring the load, significantly improving the safety margin and reliability of the post-disaster recovery process. Furthermore, all constraints are indexed by the time variable t and linked to the line state variable s. i,j,t Coupling allows the model to adapt to topological changes brought about by network reconstruction. For example, when a line is disconnected (s i,j,t When t=0), equations (29) and (31) automatically exclude power flow, avoiding invalid calculations; meanwhile, equations (30) and (32) only take effect when connected. This dynamic response capability makes the model applicable to the entire recovery scenario from islanded operation to gradual networking, enhancing its applicability and robustness.

[0243] S6. Based on the joint optimization framework constructed in S5, the VSC operation equivalent model of S2, the multi-type maintenance resource scheduling model of S3, and the communication fault analysis results of S4 are embedded into the joint optimization framework as specific constraints or parameters. The objective function is to maximize the load recovery amount, minimize the total load reduction amount, and prioritize the recovery of high-priority loads. A collaborative optimization model for post-disaster system recovery is constructed.

[0244] In practical implementation, the objective function of the collaborative optimization model for post-disaster system recovery includes:

[0245]

[0246] In the formula, ω i This represents the priority weight coefficient of node i; This represents the active load of node i.

[0247] S7. When a disaster occurs, solve the collaborative optimization model in S5 based on actual data to obtain a post-disaster recovery plan.

[0248] Unlike existing technologies that often limit VSC to a specific recovery phase (e.g., only for islanded power supply) or a fixed control mode, this solution defines and models multiple control modes of VSC (PQ, UAC-f, UDC-Q) and constructs their operational equivalent models. This allows for flexible switching of control strategies at different stages, such as fault isolation, islanding, and network reconfiguration. For example, in the initial recovery phase, it can switch to UAC-f mode to provide voltage and frequency support to the power-loss area, ensuring power supply to critical loads; as the system gradually recovers, it switches back to PQ mode to participate in power regulation. This mechanism fully leverages the multi-energy characteristics of VSC, significantly enhancing the voltage stability and operational flexibility of the system during dynamic recovery. Furthermore, existing methods typically treat maintenance resources as a single type, failing to reflect the differences between power and communication repair tasks. This solution clearly distinguishes between multiple resource types, including power fault repair personnel (PMC), communication fault repair personnel (CMC), and emergency communication vehicles (ECV), and constructs their path planning and work time scheduling models. By optimizing the dispatch order and spatial path of different types of resources, the problem of "power equipment has been repaired but cannot be remotely controlled" caused by communication repair delays was avoided, thus improving the overall coordination and execution efficiency of resource scheduling.

[0249] To address the common oversight in existing research of "powered but uncontrolled" situations caused by communication failures, this solution constructs a communication failure analysis system capable of dynamically identifying the scope of communication blind spots after a disaster and determining whether key equipment (such as VSCs and tie switches) can restore communication and control functions once maintenance resources arrive. This mechanism uses communication status as a prerequisite for recovery operations, ensuring that critical operations such as network reconfiguration or control mode switching are only permitted when communication is available. Compared to the simplified approach of traditional methods that assume complete reliability or independent handling of communication repair, this solution significantly improves the feasibility and safety of recovery strategies in real-world environments. Furthermore, this solution innovatively integrates network reconfiguration constraints (based on spanning tree theory), power distribution system operation constraints (DistFlow and DC power flow models), and equipment control timing constraints into a unified joint optimization framework, embedding the VSC equivalent model, multi-resource scheduling model, and communication status analysis results as key parameters. This framework can simultaneously consider multiple constraints such as electrical safety, topology radiation, control logic timing, and communication reachability, generating physically feasible, informationally executable, and timing-reasonable recovery schemes. Compared to the phased and fragmented optimization strategies in existing studies, this method achieves cross-domain and full-chain collaborative decision-making, significantly improving the overall performance of post-disaster recovery.

[0250] This method can take into account the cyber-physical coupling characteristics, enabling rapid, orderly, and efficient load recovery.

[0251] Example 2

[0252] To better illustrate the AC / DC distribution network post-disaster recovery strategy considering the scheduling of multiple types of maintenance resources proposed in this invention, the following experiment is disclosed:

[0253] This invention applies the proposed joint recovery strategy to a modified IEEE 123 node test system, in which part of the AC power grid is converted to a DC power grid. The system voltage is 4.16kV, and the total load requirement is 4330kW. The CPDS is configured with one command center, three warehouses, three VSCs, eight RCSs, six DGs, and two substations. For fault conditions and recovery resources, it is assumed that 12 power lines and 10 communication links are damaged. Each warehouse is equipped with two EFRCs and one CMC, and warehouse 2 is equipped with one ECV. In addition, more practical parameter settings (such as repair time, RCS working time, VSC mode switching time, etc.) are considered in this test system, and the specific values ​​are shown in Tables 1 to 3. The time required to initiate emergency communication when the ECV arrives at the working location is set to 5 minutes. The VSC capacity is set to 1.0MVA.

[0254] Table 1 Repair Time of Damaged Power Lines

[0255]

[0256] Table 2 Repair time of damaged communication links

[0257]

[0258] Table 3 RCS Operation Runtime

[0259]

[0260] Validity analysis

[0261] The proposed collaborative optimization model has a solution time of 809.78 s, and the proposed strategy restored all loads within 330 minutes, with a total restored power of 19893.50 kWh. The scheduling path results of the PMC in the power system are as follows: Figure 3 As shown, the scheduling path results for CMC and ECV in the communication system are as follows: Figure 4 As shown in Table 4, their travel routes and schedules are also shown.

[0262] Table 4. Scheduling Table for Three Types of Maintenance Resources

[0263]

[0264] To illustrate the sequential recovery process of CPDS in detail, Table 5 lists the timeline of the sequential recovery strategy. During the recovery process, collaborative recovery tasks include:

[0265] 1) Repair damaged power lines and communication links;

[0266] 2) Restore communication functionality between RCS and VSC;

[0267] 3) The sequence of RCS switching actions;

[0268] 4) The energizing sequence and power generation sequence of each node and DG.

[0269] Table 5. Timeline of Sequential Recovery Strategy

[0270]

[0271] The communication function of RCSi-j* can only be temporarily restored and the switch can only operate normally after the ECV has remained stationary and established wireless communication for a period of time. Therefore, the ECV can only leave after the RCS has completed its operation. By repairing the damaged communication links, the communication function of VSC with other RCSs is restored. In the case of this invention, five damaged communication links were repaired, and the communication functions of the corresponding RCSs and VSCs were restored.

[0272] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit the technical solutions. Those skilled in the art should understand that any modifications or equivalent substitutions to the technical solutions of the present invention without departing from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. A method for post-disaster recovery of AC / DC distribution networks considering the scheduling of multiple types of maintenance resources, characterized by: Includes the following steps: S1. Define the control mode of the voltage source converter VSC, wherein the control mode includes DC voltage and reactive power control U. DC -Q, Active and reactive power control PQ, AC voltage and frequency control U AC -f; S2. Construct an equivalent model of VSC operation to analyze the ability of VSC to support voltage in non-fault areas through control mode switching during fault isolation and recovery. S3. Construct a scheduling model for multiple types of maintenance resources to optimize the path and time of each type of maintenance resource; among which, the types of maintenance resources include power fault repair personnel (PMC), communication fault repair personnel (CMC), and emergency communication vehicles (ECV); S4. Construct a communication fault analysis system to identify the range of communication blind spots and determine whether each device can restore its control function after maintenance resources arrive. S5. Taking into account the coupling characteristics of information and physical systems in the power distribution system, a joint optimization framework is constructed that includes network reconfiguration constraints, power distribution system operation constraints, and equipment control timing constraints. Among them, the network reconfiguration constraint is constructed based on the spanning tree theory method, which treats the distribution network as a graph, where nodes represent buses and edges represent lines or switches. A radially connected network is equivalent to a spanning tree of this graph. The network reconfiguration constraint is used to ensure that at any time during the post-disaster recovery process, the topology of the AC distribution network always remains radial and connected, avoiding the formation of loops, and only allowing the formation of controllable islands with the support of VSC or DG. The power distribution system operation constraints are constructed using the DistFlow model for AC power grids and a simplified DC power flow model for DC power grids to ensure that at each recovery time point, the electrical operating state of the system meets physical laws and safety specifications, thus guaranteeing power supply quality and equipment safety. Equipment control timing constraints are constructed by introducing time variables and logical constraints to characterize the logical dependencies and temporal sequence of various operations during the recovery process, ensuring that the recovery process proceeds in an orderly and safe manner. S6. Based on the joint optimization framework constructed in S5, the VSC operation equivalent model of S2, the multi-type maintenance resource scheduling model of S3, and the communication fault analysis results of S4 are embedded into the joint optimization framework as specific constraints or parameters. The objective function is to maximize the load recovery amount, minimize the total load reduction amount, and prioritize the recovery of high-priority loads. A collaborative optimization model for post-disaster system recovery is constructed. S7. When a disaster occurs, solve the collaborative optimization model in S5 based on actual data to obtain a post-disaster recovery plan.

2. The AC / DC distribution network post-disaster recovery method considering multi-type maintenance resource scheduling as described in claim 1, characterized in that: In S2, if the VSC runtime equivalent model adopts U DC If -Q or Uac-f control is applied, the voltage on the fault side should meet the following constraints: In the formula, U is the voltage at faulty node i, and U0 is the preset voltage.

3. The AC / DC distribution network post-disaster recovery method considering multi-type maintenance resource scheduling as described in claim 1, characterized in that: In S2, when constructing the VSC operation equivalent model, an equivalent circuit diagram of VSC consisting of equivalent impedance and ideal VSC is constructed. VSC is connected to AC side bus ka and DC side bus kd through circuit breakers for isolation, and it is assumed that the circuit breaker and the bus connected on both sides are included in the VSC station. The constraints of the VSC equivalent model include: In the formula, Ω VSC For VSC site collection; U represents the capacity of the k-th VSC. i,t U represents the voltage magnitude of node i at time t. j,t P represents the voltage magnitude of node j at time t. dk,t P represents the active power of dk connected to the VSC branch at time t. i,ka,t Q i,ka,t P represents the active power and reactive power of AC node i at time t, respectively; kd,j,t Let I be the active power at DC node j at time t; i,ka,t I kd,j,t Ri represents the current at AC node i and DC node j at time t, respectively; ka R kd These are the resistances of the AC and DC circuits, respectively; X k Reactance of AC lines; Let VSC k be the active power and reactive power at time t; These are the upper and lower limits of the reactive power output of VSC k, respectively; Let be the AC bus voltage and DC bus voltage at time t; Let i be the resistance and reactance of AC line i; Let be the resistance of DC line j.

4. The AC / DC distribution network post-disaster recovery method considering multi-type maintenance resource scheduling as described in claim 3, characterized in that: In S3, the constraints of the scheduling model include routing constraints and time constraints; The constraints of the routing problem include: In the formula, x dp(γ),T(γ),γ Indicates whether maintenance resource γ is from the warehouse. dp(γ) Heading to work T(γ) ;x O(γ),dp(γ),γ Indicates whether maintenance resource γ is from the work point O(γ) Heading to work dp(γ) dp(γ) represents the warehouse to which the maintenance resource belongs; T(γ) represents the work point reached by the maintenance resource γ; O(γ) represents the work point from which the maintenance resource γ departs; γ represents a certain type of maintenance resource; In the formula, x dp,T(γ),γ Indicates whether maintenance resource γ is from the warehouse. dp Heading to work T(γ), ;x O(γ),dp,γ This indicates whether maintenance resources γ originate from the work point. O(γ) Head to the warehouse dp ; DP / {dp(γ)} represents a warehouse that does not belong to maintenance resources; In the formula, x O(γ),T(γ),γ Indicates whether maintenance resource γ is from the work point O(γ) Heading to work T(γ) V MC DP represents the set of work points for maintenance personnel; DP represents the set of all maintenance resource repositories; k represents the index of the work point. In the formula, x m,n,pmc This indicates whether power fault repair personnel have traveled from work point m to work point n; D represents the set of power failure points; D represents the set of warehouses. In the formula, x p,q,cmc Indicates whether the communication fault repair personnel have traveled from work point m to work point n; This represents the set of work locations for communication fault repair personnel; cmc represents the index of the communication fault repair personnel. In the formula, x a,b,ecv Indicate whether the emergency communication vehicle is traveling from work point a to work point b; This represents the set of emergency communication vehicle work points; ecv represents the index of the emergency communication vehicle.

5. The AC / DC distribution network post-disaster recovery method considering multi-type maintenance resource scheduling as described in claim 4, characterized in that: The time constraints include: In the formula, This indicates that maintenance resources γ have arrived at the work point. T(γ) Time; This indicates that maintenance resources γ have arrived at the work point. O(γ) Time; This indicates that maintenance resource γ is at the working point. O(γ) Required working hours; Indicates that maintenance resources γ originate from the work point O(γ) Heading to work T(γ) Required travel time; M represents an integer greater than the preset value; In the formula, This indicates that maintenance resource γ has left the work point. T(γ) Time; This indicates that maintenance resource γ is at the working point. T(γ) Required working hours; In the formula, This indicates the time when the emergency communication vehicle arrived at work point b; This indicates the time when the emergency communication vehicle arrived at work point a; This indicates the working time required for the emergency communication vehicle to reach work point a; This indicates the travel time required for the emergency communication vehicle to travel from work point A to work point B; In the formula, Indicates the time when the emergency communication vehicle left work point b; In the formula, This indicates the working time required for the emergency communication vehicle to reach work point b; In the formula, x b,a,ecv This indicates whether the emergency communication vehicle is traveling from work point a to work point b; 1 indicates that it is traveling, and 0 indicates that it is not traveling. This indicates the required operation time for the equipment located at work point a; This indicates the operation time required for the emergency communication vehicle.

6. The AC / DC distribution network post-disaster recovery method considering multi-type maintenance resource scheduling as described in claim 5, characterized in that: In S4, when constructing the communication fault analysis system, it is assumed that the power grid and communication network in the Cyber-Physical System (CPDS) are geographically isomorphic, and the communication network adopts a radial topology, corresponding one-to-one with the power nodes. When a communication link is damaged, the downstream communication nodes cannot communicate with the command center, forming a communication blind zone. Within the communication blind zone, the remote control switches RCS and VSC lose their remote control capabilities, affecting system reconstruction and recovery operations. The range of the communication blind zone is identified by the shortest path method, and constraints are established to determine whether each device can restore its control function after maintenance resources arrive.

7. The AC / DC distribution network post-disaster recovery method considering multi-type maintenance resource scheduling as described in claim 6, characterized in that: The constraints of the communication fault analysis system include: In the formula, c is the communication blind zone, C is the set of communication blind zones; e(c) represents the set of all damaged communication lines located at vertex e that cause the formation of the communication blind zone c; The time required to complete repairs of the i-communication function in the communication blind zone; The time required to complete repairs for communication fault e(c); x is the time required to complete repairs for all communication faults within the communication dead zone c; f,e(c),cmc Whether communication maintenance personnel should go to the communication fault e(c); N c A collection of communication blind spots; In the formula, binary variables A value of 1 indicates that the communication function of vertex a is restored by ECV; binary variable. A value of 1 indicates that the communication function of vertex a is restored by the CMC; Ω VSC For the VSC set; Ω RCS For RCS set; In the formula, The time it takes for equipment a to be repaired by ECV; Let ecv be the dwell time at device a; The time it takes for CMC to complete the maintenance of equipment a; The time required for node j to restore its communication function; In the formula, This is the final recovery time for device a.

8. The AC / DC distribution network post-disaster recovery method considering multi-type maintenance resource scheduling as described in claim 7, characterized in that: In S5, network reconstruction constraints include: In the formula, This indicates the connection relationship of AC lines ij at time t; This indicates the connection relationship of AC line ji at time t; B represents the on / off state of AC line ij at time t; AC Indicates a set of communication lines; This indicates the connection relationship of DC lines ij at time t; This indicates the connection relationship of the DC line ji at time t; B represents the on / off state of DC line ij at time t; DC Represents a set of DC lines; In the formula, the binary variable r i,t When N is 1, it indicates that node i is the root node at time t; AC N represents the set of communication nodes; DC Represents the set of DC nodes; In the formula, s i,t This represents the state of node i at time t; This represents the set of VSC communication side nodes; Let N represent the set of DC-side nodes of the VSC; N represents the set of all nodes; N sub This represents the set of nodes where the substation is located; In the formula, This indicates the connection state of line ij at time t. If node i is the parent node of node j, then... otherwise This indicates the energized state of node i at time t; This indicates the connection relationship of the DC-side line ik at time t; This indicates the connection relationship of AC side line ki at time t; This indicates the connection relationship of DC-side line jk at time t; B represents the on / off state of AC line kj at time t; VSC This represents the set of lines where VSC is located.

9. The AC / DC distribution network post-disaster recovery method considering multi-type maintenance resource scheduling as described in claim 8, characterized in that: In S5, the operating constraints of the power distribution system include: Power flow constraints in AC power grids: In the formula, ds(i) represents the set of downstream nodes connected to node i; us(i) represents the set of upstream nodes; P i,j,t P represents the active power of line ij at time t; j,i,t This represents the active power of line ji at time t; P represents the active power of the generator at node i at time t; i load Q represents the active load at node i; i,j,t Q represents the reactive power of ij at time t; j,i,t This represents the reactive power of ji at time t; This represents the reactive power of the generator at node i at time t; N represents the reactive load at node i; AC T represents the set of communication nodes; T represents the time set. In the formula, U i,t U represents the voltage magnitude of node i at time t; j,t R represents the voltage magnitude of node j at time t; i,j X represents the resistance of line ij; i,j Q represents the reactance of line ij; i,j,t This represents the reactive power of line ij at time t; s ij,t This indicates the on / off state of line ij at time t; Power flow constraints in DC power grids: Safety constraints: In the formula, This represents the maximum active power of line ij; s i,j,t B represents the state of line ij at time t; B represents the set of branches. In the formula, P i max This represents the upper limit of active power of node i; N represents the upper limit of reactive power of node i; G Represents the set of nodes where the generator is located; In the formula, These represent the upper and lower limits of the voltage amplitude at node i, respectively.

10. The AC / DC distribution network post-disaster recovery method considering multi-type maintenance resource scheduling as described in claim 9, characterized in that: In S6, the objective function of the collaborative optimization model for post-disaster system recovery includes: In the formula, ω i P represents the priority weight coefficient of node i; i load This represents the active load of node i.

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