Method and system for generating information-physical collaborative recovery plan for distribution network after disaster considering satellite communication support

Abstract

The present invention discloses a method and system for generating a post-disaster information-physical collaborative recovery plan for a distribution network considering satellite communication support, which relates to the field of distribution networks. The post-disaster information-physical collaborative recovery process of a distribution network supported by satellite communication is modeled as a MILP problem, and the initial data of the information-physical system recovery of the distribution network is used as input. The repair sequence of each node in the power-information network, the information flow distribution path, the load and unit operation plan, the satellite communication terminal deployment and the disaster scheduling plan are output, so as to realize the efficient generation of the information-physical collaborative recovery plan. Compared with the prior art, the present invention comprehensively takes into account the complex coupling relationship between the information-physical systems of the distribution network, and considers the supporting role of satellite communication in collaborative recovery under the background of technological development in the new era, which is conducive to guiding the efficient recovery of the distribution network after a disaster and improving the resilience of the distribution network.

Description

Technical Field

[0001] The present invention relates to the field of post-disaster recovery plan generation for power systems, and in particular to a method and system for generating a post-disaster information-physical collaborative recovery plan for a distribution network taking into account satellite communication support. Background Art

[0002] In recent years, extreme natural disasters such as floods, typhoons, and ice disasters caused by global climate change have occurred frequently, exacerbating the risk of post-disaster power outages in distribution networks. In the context of the development of informatization, the information-physical coupling of power systems has become increasingly close. While deepening the perception depth of distribution network operation, it has also increased the hidden dangers of post-disaster information-physical chain failures. The physical strength of the existing traditional distribution network communication system is not high and is easily damaged by natural disasters. In extreme events, a failure in the communication network may reduce the control and perception capabilities of the control master station over primary equipment, causing chain failures and expanding the scope of power outages. At the same time, satellite Internet technology has the technical advantages of wide coverage, low latency, and high bandwidth, and is not affected by extreme meteorological conditions. It can respond quickly to assist in the post-disaster reconstruction of the information network when extreme natural disasters cause damage to power communication terminals or communication equipment, and accelerate the information-physical collaborative recovery process of the distribution network. At present, the relevant recovery plan generation strategies are mostly based on the complete observability of each node information, without considering its information-physical coupling relationship and the post-disaster recovery process of the information network, and without considering the collaborative support role of satellite Internet development in the repair of post-disaster information-physical systems. In summary, it is necessary to propose a method for generating a distribution network post-disaster information-physical collaborative recovery plan considering satellite communication support, so as to achieve efficient information-physical collaborative recovery of distribution networks after disasters under the background of new technologies. Summary of the invention

[0003] In view of the shortcomings of the existing information-physical collaborative recovery plan generation strategy, which does not fully consider the information-physical coupling relationship and does not take into account the support role of satellite communications, the present invention proposes a distribution network post-disaster information-physical collaborative recovery plan generation method and system that considers satellite communication support, so as to realize the site selection of satellite communication terminal deployment locations and the generation of post-disaster emergency recovery plans. By inputting the power grid and information network topology structure, line parameters and damage status of the distribution network to be restored, the method can obtain the global optimal strategy for post-disaster recovery of the information-physical system, satellite communication terminal deployment and disaster communication scheduling plan through optimization problem solving, guide and assist the efficient post-disaster recovery of the distribution network information-physical system, so as to solve the problems raised in the above-mentioned background technology.

[0004] To achieve the above object, the present invention provides the following technical solutions:

[0005] The present invention relates to a method for generating a post-disaster information-physical collaborative recovery plan for a distribution network considering satellite communication support. Firstly, with distribution network recovery, information network recovery, coupling relationship between distribution network and information network and satellite communication function as constraint conditions, and with optimal post-disaster load recovery and minimum total cost of satellite communication terminal deployment as optimization goals, the recovery plan generation problem is established as a mathematical optimization model to achieve accurate characterization of the internal coupling interaction relationship of the information-physical system and the satellite communication function; then, the information-physical collaborative recovery problem is converted into a mixed integer linear programming (MILP) optimization problem through a linearization method, the MILP problem inputs the initial data of the information-physical system recovery of the distribution network, and outputs the globally optimal information-physical collaborative recovery plan, so as to achieve efficient solution of the recovery plan.

[0006] The distribution network information-physical system recovery initial data includes: information-physical network topology and line parameters, coupling relationship between information-physical nodes, initial disconnection and damage status of lines after disasters, and alternative nodes for satellite communication terminal deployment.

[0007] The information-physical collaborative recovery plan generation content includes: the repair order of each node in the information network, the traffic distribution path; the dispatch order of the power grid repair team, the load and unit operation plan; the satellite communication terminal deployment and disaster dispatch plan.

[0008] The linearization methods include: Big M method, 0-1 variable introduction method, SOS-2 method, etc.

[0009] The optimization problem is a mathematical problem of determining the values ​​of certain optional variables under certain constraints so that the selected objective function reaches the optimal value.

[0010] The mixed integer linear programming (MILP) problem refers to an optimization problem in which the objective function and all constraints are linear and the decision variables only contain continuous variables and integer variables.

[0011] The present invention also relates to a system for implementing the above method, comprising: a recovery data initialization unit, a model building and recovery plan generation unit, and a collaborative recovery effect evaluation unit. Among them: the recovery data initialization unit processes the data to be recovered of the information-physical system of the distribution network, and inputs the information-physical collaborative recovery plan generation model to be required; the model building and recovery plan generation unit models and characterizes the information-physical collaborative recovery relationship of the distribution network supported by satellite communication and solves the MILP problem, and outputs the optimal post-disaster recovery strategy; the collaborative recovery effect evaluation unit evaluates the collaborative recovery benefit according to the load recovery amount and the satellite communication terminal deployment benefit, and makes a post-disaster recovery decision.

[0012] Compared with the prior art, the beneficial effect of the present invention is that the present invention models the post-disaster information-physical collaborative recovery process of the distribution network supported by satellite communications as a MILP problem, and uses the initial data of the information-physical system recovery of the distribution network as input to achieve efficient generation of information-physical collaborative recovery solutions. Compared with the prior art, the present invention comprehensively takes into account the complex coupling relationship between the information-physical system of the distribution network, and considers the supporting role of satellite communications in collaborative recovery under the background of technological development in the new era, which is conducive to guiding the efficient recovery of the distribution network after a disaster and improving the resilience of the distribution network. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a flow chart of the present invention;

[0014] Figure 2 It is the circuit diagram of the 9-node information network-IEEE 33-node distribution network coupling system;

[0015] Figure 3 Comparison chart of weighted load recovery during post-disaster recovery of distribution network with and without satellite communication access;

[0016] Figure 4 This is a schematic diagram of the post-disaster island division and line closure sequence of the power distribution network;

[0017] Figure 5 This is a schematic diagram of the post-disaster traffic distribution and line repair sequence of the distribution network information network. DETAILED DESCRIPTION

[0018] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0019] like Figure 1 As shown, this embodiment involves a method for generating a post-disaster information-physical collaborative recovery plan for a distribution network considering satellite communication support, including:

[0020] Step S1: Input the data of the information network-power network to be restored, including the information-physical network topology and line parameters, the coupling relationship between information-physical nodes, the initial disconnection and damage status of the line after the disaster, and the deployment of alternative nodes for satellite communication terminals, and initialize the corresponding constraints in the optimization problem of restoring the plan generation.

[0021] Step S2: Model the post-disaster information-physical coordinated recovery process of the distribution network supported by satellite communication as an optimization problem to fully consider the post-disaster information-physical coupling recovery relationship and the satellite communication effect. The modeling method specifically includes:

[0022] Step S21: Determine the objective function of the optimization problem with the goal of minimizing the post-disaster load loss and satellite communication terminal deployment cost. The objective function includes the sum of two parts of cost: load loss cost c loss and satellite communication terminal deployment cost c deploy , its specific expression is:

[0023] min c loss +c deploy (1)

[0024]

[0025] Where: τ is the time interval of model analysis, T is the total number of time periods; N P is the set of distribution network nodes, is the set of distribution network nodes where satellite communication terminals can be deployed; ε i is the load weight coefficient of distribution network node i; is the load recovery amount of distribution network node i at time t; ω is the load-money conversion coefficient of deploying satellite communication terminals, c S is the deployment cost of satellite communication terminals, is a 0-1 variable indicating whether node i is deployed with a satellite communication terminal, where 1 indicates that node i is deployed, and 0 indicates that it is not deployed.

[0026] Step S22: Based on the physical network repair logic in the cyber-physical coupling network, establish the distribution network restoration constraints of the optimization problem, including the distribution network restoration path constraints, the distribution network restoration time constraints, the distribution network restoration initial state constraints and the distribution network power flow constraints. The distribution network restoration path constraints refer to: describing the restoration process of the distribution network topology in the form of an energized agent (EA). P ×n P , the path table composed of 0-1 variables describes the repair path of the distribution network (n P is the total number of distribution network nodes), its elements The EA of the distribution network moves from node i to node j. The constraints of each element in the path table are as follows:

[0027]

[0028] Where: N P represents the node set in the distribution network, L P represents the set of lines in the distribution network, Represents a set of black start power supply nodes in the distribution network; is the node connection matrix in the distribution network, Indicates that there is a recoverable path between i and j. Formula (4) indicates that EA takes the black start power supply as the starting point; Formula (5) indicates that the black start power supply cannot be used as the target node for recovery to prevent the topology from forming a loop; Formula (6) constrains that the same line cannot be passed through in both the forward and reverse directions at the same time to prevent the formation of a loop; Formula (7) indicates that the same node can only be repaired once at most; Formula (8) constrains that a recovery path is used only if its starting node has been successfully recovered; Formula (9) indicates that EA can only move on a recoverable path.

[0029] The distribution network restoration time constraint means that on the basis of obtaining the distribution network restoration path by EA, the restoration time of each node in the distribution network is further described by the following constraint, and its expression is as follows:

[0030]

[0031] in: Indicates the time when power supply is restored at distribution network node i; is the switch action time matrix between nodes in the distribution network, whose elements represents the time required for the switch action between nodes i and j, represents the self-start time of the black start power supply at node i; It indicates the time when the power supply of the distribution network node i has been restored and the target node j of the restoration path has recovered information. It takes considerable time for the distribution network node i to restore the wired information network. represents the satellite communication access time of distribution network node i, M is a sufficiently large constant;

[0032] is a 0-1 variable matrix used to represent the recovery status of distribution network nodes in each period, and its elements Indicates that the distribution network node resumes power supply in time period t. Formula (10) indicates that after the black start power supply node is restored, the black start power supply starts automatically and supplies power to the node where it is located; Formulas (11), (12) and (13) indicate that if there is a recovery path between nodes i and j and i resumes power supply and j resumes observably, then after the switch action time, node j resumes power supply, otherwise formulas (11), (12) and (13) do not work; Formulas (14) and (15) indicate that if there is no power supply path to be restored passing through node j, then its power supply restoration time is the maximum power outage duration + 1, otherwise (14) and (15) do not work. Formula (16) indicates that the premise for node i to resume power supply is that there is a recovery path passing through the node; Formula (17) indicates that node i resumes power supply after the time point when its restoration is completed; Formula (18) constrains the node that has resumed power supply to no longer be powered off.

[0033] The distribution network recovery initial state constraint means: during post-disaster recovery, if some distribution network line switches and nodes are damaged and power supply cannot be restored, the initial state constraint expression constraining its recovery is as follows:

[0034]

[0035] in: and They represent the set of distribution network nodes that cannot be restored and the set of lines that cannot be closed respectively.

[0036] The power flow constraint of the distribution network refers to the constraint that the power flow relationship of the distribution network needs to satisfy. The present invention describes the power flow relationship within the distribution network based on the linearized Distflow model, and its specific expression is as follows:

[0037]

[0038] Where: Equations (21)-(23) are black start power constraints, where and represents the active and reactive output of the black start power supply at node i at time t; P i G,min and P i G,max Indicates the lower and upper limits of the active output of the black start power supply at node i; and represents the lower and upper limits of reactive power output of the black start power supply at node i; and The maximum power down / up rate is represented by equations (21) and (22) which constrain the active and reactive output of the black start power supply, and equation (23) constrains the ramp rate of the black start power supply. Equations (24)-(26) are load-related constraints, where and represents the active and reactive load recovery of distribution network node i at time t; P i L,max represents the maximum value of the load that can be restored at node i; η is the power factor of the load. Formula (24) constrains the upper and lower limits of the load recovery amount of each node; Formula (25) represents the active and reactive load recovery relationship under the condition of constant power factor; Formula (26) constrains the stability of load recovery and ensures that the load recovery amount of each node increases over time. Formulas (27)-(34) are line flow constraints, where is a 0-1 variable representing the recovery status of distribution network line k at time t, Indicates line recovery; Indicates the maximum active and reactive capacity of line k; is the connection relationship variable between line k and node i. If k = (i, j), that is, line k connects nodes i and j and the connection direction is from i to j, then Formula (27) constrains the voltage amplitude of the restored node; Formula (28) constrains the output voltage of the black start power supply to always maintain the standard value; Formula (29) indicates that if the two nodes connected to line k have been restored at time t and the line is on the EA path, the line will be restored at time t; Formulas (30) and (31) constrain the active and reactive capacity on the restored path; Formulas (32) and (33) are the power balance constraints of each node; Formula (34) is the node voltage amplitude relationship of the linearized Dist-Flow model.

[0039] Step S23: Based on the information network repair logic in the information-physical coupling network, establish information network recovery constraints for the optimization problem, including information network recovery path constraints, information network recovery time constraints, information network flow constraints, information network initial state constraints and information network energy supply constraints.

[0040] The information network restoration path constraint refers to: using the "information agent" path to describe the repair process of the distribution network, and its expression is:

[0041]

[0042]

[0043] Where: N C represents the set of information network nodes, L C Represents a collection of information network lines. Indicates the node where the central server in the information network is located; It is the node connection matrix in the information network.

[0044] The information network recovery time constraint means that the post-disaster emergency recovery relationship of the distribution network is described by the repair process of the repair team on the damaged information network lines connecting each switch, and its expression is:

[0045]

[0046] in: represents the time it takes for the repair team to complete the dth step of repair; T r (x) represents the repair time function, whose value is the repair time required to repair x information network nodes at the same time, which increases with the increase of the number of nodes repaired at the same time; freq(d) represents the total number of information network nodes with repair order d; d a represents the repair order of node a; F C (d a ) represents the repair order of the parent nodes of node a in the emergency repair topology; Indicates the recovery completion time of information network node a; I d,a is the judgment variable, in d a =d, its value is 1, otherwise it is 0. Formula (41) indicates that for the central server that does not need to be repaired (repair order is 1), its repair completion time is 1, and the completion time of each subsequent repair step is equal to the sum of the time required for each previous repair step; Formula (42) constrains the repair order of the central server to be 1; Formula (43) indicates that the repair order of the child node on the repair path must be greater than its parent node; Formulas (44) and (45) indicate that if the repair path is a→b, the parent node of node b is node a, otherwise Formulas (44) and (45) do not work; (46) indicates that due to the existence of energy supply constraints, the recovery time of information network node a is later than the completion time of the emergency repair work of its corresponding number of steps.

[0047] The information network flow constraint refers to the constraint composed of flow conditions that need to be satisfied in the recovery process due to the limitation of the flow that can be passed through each line in the information network. The specific expression is:

[0048]

[0049] in: A -1 variable matrix representing the recovery status of information network nodes in each period, whose elements It means that the information network node a repairs the wired path in time period t; It is a 0-1 variable matrix representing the situation of the distribution network nodes in the information network recovering observably in each period, and its element is 1, indicating that the corresponding node has recovered observably; It represents the time for the distribution network node i to restore the wired information network; It represents the information network node where the switch responsible for forwarding the observation data obtained by the sensor at the distribution network node i is located. represents the set of distribution network nodes connected to the switch at information network node a, f i C The data traffic generated by the sensor observing the power distribution node i; represents the data flow input by information network node a at time t, Indicates the output data flow; is a 0-1 variable representing the recovery status of distribution network line g at time t, Indicates line recovery; Indicates the maximum data flow through line g; is the connection relationship variable between line g and node a. If g = (a, b), that is, line g connects nodes a and b and the connection direction is from a to b, then Formula (54) indicates that the traffic forwarded by switch a is the total data traffic generated by the distribution network nodes under its subordinate restoration observation; Formula (55) indicates that if the two nodes connected by line g have been restored at time t and the line is on the repair path, then the line is restored at time t; Formula (56) constrains the maximum data traffic that can pass through the repaired line; Formula (57) indicates that the data traffic is only output at the processing center, and its value is the total amount of data to be processed in the current period, and the other nodes have no data output; Formula (58) represents the traffic balance constraint of each node.

[0050] The initial state constraint of the information network means that during post-disaster recovery, considering that part of the distribution network has not been damaged before the start of repair, the initial state of its recovery is constrained as follows:

[0051]

[0052] in: and They represent the set of nodes and lines in the information network that do not need to be restored. In addition, there are no constraints (43)-(45) on the nodes and lines that are intact in the initial state.

[0053] The information network energy supply constraint means that in the wired communication network, the measurement data generated by the sensors at each node of the distribution network needs to be processed by the switch and then forwarded to the central server, and the normal operation of the switch depends on the corresponding main / backup power supply lines in the distribution network for energy supply, and its expression is:

[0054]

[0055] in: is a 0-1 variable matrix representing the energy recovery status of the information network nodes in each period, and its elements Indicates that the switch at node a of the information network resumes power supply in time period t; It represents the set of distribution network nodes that supply power to the switch at information network node a, including the main power supply line access node and the backup power supply line access node; is a 0-1 variable indicating whether the distribution network node i meets the switch power supply requirement at time t, It means that the load recovery ratio at time t is greater than the minimum ratio α required for power supply, and the power supply of the switch can be restored; Indicates the time point when the information network node a resumes power supply. Formulas (61) and (62) indicate that the time when the switch at the information network node a resumes power supply depends on the earliest time when the minimum power supply ratio is restored in the corresponding distribution network main / backup power supply node, and the information center does not need to consider the power supply problem; Formulas (63) and (64) constrain the relationship between the time point when node a resumes power supply and the recovery state in each time period; Formula (65) indicates that due to the existence of the repair path constraint, the time when the information network node a is fully restored should be later than the time when its power supply is restored.

[0056] Step S24: Based on the supporting role of satellite communications in information-physical collaborative recovery, satellite communication constraints for the optimization problem are established, including satellite communication terminal deployment constraints, satellite communication capacity constraints, and satellite communication duration constraints.

[0057] The satellite communication terminal deployment constraint means that in order for the distribution network nodes to realize satellite communication, satellite communication terminals need to be deployed in advance, and the expression is as follows:

[0058]

[0059] in: It is an alternative distribution network node where satellite communication terminals can be deployed; is the time when node i accesses satellite communication, is the time when node i loses satellite communication, if It means that node i has no satellite communication access during the recovery process; A 0-1 variable representing the satellite terminal deployment, Indicates that the terminal is configured at node i. Equations (66) and (67) constrain the upper and lower limits of the satellite access and departure times; Equation (68) indicates that the time of losing satellite communication should be later than the access time; Equation (69) indicates that if node i does not deploy a communication terminal, it cannot access satellite communication.

[0060] The satellite communication capacity constraint means that since there is an upper limit on the maximum number of nodes and the maximum communication flow that a single satellite communication can simultaneously support, its maximum communication flow needs to be constrained, and its expression is as follows:

[0061]

[0062] in: is a 0-1 variable matrix representing the satellite communication status of the distribution network nodes in each period, and its elements Indicates that there is a satellite communication signal M at distribution network node i in time period t S and M FThey represent the node number limit and maximum flow limit of satellite communication respectively. Formula (70) indicates that between the satellite communication access time and the departure time, node i is in an effective communication state; Formulas (71) and (72) constrain the maximum number of nodes and flow of satellite communication in the same time.

[0063] The satellite communication duration constraint means that if the satellite communication is used to restore the observable state of the distribution network node in advance and close the telecontrol switch to restore the load of the corresponding node before the wired information network is repaired, the satellite communication signal cannot be removed before the wired information network corresponding to the node is restored, otherwise it will cause the restored line to trip again due to loss of observability. Its expression is This means that the satellite communication signal removal time of any distribution network node i must be later than the considerable time of its wired information network restoration.

[0064] Step S3: By means of constrained linearization and limiting the feasible domain, the established optimization model is simplified and transformed into a MILP problem to improve the solution efficiency. The simplification method specifically includes:

[0065] Step S31: Linearize the nonlinear constraints contained in the original problem, including the linearization of distribution network restoration constraints, the linearization of information network restoration constraints and the linearization of satellite cooperative communication constraints.

[0066] The linearization of the distribution network restoration constraint is as follows: by introducing a 0-1 variable and the large M method (M is a sufficiently large constant), replacing the nonlinear constraints (10), (13) and (29) in the distribution network constraints with linear constraints, where equation (10) is transformed into: (13) is transformed into: (29) is transformed into:

[0067] The linearization of the information network recovery constraint refers to: by introducing 0-1 variables The Big M method and the SOS2 method replace the nonlinear constraints (41), (47), (55), (61) and (62) in the distribution information network related constraints with linear constraints, where equation (41) is transformed into: (47) is transformed into: Where: n d is the maximum number of repair steps allowed; (55) is converted to: (61) is transformed into: (62) is transformed into:

[0068] The linearization of satellite cooperative communication constraints refers to: converting the nonlinear constraint formula (70) in satellite cooperative communication into a linear constraint by the big M method, and its expression is:

[0069] Step S32: According to the principle of shortest satellite communication access time, the feasible domain of the optimization problem is restricted to improve its solution efficiency.

[0070] The principle of shortest satellite communication access time refers to: 1) if (the access time of satellite communication to node i is later than the recovery time of its wired communication network), then satellite communication does not access this node, that is, 2) If (The load recovery time of node i is earlier than the expected recovery time of its wired communication network), indicating that satellite communication access enables the load of the node to recover in advance. The access time point of satellite communication is the time when the corresponding remote switch on its recovery path starts to act / the black start power supply starts to self-start, that is, (The time it takes for node i to restore power minus the time it takes for the restoration path to take effect). 3) If The time point of satellite communication removal is the time it takes to recover in the wired communication network, that is, Assumption 1 ensures that satellite communication does not make meaningless access after node i is restored; Assumption 2 ensures that satellite communication is accessed at the latest time point that can achieve the recovery effect; Assumption 3 ensures that satellite communication ends at the earliest time point that can be removed.

[0071] The restricted feasible domain means that since the MILP problem is NP-Hard, if no constraints are added and some invalid feasible domains are cut, there will be too many feasible solution combinations, making the problem extremely difficult to solve. ) with: Where: T i FP Refers to the parent node j of i in the recovery topology = F P (i) The switching time required for the line to i to recover; is the auxiliary continuous variable introduced, An auxiliary 0-1 variable introduced.

[0072] Step S4: Solve the MILP problem, analyze the problem-solving results, and obtain the repair order of each node in the information network, the traffic distribution path, the dispatch order of the power grid repair team, the load and unit operation plan, the satellite communication terminal deployment and disaster dispatch plan.

[0073] Step S5: Evaluate the collaborative recovery benefits based on the load recovery amount and satellite communication terminal deployment benefits to guide post-disaster recovery decisions.

[0074] After specific practical experiments, the above method is implemented on the following 33-node distribution network-10-node information network coupling system: Figure 2 As shown in the figure, the information network contains an information processing center (node ​​1) and 9 switch nodes (nodes 2-10). The switch at each information network node is responsible for forwarding the status information collected by the sensor devices at multiple distribution network nodes. The distribution network adopts the IEEE 33-node distribution network topology. Node 1 is a balancing node. Two distributed generators are connected at nodes 15 and 33, and their output ranges are [0, 0.7], [0, 0.5] (active power) and [-0.9, 0.9], [-0.4, 0.4] (reactive power). Nodes 1, 15, and 33 are all regarded as black start power sources during post-disaster recovery.

[0075] In this embodiment, when performing the calculation of the satellite communication terminal deployment and the post-disaster information-physical collaborative recovery model of the distribution network, it is assumed that the information network lines are all disconnected due to the disaster under the initial conditions, and all the remote switches of the distribution network transmission lines are tripped but do not include the damaged switches that cannot be closed, and the physical-information coupling system starts the post-disaster recovery from the completely black state. When setting the model parameters, the analysis time interval τ = 10min, the analysis period number T = 20; for the distribution network, the data flow generated by the sensor device at each node is taken as f i C =0.5MB / s, the flow related parameters are the same as those of the IEEE 33-node distribution network; for the information network, the flow capacity of each line is The distribution network load recovery ratio α required to restore the switch power supply is 0.3. It is assumed that the repair team can repair up to three information channels at the same time, and the time required to repair 1, 2, and 3 information channels at the same time is 20 minutes, 30 minutes, and 60 minutes respectively; for satellite communication, the deployable nodes are distribution network nodes 6-8, 14-15, 31-33, and the flow limit is M F =2MB / s, the maximum number of communications is limited to M S =3; in the objective function, take the deployment cost c of the satellite communication terminal S =1000, the load-money conversion coefficient of deploying satellite communication terminals ω=0.005, and the weight coefficients of each distribution network load are shown in Table 1.

[0076] Table 1 Load weight coefficient of each node

[0077]

[0078] This implementation uses the GUROBI solver to solve the MILP problem, and the duality gap is set to MIPGap = 0.01%. The example simulation is tested under MATLAB R2022a, and the hardware environment is 32GB memory and Intel core i5-12400 CPU.

[0079] The input-output samples obtained from 5000 sets of input data samples are used to establish low-fidelity models corresponding to the analytical method and SPCE proxy model method, where the highest order of the SPCE model is set to 2. The high / low fidelity models are calculated 1000 times each, and the computational burden required for each model is shown in Table 1.

[0080] The above example is solved using the method proposed by the present invention, and the satellite communication terminal deployment results are shown in Table 2. It can be seen from Table 2 that in the distribution network satellite communication terminal deployment strategy, satellite communication terminals are deployed at three distribution network nodes (15, 32, and 33), and the total deployment cost is 3000. Among them, nodes 15 and 33 are the nodes where the black start power supply is located, and the satellite signal is connected at time 1; the satellite signal of node 32 is connected at time 2. In order to maximize the use of the satellite terminal deployment cost, the satellite signal is no longer removed after accessing these three nodes, and assists the deployed nodes to complete the forwarding of the sensor signal until the post-disaster recovery process is completed. Under the influence of the satellite communication deployment and access strategy, nodes 15 and 32 after time 1, and node 33 after time 2, the satellite communication link recovery information is considerable. After the recovery information is considerable, the black start power supplies of nodes 15 and node 33 start to self-start. After the self-start is completed, an island can be formed to restore the energy supply of the corresponding area. After the power supply of node 33 is self-started (time 2), since the load weight coefficient at node 32 is relatively high (0.5), satellite communication is used to restore its observability. After that, both nodes 32 and 33 restore observable information, and the corresponding remote switches can be closed to achieve load recovery.

[0081] Table 2 Satellite communication terminal deployment nodes and satellite access time

[0082]

[0083] The method proposed in the invention is used to solve the example, and the collaborative recovery effect of satellite communication access is compared and analyzed. Under the coordination of satellite communication in this paper, the lines of the distribution network are closed in sequence under the premise of considerable recovery information, the load recovery amount gradually increases, and the recovery speed is relatively stable. Finally, after 170 minutes, the load recovery amount of the system reaches the maximum value; after accessing satellite communication, the weighted load recovery amount of the distribution network in each period during the post-disaster recovery process is greater than that without satellite communication access, and compared with the case of not accessing satellite communication, accessing satellite communication can restore the load to the maximum value 10 minutes in advance. As shown in Table 3, accessing satellite communication can reduce the post-disaster load loss cost of the power system by 23.86%. After considering the deployment cost of satellite communication terminals, the objective function value can still be reduced by 8.49%.

[0084] Table 3 Comparison of recovery results with and without satellite communication access

[0085]

[0086] In this embodiment, the distribution network post-disaster island division and the closing time of each line switch are as follows: Figure 4 .Depend on Figure 4 It can be seen that after the disaster, the distribution network forms three radial islands with the nodes where the black start power sources are located as the power supply center. Among them, since node 1 is a balanced node, it supplies power to 21 nodes (1-7, 12, 13, 19-30), forming a large island range; nodes 15 and 33 only supply power to 8 nodes (8-11, 14-17) and 4 nodes (31-33, 18) respectively due to limited unit output, and the island range is relatively small.

[0087] In this embodiment, the information network post-disaster line repair time and node recovery time are as follows: Figure 5 .Depend on Figure 5 It can be seen that the information network repaired the emergency communication network in a radial manner after the disaster, among which the path of node 1-6 was repaired, and the path of node 7 was not repaired. When the repair was completed, the data flow on each line met the line capacity constraint (10MB / s). In the first repair sequence, the repair team repaired lines 1-2 and 1-3 at the same time, and then completed the repair of 2-4, 4-9, 1-8, 9-10, 4-5, and 4-6 in sequence. Since the observation data of the observation area of ​​switch 7 (distribution nodes 32 and 33) can be completely forwarded by satellite, the wired path of node 7 was not repaired.

[0088] Compared with the existing technology, the present invention comprehensively takes into account the complex coupling relationship between the information-physical system of the distribution network, and considers the supporting role of satellite communication in collaborative recovery under the background of new-era technological development. It takes the distribution network parameters and its initial state of post-disaster recovery as input, and outputs the information-physical collaborative recovery plan supported by satellite communication, which is conducive to guiding the efficient post-disaster recovery of the distribution network and improving the resilience of the distribution network.

[0089] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other specific forms without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations falling within the meaning and scope of the equivalent elements of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0090] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A method for generating a post-disaster information-physical collaborative recovery plan for a distribution network supported by satellite communications, characterized in that: The steps include: Step S1: input the data of the information network-power network to be restored, including the information-physical network topology and line parameters, the coupling relationship between information-physical nodes, the initial disconnection and damage status of the line after the disaster, and the deployment candidate nodes of the satellite communication terminal, and initialize the corresponding constraints in the optimization problem of restoring solution generation; Step S2: Modeling the post-disaster information-physical collaborative recovery process of the distribution network supported by satellite communication as an optimization problem. The modeling method specifically includes: Step S21: determining the objective function of the optimization problem with the goal of minimizing the post-disaster load loss and the satellite communication terminal deployment cost; The objective function includes the sum of two costs: load loss cost c loss and satellite communication terminal deployment cost c deploy , its specific expression is: my c loss +c deploy (1) Where: τ is the time interval of model analysis, T is the total number of time periods; N P is the set of distribution network nodes, is the set of distribution network nodes where satellite communication terminals can be deployed; ε i is the load weight coefficient of distribution network node i; is the load recovery amount of distribution network node i at time t; ω is the load-money conversion coefficient of deploying satellite communication terminals, c S is the deployment cost of satellite communication terminals, is a 0-1 variable indicating whether node i is deployed with a satellite communication terminal, where 1 means node i is deployed and 0 means it is not deployed; Step S22: Based on the physical network repair logic in the cyber-physical coupling network, distribution network restoration constraints of the optimization problem are established, including distribution network restoration path constraints, distribution network restoration time constraints, distribution network restoration initial state constraints, and distribution network power flow constraints; The distribution network restoration path constraint refers to: describing the restoration process of the distribution network topology in the form of an energized agent EA, with an n P ×n P , the path table composed of 0-1 variables describes the repair path of the distribution network, n P is the total number of distribution network nodes, and its elements The energized agent EA representing the distribution network moves from node i to node j. The constraints of each element in the path table are as follows: Where: N P represents the node set in the distribution network, L P represents the set of lines in the distribution network, Represents a set of black start power supply nodes in the distribution network; is the node connection matrix in the distribution network, = ... The distribution network restoration time constraint means that on the basis of obtaining the distribution network restoration path by the energized agent EA, the restoration time of each node in the distribution network is described by the following constraint, and its expression is as follows: in: Indicates the time when power supply is restored at distribution network node i; is the switch action time matrix between nodes in the distribution network, whose elements represents the time required for the switch action between nodes i and j, represents the self-start time of the black start power supply at node i; It indicates the time when the power supply of the distribution network node i has been restored and the target node j of the restoration path has recovered information. It takes considerable time for the distribution network node i to restore the wired information network. represents the satellite communication access time of distribution network node i, M is a sufficiently large constant; is a 0-1 variable matrix used to represent the recovery status of distribution network nodes in each period, and its elements = represents the restoration of power supply at the distribution network node in time period t. Formula (10) indicates that after the restoration information of the node where the black start power supply is located is observable, the black start power supply starts automatically and supplies power to the node where it is located. Formulas (11), (12) and (13) indicate that if there is a restoration path between nodes i and j and i restores power supply and j restores observably, then after the switch action time, node j restores power supply, otherwise formulas (11), (12) and (13) do not work. Formulas (14) and (15) indicate that if there is no power supply path to be restored passing through node j, then its power restoration time is the maximum power outage duration + 1, otherwise (14) and (15) do not work. Formula (16) indicates that the premise for node i to restore power supply is that there is a restoration path passing through the node. Formula (17) indicates that node i will restore power supply after the time point when its restoration is completed. Formula (18) constrains the node that has restored power supply to no longer be powered off. The distribution network recovery initial state constraint means: during post-disaster recovery, if some distribution network line switches and nodes are damaged and power supply cannot be restored, the initial state constraint expression constraining its recovery is as follows: in: and They represent the set of distribution network nodes that cannot be restored and the set of lines that cannot be closed respectively; The distribution network flow constraint refers to the constraint that the distribution network flow relationship needs to satisfy. The linearized Distflow model is used to describe the internal flow relationship of the distribution network. The specific expression is as follows: Where: Equations (21)-(23) are black start power constraints, where and represents the active and reactive output of the black start power supply at node i at time t; P i G,min and P i G,max Indicates the lower and upper limits of the active output of the black start power supply at node i; and represents the lower and upper limits of reactive power output of the black start power supply at node i; and It represents the maximum power down / up rate. Formula (21) (22) constrains the active and reactive output of the black start power supply. Formula (23) constrains the ramp rate of the black start power supply. Formulas (24)-(26) are load-related constraints. and represents the active and reactive load recovery of distribution network node i at time t; P i L,max represents the maximum value of the restorable load at node i; η is the power factor of the load, and formula (24) constrains the upper and lower limits of the load recovery amount of each node; formula (25) represents the active and reactive load recovery relationship under the condition of constant power factor; formula (26) constrains the stability of load recovery and ensures that the load recovery amount of each node increases over time. Formulas (27)-(34) are line flow constraints, where is a 0-1 variable representing the recovery status of distribution network line k at time t, Indicates line recovery; Indicates the maximum active and reactive capacity of line k; is the connection relationship variable between line k and node i. If k = (i, j), that is, line k connects nodes i and j and the connection direction is from i to j, then n≠i or j, formula (27) constrains the voltage amplitude of the restored node; formula (28) constrains the output voltage of the black start power supply to always maintain the standard value; formula (29) indicates that if the two nodes connected to line k have been restored at time t, and the line is on the energized proxy EA path, then the line is restored at time t; formulas (30) and (31) constrain the active and reactive capacity on the restored path; formulas (32) and (33) are the power balance constraints of each node; formula (34) is the node voltage amplitude relationship of the linearized Dist-Flow model; Step S23: Based on the information network repair logic in the information-physical coupling network, establish information network recovery constraints for the optimization problem, including information network recovery path constraints, information network recovery time constraints, information network flow constraints, information network initial state constraints, and information network energy supply constraints; The information network restoration path constraint refers to: using the "information agent" path to describe the repair process of the distribution network, and its expression is: Where: N C represents the set of information network nodes, L C Represents a collection of information network lines. Indicates the node where the central server in the information network is located; It is the node connection matrix in the information network; The information network recovery time constraint means that the post-disaster emergency recovery relationship of the distribution network is described by the repair process of the repair team on the damaged information network lines connecting each switch, and its expression is: in: T represents the time it takes for the repair team to complete the dth step of repair; r (x) represents the repair time function, whose value is the repair time required to repair x information network nodes at the same time, which increases with the increase of the number of nodes repaired at the same time; freq(d) represents the total number of information network nodes with repair order d; d a represents the repair order of node a; F C (d a ) represents the repair order of the parent nodes of node a in the emergency repair topology; Indicates the recovery completion time of information network node a; I d,a is the judgment variable, in d a =d, its value is 1, otherwise it is 0; Formula (41) indicates that for the central server that does not need to be repaired, the repair order is 1, its repair completion time is 1, and the completion time of each subsequent repair step is equal to the sum of the time required for each previous repair step; Formula (42) constrains the repair order of the central server to be 1; Formula (43) indicates that the repair order of the child node on the repair path must be greater than its parent node; Formulas (44) and (45) indicate that if the repair path is a→b, the parent node of node b is node a, otherwise Formulas (44) and (45) do not work; (46) indicates that due to the existence of energy supply constraints, the recovery time of information network node a is later than the completion time of the emergency repair work of its corresponding number of steps; The information network flow constraint refers to the constraint composed of flow conditions that need to be satisfied in the recovery process due to the limitation of the flow that can pass through each line in the information network. The specific expression is: in: A -1 variable matrix representing the recovery status of information network nodes in each period, whose elements It means that the information network node a repairs the wired path in time period t; It is a 0-1 variable matrix representing the situation of the distribution network nodes in the information network recovering observably in each period, and its element is 1, indicating that the corresponding node has recovered observably; It represents the time for the distribution network node i to restore the wired information network; represents the information network node where the switch responsible for forwarding the observation data obtained by the sensor at the distribution network node i is located, represents the set of distribution network nodes connected to the switch at information network node a, f i C The data traffic generated by the sensor observing the power distribution node i; represents the data flow input by information network node a at time t, Indicates the output data flow; is a 0-1 variable representing the recovery status of distribution network line g at time t, Indicates line recovery; Indicates the maximum data flow through line g; is the connection relationship variable between line g and node a. If g = (a, b), that is, line g connects nodes a and b and the connection direction is from a to b, then n≠a or b, formula (54) indicates that the traffic forwarded by switch a is the total data traffic generated by the distribution network nodes under its subordinate restoration observation; formula (55) indicates that if the two nodes connected by line g have been restored at time t and the line is on the repair path, then the line is restored at time t; formula (56) constrains the maximum data traffic that can pass through the repaired line; formula (57) indicates that the data traffic is only output at the processing center, and its value is the total amount of data to be processed in the current period, and the other nodes have no data output; formula (58) represents the traffic balance constraint of each node; The initial state constraint of the information network means that during post-disaster recovery, considering that part of the distribution network has not been damaged before the start of repair, the initial state of its recovery is constrained as follows: in: and They represent the set of nodes and lines of the information network that do not need to be restored. In addition, there are no constraints on the nodes and lines that are intact in the initial state (43)-(45); The information network energy supply constraint means that in the wired communication network, the measurement data generated by the sensors at each node of the distribution network needs to be processed by the switch and then forwarded to the central server, and the normal operation of the switch depends on the corresponding main / backup power supply lines in the distribution network for energy supply, and its expression is: in: is a 0-1 variable matrix representing the energy recovery status of the information network nodes in each period, and its elements Indicates that the switch at node a of the information network resumes power supply in time period t; It represents the set of distribution network nodes that supply power to the switch at information network node a, including the main power supply line access node and the backup power supply line access node; is a 0-1 variable indicating whether the distribution network node i meets the switch power supply requirement at time t, It means that the load recovery ratio at time t is greater than the minimum ratio α required for power supply, and the switch power supply can be restored; represents the time point when the information network node a resumes power supply. Formulas (61) and (62) indicate that the time when the switch at the information network node a resumes power supply depends on the earliest time when the minimum power supply ratio is restored in the corresponding distribution network main / backup power supply node, and the information center does not need to consider the power supply problem; Formulas (63) and (64) constrain the relationship between the time point when node a resumes power supply and the recovery status in each time period; Formula (65) indicates that due to the existence of the repair path constraint, the time when the information network node a is fully restored should be later than the time when its power supply is restored; Step S24: Based on the supporting role of satellite communication in information-physical collaborative recovery, satellite communication constraints for the optimization problem are established, including satellite communication terminal deployment constraints, satellite communication capacity constraints, and satellite communication duration constraints; The satellite communication terminal deployment constraint means that in order for the distribution network nodes to realize satellite communication, satellite communication terminals need to be deployed in advance, and the expression is as follows: in: It is an alternative distribution network node where satellite communication terminals can be deployed; is the time when node i accesses satellite communication, is the time when node i loses satellite communication, if It means that node i has no satellite communication access during the recovery process; A 0-1 variable representing the satellite terminal deployment, Indicates that the terminal is configured at node i; Equations (66) and (67) constrain the upper and lower limits of satellite access and departure times; Equation (68) indicates that the time of losing satellite communication should be later than the access time; Equation (69) indicates that if node i does not deploy a communication terminal, it cannot access satellite communication; The satellite communication capacity constraint means that since there is an upper limit on the maximum number of nodes and the maximum communication flow that a single satellite communication can simultaneously support, its maximum communication flow needs to be constrained, and its expression is as follows: in: is a 0-1 variable matrix representing the satellite communication status of the distribution network nodes in each period, and its elements Indicates that there is a satellite communication signal M at distribution network node i in time period t S and M F They represent the node number limit and maximum flow limit of satellite communication respectively. Formula (70) indicates that node i is in an effective communication state between the satellite communication access time and the departure time. Formulas (71) and (72) constrain the maximum number of nodes and flow of satellite communication in the same time. The satellite communication duration constraint means that if the satellite communication is used to restore the observable state of the distribution network node in advance and close the telecontrol switch to restore the load of the corresponding node before the wired information network is repaired, the satellite communication signal cannot be removed before the wired information network corresponding to the node is restored. Otherwise, the restored line will be tripped again due to loss of observability. Its expression is: This means that the satellite communication signal removal time of any distribution network node i must be later than the considerable time of its wired information network restoration; Step S3: By means of constrained linearization and limiting the feasible domain, the established optimization model is simplified and transformed into a MILP problem to improve the solution efficiency; the simplification method specifically includes: Step S31: linearizing the nonlinear constraints contained in the original problem, including the linearization of distribution network restoration constraints, the linearization of information network restoration constraints, and the linearization of satellite cooperative communication constraints; The linearization of the distribution network restoration constraint is as follows: by introducing a 0-1 variable and the large M method, where M is a constant. The nonlinear constraints (10), (13) and (29) in the distribution network constraints are replaced by linear constraints, where equation (10) is transformed into: (13) is transformed into: (29) is transformed into: The linearization of the information network recovery constraint refers to: by introducing 0-1 variables The Big M method and the SOS2 method replace the nonlinear constraints (41), (47), (55), (61) and (62) in the distribution information network related constraints with linear constraints, where equation (41) is transformed into: (47) is transformed into: Where: n d is the maximum number of repair steps allowed; (55) is converted to: (61) is transformed into: (62) is transformed into: The linearization of satellite cooperative communication constraints refers to: converting the nonlinear constraint formula (70) in satellite cooperative communication into a linear constraint by the big M method, and its expression is: Step S32: According to the principle of shortest satellite communication access time, the feasible domain of the optimization problem is restricted to improve its solution efficiency; The principle of shortest satellite communication access time refers to: 1) if That is, the time when the satellite communication accesses the node i is later than the recovery time of its wired communication network, then the satellite communication does not access the node, that is, 2) If That is, the load recovery time of node i is earlier than the considerable recovery time of its wired communication network, indicating that satellite communication access enables the load of the node to recover in advance. Then the access time point of satellite communication is the time when the corresponding remote switch on its recovery path starts to act / the black start power supply starts to self-start, that is, The time for node i to restore power minus the time for restoring the path action; 3) If The time point of satellite communication removal is the time it takes to recover in the wired communication network, that is, Assumption 1 ensures that satellite communication does not make meaningless access after node i is restored; Assumption 2 ensures that satellite communication is accessed at the latest time point that can achieve the recovery effect; Assumption 3 ensures that satellite communication ends at the earliest time point that can be removed; The restricted feasible domain is: constraining the duration of satellite communication, that is, Replace with: Where: T i FP Refers to the parent node j of i in the recovery topology = F P (i) The switching time required for the line to i to recover; is the auxiliary continuous variable introduced, is the auxiliary 0-1 variable introduced; Step S4: Solve the MILP problem, analyze the problem-solving results, and obtain the repair order of each node in the information network, the flow distribution path, the dispatch order of the power grid repair team, the load and unit operation plan, the satellite communication terminal deployment and disaster dispatch plan; Step S5: Evaluate the collaborative recovery benefits based on the load recovery amount and satellite communication terminal deployment benefits to guide post-disaster recovery decisions.

2. A system for implementing the method for generating a post-disaster information-physical collaborative recovery plan for a distribution network considering satellite communication support as described in claim 1, characterized in that: include: Recovery data initialization unit, model building and recovery plan generation unit, collaborative recovery effect evaluation unit; wherein: the recovery data initialization unit processes the data to be recovered of the distribution network information-physical system, and inputs the information-physical collaborative recovery plan generation model to be required; the model building and recovery plan generation unit models and characterizes the information-physical collaborative recovery relationship of the distribution network supported by satellite communication and solves the MILP problem, and outputs the optimal post-disaster recovery strategy; the collaborative recovery effect evaluation unit evaluates the collaborative recovery benefits based on the load recovery amount and the satellite communication terminal deployment benefits, and makes post-disaster recovery decisions.

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