Power distribution network disaster-mid-disaster and post-disaster two-stage collaborative resilience recovery decision method

Abstract

The application relates to a disaster-mid-disaster-post-disaster two-stage coordinated resilience recovery decision method in a power distribution network technical field, which plays the independent power supply advantage of a distributed power supply, establishes a disaster-mid-disaster-post-disaster recovery interaction model, and guarantees the optimality of disaster-mid-disaster-post-disaster recovery decision. The method comprises the following steps: in the disaster-mid stage, a disaster-mid cell recovery model is established by modeling a DG black start sequence and a cell recovery time; in the disaster-post stage, a maintenance personnel scheduling model, a cell recovery model and a power supply path model are established to jointly decide the maintenance path, the load recovery time, the switch state and the time in the disaster-post stage; the interaction between the disaster-mid stage and the disaster-post stage is fully considered, a topology adjustment model and a load recovery model under the disaster-mid-disaster-post coordination are established, and the rapid recovery of the load is realized. Through modeling the interaction relationship between the disaster-mid stage and the disaster-post stage, the optimality in the disaster-mid and disaster-post recovery processes can be guaranteed, and the rapid recovery of the load is realized.

Description

Technical Field

[0001] This invention relates to the field of power distribution network technology, specifically a two-stage collaborative resilience recovery decision-making method for power distribution networks during and after disasters. Background Technology

[0002] Currently, during the disaster phase, certain emergency measures are typically taken to reduce the scope of power outages and lay the foundation for post-disaster recovery. Commonly used measures include the scheduling of distributed generators (DG), network reconfiguration, and emergency energy supply. After a disaster, utilizing various flexible resources to ensure the power supply to critical loads and dispatching maintenance teams to repair faulty components, restoring the distribution network to normal power supply status, is a key link in reducing power outage losses and improving the resilience of the distribution network. The literature "Zhang Gang, Zhang Feng, Zhang Xin, et al. Sequential post-disaster recovery model of distribution system maintenance and emergency repair personnel scheduling collaboration optimization [J]. IEEE Smart Grid Bulletin, 2019.10(1):204-215." considers the relationship between the scheduling of fault repair personnel, switch operators and distribution network recovery, and constructs a distribution network post-disaster recovery model under personnel collaboration. The paper “Wang Yuehan, Liu Wenxia, ​​Yao Qi, et al. Pre-deployment and dynamic scheduling strategy of mobile energy storage for improving the resilience of distribution networks [J]. Automation of Electric Power Systems, 2022, 46(15):37-45.” considers the impact of various distributed power sources such as mobile generators, renewable energy and energy storage systems. It restores the load by forming dynamic islands through network reconfiguration and proposes an optimized scheduling model for fault maintenance personnel and mobile emergency power sources to achieve multi-source collaborative recovery.

[0003] It is evident that existing research has made certain contributions to system recovery during and after disasters. However, these studies generally make independent decisions regarding emergency measures during a disaster and the recovery process after the disaster, neglecting the continuity and correlation between the recovery sequence during and after a disaster. For example, temporary power supply decisions during a disaster may delay post-disaster recovery and prolong the time of power outages. Summary of the Invention

[0004] The purpose of this invention is to provide a two-stage collaborative resilience recovery decision-making method for distribution networks during and after disasters, which leverages the independent power supply advantages of distributed power sources and ensures the optimality of the recovery decision-making during and after disasters by establishing an interaction model for disaster recovery.

[0005] The technical solution adopted by this invention to solve its technical problem is: a two-stage collaborative resilience recovery decision-making method for distribution networks during and after disasters, including the following steps:

[0006] I. During the disaster phase, a cell recovery model is established by modeling the DG black start sequence and cell recovery time.

[0007] Second, in the post-disaster phase, establish a maintenance personnel scheduling model, a cell recovery model, and a power supply path model to jointly decide on the maintenance path, load recovery time, switch status, and timing during the post-disaster phase.

[0008] Third, fully consider the interaction between the disaster-prone and post-disaster processes, establish a topology adjustment model and load recovery model under the coordination of disaster-prone and post-disaster processes, and achieve rapid load recovery;

[0009] The objective function for minimizing power outage losses throughout the entire disaster period is as follows:

[0010]

[0011] in ω represents the power supply time of the load at node i. i The importance of the load on node i, Let be the load power of node i.

[0012] Furthermore, before constructing the disaster-post-disaster collaborative recovery model, a disaster-post-disaster collaborative recovery framework is constructed; based on whether there is a DG and faulty components inside the cell, the cells are divided into four categories: A / B / C / D, and the substation is regarded as a cell; (1) During the disaster phase, the A and D cells without faulty components are powered by DG black start; at the same time, considering that ordinary switches do not have the ability to self-synchronize, some ordinary switches are closed during the disaster phase to initially adjust the network topology; (2) In the post-disaster phase, based on the network topology during the disaster, maintenance personnel are dispatched to repair the faulty components; after the fault is repaired, the B cells are restored by DG black start; at the same time, for the C cells without DG and the remaining unrestored D cells, power supply is restored by establishing a power supply path between them and the restored A / B cells or the restored substation.

[0013] Furthermore, the steps for establishing a disaster-recovery cellular recovery model include:

[0014] I. Constrain the black start variables of DG according to Equations (2)-(4); where Equation (2) means that when the ordinary switch between two A or B cells is closed, cell A or B will be black started; Equations (3) and (4) mean that when the ordinary switch between two A or B cells is closed, the DG with the shorter black start time will be selected for start-up.

[0015]

[0016]

[0017]

[0018] In the formula: I m N represents the set of nodes within cell m. A N B Represent the sets of cells of type A and type B respectively; 0-1 variables This represents the DG black-start state of node i located in cell m. This indicates a black start; otherwise, it indicates grid connection. Indicates the time of DG black start within cell m; a 0-1 variable. This represents the state of a normal switch between cells m and n. This indicates that the switch is closed, and vice versa;

[0019] II. According to equations (5)-(6), type A cells recover through DG black start or grid connection; according to equations (7)-(8), type D cells recover by interacting with type A cells; according to equation (9), the internal load of a cell after recovery is delayed by T after cell recovery. c After recovery; according to equation (10), the normal power supply time of DG is equal to the cell recovery time;

[0020]

[0021]

[0022]

[0023]

[0024]

[0025]

[0026] In the formula: This represents the recovery time of cell m; Represents the closing time of a normal switch between cells m and n; a 0-1 variable. This indicates the state of the smart switch between cells m and n. Indicates that the switch is closed, and vice versa; T bw This is the time required for DG to connect to the grid; N D The set representing D-class cells; and These represent the remote control time for the closing of the smart switch and the ordinary switch, respectively; and T represents the power restoration time of load node i and DG node within cell m, respectively; c Indicates the time of load delay; I DG This represents the set of DG nodes.

[0027] Furthermore, the post-disaster modeling is divided into four parts: maintenance personnel scheduling modeling, load restoration modeling, power supply path modeling, and safe operation constraints.

[0028] Furthermore, the scheduling of maintenance personnel is modeled as follows: Equation (11) indicates that the maintenance personnel depart from the station and return to the station from which they depart; Equation (12) indicates that after the maintenance personnel have repaired the fault at node k, they continue to repair the fault at node l; Equation (13) indicates that each faulty component is repaired by one maintenance personnel; Equation (14) indicates that the time for the maintenance personnel to reach node l = the time to reach the previous node + the repair time of the previous component + the time required for transportation between the two nodes; Equation (15) indicates that the time for the maintenance personnel to repair node k = the time to reach node k + the time to repair component k;

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[0030]

[0031]

[0032]

[0033]

[0034] In the formula: This indicates the time it takes for maintenance personnel mc to arrive at node k; This indicates the time required for the repair of the faulty component at node k to be completed. This represents the time required for personnel mc to repair the component at node k. This represents the time required for person mc to travel from node k to node l.

[0035] Furthermore, load recovery modeling in the post-disaster phase includes substation recovery and B and C / D type cell recovery; there are two cases in which the DG of type B cells does not need black start. Case 1 is when a power supply path is formed between A cell and B cell. Since A cell has been recovered in the disaster phase, the DG of B cell only needs to be connected to the grid, satisfying equation (16); Case 2 is when a power supply path is established between two type B cells, and the impact of the network topology in the disaster phase needs to be considered.

[0036]

[0037] Substation repair is related to the upstream transmission line. Assume the substation repair time is... The substation restoration time is As shown in equation (17); equation (18) indicates that when time t is greater than At that time, the substation resumed power supply;

[0038]

[0039]

[0040] Where: N S This represents the set of cells in a substation; and introduces 0-1 variables. Indicates whether the substation has been restored. This indicates that the substation has resumed power supply; otherwise, it has not.

[0041] The recovery of B-type cells requires the completion of the fault repair within the cell. DG will then supply power to the load within the cell through black start or grid connection. Equation (19) indicates that the recovery time of B-type cells through DG black start is the sum of the fault repair completion time in the region and the DG black start time. Equation (20) indicates that when a power supply path is formed between A and B-type cells, the recovery time of B-type cells through DG grid connection is the sum of the switch closing time and the DG grid connection time.

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[0043]

[0044] The recovery model for C / D cells is as follows: Equation (21) indicates that the premise for the recovery of C cells is that all internal faults must be repaired; Equation (22) indicates the recovery time of C and D cells powered by A / B cells; Equation (23) indicates the recovery time of C and D cells powered by the substation.

[0045]

[0046]

[0047]

[0048] Where: N C This represents the set of C cells.

[0049] Furthermore, the energy supply path modeling is divided into two sub-models: an energy supply path decision model and an energy supply time model.

[0050] (1) Energy supply path decision model

[0051] The single commodity flow method is used to model the power supply path. Equation (24) indicates that the total number of closed switches is equal to the total number of cells minus the number of substations, thus avoiding the formation of a loop network. Equation (25) indicates that after the upstream substation is repaired, each cell is connected to the substation to ensure continuous power supply to the load. Equation (26) indicates that there can only be one type of switch between cells m and n: a regular switch or a smart switch.

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[0053]

[0054]

[0055] In the formula: N represents the total number of cells, F mn,t The virtual power flow represents the energy supply path between cells m and n at time t; It is a 0-1 variable, and its value indicates whether cell n is a substation cell. If it is a substation cell, it is 1, otherwise it is 0; a(n) and b(n) are the sets of child nodes and parent nodes when each cell is regarded as a node.

[0056] (2) Energy supply time model

[0057] Considering the differences between ordinary switches and smart switches, the time required for the two types of switches to form a power supply path is modeled separately:

[0058] Ordinary switches: According to the different cell types at both ends of the ordinary switch, there are 6 cases: Case 1 (cells on both sides of the switch are A1-A2), Case 2 (cells on both sides of the switch are B1-B2), Case 3 (cells on both sides of the switch are A1-D1), Case 4 (cells on both sides of the switch are A1-B1), Case 5 (cells on both sides of the switch are A1-C1), and Case 6 (cells on both sides of the switch are B1-C1 / D1). Cases 1 and 2 need to be formed under the coordination of disaster prevention and disaster relief. Equation (27) represents Case 4, where the power supply path is formed after the B cell fault is repaired. Equation (28) represents Cases 5 and 6. If the DG capacity in A / B cells is sufficient to restore the load of C cell, then after A / B cells are restored, the switch is closed to form a power supply path to power C cell. Otherwise, the switch is closed to power C cell after the substation is repaired.

[0059]

[0060]

[0061] Smart switch: According to the different cell types at both ends of the smart switch, there are 7 cases: Case 1 (cells on both sides of the switch are A1-D1), Case 2 (cells on both sides of the switch are A1-A2), Case 3 (cells on both sides of the switch are B1-B2), Case 4 (cells on both sides of the switch are A1-B1), Case 5 (cells on both sides of the switch are A1-C1), Case 6 (cells on both sides of the switch are B1-C1 / D1) and Case 7 (cells ABCD of the substation); Equation (29) represents the power supply time of cell cases 2, 3 and 4. After both sides of the cells are restored, the switch is closed after synchronization. Equation (30) represents the power supply time under cases 5 and 6. Equation (31) represents that under case 7, the smart switch connected to the substation is closed after the power supply path is formed.

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[0063]

[0064]

[0065] In the formula: The time required for the intelligent switch to synchronize the microgrids on both sides; This represents the power generation of DG within cell m; These represent the load demand within cells m and n, respectively;

[0066] After obtaining the power distribution network recovery time and power supply path, the power supply status of load i within the cell at time t is introduced. Normal working state of intracellular DG Non-switch circuit power supply status and the power supply status of the switching circuit in Equations (32) and (33) indicate that the load / DG power supply state is 1 when the time is greater than the load / DG power supply time; Equation (34) indicates that the power supply state of the internal non-switching circuit is 1 after the cell is restored; Equations (35) and (36) indicate that the switch state is 1 only after the switch is closed and the time is greater than the switch closing time.

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[0068]

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[0070]

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[0072] In the formula: B is the set of all load power supply times, and B is the set of distribution network branches.

[0073] Furthermore, the modeling steps for safe operation constraints are as follows:

[0074] A distribution network recovery model with variable time step based on power supply time is adopted, and safety constraint verification is performed at each power supply moment; where Equations (37) and (38) represent the output constraints of substations and distributed power sources, Equation (39) represents the active and reactive power balance equation of the node, Equation (40) represents the line voltage drop, Equation (41) represents the upper and lower limits of power flow constraints borne by the line, Equation (42) represents the upper and lower limits of voltage constraints of the node, and Equation (43) represents that all loads must eventually be restored;

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[0080]

[0081]

[0082] In the formula: This represents the active and reactive power output of the substation at node i at time t; This represents the upper limit of active and reactive power output of the distributed generation or substation of node i; This represents the lower limit of active and reactive power output of the distributed generation or substation at node i. This represents the active and reactive power output of the distributed power source at node i at time t; These represent the active and reactive loads of node i, respectively; P i,j,t Q i,j,t R represents the active and reactive power of line ij at time t; i,j X i,j Let Uij be the resistance and reactance of line ij; and U0 be the reference voltage. Let be the active and reactive power transmission capacity of line ij; and Let a(i) be the upper and lower limits of the voltage amplitude of node i; and let a(i) and b(i) be the sets of child nodes and parent nodes of node i.

[0083] Furthermore, the steps for establishing a disaster-prone and post-disaster network topology adjustment model are as follows:

[0084] Based on the power supply path model in the post-disaster phase, the switching decision quantity is obtained. By modeling the switching closing time, it is ensured that the switching closes during the disaster phase, achieving network topology adjustment under disaster-post-disaster coordination. During the disaster phase, network topology adjustments are made for cases 1 and 2 of ordinary switches:

[0085] (1) A1-A2 cells

[0086] When there are two Class A cells on both sides of the ordinary switch, the switch is closed in advance during the disaster phase and before the Class A cells recover to form a switch; the following constraint is established for this: Equation (44) indicates that the time for the ordinary switch to close between the two Class A cells is equal to the cell recovery time of the DG black start plus the remote control time for the switch to close.

[0087]

[0088] (2) B1-B2 cells

[0089] Similar to A1-A2, if cells 1 and 2 are type B cells, firstly, based on the post-disaster recovery model, the two type B cells undergo a black start of the DG after fault repair; then, based on the power supply path model, by pre-closing the switch during a disaster, the following constraints are established for this situation:

[0090]

[0091] In the formula, T mid This indicates the duration of the emergency response phase during a disaster.

[0092] Furthermore, the steps for establishing a disaster-prone and post-disaster load recovery model are as follows:

[0093] The impact of disaster topology on class B cells is specifically twofold: the DG black start sequence and the cell recovery time. These two impacts are modeled below:

[0094] The constraints of the DG black start sequence are the same as those in equations (3) and (4), that is, if the switch between two B cells is closed in the disaster, then the DG black start time with the shorter black start time is allowed to perform black start.

[0095] The impact of B-type cell recovery time is shown in Equations (46) and (47): Equation (46) indicates that if the ordinary switch between two B cells is closed, the recovery time of the cell that is black-started by the DG is still greater than the fault repair time of the other B-type cell; Equation (47) indicates that the B cells that are not black-started by the DG need to wait for the DG to be connected to the grid before the power supply to all loads in the area can be restored.

[0096]

[0097]

[0098] Equations (46)-(47) and Equations (19)-(20) of the post-disaster model together determine the recovery time of B-type cells after the disaster.

[0099] The beneficial effects of this invention are as follows: By modeling the interaction between disaster and post-disaster recovery, a collaborative recovery model is established, ensuring optimality during and after the disaster and achieving rapid load recovery. Compared to non-collaborative models, collaborative models can restore more load and reduce power outage losses in the distribution network. In the event of upstream grid outages, fully utilizing the inherent power supply advantages of distributed generation sources to form regional microgrids can provide temporary power to surrounding critical loads, reducing load outage losses and improving the power supply guarantee capability of the distribution network. Attached Figure Description

[0100] Figure 1 The response diagram of a resilient distribution network after a disaster;

[0101] Figure 2 Cellular classification diagram;

[0102] Figure 3 A framework diagram for coordinated recovery in the two phases of disaster response and post-disaster recovery;

[0103] Figure 4 Diagram of a collaborative recovery model during and after a disaster;

[0104] Figure 5 This is a diagram illustrating the DG black boot process.

[0105] Figure 6 Diagrams showing six possible scenarios for a standard switch;

[0106] Figure 7 Diagram showing seven scenarios for a smart switch;

[0107] Figure 8a Example 1 of a disaster-prone collaborative model;

[0108] Figure 8b Example 2 of a disaster-prone collaborative model;

[0109] Figure 9 Diagram of the IEEE 123 node distribution network system;

[0110] Figure 10 This is a diagram showing the load conditions of the node cells;

[0111] Figure 11 This is a diagram showing the output range of the DG.

[0112] Figure 12 This is a clustering diagram of faulty equipment;

[0113] Figure 13a Road traffic time map for station 1;

[0114] Figure 13b Road traffic time map for station 2;

[0115] Figure 13c Road traffic time map for station 3;

[0116] Figure 14 A timeline for equipment maintenance;

[0117] Figure 15 A schedule for maintenance personnel;

[0118] Figure 16 This is a diagram showing the power distribution network restoration sequence.

[0119] Figure 17 Diagrams showing the restoration of cells 2, 3, and 4;

[0120] Figure 18 This is a sequence diagram of the phased recovery of the distribution network during a disaster under non-cooperative conditions.

[0121] Figure 19 This is a sequence diagram of the post-disaster recovery of the distribution network under non-cooperative conditions.

[0122] Figure 20 This is a comparison chart of the collaborative model and the non-collaborative model. Detailed Implementation

[0123] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0124] I. Establishing a framework for collaborative recovery during and after a disaster

[0125] like Figure 1(The shaded area represents system load loss.) This illustrates the response of a resilient distribution network after a disaster, specifically divided into three stages: pre-disaster planning (t0-t1), emergency response (t1-t2), and post-disaster recovery (t2-t3). The pre-disaster planning stage enhances the distribution network's resilience to disasters through line reinforcement and pre-adjustment of distributed power sources. The emergency response stage ensures power supply to critical loads and reduces the scope of power outages by utilizing distributed power sources and altering network topology. The post-disaster recovery stage, through dispatching maintenance personnel to repair faults and utilizing flexible resources such as distributed power sources, quickly restores the distribution network to its pre-disaster state by altering the network topology. It is evident that the recovery time during and after a disaster is continuous, with the disaster stage forming the foundation for post-disaster recovery. Furthermore, both stages share similar recovery resources. Implementing measures during a disaster to coordinate with the post-disaster recovery process leads to better post-disaster recovery. Considering the coupling relationship between the emergency response and recovery stages, fully coordinating recovery resources in both stages ensures the continuity of decision-making during the recovery process and improves the recovery speed of the distribution network.

[0126] Considering the large scale and complex network structure of my country's urban power distribution network, the following assumptions are made in this paper:

[0127] (1) Distribution network switches include smart switches and ordinary switches. Smart switches have voltage and current sensors at both ends, which can remotely control the regional microgrids on both sides of the switch to synchronize and close the switch. Ordinary switches only have the ability to remotely control closing and do not have the ability to synchronize.

[0128] (2) Distributed power sources all have black start capability and can provide a reference frequency and relatively stable voltage. Among them, intermittent distributed power sources such as photovoltaic and wind power have black start capability by equipping them with synchronous power sources such as diesel engines in advance before a disaster.

[0129] (3) To simplify the analysis, the power distribution network restoration model is performed on a cell-by-cell basis. Each cell region is a set of nodes connected by non-switch lines. To ensure the radiation of the power distribution network, each cell is interconnected with other cells through at least one switch, and two adjacent cells can only be connected by one switch.

[0130] Regarding hypothesis (3), depending on whether there are DGs and faulty components inside the cell, such as Figure 2 As shown, cells are divided into four categories: A, B, C, and D; simultaneously, substations are treated as separate cells. Based on these assumptions, a framework for a rapid distribution network recovery method based on two-stage collaborative decision-making during and after a disaster is proposed, as follows: Figure 3As shown. Specifically: (1) During the disaster phase, Class A and Class D cells without faulty components are powered by DG black start. At the same time, considering that ordinary switches do not have self-synchronization capabilities, in order to ensure the rapid restoration of the power supply path after the disaster, it is necessary to close some ordinary switches during the disaster phase and initially adjust the network topology. (2) In the post-disaster phase, based on the network topology during the disaster, maintenance personnel are dispatched to repair faulty components first; after the fault is repaired, Class B cells can restore the load within the cell through DG black start; at the same time, for Class C cells without DG and the remaining unrestored Class D cells, power supply can be restored by establishing a power supply path between them and the restored Class A / B cells or the restored substation.

[0131] II. Establishing a Collaborative Recovery Model During and After Disasters

[0132] The disaster recovery and post-disaster phases exhibit continuity and coupling. Therefore, to improve the recovery speed of the distribution network, a two-stage collaborative recovery model for the disaster recovery and post-disaster phases is established, such as... Figure 4 As shown, firstly, during the disaster phase, a cellular recovery model is established by modeling the DG black start sequence and cell recovery time. Secondly, in the post-disaster phase, a maintenance personnel scheduling model, a cellular recovery model, and a power supply path model are established to jointly determine the maintenance path, load recovery time, and switch status and timing in the post-disaster phase. Finally, fully considering the interaction between the disaster-prone and post-disaster processes, a topology adjustment model and a load recovery model under disaster-prone-post-disaster coordination are established to achieve rapid load recovery.

[0133] To improve the recovery speed of the distribution network and reduce load outage losses, the objective function is to minimize the outage losses throughout the entire disaster period:

[0134]

[0135] in ω represents the power supply time of the load at node i. i The importance of the load on node i, Let be the load power of node i.

[0136] 2.1 Disaster Phase Modeling

[0137] During the disaster phase, measures such as distributed power generation and network topology modifications are implemented to ensure power supply to critical loads and support rapid post-disaster recovery. To this end, a disaster recovery cellular model is established, centered on distributed generation black start. This model uses distributed generation black start to power critical loads. It is modeled as two sub-problems: the distributed generation black start problem and the cellular recovery time problem.

[0138] (1) DG Black Boot Issue

[0139] Because only type A cells possess the conditions for DG (Distributed Generation) and fault-free operation within the region during the disaster phase, this part of the modeling focuses on type A cells. Considering the implementation of post-disaster power supply paths, a black start of all DGs within type A cells during the disaster might render post-disaster power supply paths infeasible. For example, in... Figure 5 In this case, both cells 1 and 2 of type A have a generator (DG). The DG with the shorter black-start time is selected for black-start to establish the reference voltage and frequency, and the other DG can then be connected to the grid for power generation. Therefore, the black-start variables of the DG need to be constrained, as shown in equations (2)-(4). Equation (2) indicates that when the ordinary switch between two cells A or B is closed, cells A or B both undergo black-start. Equations (3) and (4) indicate that when the ordinary switch between two cells A or B is closed, the DG with the shorter black-start time is selected for startup. In all other cases, the DGs of type A cells undergo black-start.

[0140]

[0141]

[0142]

[0143] In the formula: I m N represents the set of nodes within cell m. A N B Represent the sets of cells of type A and type B respectively; 0-1 variables This represents the DG black-start state of node i located in cell m. This indicates a black start; otherwise, it indicates grid connection. Indicates the time of DG black start within cell m; a 0-1 variable. This represents the state of a normal switch between cells m and n. This indicates that the switch is closed, and vice versa.

[0144] (2) Cell recovery time problem

[0145] This part of the model realizes load power supply within the fault-free zone. Among them, Class A cells are restored through DG black start or grid connection, i.e., Equations (5)-(6); Equations (7)-(8) indicate that Class D cells are restored through interaction with Class A cells; Equation (9) indicates that after cell restoration, its internal load can be delayed by T after cell restoration. c After recovery; Equation (10) indicates that the normal power supply time of DG is equal to the cell recovery time. This paper assumes that the upstream substation is disconnected, so the situation where the substation supplies power to D cells is not considered during the disaster phase.

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[0147]

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[0149]

[0150]

[0151]

[0152] In the formula: This represents the recovery time of cell m; Represents the closing time of a normal switch between cells m and n; a 0-1 variable. This indicates the state of the smart switch between cells m and n. Indicates that the switch is closed, and vice versa; T bw This is the time required for DG to connect to the grid; N D The set representing D-class cells; and These represent the remote control time for the closing of the smart switch and the ordinary switch, respectively; and T represents the power restoration time of load node i and DG node within cell m, respectively; c Indicates the time of load delay; I DG This represents the set of DG nodes.

[0153] 2.2 Post-disaster phase modeling

[0154] In the post-disaster phase, building upon the recovery efforts during the disaster, a robust operational plan is crucial for the rapid restoration of the distribution network. This plan involves the rational allocation of repair teams to restore power equipment, coupled with measures such as distributed generation and network reconfiguration to ensure continuous power supply to the loads. The post-disaster model restores power to the affected areas by making decisions regarding repair paths, distributed generation black-start sequences, cell recovery times, and power supply paths. Therefore, the post-disaster modeling is divided into four parts: maintenance personnel scheduling modeling, load recovery modeling, power supply path modeling, and safe operation constraints.

[0155] 2.2.1 Maintenance Personnel Dispatch Model

[0156] First, establish the network topology G of the faulty component. M (V M E M ), where V M With E M Let represent the set of nodes and branches in the faulty network, respectively. A node represents a maintenance station (denoted by dp) and a faulty component. A branch represents a traffic path that connects two nodes. 0-1 variables are introduced. This indicates whether maintenance personnel mc has been scheduled from node k to node l. A value of 1 indicates that a maintenance worker is scheduled from node k to node l. Otherwise, the value is 0.

[0157] In summary, the scheduling of maintenance personnel is modeled as follows: Equation (11) indicates that the maintenance personnel depart from the station and return to the station from which they depart; Equation (12) indicates that after the maintenance personnel have repaired the fault at node k, they continue to repair the fault at node l; Equation (13) indicates that each faulty component is repaired by one maintenance personnel; Equation (14) indicates that the time for the maintenance personnel to reach node l = the time to reach the previous node + the repair time of the previous component + the time required for transportation between the two nodes; Equation (15) indicates that the time for the maintenance personnel to repair node k = the time to reach node k + the time to repair component k.

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[0159]

[0160]

[0161]

[0162]

[0163] In the formula: This indicates the time it takes for maintenance personnel mc to arrive at node k; This indicates the time required for the repair of the faulty component at node k to be completed. This represents the time required for personnel mc to repair the component at node k. This represents the time required for person mc to travel from node k to node l.

[0164] 2.2.2 Load Recovery Model

[0165] The load recovery in the post-disaster phase includes the restoration of substations and the restoration of B and C / D class cells. Similar to the during-disaster phase, the cell recovery model is also divided into two parts: DG black-start modeling and cell recovery time modeling. The black-start variables of class A cells have been modeled in the during-disaster phase, so the DG black-start variable modeling in the post-disaster phase mainly targets class B cells. There are two cases in which the DG of class B cells does not require black-start. Case 1 is when a power supply path is formed between class A cells and class B cells. Since class A cells have been restored in the during-disaster phase, the DG of class B cells only needs to be connected to the grid, satisfying equation (16); Case 2 is when a power supply path is established between two class B cells, and the impact of the network topology in the during-disaster phase needs to be considered.

[0166]

[0167] Substation repair is related to the upstream transmission line. Assume the substation repair time is... The substation restoration time is As shown in equation (17). Equation (18) indicates that when time t is greater than... At that time, the substation resumed power supply.

[0168]

[0169]

[0170] Where: N S This represents the set of cells in a substation; and introduces 0-1 variables. Indicates whether the substation has been restored. This indicates that the substation has resumed power supply; otherwise, it indicates that power supply has not been resumed.

[0171] The recovery of type B cells requires the completion of fault repair within the cell, after which the DG supplies power to the load within the cell via black start or grid connection. Equation (19) indicates that the recovery time of type B cells via DG black start is the sum of the fault repair completion time within the area and the DG black start time. Equation (20) indicates that when a power supply path is formed between cells A and B, the recovery time of type B cells via DG grid connection is the sum of the switch closing time and the DG grid connection time.

[0172]

[0173]

[0174] It should be noted that Equation (19) is only a time range for the recovery time of B cells. The specific recovery time of B cells also needs to take into account the impact of decision-making during the disaster.

[0175] After the fault repair within a C-cell is completed, a power supply path needs to be formed from the upstream substation or nearby A / B cells before power can be restored. Since there is no fault within a D-cell, the fault repair time can be considered zero, and its load restoration also requires power from the substation or A / B cells. When the DG capacity of an A / B cell is sufficient to restore itself and adjacent C / D cells, power is supplied by the A / B cells; otherwise, it waits for the substation to restore. Therefore, the restoration model for C / D cells is as follows: Equation (21) indicates that the prerequisite for the restoration of a C-cell is that all internal faults must be repaired. Equation (22) indicates the restoration time for C and D cells powered by A / B cells.

[0176] Equation (23) represents the recovery time of cells C and D when they are powered by the substation.

[0177]

[0178]

[0179]

[0180] Where: N C This represents the set of C cells.

[0181] 2.2.3 Energy Supply Path Model

[0182] 0-1 variables This indicates the state of the switching circuit between cells m and n. A value of 1 indicates that the switch between cells m and n is closed. That is, if the switch between substation cells m and n is closed, forming a circuit, a power supply path is considered to have been established between the substation and cell n.

[0183] After a Class C cell is repaired from a fault, a power supply path needs to be established between it and a Class A / B cell containing a power source or a substation to supply power. The restored Class A / B cells also need to be connected to an upstream substation to ensure a continuous and stable power supply to the load. Therefore, establishing a power supply path is the key to restoring power to all loads. The model is then divided into two sub-models: a power supply path decision model and a power supply time model.

[0184] (1) Energy supply path decision model

[0185] The single commodity flow method is used to model the power supply path. Equation (24) indicates that the total number of closed switches is equal to the total number of cells minus the number of substations, avoiding the formation of a loop network. Equation (25) indicates that after the upstream substation is repaired, each cell is connected to the substation to ensure continuous power supply to the load. Equation (26) indicates that the connection between cells m and n can only be either a regular switch or a smart switch.

[0186]

[0187]

[0188]

[0189] In the formula: N represents the total number of cells, F mn,t This represents the virtual power flow of the energy supply path between cells m and n at time t. It is a 0-1 variable, whose value indicates whether cell n is a substation cell. If it is a substation cell, it is 1, otherwise it is 0; a(n) and b(n) are the sets of child nodes and parent nodes when each cell is regarded as a node.

[0190] (2) Energy supply time model

[0191] Considering the differences between ordinary switches and smart switches, the time required for the two types of switches to form a power supply path is modeled separately.

[0192] Ordinary switches: Based on the different cell types at both ends of an ordinary switch, there are 6 cases, such as... Figure 6 As shown. Situations 1 and 2 require coordination during and after a disaster. Equation (27) represents situation 4, where the power supply path is formed after the B cell fault is repaired. Equation (28) represents situations 5 and 6. If the DG capacity in the A / B cells is sufficient to restore the load of the C cell, then after the A / B cells are restored, the switch is closed to form a power supply path to power the C cell; otherwise, the switch is closed to power the C cell after the substation is repaired.

[0193]

[0194]

[0195] Smart switches: Based on the different cell types at both ends of the smart switch, there are 7 types, such as... Figure 7 As shown. Compared with ordinary switches, smart switches have an additional cell type 7 at both ends. This is because it is assumed that the switch at the upstream substation can generally be synchronously connected to the power grid. Case 1 has been introduced in disaster modeling. Equation (29) represents the power supply time of cell cases 2, 3 and 4. After both cells on both sides are restored, the switch is closed after synchronization. Equation (30) represents the power supply time under cases 5 and 6. Equation (31) represents that under case 7, the smart switch connecting the substation closes after the power supply path is formed.

[0196]

[0197]

[0198]

[0199] In the formula: The time required for the intelligent switch to synchronize the microgrids on both sides; This represents the power generation of DG within cell m; These represent the load demand within cells m and n, respectively.

[0200] After obtaining the power distribution network recovery time and power supply path, the power supply status of load i within the cell at time t is introduced. Normal working state of intracellular DG Non-switch circuit power supply status and the power supply status of the switching circuit in Equations (32) and (33) indicate that the load / DG power supply state is 1 when the time is greater than the load / DG power supply time; Equation (34) indicates that the power supply state of the internal non-switching circuit is 1 after the cell is restored; Equations (35) and (36) indicate that the switch state is 1 only after the switch is closed and the time is greater than the switch closing time.

[0201]

[0202]

[0203]

[0204]

[0205]

[0206] In the formula: B is the set of all load power supply times, and B is the set of distribution network branches.

[0207] 2.2.4 Safety Operation Constraints

[0208] A distribution network restoration model based on power supply time-driven variable time step is adopted, which only requires safety constraint verification at each power supply moment. Among them, equations (37) and (38) represent the output constraints of substations and distributed power sources, and equation (39) represents the active and reactive power balance equation of the node. Equation (40) represents the line voltage drop, equation (41) represents the upper and lower limits of power flow constraints on the line, equation (42) represents the upper and lower limits of node voltage constraints, and equation (43) indicates that all loads must eventually be restored.

[0209]

[0210]

[0211]

[0212]

[0213]

[0214]

[0215]

[0216] In the formula: This represents the active and reactive power output of the substation at node i at time t; This represents the upper limit of active and reactive power output of the distributed generation or substation of node i; This represents the lower limit of active and reactive power output of the distributed generation or substation at node i. This represents the active and reactive power output of the distributed power source at node i at time t; These represent the active and reactive loads of node i, respectively; P i,j,t Q i,j,t R represents the active and reactive power of line ij at time t; i,j X i,j Let Uij be the resistance and reactance of line ij; and U0 be the reference voltage. Let be the active and reactive power transmission capacity of line ij; and Let a(i) be the upper and lower limits of the voltage amplitude of node i; and let a(i) and b(i) be the sets of child nodes and parent nodes of node i.

[0217] 2.3 Disaster-Post-Disaster Coupling Constraints

[0218] Since ordinary switches do not have self-synchronization capabilities, some power supply paths need to be constructed in coordination with those constructed during the disaster. At the same time, the network topology changes caused by constructing power supply paths during the disaster will also directly affect the recovery of the post-disaster load.

[0219] by Figure 8a For example, assuming cells 1 and 2 are type A cells, based on the disaster recovery model, cells 1 and 2 restore power during a disaster. Based on the post-disaster power supply path model, ordinary switches 3-5 need to be closed to power cell 3, but since the area microgrids formed by two distributed generation (DG) units are located on either side of the switches, they cannot be closed. Therefore, the switches must be closed before the cells recover during the disaster phase to form a power supply path. Let's take... Figure 8b For example, since switch 3-5 was closed during the disaster, cells 1 and 2 became connected. Therefore, the condition for cell 1 to recover after the disaster becomes that there are no faulty components in cells 1 and 2.

[0220] Therefore, considering the mutual influence of the disaster recovery process and establishing a collaborative recovery model for the disaster recovery process is crucial for improving the recovery speed of the power distribution network. The interaction between them is modeled below.

[0221] 2.3.1 Disaster-Post-Disaster Network Topology Adjustment Model

[0222] Based on the power supply path model in the post-disaster phase, the switching decision quantity is obtained. By modeling the switching closing time, it is ensured that the switching closes during the disaster phase, achieving network topology adjustment under disaster-post-disaster coordination. During the disaster phase, network topology adjustments are needed for scenarios 1 and 2 involving ordinary switches:

[0223] (1) A1-A2 cells

[0224] like Figure 8aAs shown, when there are two Class A cells on both sides of the ordinary switch, the switch must be closed in advance during the disaster phase and before the Class A cells recover to form the switch. To this end, the following constraint is established: Equation (44) indicates that the time for the ordinary switch to close between the two Class A cells is equal to the cell recovery time of the DG black start plus the remote control time for the switch to close.

[0225]

[0226] (2) B1-B2 cells

[0227] Similar to (A1-A2), if Figure 8a Cells 1 and 2 are Class B cells. Firstly, based on the post-disaster recovery model, the two Class B cells undergo a black start in the DG after fault repair. Then, based on the power supply path model, switches 3-5 need to be closed, but ordinary switches lack self-synchronizing power supply and cannot be closed. Therefore, this must be achieved by closing switches in advance during a disaster. For this situation, the following constraints are established:

[0228]

[0229] In the formula T mid This indicates the duration of the emergency response phase during a disaster.

[0230] Unlike the A1-A2 case, since cell B only recovers during the post-disaster phase, the opening and closing time only needs to be constrained during the disaster phase. However, in the A1-A2 case, cell A recovers during the disaster, so it needs to be strictly constrained to close before both A-class cells recover.

[0231] 2.3.2 Disaster-Post-Disaster Load Recovery Model

[0232] As the foregoing analysis shows, network topology adjustments are carried out in conjunction with the disaster recovery phase. Furthermore, the impact of these network adjustments needs to be modeled during post-disaster recovery.

[0233] The changes in topology during a disaster primarily affect the recovery of B-cells after the disaster. Figure 8b For example, if cells 1 and 2 are type B cells, and switches 3-5 are closed prematurely during a disaster, merging them into one cell, then during the post-disaster recovery phase, recovery can only be achieved if both cells are fault-free. Furthermore, only one of the two DGs needs to be black-started. Therefore, the impact of the disaster topology on type B cells is specifically reflected in two aspects: the DG black-start sequence and the cell recovery time. These two impacts are modeled below:

[0234] The constraints of the DG black start sequence are the same as those in equations (3) and (4), that is, if the switch between two B cells is closed in the disaster, then the DG black start time is shorter and black start is performed.

[0235] The impact of B-type cell recovery time is shown in Equations (46) and (47): Equation (46) indicates that if the ordinary switch between two B cells is closed, the recovery time of the cell that started the DG black is still longer than the fault repair time of the other B-type cell; Equation (47) indicates that the B cells that did not start the DG black need to wait for the DG to be connected to the grid before the power supply to all loads in the area can be restored.

[0236]

[0237]

[0238] Equations (46)-(47) and Equations (19)-(20) of the post-disaster model jointly determine the recovery time of Class B cells after a disaster. Finally, the two-stage collaborative model based on distributed power supply during and after a disaster is obtained as follows: Objective function:

[0239] The constraints include:

[0240] (1) Cellular recovery model during disaster phase (2)-(10);

[0241] (2) Post-disaster maintenance personnel dispatch model (11)-(15);

[0242] (3) Post-disaster power distribution network recovery model (16)-(23);

[0243] (4) Energy supply path model equations (24)-(36);

[0244] (5) Safety operation constraint formulas (37) and (43);

[0245] (6) Disaster-post-disaster coupling constraint equations (44) and (47).

[0246] 2.4 Model Solving

[0247] The above recovery model is a mixed integer nonlinear programming model. As shown in equations (44) and (46), there are nonlinear terms in which 0-1 variables are multiplied by continuous variables. Equations (32)-(36) are nonlinear constraints, and the above nonlinear terms need to be linearized.

[0248] First, for the nonlinear term resulting from the multiplication of a 0-1 variable with a continuous variable, equation (46) is linearized by introducing an auxiliary 0-1 variable α in the following manner:

[0249]

[0250] Secondly, by introducing a smaller number ε, equations (32)-(33) are linearized in the manner of equation (49):

[0251]

[0252] Finally, by introducing an assignment variable β, as shown in equation (50), and adding the variable ε to linearize equation (34), the final linearized equation is (51):

[0253]

[0254]

[0255] By linearizing the nonlinear terms using the above methods, the model is transformed into a mixed integer linear programming (MILP) model, which is then solved using CPLEX.

[0256] III. Case Analysis

[0257] The proposed model was validated using an IEEE 123-node distribution network. All simulations were performed on a computer with an i5 processor and 16GB of RAM, running GAMS 25.1.3 / CPLEX 25.1.3.

[0258] 3.1 Simulation Example Design

[0259] like Figure 9 As shown, the tested IEEE 123 node distribution network system includes one substation, five distributed generation (DG) units, eight remote intelligent control switches, and four remote ordinary control switches, with a total load of 3490kW. There were seven line faults, and three maintenance stations were set up. Based on the DG and fault information, the IEEE 123 node distribution network is divided into three Class A cells, two Class B cells, four Class C cells, and one Class D cell, marked with different colors. The load conditions and DG output conditions within the cells are as follows: Figure 10 and Figure 11 As shown: To simplify the scheduling model for maintenance personnel, a clustering method is used in advance to assign faulty components to the nearest stations. Due to the lack of real-world data, a random number generator is used in MATLAB to randomly generate the repair time of the faulty components, traffic time, and synchronization time of the smart switches, such as... Figures 12-14 As shown.

[0260] 3.2 Simulation Results

[0261] By solving the proposed model, the dispatch path for maintenance personnel is obtained as follows: Figure 15 As shown in Table 3, the restoration sequence of the distribution network is indicated by 0 / 1. A value of 1 indicates a black start, while a value of 0 indicates only grid connection.

[0262] Using the proposed recovery model, the distribution network is ultimately restored to a substation-powered distribution system, and all loads are restored. The final topology of the distribution network is as follows: Figure 10 As shown.

[0263] During the disaster phase, distributed generation systems use black start to supply power to loads in fault-free areas, reducing outage time. Figure 16 Taking Class A cells 7 and Class D cells 8 as examples, at t=7min, the DG in cell 7 starts up and restores the load in cell 7; at t=8min, switches 76-77 close and the DG in cell 7 supplies power to the load in cell 8.

[0264] from Figure 16 This demonstrates that coordination during and after a disaster is crucial for load recovery. Figure 17 (Among them, ② and ③ at t=0min, ② at t=3min, ④ at t=351min, and ④ at t=188min are unpowered cells; the remaining ②, ③, and ④ are powered cells.) Taking the recovery of Class A cells 2 and 3 and Class C cells 4 as an example: ① Based on the distributed generation black-start model and cell recovery model during the disaster phase, the DG in cell 3 performs a black start. At t=3min, the DG black start is successful, restoring the load in cell 3. At the same time, based on the topology adjustment model under disaster-disaster coordination, switches 13-18 are closed in advance during the disaster phase. ② After cell 3 recovers and switches 13-18 are closed, a reference voltage and frequency have been established. Based on the disaster-disaster cell recovery model, the DG in cell 2 completes grid connection at t=4min, restoring the load in cell 2. ③ In the post-disaster phase, based on the maintenance personnel scheduling model, the fault in cell 4 is repaired at t=188min. ④ Based on the post-disaster power supply path model, switches 23-25 ​​are closed at t=351min, along with switches 13-18 closed during the disaster phase, thus forming a power supply path between cell 4 and the substation. ⑤ After the substation is connected to the distribution network at t=352min, the loads within cell 4 are restored to power supply.

[0265] In the post-disaster phase, through the dispatch of maintenance personnel and in conjunction with measures such as distributed power sources and network topology adjustments, power supply to the load can be restored quickly. Figure 16Taking cells 7 and 10 as examples, based on the post-disaster cell recovery model, at t=333min, switches 97-197 close. Since cell 7 (class A) has already recovered during the disaster, the distributed generation (DG) within cell 10 can directly connect to the grid and generate electricity, thus restoring power to cell 7. This switching operation saves the black-start time of the DG and improves the recovery speed. For instance, at t=132min, the fault in cell 1 is repaired. At the next moment, t=133min, switches 1-14 close, forming a path for the DG in class A to power class C cells, restoring power to the load in cell 1. This demonstrates that utilizing the inherent power supply capacity of distributed generation can provide support for critical loads before the substation is restored, reducing losses caused by power outages.

[0266] from Figure 16 As can be seen, based on the power supply path model, power supply paths between all cells and the substation were established, while ensuring the radiation requirements of the power grid. At t = 352 min, the substation was connected to the distribution system, achieving stable power supply to all loads.

[0267] 3.3 Advantages of the Model

[0268] The superiority of the proposed in-disaster and post-disaster optimization model is verified by comparing it with a non-cooperative optimization model. In the non-cooperative model, the recovery during the disaster phase only needs to minimize the power outage loss during the disaster phase. Only the black-start variables of the distributed generation (DG) and the cell recovery time are modeled. Then, the topology after disaster recovery is used as the input information for post-disaster recovery. The path of maintenance personnel, the black-start variables of the DG, and the switching variables are then solved to obtain the load recovery time, using the minimum power outage loss in the post-disaster phase as the starting point. The results of the non-cooperative model are as follows: Figure 18 and Figure 19 As shown in the non-cooperative model, the optimization objective in both the disaster-prone and post-disaster phases is to minimize the power outage loss in the current phase. Individually, this is optimal for each phase. However, it may not be optimal for the entire recovery process. Taking the above model as an example, in the non-cooperative model, the load in cell 4 was not restored. The main reason is that the role of the power supply path in the post-disaster phase was not considered during the recovery process in the disaster-prone phase. Switches 18-23 were not closed during the disaster-prone phase, resulting in the inability to form a power supply path for cell 4 in the post-disaster phase due to the open switch 18-13, ultimately leading to the failure to restore the load in cell 4.

[0269] Figure 20 This paper compares the final recovery results of the cooperative model and the non-cooperative model. It can be seen that the cooperative model proposed in this paper can recover 3490kW of load, which is 200kW more than the non-cooperative model. Furthermore, the cooperative model can recover 15259kWh of electricity, which is 24.7% more than the 12238kWh recovered by the non-cooperative model.

[0270] Therefore, in the recovery model of the distribution network, by fully considering the interaction between decision-making during and after the disaster and making coordinated decisions during and after the disaster, the optimal solution for rapid and effective recovery of the distribution network can be obtained, and load recovery can be achieved after a large-scale failure of the distribution network.

Claims

1. A two-stage collaborative resilience recovery decision-making method for distribution networks during and after disasters, characterized in that: Includes the following steps: I. During the disaster phase, a disaster cell recovery model is established by modeling the DG black start sequence and cell recovery time. A cell is a set of nodes connected by non-switching lines. Based on whether there are DGs and faulty components inside the cell, the cells are divided into four categories: A, B, C, and D. Second, in the post-disaster phase, establish a maintenance personnel scheduling model, a cell recovery model, and a power supply path model to jointly decide on the maintenance path, load recovery time, switch status, and timing during the post-disaster phase. Third, fully consider the interaction between the disaster-prone and post-disaster processes, establish a topology adjustment model and load recovery model under the coordination of disaster-prone and post-disaster processes, and achieve rapid load recovery; The objective function for minimizing power outage losses throughout the entire disaster period is as follows: （1） in ω represents the power supply time of the load at node i. i The importance of the load on node i, Let be the load power of node i; The steps to establish a disaster-prone and post-disaster network topology adjustment model are as follows: Based on the power supply path model in the post-disaster phase, the switching decision quantity is obtained. By modeling the switching closing time, it is ensured that the switching closes during the disaster phase, achieving network topology adjustment under disaster-post-disaster coordination. Smart switches can remotely control the regional microgrids on both sides of the switch to tend to synchronize, while ordinary switches only have the ability to remotely control closing and do not have synchronization capabilities. During the disaster phase, network topology adjustments are made for ordinary switches in scenarios 1 and 2. Case 1: The cells on both sides of the ordinary switch are A1-A2. The switch is closed in advance during the disaster phase and before the A-type cells recover. The following constraint is established for this: Equation (2) means that the time for the ordinary switch to close between the two A-type cells is equal to the cell recovery time of the DG black start plus the remote control time for the switch to close. （2） in, This represents the closing time of a normal switch between cells m and n; This represents the recovery time of cell m; 0-1 variables This represents the DG black-start state of node i located in cell m. This indicates a black start; otherwise, it indicates grid connection. Represents the remote control time of a normal switch closing; 0-1 variable. This represents the state of a normal switch between cells m and n. Indicates that the switch is closed, and vice versa; N A Represents the set of cells of class A; Scenario 2: The cells on both sides of the ordinary switch are B1-B2. First, based on the post-disaster recovery model, the two B-type cells undergo a black start of the DG after fault repair. Then, based on the power supply path model, by closing the switch in advance during a disaster, the following constraints are established for this scenario: （3） In the formula, Indicates the duration of the emergency response phase during a disaster; N B This represents the set of cells of type B.

2. The decision-making method for coordinated resilience recovery of distribution networks in two stages during and after disasters, as described in claim 1, is characterized in that... Before constructing the disaster-post-disaster collaborative recovery model, a disaster-post-disaster collaborative recovery framework is constructed; at the same time, the substation is regarded as a cell; (1) During the disaster phase, the A and D cells without faulty components are powered by DG black start; at the same time, considering that ordinary switches do not have self-synchronization capabilities, some ordinary switches are closed during the disaster phase to initially adjust the network topology; (2) In the post-disaster phase, based on the network topology during the disaster, maintenance personnel are dispatched to repair faulty components; after the fault is repaired, the B cells are restored by DG black start; at the same time, for the C cells without DG and the remaining unrestored D cells, power supply is restored by establishing a power supply path between the restored A / B cells or the restored substation.

3. The decision-making method for coordinated resilience recovery of distribution networks in two stages during and after disasters, as described in claim 2, is characterized in that... The steps to establish a cellular recovery model during a disaster include: I. Constrain the black start variables of DG according to Equations (4)-(6); where Equation (4) means that when the ordinary switch between two A or B cells is closed, cell A or B will be black started; Equations (5) and (6) mean that when the ordinary switch between two A or B cells is closed, the DG with the shorter black start time will be selected for start-up. （4） （5） （6） In the formula: I m This represents the set of nodes within cell m; This indicates the time of DG black start within cell m; II. According to equations (7)-(8), type A cells recover through DG black start or grid connection; according to equations (9)-(10), type D cells recover by interacting with type A cells; according to equation (11), the internal load of a cell after recovery is delayed by T after cell recovery. c After recovery; according to equation (12), the normal power supply time of DG is equal to the cell recovery time; （7） （8） （9） （10） （11） （12） In the formula: 0-1 variables This indicates the state of the smart switch between cells m and n. Indicates that the switch is closed, and vice versa; T bw This is the time required for DG to connect to the grid; N D The set representing D-class cells; Indicates the remote control time for the smart switch to close; and T represents the power restoration time of load node i and DG node within cell m, respectively; c Indicates the time of load delay; I DG This represents the set of DG nodes.

4. The decision-making method for coordinated resilience recovery of distribution networks in two stages during and after disasters, as described in claim 3, is characterized in that... The post-disaster modeling is divided into four parts: maintenance personnel scheduling modeling, load restoration modeling, power supply path modeling, and safe operation constraints.

5. The decision-making method for coordinated resilience recovery of distribution networks in two stages during and after disasters, as described in claim 4, is characterized in that... The maintenance personnel scheduling model is as follows: Equation (13) indicates that the maintenance personnel depart from the station and return to the station from which they depart; Equation (14) indicates that after the maintenance personnel have repaired the fault at node k, they continue to repair the fault at node l; Equation (15) indicates that each faulty component is repaired by one maintenance personnel; Equation (16) indicates that the time for the maintenance personnel to arrive at node l = the time to arrive at the previous node + the repair time of the previous component + the time required for transportation between the two nodes; Equation (17) indicates that the time for the maintenance personnel to repair node k = the time to arrive at node k + the time to repair component k; （13） （14） （15） （16） （17） In the formula: This indicates the time it takes for maintenance personnel mc to arrive at node k; This indicates the time required for the repair of the faulty component at node k to be completed. This represents the time required for personnel mc to repair the component at node k. This represents the time required for person mc to travel from node k to node l.

6. The decision-making method for coordinated resilience recovery of distribution networks in two stages during and after disasters, as described in claim 5, is characterized in that... The load recovery modeling in the post-disaster phase includes the recovery of substations and the recovery of B and C / D type cells; there are two cases in which the DG of B type cells does not need to be black-started. Case 1 is when a power supply path is formed between A cell and B cell. Since A cell has been recovered in the disaster phase, the DG of B cell only needs to be connected to the grid, which satisfies equation (18); Case 2 is when a power supply path is established between two B type cells, and the impact of the network topology in the disaster phase needs to be considered. （18） Substation repair is related to the upstream transmission line. Assume the substation repair time is... The substation recovery time is... As shown in equation (19); equation (20) indicates that when time t is greater than At that time, the substation resumed power supply; （19） （20） Where: N S This represents the set of cells in a substation; and introduces 0-1 variables. Indicates whether the substation has been restored. This indicates that the substation has resumed power supply; otherwise, it has not. The recovery of B-type cells requires the completion of the fault repair within the cell. DG will then supply power to the load within the cell through black start or grid connection. Equation (21) indicates that the recovery time of B-type cells through DG black start is the sum of the fault repair completion time in the region and the DG black start time. Equation (22) indicates that when a power supply path is formed between A and B-type cells, the recovery time of B-type cells through DG grid connection is the sum of the switch closing time and the DG grid connection time. （21） （22） The recovery model for C / D cells is as follows: Equation (23) indicates that the premise for the recovery of C cells is that all internal faults must be repaired; Equation (24) indicates the recovery time of C and D cells powered by A / B cells; Equation (25) indicates the recovery time of C and D cells powered by the substation. （23） （24） （25） Where: N C This represents the set of C cells.

7. The decision-making method for coordinated resilience recovery of distribution networks in two stages during and after disasters, as described in claim 6, is characterized in that... The energy supply path modeling is divided into two sub-models: the energy supply path decision model and the energy supply time model. (1) Energy supply path decision model The power supply path is modeled using a single-object network flow model. Equation (26) indicates that the total number of closed switches is equal to the total number of cells minus the number of substations, thus avoiding the formation of a ring network. Equation (27) indicates that after the upstream substation is repaired, each cell is connected to the substation to ensure the continuous power supply to the load. Equation (28) indicates that there can only be one type of switch between cells m and n: a regular switch or a smart switch. （26） （27） （28） In the formula: N represents the total number of cells, F mn,t The virtual power flow represents the energy supply path between cells m and n at time t; It is a 0-1 variable, and its value indicates whether cell n is a substation cell. If it is a substation cell, it is 1, otherwise it is 0; a(n) and b(n) are the sets of child nodes and parent nodes when each cell is regarded as a node. (2) Energy supply time model Considering the differences between ordinary switches and smart switches, the time required for the two types of switches to form a power supply path is modeled separately: Ordinary switches: According to the different cell types at both ends of the ordinary switch, there are 6 cases: Case 1: the cells on both sides of the switch are A1-A2, Case 2: the cells on both sides of the switch are B1-B2, Case 3: the cells on both sides of the switch are A1-D1, Case 4: the cells on both sides of the switch are A1-B1, Case 5: the cells on both sides of the switch are A1-C1, Case 6: the cells on both sides of the switch are B1-C1 / D1; Cases 1 and 2 need to be formed under the coordination of disaster-on-disaster. Equation (29) represents Case 4, where the power supply path is formed after the B cell fault is repaired; Equation (30) represents Cases 5 and 6. If the DG capacity in the A / B cells is sufficient to restore the load of the C cell, then after the A / B cells are restored, the switch is closed to form a power supply path to supply power to the C cell; otherwise, wait for the substation to be repaired before closing the switch to supply power to the C cell. （29） （30） Intelligent switch: According to the different cell types at both ends of the intelligent switch, there are 7 cases: Case 1: the cells on both sides of the switch are A1-D1, Case 2: the cells on both sides of the switch are A1-A2, Case 3: the cells on both sides of the switch are B1-B2, Case 4: the cells on both sides of the switch are A1-B1, Case 5: the cells on both sides of the switch are A1-C1, Case 6: the cells on both sides of the switch are B1-C1 / D1, and Case 7: the substation ABCD cells; Equation (31) represents the power supply time of cell cases 2, 3 and 4. After both sides of the cells are restored, the switch is closed after synchronization. Equation (32) represents the power supply time under cases 5 and 6. Equation (33) represents that under case 7, the intelligent switch connected to the substation is closed after the power supply path is formed. （31） （32） （33） In the formula: The time required for the intelligent switch to synchronize the microgrids on both sides; This represents the power generation of DG within cell m; , These represent the load demand within cells m and n, respectively; After obtaining the power distribution network recovery time and power supply path, the power supply status of load i within the cell at time t is introduced. Normal working state of intracellular DG Non-switch circuit power supply status and the power supply status of the switching circuit , ,in , Equations (34) and (35) indicate that the load / DG power supply status is 1 when the time is greater than the load / DG power supply time; Equation (36) indicates that the power supply status of the internal non-switching circuit is 1 after the cell is restored; Equations (37) and (38) indicate that the switch status is 1 only after the switch is closed and the time is greater than the switch closing time. （34） （35） （36） （37） （38） In the formula: B is the set of all load power supply times, and B is the set of distribution network branches.

8. The decision-making method for coordinated resilience recovery of distribution networks in two stages during and after disasters, as described in claim 7, is characterized in that... The modeling steps for safe operation constraints are as follows: A distribution network recovery model based on power supply time and variable time step is adopted, and safety constraint verification is performed at each power supply moment; where Equations (39) and (40) represent the output constraints of substations and distributed power sources, Equation (41) represents the active and reactive power balance equation of the node, Equation (42) represents the line voltage drop, Equation (43) represents the upper and lower limits of power flow constraints borne by the line, Equation (44) represents the upper and lower limits of voltage constraints of the node, and Equation (45) represents that all loads must eventually be restored; （39） （40） （41） （42） （43） （44） （45） In the formula: , This represents the active and reactive power output of the substation at node i at time t; , This represents the upper limit of active and reactive power output of the distributed generation or substation of node i; , This represents the lower limit of active and reactive power output of the distributed generation or substation at node i. , This represents the active and reactive power output of the distributed power source at node i at time t; , These represent the active and reactive loads of node i, respectively. , R represents the active and reactive power of line ij at time t; i,j X i,j Let Uij be the resistance and reactance of line ij; and U0 be the reference voltage. , Let be the active and reactive power transmission capacity of line ij; and Let a(i) be the upper and lower limits of the voltage amplitude of node i; and let a(i) and b(i) be the sets of child nodes and parent nodes of node i.

9. The decision-making method for coordinated resilience recovery of distribution networks in two stages during and after disasters, as described in claim 1, is characterized in that... The steps to establish a disaster-in-disaster load recovery model are as follows: The impact of disaster topology on class B cells is specifically twofold: the DG black start sequence and the cell recovery time. These two impacts are modeled below: The constraints of the DG black start sequence are the same as those in equations (5) and (6), that is, if the switch between two B cells is closed in the disaster, then the DG black start time with the shorter black start time is allowed to perform black start. The impact of B-type cell recovery time is shown in Equations (46) and (47): Equation (46) indicates that if the ordinary switch between two B cells is closed, the recovery time of the cell that is black-started by the DG is still longer than the fault repair time of the other B-type cell; Equation (47) indicates that the B cells that are not black-started by the DG need to wait for the DG to be connected to the grid before the power supply to all loads in the area can be restored. （46） （47） Equations (46)-(47) and Equations (21)-(22) of the post-disaster model together determine the recovery time of the B-type cells after the disaster.

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