Distribution network fault maintenance optimization method and system based on information physical system, terminal and medium

Abstract

The invention provides a distribution network fault maintenance optimization method and system based on an information physical system, a terminal and a medium, and belongs to the technical field of distribution network fault recovery scheduling optimization, and the method comprises the steps: constructing a network maintenance personnel and equipment maintenance personnel scheduling model, and obtaining a maintenance path of the maintenance personnel through the scheduling model; establishing a time unification model for parallel scheduling of multiple maintenance personnel, integrating network maintenance personnel and equipment maintenance personnel on the same time axis, obtaining a time sequence according to a maintenance sequence, and establishing a power distribution network reconstruction model; establishing a collaborative recovery model with an association relationship among equipment maintenance personnel, network maintenance personnel and a power distribution network recovery system; a single commodity flow model is adopted to determine connectivity of network nodes of the collaborative recovery model, nonlinear constraints are converted into linear sub-problems, constraints are added, and a mixed integer linear programming model is obtained; and solving the mixed integer linear programming model to obtain the minimum time required for maintaining the remaining fault parts.

Description

Technical Field

[0001] The present invention relates to the technical field of distribution network fault recovery scheduling optimization, and in particular to a distribution network fault maintenance optimization method and system based on an information-physical system, as well as a corresponding computer terminal and a computer-readable storage medium. Background Art

[0002] As the degree of coupling between physical networks and communication networks accelerates the development of intelligent power grids, the operating environment of cyber-physical distribution systems (CPDPS) has become increasingly complex, which makes them prone to large-scale cascading failures, for example, of power lines and communication links, caused by natural disasters. Therefore, it is critical to develop an effective recovery strategy to quickly restore loads after a power outage, considering the coupling effect of the physical network and the communication network. At present, a variety of distribution network post-disaster recovery strategies have been proposed. These strategies can make good use of various resources on the physical side to reduce the losses caused by natural disasters, such as improving the resilience of the system through flexible reconstruction of microgrids and distributed generation. However, the above studies do not show the impact of maintenance personnel on the improvement of resilience. The routing problem of the maintenance team is a linear programming difficult combinatorial optimization problem that has been studied in operations research for a long time. In addition, the routing problem of maintenance personnel assigned to different systems is coupled to the distribution system recovery model, further increasing the complexity of the model. Due to the deepening coupling of the physical network and the communication network, faults on the network side often affect the operation of components in the physical network, resulting in deviations from the original recovery measures. Therefore, the coupling characteristics of the physical network and the communication network are crucial to enhancing the resilience of the distribution network.

[0003] At present, people have conducted extensive research on virtual physical power distribution systems (CPPS). The vulnerability of virtual distribution networks has been studied from a physical perspective, and robustness has been discussed from a network perspective. In the study of the resilience of distribution networks, a survivability-aware path recovery strategy for the core network of virtual physical distribution systems under large-scale communication failures caused by natural disasters is proposed. However, as the resilience is restored, the topology of the distribution network and the working status of the components will undergo new changes, affecting the distribution network recovery decision. Therefore, it is necessary to explore the recovery order of faulty components in virtual physical distribution systems to achieve rapid load recovery after natural disasters. In addition, when determining the maintenance order, the travel time of maintenance personnel is an important factor that cannot be ignored. Theoretically, equipment maintenance personnel and network maintenance personnel are parallel in time and space, which means that they repair faulty components belonging to two subsystems. However, from a global perspective, the scheduling order of the two depends on the impact on the power grid recovery effect, so it is necessary to establish a coordination model of network maintenance personnel, equipment maintenance personnel and distribution network recovery system that considers the coupling relationship between the three. At present, no description or report of similar technologies to the present invention has been found, and similar materials at home and abroad have not yet been collected. Summary of the invention

[0004] In view of the above-mentioned deficiencies in the prior art, the present invention provides a distribution network fault maintenance optimization method and system based on an information-physical system, and also provides a corresponding computer terminal and a computer-readable storage medium.

[0005] According to one aspect of the present invention, a distribution network fault maintenance optimization method based on a cyber-physical system is provided, comprising: Construct a network maintenance personnel scheduling model and an equipment maintenance personnel scheduling model, and use the two scheduling models to obtain the maintenance path of the corresponding maintenance personnel; Based on the maintenance path, a unified time model for parallel scheduling of multiple maintenance personnel is established, network maintenance personnel and equipment maintenance personnel are integrated into the same timeline, a time series is obtained according to the maintenance sequence, and a distribution network reconstruction model is established; Based on two dispatch models, a time unified model and a distribution network reconstruction model, a collaborative restoration model with the association relationship between equipment maintenance personnel, network maintenance personnel and distribution network system is established; A single commodity flow model is used to determine the connectivity of the network nodes of the collaborative recovery model, and the connectivity judgment constraint of the network nodes is transformed from a highly nonlinear problem to a linear sub-problem; The constraints of the time unified model and the objective function of the collaborative recovery model are linearized to obtain a mixed integer linear programming model; The mixed integer linear programming model is solved to obtain the minimum time required to repair the remaining faulty components, thereby minimizing the distribution network fault maintenance time loss.

[0006] Preferably, the construction of the network maintenance personnel scheduling model and the equipment maintenance personnel scheduling model, and obtaining the maintenance path of the maintenance personnel by using the scheduling model, includes: Integrating maintenance personnel scheduling with maintenance time and travel time, the scheduling model for equipment maintenance personnel and network maintenance personnel is obtained as follows: (1) (2) In the formula, Indicates the time to complete the repair of the faulty components in the virtual physical power system. g Indicates the end point of the physical system failure, h Indicates the end location of the faulty component of the network system. p Indicates equipment maintenance personnel, po Indicates the status of the equipment maintenance personnel before the failure. v po Indicates the site of the equipment maintenance personnel before the failure. Indicates equipment maintenance personnel,v co Indicates the site of the network maintenance personnel before the failure. Indicates network maintenance personnel. M p Represents a collection of equipment maintenance personnel. M c Represents a collection of network maintenance personnel. Indicates whether the equipment maintenance personnel have reached the power fault component and completed the repair of the fault point within the repairable time. Indicates whether the network maintenance personnel reached the network fault component and completed the repair of the fault point within the repairable time; Equations (1) and (2) describe the departure paths of equipment maintenance personnel and network maintenance personnel, respectively; For a certain fault repair time When only one faulty component is repaired by its corresponding maintenance personnel, then: (3) In the formula, f is the starting point of the physical system failure, g is the physical system failure endpoint, l The starting point of the network system failure. h The network system failure endpoint. T f is the set of repair completion times of the faulty components, Indicates the time it takes for equipment maintenance personnel to complete repairs of all physical system failures. Indicates the time it takes for network maintenance personnel to complete repairs of all network system faults; When multiple maintenance personnel complete maintenance work at the same time, the corresponding fault repair time is recorded as and ,in ; When only one maintenance personnel handles the corresponding faulty component, there are: (4) (5) In the formula, represents the set of failure points in the physical system, Represents the set of failure points in a network system; When a faulty component is repaired, the scheduling model in which equipment maintenance personnel and network maintenance personnel are involved in the repair is as follows: (6) (7) Equations (6) and (7) give the mathematical expressions that at most one maintenance team can leave when a faulty component is repaired; If the current faulty component is a maintenance or If the last component in the restoration process requires repair, the maintenance personnel or Return to the maintenance center, at this time the left side of equation (6) or equation (7) is equal to 0; For the first fault repair completion time, a maintenance person must be or To reach a faulty component and perform repair work, there are: (8) When maintenance personnel or During troubleshooting time If the faulty part is successfully repaired, the maintenance personnel or Subsequent maintenance activities must start from the faulty component, so the path model of a single maintenance personnel is established as follows: (9) (10) In the formula, M represents the fault repair coefficient that ensures the continuity of a single maintenance team's path, Indicates the time when the fault repair is completed. Completed before; Equations (9) and (10) are used to describe the continuity of the path model of a specific maintenance worker.

[0007] Preferably, based on the maintenance path, a unified time model for parallel scheduling of multiple maintenance personnel is established, network maintenance personnel and equipment maintenance personnel are integrated into the same timeline, a time series is obtained according to the maintenance sequence, and a distribution network reconstruction model is established, including: A time unified model is established, and the time unified model is expressed as: (11) (12) In the formula, Indicates that the equipment maintenance personnel have left the fault starting point f and reaches the fault end point g The shortest time, Indicates that the network maintenance personnel have left the fault origin. l and reaches the fault end point h The shortest time, Indicates the repair time of a faulty component in the physical network, represents the repair time of a faulty component in a communication network, Indicates that the equipment maintenance personnel start from the fault f Travel to the fault end g and the time required to complete the repair task and trigger the network reconfiguration, Indicates that network maintenance personnel start from the fault point l Travel to the fault end h The time required to complete the repair task and trigger network reconfiguration; the shortest time or It can be obtained by Floyd's algorithm; Maintaining personnel or The time interval between two adjacent maintenance activities is represented on the time axis, and the time interval for each maintenance personnel is obtained as: (13) (14) In the formula, Indicates maintenance personnel The time interval between two adjacent maintenance activities, Indicates maintenance personnel The time interval between two adjacent maintenance activities; When the faulty component is a maintenance or exist or The first maintenance is equal to the maintenance personnel or The time it takes to travel from the depot to the faulty component and complete the repair task; for other maintenance personnel, or During troubleshooting time The inner value is equal to 0; (15) (16) In the formula, and is a binary variable, indicating the maintenance personnel and exist status; if the maintenance personnel If the maintenance activity is completed, the binary variable is equal to 1, otherwise it is 0; No. k The actual time of maintenance events is equal to the previous k The sum of time intervals is: (17) (18) In the formula, and For maintenance personnel and Actual repair time; For other maintenance personnel who did not completely repair the faulty part, the status or To be used by maintenance personnel or Actual repair time or Set to 0 to get a unified time by adding the actual times corresponding to different maintainers. for: (19) (20) In the formula, Actual time and for different maintenance personnel; Represents the time interval between each network reconfiguration; Formula (20) represents the time interval between each network reconfiguration, and adds the following constraints to ensure that different maintenance personnel are sorted in chronological order when the time axis is unified: (twenty one) Let binary variable Indicated in k Power failure endpoint after reconfiguration g Is it connected, and Indicates the end point of power failure g or h Whether it is maintained by the maintenance personnel or Maintenance; binary variable Respectively expressed in k Network nodes after repair activity i and network nodes j If the network node is working properly, then is equal to 1, otherwise, =0; based on this, the coupling effect of the physical network and the communication network is established, expressed as: (twenty two) (twenty three) (twenty four) (25) (26) In the formula, Represents the system generator network node i exist k The power after repair, Represents the system generator network node i Maximum power; in: Formula (22) and Formula (23) are used to obtain the fault component in the communication network or physical network at the time of fault repair. Working status; Formula (24) is used to describe the effect of the current fault status on whether the line can be repaired within the repair time when the fault repair event triggers the network reconfiguration decision. Closure then has an effect; if the faulty component is defective and has not been repaired, the line cannot be closed; Formula (25) is used to describe that if the corresponding network nodes on both sides of the line cannot be operated, the remote control switch of the line will not be able to receive the control signal and will stop operating; Equation (26) is used to describe that when the system is disturbed by the set conditions, the generator will be forced to shut down for protection and other reasons; make Indicates the time to repair the fault Time fault end point g Products on i' , and let the binary variable Indicates fault endpoint g Is it included in the spanning tree, and let the binary variable It is a virtual switch, the fault endpoint g exist If it is closed when , the virtual switch is equal to 1; based on this, the radial topology constraint of the distribution network reconstruction model is constructed as follows: (27) (28) (29) (30) (31) (32) (33) In the formula, represents the collection of power nodes in the physical network, Indicates the node current of the substation to which the system is connected; Formula (27) makes 1 unit of commodity i'From the substation node outflow; Formula (28) requires that 1 unit of commodity i' Inflow Node i' ; Formula (29) prohibits each commodity i' Flow into other nodes; Equation (30) is used as a constraint to define the arc only when it is included by the variable Each commodity can flow on the arc only when it is in the defined directed spanning tree; Equation (31) specifies the number of arcs in the spanning tree; Formula (32) obtains the virtual connection state of the branch according to the arcs contained in the spanning tree ; Through equations (27) to (32), we obtain the set of all associated vectors of the spanning tree topology formed by the reconstruction of the physical network, and through equation (33), we restrict the closure of the physical network to Determine the subset of closed branches in the spanning tree.

[0008] Preferably, the collaborative restoration model with the association relationship between equipment maintenance personnel, network maintenance personnel and distribution network system is established based on the two scheduling models, the time unified model and the distribution network reconstruction model, including: The distance matrix d is initialized according to the information of the traffic network during the distribution network restoration process, and the Floyd algorithm is used to solve the shortest path between two members through matrix iteration to build a traffic network model; where: d ( i , j )yes i and j The distance between i and j If there is a road available between d ( i , j ) is equal to the distance value of the road; if i = j ,but d ( i , j ) = 0, and if in i and j If there is no available road between d ( i , j ) = ∞; then, the vertex k as a midpoint; if d ( i , k )+ d ( k , j )<d ( i , j ),but d ( i , j )= d ( i , k )+ d ( k , j );otherwise, d ( i , j ) remains unchanged; Based on the traffic network model, a collaborative restoration model considering equipment maintenance personnel, network maintenance personnel and distribution network system is constructed, including: set up For Node i The load at For Node i The priority and weight of the load at the location are considered, and the objective function of the collaborative recovery model is to minimize the load reduction during a failure. Then: (34) In the formula, Indicates k Network nodes after repair i Working status; The constraints for establishing the objective function are: The constraints for maintenance personnel scheduling are: Equation (1) to (10); The constraints of the time unified model are: Equation (11) to Equation (21); The constraints of the coupling characteristics of the physical network and the communication network are: Equation (22) to Equation (27); The constraints of the distribution network reconstruction model are: Equation (28) to Equation (33); When the load is fully restored, the objective function is changed to minimize the time cost in repairing the remaining faulty components: (35) The constraints of the changed objective function are: Constraints for maintenance personnel scheduling: Equation (1) to (10); Constraints of the time unified model: Equation (11) to Equation (21).

[0009] Preferably, the method of using a single commodity flow model to determine the connectivity of the network nodes of the collaborative recovery model and converting the connectivity judgment constraint of the network nodes from a highly nonlinear problem to a linear sub-problem includes: A single commodity flow model is provided, wherein the central control node and the sub-node in the communication network are respectively regarded as a power node and a load in the physical network, and the connectivity of the network node is whether the central control node restores the sub-node; In the single commodity flow model, let Represents a network node i The load of is equal to 1 for the child nodes in the communication network; represents the output of the central control node, and let Indicates the time to repair the fault Passing the fault starting point l ; let the binary variable Indicates the time to repair the fault The starting point of the failure after reconfiguration l The actual working status; Indicates the time to repair the fault Time failure start l The commodity flow in the network; based on this, the connectivity judgment model of the network nodes is constructed as follows: (36) The constraints for establishing the connectivity judgment model of the network nodes include: (37) (38) (39) (40) (41) The objective function of the connectivity judgment model of the network node is to minimize the load loss, and the constraints are shown in equations (36) to (41); wherein equation (36) is used to constrain all nodes to satisfy flow balance, and equations (37) to (41) are topological constraints; If the child node recovers power, the load recovery factor Equal to 1, indicating a node i Connect to the central control node v , and the node i Works normally; otherwise, If it is equal to 0, it means the node cannot work; (42) (43) Add an appropriate data The converter converts the connectivity judgment model of the network nodes into the following form: (44)

[0010] Preferably, the constraints of the time unified model and the objective function of the collaborative recovery model are linearized to obtain a mixed integer linear programming model, including: Linearize the constraints (17) and (18) in the time unified model; for (17), introduce the auxiliary binary variable , and let , transform equation (17) into: (45) and The following constraints are met: (46) make: (47) (48) There are continuous variables in the objective function (34) and binary variables , so we introduce auxiliary variables Linearize the objective function and transform the mixed integer quadratic programming problem into a mixed integer linear programming problem: (49) in, The following additional constraints are met: (50) Get a complete mixed integer linear programming model; By solving the mixed integer linear programming model, the minimum time required to repair the remaining faulty components is obtained.

[0011] According to another aspect of the present invention, a distribution network fault maintenance optimization system based on a cyber-physical system is provided, comprising: A scheduling model building module is used to build a network maintenance personnel scheduling model and an equipment maintenance personnel scheduling model. The two scheduling models are used to obtain the maintenance path of the corresponding maintenance personnel. A time unified model building module, which builds a time unified model for parallel scheduling of multiple maintenance personnel based on the maintenance path, integrates network maintenance personnel and equipment maintenance personnel on the same time axis, obtains a time series according to the maintenance sequence, and builds a distribution network reconstruction model; A collaborative restoration model building module, which builds a collaborative restoration model with the relationship between equipment maintenance personnel, network maintenance personnel and distribution network system based on two scheduling models, a time unified model and a distribution network reconstruction model; A linear programming module, which uses a single commodity flow model to determine the connectivity of the network nodes of the collaborative recovery model, converts the connectivity judgment constraints of the network nodes from highly nonlinear to linear sub-problems; linearizes the constraints of the time unified model and the objective function of the collaborative recovery model to obtain a mixed integer linear programming model; A maintenance optimization module is used to obtain the minimum time required to repair the remaining faulty components by solving the mixed integer linear programming model.

[0012] According to a third aspect of the present invention, there is provided a computer terminal comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, can be used to execute any of the above-described methods of the present invention, or to run any of the above-described systems of the present invention.

[0013] According to a fourth aspect of the present invention, there is provided a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, can be used to execute any of the methods described above in the present invention, or to run any of the systems described above in the present invention.

[0014] Due to the adoption of the above technical solution, the present invention has at least one of the following beneficial effects compared with the prior art: The distribution network fault maintenance optimization method and system based on the cyber-physical system provided by the present invention takes into account the mutual coupling between the network system and the physical system, and proposes a sequential disaster recovery strategy based on the coordinated optimization of network maintenance personnel, equipment maintenance personnel and distribution network recovery model. In the time unified model, the equipment maintenance personnel and the network maintenance personnel are integrated into the same time axis according to the repair order to obtain a time series, thereby matching the distribution network recovery model, minimizing the load loss of the distribution network after the disaster, and solving the problem that the distribution network recovery model is difficult to couple.

[0015] The distribution network fault maintenance optimization method and system based on the information-physical system provided by the present invention establish a parallel scheduling model for multiple maintenance personnel and a unified time model, integrate network maintenance personnel and equipment maintenance personnel on the same timeline, obtain a time series according to the maintenance sequence, and thus match the distribution network recovery model, which can effectively reduce the load loss of the distribution network after a disaster.

[0016] The present invention provides a distribution network fault maintenance optimization method and system based on an information-physical system. The connectivity of network nodes is determined using a modified single commodity flow model, which is used to transform highly nonlinear constraints into linear sub-problems, and thereby establish a MILP model, thereby solving the problem of difficulty in solving the model using a computer. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings: Figure 1 This is a workflow diagram of a distribution network fault maintenance optimization method based on an information-physical system in one embodiment of the present invention.

[0018] Figure 2 This is a working architecture diagram of a distribution network fault maintenance optimization method based on an information-physical system in a preferred embodiment of the present invention.

[0019] Figure 3 Schematic diagram of component modules of a distribution network fault maintenance and optimization system based on an information-physical system in one embodiment of the present invention. DETAILED DESCRIPTION

[0020] The following is a detailed description of the embodiments of the present invention: This embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation method and a specific operation process are given. It should be pointed out that for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

[0021] Based on the problem that the prior art lacks consideration of the impact of maintenance personnel on resilience improvement, an embodiment of the present invention provides a distribution network fault maintenance optimization method based on a cyber-physical system (CPS), aiming to improve the resilience and efficiency of the power distribution network after encountering a fault.

[0022] Specifically, Figure 1 As shown, the distribution network fault maintenance optimization method based on the cyber-physical system provided in this embodiment may include the following operations: S100, constructing a network maintenance personnel scheduling model and an equipment maintenance personnel scheduling model, and using the two scheduling models to obtain a maintenance path for the corresponding maintenance personnel; S200, based on the maintenance path, a unified time model for parallel scheduling of multiple maintenance personnel is established, network maintenance personnel and equipment maintenance personnel are integrated into the same time axis, a time series is obtained according to the maintenance sequence, and a distribution network reconstruction model is established; S300, based on two scheduling models, a time unified model and a distribution network reconstruction model, a collaborative restoration model with associations among equipment maintenance personnel, network maintenance personnel and a distribution network system is established; S400, using a single commodity flow model to determine the connectivity of the network nodes of the collaborative recovery model, transforming the connectivity judgment constraint of the network nodes from a highly nonlinear problem to a linear sub-problem; S500, linearizing the constraints of the time unified model and the objective function of the collaborative recovery model to obtain a mixed integer linear programming model; S600, solving the mixed integer linear programming model to achieve the minimum time required to repair the remaining faulty components based on the cyber-physical system, thereby minimizing the distribution network fault maintenance time loss.

[0023] The technical solution provided by the above embodiment of the present invention is further described in detail below in conjunction with the preferred implementation manner.

[0024] Figure 2 This is a working architecture diagram of the distribution network fault maintenance optimization method provided by the above embodiment of the present invention. Figure 1 and Figure 2 As shown, the distribution network fault maintenance optimization method includes the following steps: S1, considering the mutual coupling between the network system and the physical system, establish a network maintenance personnel scheduling model and an equipment maintenance personnel scheduling model, and use the scheduling model to obtain the maintenance path of the maintenance personnel; S2, establish a unified time model for parallel scheduling of multiple maintenance personnel, integrate network maintenance personnel and equipment maintenance personnel belonging to the two subsystems of network system and physical system into the same timeline, obtain the time series according to the maintenance sequence, and establish a distribution network reconstruction model to match the distribution network recovery system and reduce the load loss of the distribution network after the disaster; S3, based on two scheduling models, the time unified model and the distribution network reconstruction model, a collaborative recovery model considering equipment maintenance personnel, network maintenance personnel and the distribution network system is established; through this step, after a disaster occurs, the network can be reconfigured to restore power supply as much as possible, and then equipment maintenance personnel and network maintenance personnel can be arranged to repair the faulty components; each repaired component may cause a change in the operating state of the network, and therefore each recovery behavior will trigger a network reconfiguration decision to minimize the load loss after the disaster; S4, the ability of a network node to operate normally depends on the connectivity of the node to the central control node; a single commodity flow model is used to determine the connectivity of network nodes, converting highly nonlinear constraints into linear sub-problems; S5, linearizes the constraints of the time unified model and the objective function of the collaborative recovery model, and then obtains a complete mixed integer linear programming model; S6, by solving the mixed integer linear programming model, the minimum time required to repair the remaining faulty components is obtained, thereby minimizing the distribution network fault maintenance time loss.

[0025] In some preferred implementations, the above S1 may further include the following operations: S11, the maintenance duration can be determined according to the number of faulty components of the physical system of the distribution network caused by natural disasters, and each fault repair corresponds to the fault repair completion time, which means that the number of faulty components is equal to the number of repairs; on this basis, the maintenance personnel scheduling is integrated with the maintenance time and travel time, and the scheduling model for the departure of equipment maintenance personnel and network maintenance personnel is obtained as: (1) (2) In the formula, Indicates the time to complete the repair of the faulty components in the virtual physical power system. g Indicates the end point of the physical system failure, h Indicates the end location of the faulty component of the network system. p Indicates equipment maintenance personnel, po Indicates the status of the equipment maintenance personnel before the failure. v po Indicates the site of the equipment maintenance personnel before the failure. Indicates equipment maintenance personnel, v co Indicates the site of the network maintenance personnel before the failure. Indicates network maintenance personnel. M p Represents a collection of equipment maintenance personnel. M c Represents a collection of network maintenance personnel. Indicates whether the equipment maintenance personnel have reached the power fault component and completed the repair of the fault point within the repairable time. Indicates whether the network maintenance personnel reached the network fault component and completed the repair of the fault point within the repairable time; Formula (1) and Formula (2) describe the departure path of maintenance personnel; after a natural disaster, maintenance personnel leave the maintenance center and arrive at one of the faulty components, and then repair the faulty components at the repair time. Complete the repair; maintenance personnel go from one faulty component to another in turn until all faulty components are repaired; during the entire repair process, for a specific maintenance personnel or , it leaves the depot only once, so during all failure times or The sum is equal to 1; or is a binary variable, so the right side of formula (1) or formula (2) can be made equal to 1, which ensures that for a specific maintenance personnel or , there is only one or =1; therefore, formula (1) and formula (2) guarantee that at all repair times , or Starting from the station only once avoids the situation of starting from the station multiple times to reach the faulty component, further ensuring the continuity of the path. In addition, when the number of faulty components is less than the number of maintenance personnel, or the maintenance personnel are too far away from the faulty components, the maintenance personnel are not assigned specific maintenance tasks. In this case, the maintenance personnel do not leave the depot to perform maintenance work; therefore, the left side of the equation is less than or equal to 1; (3) In the formula, f is the starting point of the physical system failure, g is the physical system failure endpoint, l The starting point of the network system failure. h The network system failure endpoint. T f is the set of repair completion times of the faulty components, Indicates the time it takes for equipment maintenance personnel to complete repairs of all physical system failures. Indicates the time it takes for network maintenance personnel to complete repairs of all network system faults; Because each fault repair event corresponds to a fault repair time, for a certain repair time , only one faulty component is repaired by its corresponding maintenance personnel, as shown in formula (3). In addition, if there are specific times when multiple maintenance personnel complete the maintenance tasks at the same time, they are regarded as different fault repair times with a time interval of 0; therefore, under this premise, the fault repair time corresponds to only one maintenance worker completing the repair work; in other words, if more than two maintenance workers complete the repair work at the same time, they are considered and ,in ; For failed parts in the communication network or physical network, there is only one maintainer to handle them, unlike other failed parts, as shown below: (4) (5) In the formula, represents the set of failure points in the physical system, Represents the set of failure points in a network system; S12, if the faulty component is repaired, the scheduling model in which the equipment maintenance personnel and the network maintenance personnel are participating in the maintenance is as follows: (6) (7) Equations (6) and (7) give the mathematical expressions that at most one maintenance team can leave when a faulty component is repaired; In addition, if the faulty component is a maintenance or If the last component in the restoration process requires repair, the maintenance personnel or Return to the maintenance center, and the left side of the above formula is equal to 0; For the first fault repair completion time, a maintenance person must be or To reach a faulty component and perform repair work, there are: (8) In addition, if the maintenance personnel or During troubleshooting time If the faulty part is successfully repaired, the maintenance personnel or The subsequent maintenance activities must start from the faulty component; in other words, because different maintenance personnel are dispatched at the same time, the following description is made to maintain the continuity of the path model of a single maintenance personnel: (9) (10) In the formula, M represents the fault repair coefficient that ensures the continuity of a single maintenance team's path, and has the same meaning, indicating the time when the fault repair is completed. express The time when the previous fault repair was completed; Formulas (9) and (10) maintain the continuity of the path model for a specific maintenance worker; for example, in formula (9), if is equal to 1, then from f Started maintenance staff Will reach the end of the failure g and in time to complete the repair task; in this case, there must be a fault repair time At this time, the maintenance personnel from other fault endpoints g 'arrive f , and in Otherwise, if If the maintenance task is not completed by the maintenance personnel, The sum is equal to 0, and since M Item, the constraint does not exist; in addition, it is the same as the scheduling formula (10) representing the network maintenance personnel in the communication network.

[0026] In some preferred implementations, the above S2 may further include the following operations: A time unified model is established to integrate the equipment maintenance personnel and network maintenance personnel of the two subsystems of the physical system and the network system into the same timeline according to the maintenance order to obtain a time series, thereby matching the distribution network recovery system and minimizing the load loss of the distribution network after the disaster. The time unified model is expressed as: (11) (12) In the formula, Indicates that the equipment maintenance personnel have left the fault starting point f and reaches the fault end point g The shortest time, Indicates that the network maintenance personnel have left the fault origin. l and reaches the fault end point h The shortest time, Indicates the repair time of a faulty component in the physical network, represents the repair time of a faulty component in a communication network, Indicates that the equipment maintenance personnel start from the fault f Travel to the fault end g and the time required to complete the repair task and trigger the network reconfiguration, Indicates that network maintenance personnel start from the fault point l Travel to the fault end h The time required to complete the repair task and trigger network reconfiguration; the shortest time or It can be obtained by Floyd's algorithm; The relationship between the equipment maintenance personnel and the network maintenance personnel of the two subsystems of the physical system and the network system is shown in equations (11) and (12): (13) (14) Equations (13) and (14) describe the maintenance personnel or The time interval between two adjacent maintenance activities is As shown in; set up and Respectively indicates maintenance personnel or The time interval between two adjacent maintenance activities; if the faulty component is a maintenance personnel or exist or The first maintenance is equal to the maintenance personnel or The time it takes to travel from the depot to the faulty component and complete the repair task; for other maintenance personnel and During troubleshooting time The inner value is equal to 0.

[0027] (15) (16) Binary variables and It is the maintenance personnel status; if the maintenance personnel If the maintenance activity is completed in the process, then the binary variable will be equal to 1, otherwise it will be 0; (17) (18) (19) In the formula, and For maintenance personnel and Actual repair time; Actual time and for different maintenance personnel; The time interval for each maintenance personnel can be obtained through equations (13) and (14); k The actual time of maintenance events is equal to the previous k The sum of the time intervals is shown in equations (17) and (18); for other maintenance personnel who have not completely repaired the faulty component, the state or To be used by maintenance personnel or Actual repair time or Set to 0, for example As shown in formula (19), the unified time can be obtained by adding the actual times corresponding to different maintenance personnel

[0028] (20) In the formula, Represents the time interval between each network reconfiguration; Equation (20) represents the time interval between each network reconfiguration; in addition, the following constraints are added to ensure that different maintainers are sorted in chronological order when unifying the timeline: (twenty one) S22. In the process of post-disaster recovery of distribution networks, network reconstruction is the key to the classification and rapid recovery of critical load faults. A distribution network reconstruction model that takes into account the coupling characteristics of the physical network and the communication network and the repair is established, including: Let binary variable Instructions in k Power failure endpoint after reconfiguration g Is it connected, and Indicates the end point of power failure g Whether it was repaired by maintenance personnel; binary variable Indicated in k Network nodes after repair activity i If the network node is working properly, then is equal to 1; otherwise, = 0. Based on these definitions, the coupling effect between the physical network and the communication network can be expressed by the following formula: (twenty two) (twenty three) (twenty four) (25) (26) Formula (22) and Formula (23) are used to obtain the fault component in the communication network or physical network at the time of fault repair. working state; Formula (24) shows that when a fault repair event triggers a network reconfiguration decision, the current fault state affects whether the line can be repaired within the repair time. After closing, it has an impact; if the faulty component is defective and has not been repaired, it cannot be closed; in addition, with the improvement of the level of grid automation, most power lines are equipped with remote control switches; Equation (25) indicates that if the corresponding network nodes on both sides of the line cannot be operated, the remote control switch of the line will not be able to receive the control signal and will stop operating; in addition, when the system is subject to considerable interference, the generator will be forced to shut down for protection and other reasons, as shown in Equation (26).

[0029] In order to ensure that the distribution network still has a radial topology after reconstruction, a directed multi-commodity flow model is used to model its topology; let Indicates the time to repair the fault Time fault end pointg Products on i' , and let the binary variable Indicates fault endpoint g Is it included in the spanning tree, and let the binary variable is a virtual switch. If the fault endpoint g exist If it is closed when , the virtual switch is equal to 1; Based on these definitions, the radial topology constraint can be expressed as follows: (27) (28) (29) (30) (31) (32) (33) Formula (27) makes 1 unit of commodity i' From the substation node Outflow, formula (28) requires 1 unit of commodity i' Inflow Node i' , Formula (29) prohibits each commodity i' Flowing into other nodes, Equation (30) is a constraint, which means that only when the arc is included by the variable Each commodity can flow on the arc when it is in the defined directed spanning tree. Formula (31) specifies the number of arcs in the spanning tree. Formula (32) obtains the virtual connection state of the branch according to the arcs contained in the spanning tree. ; According to these definitions, Equations (27) to (32) can obtain the set of all associated vectors of the spanning tree topology that the network can form by reconstruction, and Equation (33) restricts the physical network closure to Determine the subset of closed branches in the spanning tree.

[0030] In some preferred implementations, the above S3 may further include the following operations: S31, during the restoration of the distribution network system, the transportation network uses many path selection methods, which may lead to a large difference in the travel time between two faulty components, thereby impairing load restoration; therefore, it is crucial to select the shortest path between the faulty components from the numerous path selections in the transportation network so that maintenance personnel can reach the faulty components in the physical network or communication network and complete the maintenance task as quickly as possible: First, initialize the distance matrix d according to the information of the traffic network. d (i , j )yes i and j The distance between i and j If there is a road available between d ( i , j ) is equal to the distance value of the road; if i = j ,but d ( i , j ) = 0, and if in i and j If there is no available road between d ( i , j ) = ∞; then, the vertex k as a midpoint; if d ( i , k )+ d ( k , j )< d ( i , j ),but d ( i , j )= d ( i , k )+ d ( k , j );otherwise, d ( i , j ) remains unchanged; The basic principle of Floyd's algorithm is to find the shortest path through matrix iteration; the shortest path between two components is represented by each member in the final matrix generated by iteration; Floyd's algorithm is used to determine the shortest path between any two components, so that maintenance personnel can reach the faulty component as quickly as possible and perform maintenance activities to minimize load loss; S32, based on the above model, a collaborative recovery model considering equipment maintenance personnel, network maintenance personnel and distribution network system is proposed; after the disaster occurs, the network is reconfigured to restore power supply as much as possible, and then equipment maintenance personnel and network maintenance personnel are arranged to repair the faulty components; each repaired component may cause a change in the operating state of the network, and therefore each repair activity will trigger a network reconfiguration decision to minimize the load loss after the disaster; after all loads are restored, equipment maintenance personnel should be rescheduled for repair, with the aim of eliminating the time required to repair the remaining faulty components until all faulty components are working normally; Based on the traffic network model, a collaborative restoration model considering equipment maintenance personnel, network maintenance personnel and distribution network system is constructed, including: set up For Node i The load at For Node i The priorities and weights of the loads at the locations are used to design the objective function of the collaborative recovery model to minimize the load reduction during a failure, as shown below: (34) In the formula, Indicates k Network nodes after repair i Working status; Subject to the following restrictions: The constraints for maintenance personnel scheduling are: Equation (1) to (10); The constraints of the time unified model are: Equation (11) to Equation (21); The constraints of the coupling characteristics of the physical network and the communication network are: Equation (22)~Equation (27) The constraints for reconfiguration of the distribution network are: Equation (28) to Equation (45); When the load is fully restored, the objective function is changed to minimize the time cost of repairing the remaining failed components: (35) Subject to the following restrictions: Maintenance personnel scheduling constraints: Equation (1) to (10); Constraints of the time unified model: Equation (11) to Equation (21).

[0031] In some preferred implementations, the above S4 may further include the following operations: S41, in order to correctly solve the proposed collaborative optimization model of equipment maintenance personnel, network maintenance personnel and distribution network restoration, the following problems need to be solved: 1) The connectivity judgment constraints on network nodes are highly nonlinear; 2) The constraints of the time unified model must be linearized; 3) Since the established collaborative restoration model is a mixed integer quadratic programming problem, it needs to be converted into a mixed integer linear programming problem: The ability of a virtual node to operate normally depends on the connectivity of the node to the central control node. Equation (27) uses an intuitive and simple traversal method to determine the connectivity of the network subnodes. However, since this constraint is highly nonlinear, it is difficult to solve directly on a computer. As a result of the reconstruction in the physical network, a modified single commodity flow model is proposed, which regards the central control node and the subnode in the communication network as a power node and a load in the physical network, respectively. Connectivity can be considered as whether the central control node restores the subnode. In the modified single commodity flow model, let Represents a network node i The load of is equal to 1 for the child nodes in the communication network; represents the output of the central control node, and let Indicates the time to repair the fault Passing the fault starting point l ; let the binary variable Indicates the time to repair the fault The starting point of the failure after reconfiguration l The actual working status; Indicates the time to repair the fault Time failure start l Commodity flow in; Based on these definitions, the connectivity judgment model can be expressed by the formula as follows: (36) Subject to the following restrictions: (37) (38) (39) (40) (41) Similar to the distribution network restoration model, the objective function minimizes the load loss, and the constraints are shown in Eqs. (36) to (41); Eq. (36) means that all nodes satisfy flow balance, and Eqs. (37) to (41) are topological constraints; S42, using the modified commodity flow model (i.e., the connectivity judgment model of the network nodes), determine the linear sub-problem of the connectivity judgment model of the network nodes: Through the communication network reconstruction based on the modified single commodity flow model, if the child node restores power supply, the load recovery factor is equal to 1, which means that the node i Connect to the central control node v , and the node i Normal operation. Otherwise, If it is equal to 0, it means the node cannot work; (42) (43) In addition, the subproblem is in the same direction as the main problem, so an appropriately small data Converter, which converts the model into the following form: (44) In some preferred implementations, the above S5 may further include the following operations: S51, in order to correctly solve the proposed collaborative optimization model of equipment maintenance personnel, network maintenance personnel and distribution network restoration, the time model is linearized: First, the constraints (17) and (18) in the time unified model are linearized as follows; for (17), the auxiliary binary variable is introduced , and let ; Formula (17) can be transformed into Formula (45): (45) and The following constraints should be met: (46) make: (47) (48) S52, in order to correctly solve the proposed collaborative optimization model of equipment maintenance personnel, network maintenance personnel and distribution network restoration, the mixed integer quadratic programming problem of the collaborative restoration model is converted into a mixed integer linear programming problem: there are continuous variables in the objective function of the collaborative restoration model. and binary variables , so we introduce auxiliary variables Linearize the objective function and transform the mixed integer quadratic programming problem into a mixed integer linear programming problem: (49) in, The following additional constraints are met: (50) In this section, the highly nonlinear connectivity judgment constraint is first transformed into a linear subproblem using the modified single commodity flow model. Then, using auxiliary variables, equations (17) and (18) are transformed into equations (46) and (48); finally, the nonlinear objective function of the collaborative recovery model is transformed into equation (49) and constraint (50) is added. Then, a complete mixed integer linear programming model is obtained, which is suitable for computer solution.

[0032] Based on the same inventive concept, an embodiment of the present invention provides a distribution network fault maintenance optimization system based on an information-physical system.

[0033] Specifically, Figure 3 As shown, the network distribution fault maintenance optimization system based on the cyber-physical system provided in this embodiment may include the following modules: A scheduling model building module is used to build a network maintenance personnel scheduling model and an equipment maintenance personnel scheduling model. The two scheduling models are used to obtain the maintenance path of the corresponding maintenance personnel. A time unified model building module, which builds a time unified model for parallel scheduling of multiple maintenance personnel based on the maintenance path, integrates network maintenance personnel and equipment maintenance personnel on the same timeline, obtains the time series according to the maintenance sequence, and builds a distribution network reconstruction model; A collaborative restoration model building module, which builds a collaborative restoration model with the relationship between equipment maintenance personnel, network maintenance personnel and distribution network system based on two scheduling models, a time unified model and a distribution network reconstruction model; Linear programming module, which uses a single commodity flow model to determine the connectivity of the network nodes of the collaborative recovery model, and transforms the connectivity judgment constraints of the network nodes from highly nonlinear to linear sub-problems; linearizes the constraints of the time unified model and the objective function of the collaborative recovery model to obtain a mixed integer linear programming model; The maintenance optimization module solves the mixed integer linear programming model to obtain the minimum time required to repair the remaining faulty parts.

[0034] It should be noted that the steps in the method provided by the present invention can be implemented by using the corresponding components in the system, and those skilled in the art can refer to the technical solution of the system to implement the step flow of the method, and can also refer to the technical solution of the method to implement the composition of the system, that is, the embodiments in the system and the embodiments in the method can be understood as preferred examples of each other, which will not be elaborated here.

[0035] An embodiment of the present invention further provides a computer terminal, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the processor can be used to execute any method of the above-mentioned embodiments of the present invention, or to run any system of the above-mentioned embodiments of the present invention.

[0036] Optionally, the memory is used to store programs; the memory may include volatile memory (English: volatile memory), such as random-access memory (English: random-access memory, abbreviated: RAM), such as static random-access memory (English: static random-access memory, abbreviated: SRAM), double data rate synchronous dynamic random access memory (English: Double Data Rate Synchronous Dynamic Random Access Memory, abbreviated: DDR SDRAM), etc.; the memory may also include non-volatile memory (English: non-volatile memory), such as flash memory (English: flash memory). The memory is used to store computer programs (such as applications, functional modules, etc. that implement the above method), computer instructions, etc., and the above computer programs, computer instructions, etc. can be partitioned and stored in one or more memories. And the above computer programs, computer instructions, data, etc. can be called by the processor.

[0037] The above-mentioned computer programs, computer instructions, etc. may be stored in one or more memories in partitions, and the above-mentioned computer programs, computer instructions, data, etc. may be called by a processor.

[0038] The processor is used to execute the computer program stored in the memory to implement the various steps of the method or various modules of the system involved in the above embodiments. For details, please refer to the relevant descriptions in the above method and system embodiments.

[0039] The processor and the memory may be independent structures or integrated structures. When the processor and the memory are independent structures, the memory and the processor may be coupled and connected via a bus.

[0040] An embodiment of the present invention further provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, it can be used to execute any method of the above embodiments of the present invention, or to run any system of the above embodiments of the present invention.

[0041] Among them, computer-readable media include computer storage media and communication media, wherein the communication media include any media that facilitates the transmission of computer programs from one place to another. The storage medium can be any available medium that can be accessed by a general or special-purpose computer. An exemplary storage medium is coupled to the processor so that the processor can read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be an integral part of the processor. The processor and the storage medium can be located in an ASIC. In addition, the ASIC can be located in a user device. Of course, the processor and the storage medium can also be present in a communication device as discrete components.

[0042] The distribution network fault maintenance optimization method and system based on the cyber-physical system provided in the above embodiment of the present invention aims to improve the recovery capability and efficiency of the power distribution network after encountering a fault. The method and system mainly include the following key parts: (1) First, based on the mixed integer linear programming (MILP) model, the transportation network (TN), communication network (CN) and physical network (PN) are integrated. The purpose of this integration process is to achieve effective load recovery and ensure that the power system can quickly recover to normal operation after a fault occurs. Through the optimization calculation of the MILP model, the best recovery path and solution can be found, thereby reducing the recovery time and reducing the inconvenience and loss of users. (2) In addition, in order to promote efficient collaboration between different maintenance personnel, a repair event triggering mechanism is also proposed. In the time unified model, the equipment maintenance personnel and the network maintenance personnel are integrated into the same time axis according to the repair order to obtain a time series, thereby matching the distribution network recovery model and minimizing the load loss of the distribution network after the disaster. This mechanism can monitor the fault situation in real time and automatically trigger the corresponding maintenance response when necessary, solving the problem of difficult coupling of the distribution network recovery model. The coordination and communication between the physical maintenance crew (PMC), the communication maintenance crew (CMC) and the distribution network restoration model (DNRM) are optimized to ensure that all parties can respond quickly to fault events and take effective recovery measures. (3) The rearrangement of equipment maintenance personnel and network maintenance personnel is crucial. This link focuses on repairing the remaining damaged parts with the lowest time cost after all power sources are restored. By rationally allocating human resources and equipment, it is ensured that post-fault recovery work is carried out quickly and efficiently, thereby minimizing system downtime. The present invention not only improves the fault recovery capability of the distribution network, but also provides strong support for the realization of the intelligence and automation of the power system. It has broad application prospects and can significantly enhance the resilience and reliability of the power distribution system in actual operation.

[0043] All matters not covered in the above embodiments of the present invention are well known in the art.

[0044] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art may make various modifications or variations within the scope of the claims, which do not affect the essence of the present invention.

Claims

1. A distribution network fault maintenance optimization method based on cyber-physical system, characterized in that: include: Construct a network maintenance personnel scheduling model and an equipment maintenance personnel scheduling model, and use the two scheduling models to obtain the maintenance path of the corresponding maintenance personnel; Based on the maintenance path, a unified time model for parallel scheduling of multiple maintenance personnel is established, network maintenance personnel and equipment maintenance personnel are integrated into the same timeline, a time series is obtained according to the maintenance sequence, and a distribution network reconstruction model is established; Based on two dispatch models, a time unified model and a distribution network reconstruction model, a collaborative restoration model with the association relationship between equipment maintenance personnel, network maintenance personnel and distribution network system is established; A single commodity flow model is used to determine the connectivity of the network nodes of the collaborative recovery model, and the connectivity judgment constraint of the network nodes is transformed from a highly nonlinear problem to a linear sub-problem; The constraints of the time unified model and the objective function of the collaborative recovery model are linearized to obtain a mixed integer linear programming model; The mixed integer linear programming model is solved to obtain the minimum time required to repair the remaining faulty components, thereby minimizing the distribution network fault maintenance time loss.

2. The distribution network fault maintenance optimization method based on cyber-physical system according to claim 1 is characterized in that: The method of constructing a network maintenance personnel scheduling model and an equipment maintenance personnel scheduling model, and using the scheduling model to obtain a maintenance path for the maintenance personnel, includes: Integrating maintenance personnel scheduling with maintenance time and travel time, the scheduling model for equipment maintenance personnel and network maintenance personnel is obtained as follows: （1） （2） In the formula, Indicates the time to complete the repair of the faulty components in the virtual physical power system. g Indicates the end point of the physical system failure, h Indicates the end location of the faulty component of the network system. p Indicates equipment maintenance personnel, po Indicates the status of the equipment maintenance personnel before the failure. v po Indicates the site of the equipment maintenance personnel before the failure. Indicates equipment maintenance personnel, v co Indicates the site of the network maintenance personnel before the failure. Indicates network maintenance personnel. M p Represents a collection of equipment maintenance personnel. M c Represents a collection of network maintenance personnel, Indicates whether the equipment maintenance personnel have reached the power fault component and completed the repair of the fault point within the repairable time. Indicates whether the network maintenance personnel reached the network fault component and completed the repair of the fault point within the repairable time; Equations (1) and (2) describe the departure paths of equipment maintenance personnel and network maintenance personnel, respectively; For a certain fault repair time When only one faulty component is repaired by its corresponding maintenance personnel, then: （3） In the formula, f is the starting point of the physical system failure, g is the physical system failure endpoint, l The starting point of the network system failure. h The network system failure endpoint. T f is the set of repair completion times of the faulty components, Indicates the time it takes for equipment maintenance personnel to complete repairs of all physical system failures. Indicates the time it takes for network maintenance personnel to complete repairs of all network system faults; When multiple maintenance personnel complete maintenance work at the same time, the corresponding fault repair time is recorded as and ,in ; When only one maintenance personnel handles the corresponding faulty component, there are: （4） （5） In the formula, represents the set of failure points in the physical system, Represents the set of failure points in a network system; When a faulty component is repaired, the scheduling model in which equipment maintenance personnel and network maintenance personnel are involved in the repair is as follows: （6） （7） Equations (6) and (7) give the mathematical expressions that at most one maintenance team can leave when a faulty component is repaired; If the current faulty component is a maintenance or If the last component in the restoration process requires repair, the maintenance personnel or Return to the maintenance center, at this time the left side of equation (6) or equation (7) is equal to 0; For the first fault repair completion time, a maintenance person must be or To reach a faulty component and perform repair work, there are: （8） When maintenance personnel or During troubleshooting time If the faulty part is successfully repaired, the maintenance personnel or Subsequent maintenance activities must start from the faulty component, so the path model of a single maintenance personnel is established as follows: （9） （10） In the formula, M represents the fault repair coefficient that ensures the continuity of a single maintenance team's path, Indicates the time when the fault repair is completed. Completed before; Equations (9) and (10) are used to describe the continuity of the path model of a specific maintenance worker.

3. The distribution network fault maintenance optimization method based on cyber-physical system according to claim 1 is characterized in that: Based on the maintenance path, a unified time model for parallel scheduling of multiple maintenance personnel is established, network maintenance personnel and equipment maintenance personnel are integrated into the same time axis, a time series is obtained according to the maintenance sequence, and a distribution network reconstruction model is established, including: A time unified model is established, and the time unified model is expressed as: （11） （12） In the formula, Indicates that the equipment maintenance personnel have left the fault starting point f and reaches the fault end point g The shortest time, Indicates that the network maintenance personnel have left the fault origin. l and reaches the fault end point h The shortest time, Indicates the repair time of a faulty component in the physical network, represents the repair time of a faulty component in a communication network, Indicates that the equipment maintenance personnel start from the fault f Travel to the fault end g and the time required to complete the repair task and trigger the network reconfiguration, Indicates that network maintenance personnel start from the fault point l Travel to the fault end h The time required to complete the repair task and trigger network reconfiguration; the shortest time or It can be obtained by Floyd's algorithm; Maintaining personnel or The time interval between two adjacent maintenance activities is represented on the time axis, and the time interval for each maintenance personnel is obtained as: （13） （14） In the formula, Indicates maintenance personnel The time interval between two adjacent maintenance activities, Indicates maintenance personnel The time interval between two adjacent maintenance activities; When the faulty component is a maintenance or exist or The first maintenance is equal to the maintenance personnel or The time it takes to travel from the depot to the faulty component and complete the repair task; for other maintenance personnel, or During troubleshooting time The inner value is equal to 0; （15） （16） In the formula, and is a binary variable, indicating the maintenance personnel and exist status; if the maintenance personnel If the maintenance activity is completed, the binary variable is equal to 1, otherwise it is 0; No. k The actual time of maintenance events is equal to the previous k The sum of time intervals is: （17） （18） In the formula, and For maintenance personnel and Actual repair time; For other maintenance personnel who did not completely repair the faulty part, the status or To be used by maintenance personnel or Actual repair time or Set to 0 to get a unified time by adding the actual times corresponding to different maintainers. for: （19） （20） In the formula, Actual time and for different maintenance personnel; Represents the time interval between each network reconfiguration; Formula (20) represents the time interval between each network reconfiguration, and adds the following constraints to ensure that different maintenance personnel are sorted in chronological order when the time axis is unified: （21） Establish a distribution network reconstruction model that considers the coupling characteristics of the physical network and the communication network as well as maintenance, including: Let binary variable Indicated in k Power failure endpoint after reconfiguration g Is it connected, and Indicates the end point of power failure g or h Whether it is maintained by the maintenance personnel or Maintenance; binary variable Respectively expressed in k Network nodes after repair activity i and network nodes j If the network node is working properly, then is equal to 1, otherwise, =0; based on this, the coupling effect of the physical network and the communication network is established, expressed as: （22） （23） （24） （25） （26） In the formula, Represents the system generator network node i exist k The power after repair, Represents the system generator network node i Maximum power; in: Formula (22) and Formula (23) are used to obtain the fault component in the communication network or physical network at the time of fault repair. Working status; Formula (24) is used to describe the effect of the current fault status on whether the line can be repaired within the repair time when the fault repair event triggers the network reconfiguration decision. Closure then has an effect; if the faulty component is defective and has not been repaired, the line cannot be closed; Formula (25) is used to describe that if the corresponding network nodes on both sides of the line cannot be operated, the remote control switch of the line will not be able to receive the control signal and will stop operating; Equation (26) is used to describe that when the system is disturbed by the set conditions, the generator will be forced to shut down for protection and other reasons; make Indicates the time to repair the fault Time fault end point g Products on i' , and let the binary variable Indicates fault endpoint g Is it included in the spanning tree, and let the binary variable It is a virtual switch, the fault endpoint g exist If it is closed when , the virtual switch is equal to 1; based on this, the radial topology constraint of the distribution network reconstruction model is constructed as follows: （27） （28） （29） （30） （31） （32） （33） In the formula, represents the collection of power nodes in the physical network, Indicates the node current of the substation to which the system is connected; Formula (27) makes 1 unit of commodity i' From the substation node outflow; Formula (28) requires that 1 unit of commodity i' Inflow Node i' ; Formula (29) prohibits each commodity i' Flow into other nodes; Equation (30) is used as a constraint to define the arc only when it is included by the variable Each commodity can flow on the arc only when it is in the defined directed spanning tree; Equation (31) specifies the number of arcs in the spanning tree; Formula (32) obtains the virtual connection state of the branch according to the arcs contained in the spanning tree ; Through equations (27) to (32), we obtain the set of all associated vectors of the spanning tree topology formed by the reconstruction of the physical network, and through equation (33), we restrict the closure of the physical network to Determine the subset of closed branches in the spanning tree.

4. The distribution network fault maintenance optimization method based on cyber-physical system according to claim 1 is characterized in that: The collaborative restoration model with the association relationship between equipment maintenance personnel, network maintenance personnel and distribution network system is established based on two scheduling models, a time unified model and a distribution network reconstruction model, including: The distance matrix d is initialized according to the information of the traffic network during the distribution network restoration process, and the Floyd algorithm is used to solve the shortest path between two members through matrix iteration to build a traffic network model; where: d ( i , j )yes i and j The distance between i and j If there is a road available between d ( i , j ) is equal to the distance value of the road; if i = j ,but d ( i , j ) = 0, and if in i and j If there is no available road between d ( i , j ) = ∞; then, the vertex k as a midpoint; if d ( i , k )+ d ( k , j )< d ( i , j ),but d ( i , j )= d ( i , k )+ d ( k , j );otherwise, d ( i , j ) remains unchanged; Based on the traffic network model, a collaborative restoration model considering equipment maintenance personnel, network maintenance personnel and distribution network system is constructed, including: set up For Node i The load at For Node i The priority and weight of the load at the location are considered, and the objective function of the collaborative recovery model is to minimize the load reduction during a failure. Then: （34） In the formula, Indicates k Network nodes after repair i Working status; The constraints for establishing the objective function are: The constraints for maintenance personnel scheduling are: Equation (1) to (10); The constraints of the time unified model are: Equation (11) to Equation (21); The constraints of the coupling characteristics of the physical network and the communication network are: Equation (22) to Equation (27); The constraints of the distribution network reconstruction model are: Equation (28) to Equation (33); When the load is fully restored, the objective function is changed to minimize the time cost in repairing the remaining faulty components: （35） The constraints of the changed objective function are: Constraints for maintenance personnel scheduling: Equation (1) to (10); Constraints of the time unified model: Equation (11) to Equation (21).

5. The distribution network fault maintenance optimization method based on cyber-physical system according to claim 1 is characterized in that: The method of using a single commodity flow model to determine the connectivity of the network nodes of the collaborative recovery model and transforming the connectivity judgment constraint of the network nodes from a highly nonlinear problem to a linear sub-problem includes: A single commodity flow model is provided, wherein the central control node and the sub-node in the communication network are respectively regarded as a power node and a load in the physical network, and the connectivity of the network node is whether the central control node restores the sub-node; In the single commodity flow model, let Represents a network node i The load of is equal to 1 for the child nodes in the communication network; represents the output of the central control node, and let Indicates the time to repair the fault Passing the fault starting point l ; let the binary variable Indicates the time to repair the fault The starting point of the failure after reconfiguration l The actual working status of Indicates the time to repair the fault Time fault start l The commodity flow in the network; based on this, the connectivity judgment model of the network nodes is constructed as follows: （36） The constraints for establishing the connectivity judgment model of the network nodes include: （37） （38） （39） （40） （41） The objective function of the connectivity judgment model of the network node is to minimize the load loss, and the constraints are shown in equations (36) to (41); wherein equation (36) is used to constrain all nodes to satisfy flow balance, and equations (37) to (41) are topological constraints; If the child node recovers power, the load recovery factor Equal to 1, indicating a node i Connect to the central control node v , and the node i Works normally; otherwise, If it is equal to 0, it means the node cannot work; （42） （43） Add an appropriate data The converter converts the connectivity judgment model of the network nodes into the following form: （44）。 6. The distribution network fault maintenance optimization method based on cyber-physical system according to claim 1 is characterized in that: The constraints of the time unified model and the objective function of the collaborative recovery model are linearized to obtain a mixed integer linear programming model, including: Linearize the constraints (17) and (18) in the time unified model; for (17), introduce the auxiliary binary variable , and let , transform equation (17) into: （45） and The following constraints are met: （46） make: （47） （48） There are continuous variables in the objective function (34) and binary variables , so we introduce auxiliary variables to linearize the objective function and transform the mixed integer quadratic programming problem into a mixed integer linear programming problem: （49） in, The following additional constraints are met: （50） Get a complete mixed integer linear programming model; By solving the mixed integer linear programming model, the minimum time required to repair the remaining faulty components is obtained.

7. A distribution network fault maintenance optimization system based on cyber-physical system, characterized in that: include: A scheduling model building module, which is used to build a network maintenance personnel scheduling model and an equipment maintenance personnel scheduling model, and obtain the maintenance path of the corresponding maintenance personnel using the two scheduling models; A time unified model building module, which builds a time unified model for parallel scheduling of multiple maintenance personnel based on the maintenance path, integrates network maintenance personnel and equipment maintenance personnel on the same time axis, obtains a time series according to the maintenance sequence, and builds a distribution network reconstruction model; A collaborative restoration model building module, which builds a collaborative restoration model with the relationship between equipment maintenance personnel, network maintenance personnel and distribution network system based on two scheduling models, a time unified model and a distribution network reconstruction model; A linear programming module, which uses a single commodity flow model to determine the connectivity of the network nodes of the collaborative recovery model, converts the connectivity judgment constraints of the network nodes from highly nonlinear to linear sub-problems; linearizes the constraints of the time unified model and the objective function of the collaborative recovery model to obtain a mixed integer linear programming model; A maintenance optimization module is used to obtain the minimum time required to repair the remaining faulty components by solving the mixed integer linear programming model.

8. A computer terminal comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, it can be used to perform the method described in any one of claims 1 to 6, or to run the system described in claim 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, it can be used to perform the method described in any one of claims 1 to 6, or to run the system described in claim 7.

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