Intelligent switch planning method considering pre-disaster-middle-post-disaster multi-stage cooperation and disaster uncertainty

Abstract

The invention discloses an intelligent switch planning method considering pre-disaster-middle-post multi-stage cooperation and disaster uncertainty, relates to the technical field of power grid intelligent switch planning, and is used for solving the problem that the uncertainty of disaster intensity is not considered in existing pre-disaster planning. By coupling available measures of a pre-disaster planning stage, a pre-disaster prevention stage and an in-disaster and post-disaster recovery stage, multi-stage coordination of determining the number of switches in the planning stage, completing switch site selection in the prevention stage and closing the switches to recover loads in the in-disaster and post-disaster stages is realized. In addition, the invention further provides a step-by-step hedging algorithm, the large nonlinear model is decomposed into a plurality of scene-related sub-problems to be solved, and the calculation burden is greatly reduced. A simulation result shows that compared with a pre-disaster-post-disaster two-stage planning model, the model provided by the invention not only can obtain a more flexible planning scheme, but also can reduce investment cost and load outage loss.

Description

Technical Field

[0001] The present invention relates to the technical field of power grid intelligent switch planning, and in particular to an intelligent switch planning method that takes into account multi-stage coordination before, during and after a disaster and disaster uncertainty. Background Art

[0002] In recent years, extreme natural disasters such as typhoons and floods have occurred frequently, and the infrastructure such as the distribution network is weak and easily damaged, causing large-scale power outages. Before the disaster occurs, taking a series of planning measures to configure flexible resources will help reduce the power outage losses after the disaster. In order to improve the flexibility of the distribution network's post-disaster topology adjustment, the power grid company installed smart switches with voltage and current sensors at both ends, which can remotely control the microgrids on both sides of the switch to synchronize and close the switch to form a dynamic microgrid. However, smart switches have not yet been widely used in distribution networks. How to reasonably plan and configure smart switches before a disaster occurs, thereby reducing post-disaster load losses, is an important way to improve the resilience of the distribution network.

[0003] Resilient distribution networks can be divided into three stages to deal with extreme disasters: pre-disaster stage, mid-disaster stage, and post-disaster stage. Among them, the pre-disaster stage can be divided into a long-term planning stage and a short-term prevention stage according to the time from the disaster. In the planning stage, the power grid analyzes the intensity of the disaster suffered by the power grid through historical data and known information, and conducts risk assessment, so as to plan recovery resources in advance, such as line reinforcement and preparation of a certain number of switches. In the prevention stage, after obtaining accurate disaster information through sufficient situational awareness, the planning scheme is further adjusted, such as installing the smart switches prepared in the planning stage in advance to the appropriate location, improving the flexibility of topology adjustment after the disaster occurs, and reducing power outage time. The measures in the pre-disaster planning stage are the basis of the prevention stage, and effective measures in the prevention stage can also improve the utilization rate of resources in the planning stage. In the mid-disaster stage, the performance of the power system drops significantly, and emergency measures such as distributed power generation scheduling and network reconstruction are needed to form microgrids to ensure the power supply of important loads and minimize the scope of power outages; in the post-disaster stage, it is necessary to sort out the fault information through disaster assessment, dispatch maintenance teams to repair faulty components, and use various flexible resources to quickly restore the distribution network to normal power supply. The three stages of pre-disaster, disaster and post-disaster are interrelated and complementary. Formulating plans by fully considering the recovery measures during and after the disaster can lead to the formulation of more complete pre-disaster planning schemes and effectively improve the distribution network's ability to cope with extreme disasters.

[0004] Pre-disaster planning needs to consider two aspects of extreme weather uncertainty: one is the uncertainty of disaster intensity caused by inaccurate disaster prediction information, and the other is the uncertainty of the location and number of faulty equipment caused by the vulnerability of distribution network equipment and environmental factors. At present, the two main methods used in the research on pre-disaster resource planning are robust optimization and stochastic optimization. Existing pre-disaster planning does not take into account the uncertainty of disaster intensity, and the planning decision volume is determined before the failure uncertainty occurs, and cannot be changed with the realization of uncertainty, which will result in a single planning scheme. Summary of the invention

[0005] The purpose of the present invention is to provide an intelligent switch planning method that takes into account multi-stage coordination before, during and after a disaster and disaster uncertainty, so as to solve the problem that the existing pre-disaster planning does not take into account the uncertainty of disaster intensity, and the planning decision quantity is determined before the failure uncertainty occurs and cannot be changed with the realization of uncertainty, resulting in a single planning scheme.

[0006] The technical solution adopted by the present invention to solve the technical problem is: an intelligent switch planning method considering multi-stage coordination before, during and after a disaster and disaster uncertainty, comprising the following steps:

[0007] S1. Construct a multi-stage collaborative model before, during and after a disaster

[0008] A three-stage stochastic planning model is established to determine the number of smart switches in the pre-disaster planning stage, complete the site selection of smart switches in the pre-disaster prevention stage, and close the switches to form an energy supply path in the disaster and post-disaster stages; in the pre-disaster planning stage, the number of smart switches is determined based on multiple scenarios generated based on the uncertainty of disaster intensity and fault scale; in the pre-disaster prevention stage, the site selection of smart switches is decided based on the realization of disaster intensity uncertainty; in the disaster and post-disaster recovery stage, switches are closed to form a load energy supply path based on the realization of fault uncertainty.

[0009] S2. Mathematical Expression of Three-stage Stochastic Programming Model

[0010] S2.1. Pre-disaster planning stage model

[0011] Take formula (1) as the objective function:

[0012]

[0013] In formula (1), is the planning cost of the smart switch, It is the product of the probability of each fault scenario and the sum of its corresponding switch configuration cost and load outage cost. g represents the planning cost of each smart switch; Indicates that the kth switch is determined to be planned as a smart switch in the planning stage; ρ srepresents the probability of scene s appearing; S is the set of scene s; represents the configuration cost of the kth smart switch; Indicates the configuration of the kth switch between cells m and n in scenario s. Its value is 1, indicating that switch k is configured as a smart switch, and its value is 0, indicating that it is configured as a normal switch. p is the penalty fee for power outage per unit load; i is the importance of the load; P i L is the load of node i; is the load recovery time of node i in scenario s.

[0014] The planned number of smart switches satisfies formula (2):

[0015] In formula (2), K ssw,max It is the maximum number of smart switches that can be configured.

[0016] S2.2. Pre-disaster prevention stage model

[0017] Formula (3) indicates that only switches that have been upgraded in the planning stage can be sited and configured in the prevention stage, thus establishing the coupling constraints between the pre-disaster planning stage and the pre-disaster prevention stage. Formula (4) ensures that the number of smart switches configured in the pre-disaster prevention stage is not greater than the number of switches in the planning stage. Formula (5) ensures that if a switch is not configured as a smart switch, it must be an ordinary switch.

[0018]

[0019] 2.3 Disaster Stage Model

[0020] Using 0-1 variables Indicates the opening and closing of the common switch between cells m and n in scene s; uses 0-1 variables Indicates the opening and closing of the intelligent switch between cells m and n in scenario s. The coupling relationship between the switch configuration in the pre-disaster prevention stage and the disaster and post-disaster stages is established through equation (6). If the switch is configured as an intelligent switch before the disaster, the 0-1 variable To indicate the on / off status of the switch; if it is not configured as an intelligent switch, the subsequent To express. A value of 1 indicates that in scenario s, the smart switch between cells m and n is closed, otherwise it is disconnected; A value of 1 indicates that in scenario s, the ordinary switch between cells m and n is closed, otherwise it is open.

[0021]

[0022] 2.4 Post-disaster stage model

[0023] The post-disaster recovery model is divided into maintenance personnel scheduling model, energy supply path model, load recovery time model and safe operation constraints.

[0024] (1) Maintenance personnel scheduling model

[0025] By building a maintenance personnel model, we can obtain the fault repair time under scenario s. On this basis, the network topology is adjusted to restore the load together with the distributed power sources.

[0026] (2) Energy supply path model

[0027] The single-object network flow method is used to model the energy supply path: Formula (7) indicates that the number of closed switches is equal to the total number of cells minus the number of substations; Formula (8) indicates that each cell can be connected to the substation; Formula (9) ensures that in each scenario s, the switch between cells m and n is closed at most once. If the intelligent switch between cells m and n is closed, that is, At this time must be 0; Formula (10) indicates that if there is an ordinary switch between two m and n cells with independent power sources, they cannot be closed to form an energy supply path; Formula (11) indicates that the switch investment cost before the disaster and the power outage loss during the disaster and post-disaster stages are controlled at a certain value, establishing the coupling constraints of pre-disaster planning, pre-disaster prevention, and disaster and post-disaster stages.

[0028]

[0029]

[0030] Where: F mn,s is the virtual power flow of the energy supply path between cells m and n in scenario s; R cb represents the maximum value of the sum of the investment cost and power outage loss in the three stages; M is a constant with a large value, which is used for model linearization; x t n It is a 0-1 variable, indicating whether node n is a root node;

[0031] (3) Load recovery time model

[0032] When the fault in the cell is repaired but the upstream substation is not repaired, for the cell containing the distributed generation, the distributed generation supplies power to the load in the cell, as shown in formula (12):

[0033]

[0034] For cells that do not contain distributed generation, the power supply restoration time is equal to the restoration time of the upstream substation, as shown in formula (13). For cells with internal fault components, the power supply is restored after the fault inside the cell is repaired, as shown in formula (14):

[0035]

[0036] (4) Safety operation constraints

[0037] A linearized distribution network power flow model is adopted, including the following constraints: Equation (15) represents the active power and reactive power balance equation in the line; Equation (16) is the line voltage drop equation; Equation (17) indicates that the active and reactive output of distributed power sources will be constrained by whether the distributed power sources are black started; Equation (18) represents the active and reactive output of the upstream substation; Equation (19) represents the upper and lower limit constraints of the power flow borne by the line; Equation (20) represents the upper and lower limit constraints of the node voltage.

[0038]

[0039] Where: P i,j,s is the active power of line ij in scenario s; Q i,j,s is the reactive power of line ij in scenario s; is the active power of the distributed generation at node i in scenario s; is the reactive power of the distributed generation at node i in scenario s; is the power factor of the load; U i,s is the voltage amplitude of node i in scenario s; is the lower limit of the voltage amplitude at node i; is the upper limit of the voltage amplitude at node i; R ij is the resistance of line ij; X ij is the reactance of line ij; U 0 is the reference voltage; is the non-switching line between nodes i and j in scenario s; is the active transmission capacity of line ij; is the reactive transmission capacity of line ij.

[0040] S3. Solution Algorithm

[0041] The objective function of formula (1) is simplified to the form of formula (21), the constraint condition is simplified to the form of formula (22), and the unexpected constraint is simplified to the form of formula (23):

[0042]

[0043] Where: z 1 It is a variable in the pre-disaster planning stage; are the relevant variables of the pre-disaster prevention stage under scenario s; is a relevant variable in the emergency response and post-disaster recovery stages; u T , and is the coefficient vector of the objective function; d s is the coefficient vector of the constraint conditions; U, V s and W s is the coefficient matrix of the constraints; is the decision variable in the pre-disaster prevention phase under scenario s; is the decision variable in the pre-disaster prevention stage under scenario s′; scenarios s and s′ are different fault scenarios under the same disaster intensity, and both belong to the scenario set S′.

[0044] The model is reconstructed using the step-by-step hedging algorithm, as shown in equations (24) and (25):

[0045]

[0046] Where: and is the μth iteration about and The iterative Lagrange multiplier vector of is shown in formula (26); η is the penalty coefficient; represents the 2-norm; and is the μth iteration of the stepwise hedging algorithm. and Perform weighted average, as shown in equations (27) and (28).

[0047]

[0048] Furthermore, by black starting distributed power sources during disasters to form microgrids, repairing faults after disasters and reconstructing networks, the power supply to loads can be quickly restored.

[0049] Furthermore, the unexpected constraints are used to configure the decision variables of the intelligent switch. Modeling is performed, and the unexpected constraints are as shown in formula (29), which represents the decision variables in the pre-disaster prevention stage It is only related to the realization of disaster intensity in the prevention phase, and has nothing to do with the realization of post-disaster failure uncertainty.

[0050]

[0051] Where: IU s represents the fault scenario s under the disaster intensity IU, IU s'represents the fault scenario s′ under the disaster intensity IU; S′(IU) represents the set of scenarios with the disaster intensity of IU; It indicates the configuration of the intelligent switch under the fault scenario s in the disaster intensity IU.

[0052] Furthermore, the cellular model is used to model the load recovery time. During the disaster stage, the cells without faults and with DG in the area are denoted as N A , the distributed generation recovers the load in the area through black start, as shown in formula (30); formula (31) indicates that the recovery time of the cell without fault and equipped with DG is equal to the DG black start time; formula (32) indicates that the recovery time of the load in the cell is equal to the recovery time of the cell. Considering the existence of controllable load, there may be T c Delayed recovery, T c Delayed recovery time.

[0053]

[0054] Where: K represents the black start variable of DG on node i in scenario s. Its value is 1, indicating that DG performs black start, and its value is 0, indicating that DG does not perform black start. dg Represents the number of DGs with black start capability in the distribution network; N B represents the set of cells with faults and DG in the area, represents the recovery time of cell m in scene s.

[0055] The beneficial effects of the present invention are as follows: the present invention achieves multi-stage coordination of determining the number of switches in the planning stage, completing the switch site selection in the prevention stage, and closing the switches to restore the load in the disaster and post-disaster stages by coupling the available measures in the pre-disaster planning stage, the pre-disaster prevention stage, and the disaster and post-disaster recovery stage. In addition, the present invention also proposes a step-by-step hedging algorithm, which decomposes a large nonlinear model into multiple scenario-related sub-problems for solution, greatly reducing the computational burden. Through simulation, compared with the pre-disaster-post-disaster two-stage planning model, the model proposed in the present invention can not only obtain a more flexible planning scheme, but also reduce investment costs and load power outage losses. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a relationship diagram between the uncertainty information in each stage.

[0057] Figure 2 This is the flow chart for solving the step-by-step hedging algorithm.

[0058] Figure 3 These are the six fault scenarios in the IEEE 33-node example.

[0059] Figure 4This is a comparison chart of planning schemes for different models.

[0060] Figure 5 It is a comparison chart of load loss costs with and without considering the disaster stage.

[0061] Figure 6 The topology diagram of the IEEE 123-node power distribution network. DETAILED DESCRIPTION

[0062] The intelligent switch can control the microgrids on both sides of the switch to close synchronously, increase the flexibility of the distribution network topology, and thus improve the resilience of the distribution network. Therefore, in order to reduce the power outage losses after the disaster, it is necessary to plan the number and location of the intelligent switch configuration before the disaster. To this end, the present invention considers the two types of disaster uncertainties, namely, disaster intensity and fault scale, and coordinates the flexible resources in the pre-disaster planning stage, pre-disaster prevention stage, and disaster and post-disaster recovery stage to establish a three-stage stochastic programming model for intelligent switch configuration. In the pre-disaster planning stage, the realization of the uncertainty of disaster intensity and fault scale is simulated based on multiple scenarios, and the number of intelligent switches is determined by minimizing the investment cost and load loss. In the pre-disaster prevention stage, an intelligent switch site selection model is established based on unexpected constraints to ensure that the intelligent switch site selection decision quantity only depends on the realization of the uncertainty of disaster intensity. In the disaster and post-disaster stages, a fault maintenance model, a load recovery model, and an energy supply path model are established based on distributed power sources to jointly decide the switch closure order, so that after the fault scale is determined, the load is restored by adjusting the network topology and forming a microgrid. In addition, a step-by-step hedging algorithm is proposed to solve the model; finally, the effectiveness of the model is verified based on a simulation example.

[0063] In order to improve the ability of distribution networks to cope with extreme natural disasters, this paper considers the uncertainty of pre-disaster disasters and the recovery measures during and after disasters, and establishes a three-stage stochastic programming model under multi-stage coordination of pre-disaster, mid-disaster and post-disaster. The main contributions are as follows:

[0064] (1) A multi-stage coordinated intelligent switch planning method considering pre-disaster, mid-disaster and post-disaster is proposed. By considering the process of distributed power generation forming microgrids during disasters and fault repair after disasters, a pre-disaster intelligent switch configuration and site selection plan is formulated, thereby reducing pre-disaster investment costs and load power outage losses during and after disasters.

[0065] (2) The uncertainty of two types of disasters, extreme disaster intensity and fault scale, was taken into account. The number of smart switches was determined in the planning stage, the site selection of smart switches was completed in the prevention stage, and the coordination of closing switches to restore loads in the recovery stage was achieved, thus completing the dynamic decision-making.

[0066] A planning model considering two types of disaster uncertainties, disaster intensity and fault scale, is proposed. In the pre-disaster planning stage when there is no uncertainty in disaster intensity, decisions on the number of smart switches are made; in the prevention stage, after the uncertainty in disaster intensity is realized, decisions on the location of smart switches are made; in the disaster and post-disaster recovery stages, after the uncertainty in fault scale is realized, the switch closure sequence is determined to achieve multi-stage dynamic decision-making.

[0067] The following is a description of the intelligent switch planning method of the present invention that takes into account multi-stage coordination before, during and after a disaster and disaster uncertainty:

[0068] S1. Constructing a multi-stage collaborative model framework before, during and after a disaster. The model proposed in this invention takes into account two types of disaster uncertainties: uncertainty in disaster intensity and uncertainty in fault scale. Different stages correspond to the realization of different uncertainties: ① Pre-disaster planning stage, no realization of disaster intensity and fault uncertainty; ② Pre-disaster prevention stage, realization of disaster intensity uncertainty; ③ Disaster and post-disaster recovery stage, the location and quantity information of faulty components are gradually known, and the uncertainty of fault scale is realized.

[0069] like Figure 1 As shown in the figure, it is assumed that there may be two realizations of disaster intensity in the pre-disaster prevention stage, and each disaster intensity corresponds to a disaster event, which are denoted as IU1 and IU2. Different failure scenarios will be generated under each disaster intensity. For example, disaster intensity IU1 will cause two independent failure scenarios, which are denoted as OU1-1 and OU1-2; disaster intensity IU2 will cause two independent failure scenarios, which are denoted as OU2-1 and OU2-2. The complete scenario includes the realization of disaster intensity uncertainty and the realization of failure uncertainty. The four scenarios generated are S1 = {IU1, OU1-1}, S2 = {IU1, OU1-2}, S3 = {IU2, OU2-1} and S4 = {IU2, OU2-2}, where scenarios S1 and S2 are failure scenarios under the same disaster intensity, and scenarios S3 and S4 are failure scenarios under the same disaster intensity.

[0070] In the pre-disaster planning stage, the number of smart switches is determined based on multiple scenarios generated based on the uncertainty of disaster intensity and fault scale. Since there is no uncertainty in the pre-disaster planning stage, the number of smart switches in the pre-disaster planning stage is irrelevant to the uncertainty, and the available number of smart switches is the same in any subsequent stage and scenario.

[0071] In the pre-disaster prevention stage, the site selection of intelligent switches is decided based on the realization of uncertainty in disaster intensity. In the pre-disaster prevention stage, the reserved intelligent switches are configured to appropriate locations so that they can form energy supply paths for loads in post-disaster recovery. In order to ensure that the decision conforms to the temporal logic, it is necessary to satisfy that the decision at the current stage only depends on the realization of current uncertainty, that is, to satisfy the unpredictability of the decision. In this regard, the present invention adds unpredictability constraints in the pre-disaster prevention stage to ensure that the intelligent switch configuration decision in the pre-disaster prevention stage depends only on the intensity of the disaster, and has nothing to do with the realization of post-disaster failure uncertainty.

[0072] In the disaster and post-disaster recovery stages, based on the realization of fault uncertainty, the switch is closed to form a load energy supply path. With the realization of fault uncertainty, the black start of distributed power sources in the disaster to form a microgrid, post-disaster fault repair and network reconstruction and other recovery measures are considered to quickly restore the power supply of the load. Since the uncertain information in the disaster and post-disaster stages is the same, both are the uncertainty of the scale of the fault, therefore, the present invention believes that the disaster and post-disaster stages belong to the recovery stage. In the stochastic programming model, the decision quantities in the disaster and post-disaster stages belong to the decision quantities of the third stage.

[0073] In summary, the present invention considers the two time scale stages of pre-disaster planning and pre-disaster prevention, adopts a multi-scenario method to deal with the uncertainty of disaster intensity and failure, and couples the recovery measures in the disaster and post-disaster recovery stages, and establishes a three-stage stochastic programming model for determining the number of intelligent switches in the pre-disaster planning stage, completing the site selection of intelligent switches in the pre-disaster prevention stage, and closing switches in the disaster and after the disaster to form an energy supply path. The following introduces the proposed model in detail from the pre-disaster planning stage, the pre-disaster prevention stage, the disaster emergency stage, and the post-disaster recovery stage, and then introduces the principle of the step-by-step hedging algorithm. Finally, the effectiveness of the proposed model is verified in the IEEE 33-node and IEEE 123-node distribution systems.

[0074] S2. Mathematical Expression of Three-stage Stochastic Programming Model

[0075] S2.1. Pre-disaster planning stage model

[0076] In the pre-disaster planning stage, the number of smart switches is decided based on the predicted disaster scenarios, so that the switches can be configured to appropriate locations in the pre-disaster prevention stage, and energy supply paths for loads can be formed during and after the disaster to reduce power outage losses.

[0077] In order to reduce the configuration cost of the intelligent switch, reduce the power outage loss of the load and give priority to restoring the important load, equation (1) is used as the objective function.

[0078]

[0079] In formula (1), is the planning cost of the smart switch, It is the product of the probability of each fault scenario and the sum of the corresponding switch configuration cost and load outage cost. Among them, the switch planning cost and configuration cost are both part of the investment cost of the smart switch. In formula (1), C g represents the planning cost of each smart switch; Indicates that the kth switch is determined to be planned as a smart switch in the planning stage; ρ s represents the probability of scene s appearing; S is the set of scenes s; considering that the smart switch is affected by the installation location and environmental factors, the installation cost of each smart switch may be different, so we use It is represented as the configuration cost of the k-th smart switch; Indicates the configuration of the kth switch between cells m and n in scenario s. Its value is 1, indicating that switch k is configured as an intelligent switch, and 0, indicating that it is configured as a normal switch. p is the penalty fee for power outage per unit load; i is the importance of the load; P i L is the load of node i; is the load recovery time of node i under scenario s;

[0080] Considering the high cost of smart switches, the planned number of smart switches cannot exceed the maximum budgeted number, as shown in formula (2).

[0081]

[0082] In formula (2), K ssw,max It is the maximum number of smart switches that can be configured.

[0083] S2.2. Pre-disaster prevention stage model

[0084] In the pre-disaster prevention stage, more accurate information about the intensity of the disaster can be obtained. Therefore, this period can be used to configure the smart switches to the appropriate location to improve the distribution network's ability to resist disasters. In the pre-disaster prevention stage model, formula (3) indicates that only switches that have been upgraded in the planning stage can be sited and configured in the prevention stage. Formula (3) establishes the coupling constraint between the pre-disaster planning stage and the pre-disaster prevention stage; formula (4) ensures that the number of smart switches configured in the pre-disaster prevention stage cannot be greater than the number of switches in the planning stage, and formula (5) ensures that if a switch is not configured as a smart switch, it must be an ordinary switch.

[0085]

[0086] It can be seen that the intelligent switch configuration decision variables is a dynamic variable that changes with different scenarios, but It is not an arbitrary change, it needs to satisfy the unexpectedness, that is, the decision at the current stage only depends on the realization of uncertainty at the current stage. Therefore, the unexpected constraint is used to configure the decision variables of the intelligent switch. is a characteristic of a dynamic variable to be modeled.

[0087] First, assign scenes with the same disaster intensity to the same set. Figure 1 As shown, scenario S1 = {IU1, OU1-1} and scenario S2 = {IU1, OU2-1} are scenarios under the same disaster intensity IU1, so it is defined that these two scenarios belong to S′(IU1). Similarly, scenarios S3 = {IU2, OU2-1} and S4 = {IU2, OU2-2} belong to S′(IU2). Based on this, in the pre-disaster prevention stage, when the disaster intensity is known, the intelligent switch begins to select a site. Since the disaster intensity of the scenarios in the same scenario set is the same, and considering that the decisions made in the pre-disaster prevention stage need to follow the unpredictability, that is, to ensure that the decisions made in the prevention stage only depend on the realization of the disaster intensity, therefore, for scenarios with the same disaster intensity, the intelligent switch configuration scheme in the prevention stage is the same. Figure 1 For example, scenario S1 and scenario S2 belong to the same disaster intensity scenario, so their intelligent switch configuration variables are the same, as shown in formula (6). By generalizing formula (6), we can obtain the applicable unexpected constraints, as shown in formula (7), which represents the decision variables in the pre-disaster prevention stage. It is only related to the realization of disaster intensity in the prevention phase, and has nothing to do with the realization of post-disaster failure uncertainty.

[0088]

[0089] Where: IU s represents the fault scenario s under the disaster intensity IU, IU s' represents the fault scenario s′ under the disaster intensity IU; S′(IU) represents the set of scenarios with the disaster intensity of IU; It indicates the configuration of the intelligent switch under the fault scenario s in the disaster intensity IU.

[0090] 2.3 Disaster Stage Model

[0091] In the disaster stage, the uncertainty of failure gradually becomes a reality, but maintenance personnel cannot be dispatched due to safety issues. Distributed power sources, as an important flexible power source, can form a temporary microgrid through black start in the disaster stage to supply power to important loads.

[0092] Using 0-1 variables Indicates the opening and closing of the common switch between cells m and n in scene s; uses 0-1 variables Indicates the opening and closing of the intelligent switch between cells m and n in scenario s. The coupling relationship between the switch configuration in the pre-disaster prevention stage and the disaster and post-disaster stages is established through equation (8). If the switch is configured as an intelligent switch before the disaster, the 0-1 variable To indicate the open and closed state of the switch, if it is not configured as a smart switch, the subsequent To express. A value of 1 indicates that in scenario s, the smart switch between cells m and n is closed, otherwise it is disconnected. It is the same.

[0093]

[0094] The cell model is used to model the load recovery time. The concept of node cell is: a set of nodes directly connected by non-switching lines. To simplify the analysis, the cells are divided into four categories: A, B, C, and D, according to whether there are distributed power sources DG and fault components inside the cells, as shown in Table 1. At the same time, the substation is regarded as a cell alone:

[0095] Table 1 Cell classification

[0096]

[0097] In the disaster stage, there are cells without faults and with DG in the area, denoted as N A , the distributed generation recovers the load in the area through black start, as shown in formula (9). Formula (10) indicates that the recovery time of the A-type cell is equal to the DG black start time. Formula (11) indicates that the recovery time of the load in the cell is equal to the recovery time of the cell. Considering the existence of controllable load, there may be T c Delayed recovery, T c Delayed recovery time.

[0098]

[0099] Where: K represents the black start variable of DG on node i in scenario s. Its value is 1, indicating that DG performs black start, and its value is 0, indicating that DG does not perform black start. dg Represents the number of DGs with black start capability in the distribution network; N B represents the set of cells with faults and DG in the area, represents the recovery time of cell m in scene s.

[0100] 2.4 Post-disaster stage model

[0101] After partial load restoration through distributed power generation in the disaster stage, the distribution network must be restored to the state before the power outage by repairing the fault. The post-disaster recovery model is divided into four parts: maintenance personnel scheduling model, energy supply path model, load recovery time model and safe operation constraints.

[0102] (1) Maintenance personnel scheduling model

[0103] Dispatching maintenance personnel to repair faulty components is an essential post-disaster recovery measure for distribution networks. By establishing a maintenance personnel model, the fault repair time under scenario s can be obtained. On this basis, the network topology is adjusted to restore the load together with the distributed power sources.

[0104] (2) Energy supply path model

[0105] In order to ensure that the distribution network maintains radial operation during the post-disaster recovery process, it is necessary to constrain the energy supply path. The single-object network flow method is used to model the energy supply path: Formula (12) indicates that the number of closed switches is equal to the total number of cells minus the number of substations; Formula (13) indicates that each cell can be connected to the substation; Formula (14) ensures that in each scenario s, the switch between cells m and n is closed at most once. If the intelligent switch between cells m and n is closed, that is, At this time must be 0; Formula (15) indicates that if there is an ordinary switch between two m and n cells with independent power supplies, they cannot be closed to form an energy supply path; Formula (16) indicates that the switch investment cost before the disaster and the power outage loss during the disaster and post-disaster stages cannot be infinite, and they need to be controlled at a certain value, that is, the coupling constraints of pre-disaster planning, pre-disaster prevention, and disaster and post-disaster stages are established.

[0106]

[0107] Where: F mn,s is the virtual power flow of the energy supply path between cells m and n in scenario s; R cb It represents the maximum value of the sum of investment cost and power outage loss in three stages.

[0108] From the above model, it can be seen that if there is an ordinary switch between two B-type cells m and n, considering that ordinary switches do not have synchronization function, it is impossible to form an energy supply path between two different power supply areas, that is, If we want to form an energy supply path to restore more loads, according to formula (14), It means that in the pre-disaster prevention stage, the switch between cells m and n is configured as an intelligent switch, which corresponds to equation (8). Therefore, the coupling relationship between the post-disaster stage and the pre-disaster prevention stage is established through equations (8) and (14).

[0109] (3) Load recovery time model

[0110] The load recovery model in the post-disaster stage involves the loads in the B-type cells, C-type cells, and D-type cells. Since there are distributed power sources with black start capability in the B-type cells, when the fault in the cell is repaired but the upstream substation is not repaired, the distributed power sources can supply power to the loads in the cell, as shown in formula (17):

[0111]

[0112] There is no distributed power supply inside the C and D cells, and their power supply recovery time is equal to the recovery time of the upstream substation, as shown in formula (18). At the same time, considering that there are faulty components inside the C cell, it is necessary to wait until the fault inside the cell is repaired before the power supply can be restored, as shown in formula (19):

[0113]

[0114] (4) Safety operation constraints

[0115] In order to ensure that the recovery phase in each scenario meets the power flow constraints, a linearized distribution network power flow model is adopted, including the following constraints: Equation (20) represents the active power and reactive power balance equation in the line; Equation (21) is the line voltage drop equation; Equation (22) indicates that the active and reactive output of distributed power sources will be constrained by whether the distributed power sources are black started; Equation (23) represents the active and reactive output of the upstream substation; Equation (24) represents the upper and lower limit constraints of the power flow borne by the line; Equation (25) represents the upper and lower limit constraints of the node voltage.

[0116]

[0117] Where: P i,j,s is the active power of line ij in scenario s; Q i,j,s is the reactive power of line ij in scenario s; is the active power of the distributed generation at node i in scenario s; is the reactive power of the distributed generation at node i in scenario s; is the power factor of the load; U i,s is the voltage amplitude of node i in scenario s; is the lower limit of the voltage amplitude at node i; is the upper limit of the voltage amplitude at node i; R ij is the resistance of line ij; X ij is the reactance of line ij; U 0 is the reference voltage; is the non-switching line between nodes i and j in scenario s; is the active transmission capacity of line ij; is the reactive transmission capacity of line ij.

[0118] S3. Solution Algorithm

[0119] From the above, it can be seen that the three-stage stochastic programming model of the present invention includes the realization of disaster intensity and failure uncertainty, involving a large number of scenarios. It is very difficult to solve the three-stage stochastic programming model on this basis. For this reason, a step-by-step hedging algorithm is proposed. First, in order to explain the principle of the step-by-step hedging algorithm, the planning model is rewritten into a general form; then, the solution steps of the step-by-step hedging algorithm are introduced in detail. The solution flow chart of the step-by-step hedging algorithm is as follows: Figure 2 As shown:

[0120] First, the objective function of formula (1) is simplified to the form of formula (26), the constraint condition is simplified to the form of formula (27), and the unexpected constraint is simplified to the form of formula (28):

[0121]

[0122] Where: z 1 It is a variable in the pre-disaster planning stage; are the relevant variables of the pre-disaster prevention stage under scenario s; is a relevant variable in the emergency response and post-disaster recovery stages; u T , and is the coefficient vector of the objective function; d s is the coefficient vector of the constraint conditions; U, V s and W s is the coefficient matrix of the constraints; is the decision variable in the pre-disaster prevention phase under scenario s; is the decision variable in the pre-disaster prevention stage under scenario s′; scenarios s and s′ are different fault scenarios under the same disaster intensity, and both belong to the scenario set S′.

[0123] From the above model, we can see that the variable z in the pre-disaster planning stage 1 Regardless of the scenario, the variables in the pre-disaster prevention phase Variables in the post-disaster recovery phase The value of is affected by the scenario, and due to the existence of formula (28), the scenarios are coupled with each other, which makes it difficult to solve the problem by directly calling the commercial solver. Therefore, the above model needs to be decoupled. To this end, the step-by-step hedging algorithm is used to reconstruct the above model, such as formula (29) and formula (30), which becomes an optimization problem in the augmented Lagrangian form. In this way, the originally coupled multi-scenario problem is decomposed into multiple scenario-related sub-problems for solution, which improves the solution efficiency.

[0124]

[0125] Where: and is the μth iteration about and The iterative Lagrange multiplier vector of is shown in formula (31); η is the penalty coefficient; represents the 2-norm; and is the μth iteration of the stepwise hedging algorithm. and Perform weighted average as shown in equations (32) and (33).

[0126]

[0127] It can be seen from equations (29) and (30) that the step-by-step hedging algorithm can transform the model with mutual coupling between scenarios into multiple scenario-related sub-models. Solving these sub-models in parallel can improve the computational efficiency.

[0128] S4. Example Analysis

[0129] (1) Case analysis of IEEE 33-bus distribution system

[0130] Figure 3 These are the six disaster scenarios of the tested IEEE 33-node distribution system, including 1 substation, 1 fixed distributed power source, 2 mobile distributed power sources and 7 switches to be configured, with a total load of 3490kW, of which the important loads have been marked. The locations of mobile distributed power sources are different due to the different fault intensities in the pre-disaster prevention stage. For example, scenarios S1-S3 are fault scenarios under disaster intensity 1, and the mobile distributed power sources are located at nodes 5 and 30; scenarios S4-S6 are fault scenarios under disaster intensity 2, and the mobile distributed power sources are located at nodes 11 and 15. Assume that the planned number of smart switches is up to 3, and the unit load power outage penalty fee is 10￥ / min.

[0131] Consider two disaster intensities IU1 and IU2, and consider three fault scenarios under each disaster intensity, so there are six disaster scenarios in total. The probabilities of the six disaster scenarios are 0.133, 0.133, 0.133, 0.2, 0.2, and 0.2 respectively. The fault location and maintenance time under each scenario are shown in Table 2.

[0132] Table 2 Fault location and repair time in different scenarios

[0133]

[0134] In the above scenario, the three-stage stochastic programming model proposed in the present invention is solved, and the switch configuration in the pre-disaster prevention stage under different scenarios is obtained as shown in Table 3. It can be seen from Table 3 that the number of intelligent switches prepared in the pre-disaster planning stage is two. In the pre-disaster prevention stage, the intelligent switches are configured to appropriate positions according to the realization of disaster intensity. At the same time, based on unexpected constraints, the decision variables in the pre-disaster prevention stage of scenarios with the same disaster intensity are the same. For example, in the S1, S2, and S3 scenarios under the same disaster intensity, the intelligent switches are configured at 1-2 and 6-7; in the S4, S5, and S6 scenarios under the same disaster intensity, the intelligent switches are configured at 1-2 and 6-7.

[0135] Table 3 Location and closure of smart switches in different scenarios

[0136]

[0137] After the switch configuration is completed in the pre-disaster prevention stage, with the realization of fault uncertainty, the location of the faulty component, the number of faulty components and the fault repair time, it is necessary to form a load energy supply path by closing the switch, and combine the distributed power supply black start to form a microgrid and restore the load by fault repair. For example, in scenario S1, line 4-5, line 31-32, line 11-12 and line 16-17 are faulty. The load energy supply path is formed by closing switches 1-2, 6-7, 18-33, 9-10 and 13-14, and partial load is quickly restored in combination with distributed power supply. The intelligent switch locations in the pre-disaster prevention stage under scenarios S1, S2 and S3 are the same, but due to different fault locations and fault repair times, the switch decisions in the disaster and post-disaster stages are not exactly the same. Taking scenarios S1 and S2 as examples, the prevention stage decisions of these two scenarios are the same, but the energy supply paths formed during the recovery process are different. In scenario S1, switches 13-14 are closed, while switches 8-14 are closed in scenario S2.

[0138] Table 4 shows the traditional two-stage planning model, which only considers the configuration of smart switches in the pre-disaster planning stage and the post-disaster recovery stage. As can be seen from Table 4, the smart switch configuration schemes in the six scenarios in the two-stage planning model are the same, and three smart switches are planned and configured. This is because Scheme 1 comprehensively considers all fault scenarios S1-S6 decisions, and does not consider the realization of disaster intensity in the prevention stage.

[0139] Table 4 Switch configuration in the two-stage planning model

[0140]

[0141] In comparison, the intelligent switch planning scheme of the model of the present invention is adjusted as the disaster intensity information is learned in the pre-disaster prevention stage, and can select the corresponding switch configuration scheme according to the realization of the disaster intensity, and then decide the switch opening and closing state according to the realization of fault uncertainty in the disaster and post-disaster stages. In the traditional two-stage random planning model, a relatively fixed planning scheme is obtained, while the model proposed in the present invention takes into account the implementation process of the planning scheme and obtains a dynamic planning scheme, such as Figure 4 It can be seen that the model proposed by the present invention can obtain more diverse and flexible switch configuration solutions.

[0142] As the disaster progresses, the uncertainty of the failure scale is realized during the disaster and post-disaster recovery phases, i.e. Figure 3 The fault scenario shown in Figure 1. Although the disaster has not yet completely ended during the emergency phase, its intensity has been greatly reduced. The distribution network can take measures to respond urgently and restore some loads. Figure 5 It can be seen that in scenario 3, the recovery plan considering the mid-disaster stage can reduce the power outage loss by 7.3%. Since all cells containing distributed power sources in scenario 4 are faulty and cannot be recovered during the disaster, other scenarios can also use the recovery during the disaster stage to reduce power outage losses to varying degrees. It can be seen that when formulating a recovery plan, the mid-disaster stage is also an important stage that cannot be ignored.

[0143] When the disaster is completely over and the maintenance personnel repair the faulty components, the cells with distributed power sources can resume power supply. For cells without distributed power sources, they can only be powered by surrounding distributed power sources or wait for the substation to be restored. Taking cell 3 as an example, after the fault was repaired, the power supply was restored at t = 60min, which is much earlier than the recovery time of cell 5 without distributed power sources. Therefore, considering the black start of distributed power sources in the recovery process during and after the disaster can shorten the power outage time of the load and restore power supply faster.

[0144] (2) Example Analysis of IEEE123 Node Distribution System

[0145] To further verify the effectiveness of the proposed model, it is applied to the IEEE 123-node power distribution system for simulation. Figure 6 As shown in Figure 4, the system includes 1 substation and 6 distributed power sources. The distributed power sources include 2 fixed distributed power sources and 4 mobile distributed power sources. Considering 9 fault scenarios under 3 disaster intensities, the probabilities of the 9 scenarios are 0.0666, 0.0666, 0.0666, 0.1666, 0.1666, 0.1666, 0.1, 0.1, and 0.1, respectively. The fault location and maintenance time under each fault scenario are shown in Table 4-Table 6. It is assumed that the planned number of smart switches is at most 5, and the unit load power outage penalty fee is 10￥ / min.

[0146] To further verify the effectiveness of the model proposed in the present invention, the three-stage random programming model is compared with the two-stage random programming model that only considers the pre-disaster planning stage and the post-disaster recovery stage, and the model that does not consider the planning stage. Table 5 shows the number of intelligent switches planned in the model proposed in the present invention and the two-stage planning model, as well as the location of intelligent switches in each scenario. Table 6 shows the comparison of the planning cost and load power outage loss of the model proposed in the present invention, the two-stage planning model and the model that does not consider the planning stage. Among them, the load that has not restored power supply in the two-stage model and the model that does not consider the planning stage, theoretically, the power restoration time is infinite. In order to easily calculate the power outage loss, the restoration time is uniformly set to 300min. It can be seen from Table 5 that with the model of the present invention, only 4 intelligent switches need to be prepared in the planning stage, and in scenarios S1-S3 and S4-S6, only three of them need to be sited and configured. In the two-stage model, 5 intelligent switches need to be prepared in the planning stage, and all 5 intelligent switches need to be sited and configured. It can be seen that the model proposed in the present invention can reduce the number of planned switches and the number of configurations by utilizing the information in the pre-disaster prevention stage.

[0147] Table 5 Comparison of smart switch planning

[0148]

[0149] It can be seen from Table 6 that although not considering the pre-disaster switch planning can save investment costs, the load loss is very high, with the maximum increase of 73% in load loss, which means the importance of upgrading the switch to an intelligent switch in the pre-disaster stage. Compared with the two-stage random programming model, the model proposed in the present invention not only reduces the cost of pre-disaster planning and configuration of intelligent switches, but also can reduce the power outage loss of post-disaster loads and reduce the objective function value of 43689￥. It can be seen that the present invention can effectively reduce the switch investment cost and power outage loss. It can be seen that the three-stage random programming model proposed in the present invention, which considers the pre-disaster, mid-post-disaster multi-stage coordination and disaster uncertainty, has obvious advantages in reducing investment costs and load losses.

[0150] Table 6 Comparison of costs and power outage losses of different models

[0151]

[0152] Due to the limitation of computational effort, the failure scenarios considered in the proposed model are limited, and there are inevitably some scenarios that are not considered. Although these scenarios are not taken into account when making planning decisions, when these scenarios actually occur, the disaster-post-disaster collaborative recovery model can be used to deal with them.

[0153] In summary, by considering the planning of the number of smart switches in the pre-disaster planning stage, the decision-making of smart switch sites in the pre-disaster prevention stage, and the coordination of closing switches to restore loads during and after the disaster, a more flexible switch configuration plan can be obtained, which can greatly reduce investment costs, reduce load power outage time, and improve the resilience of the distribution network.

[0154] In order to improve the resilience of the distribution network, the present invention proposes an intelligent switch planning method that considers multi-stage coordination before, during and after disasters and disaster uncertainty. By coupling the available measures in the pre-disaster planning stage, the pre-disaster prevention stage, and the mid-disaster and post-disaster recovery stages, multi-stage coordination is achieved, including determining the number of switches in the planning stage, completing the switch site selection in the prevention stage, and closing the switches to restore the load in the mid-disaster and post-disaster stages. In addition, the present invention also proposes a step-by-step hedging algorithm that decomposes large nonlinear models into multiple scenario-related sub-problems for solution, greatly reducing the computational burden. Simulation results show that compared with the two-stage planning model before and after disasters, the model proposed in the present invention can not only obtain a more flexible planning scheme, but also reduce investment costs and load power outage losses.

Claims

1. An intelligent switch planning method considering multi-stage coordination before, during and after a disaster and disaster uncertainty, characterized by: The following steps are involved: S1. Construct a multi-stage collaborative model before, during and after a disaster A three-stage stochastic planning model is established to determine the number of smart switches in the pre-disaster planning stage, complete the site selection of smart switches in the pre-disaster prevention stage, and close the switches to form the energy supply path during and after the disaster. In the pre-disaster planning stage, the number of smart switches is determined based on multiple scenarios generated based on the uncertainty of disaster intensity and fault scale. In the pre-disaster prevention stage, the site selection of smart switches is decided based on the realization of uncertainty of disaster intensity. During the disaster and post-disaster recovery phases, based on the realization of fault uncertainty, switches are closed to form load energy supply paths; S2. Mathematical Expression of Three-stage Stochastic Programming Model S2.

1. Pre-disaster planning stage model Take formula (1) as the objective function: In formula (1), is the planning cost of the smart switch, is the product of the probability of each fault scenario and the sum of its corresponding switch configuration cost and load outage cost; where C g represents the planning cost of each smart switch; Indicates that the kth switch is determined to be planned as a smart switch in the planning stage; ρ s represents the probability of scene s appearing; S is the set of scene s; represents the configuration cost of the kth smart switch; Indicates the configuration of the kth switch between cells m and n in scenario s. Its value is 1, indicating that switch k is configured as a smart switch, and its value is 0, indicating that it is configured as a normal switch. p is the penalty fee for power outage per unit load; i is the importance of the load; P i L is the load of node i; is the load recovery time of node i under scenario s; The planned number of smart switches satisfies formula (2): In formula (2), K ssw,max The maximum number of smart switches allowed to be planned; S2.

2. Pre-disaster prevention stage model Formula (3) indicates that only switches upgraded in the planning stage can be sited and configured in the prevention stage, thus establishing the coupling constraint between the pre-disaster planning stage and the pre-disaster prevention stage. Formula (4) ensures that the number of smart switches configured in the pre-disaster prevention stage is not greater than the number of switches in the planning stage. Formula (5) ensures that if a switch is not configured as a smart switch, it must be an ordinary switch. 2.3 Disaster Stage Model Using 0-1 variables Indicates the opening and closing of the common switch between cells m and n in scene s; uses 0-1 variables represents the opening and closing of the intelligent switch between cells m and n in scenario s; the coupling relationship between the switch configuration in the pre-disaster prevention stage and the disaster and post-disaster stages is established through formula (6); if the switch is configured as an intelligent switch before the disaster, the 0-1 variable is used in the subsequent recovery process To indicate the on / off status of the switch; if it is not configured as an intelligent switch, the subsequent To express; A value of 1 indicates that in scenario s, the smart switch between cells m and n is closed, otherwise it is disconnected; A value of 1 indicates that in scenario s, the ordinary switch between cells m and n is closed, otherwise it is open; 2.4 Post-disaster stage model The post-disaster recovery model is divided into maintenance personnel scheduling model, energy supply path model, load recovery time model and safe operation constraints; (1) Maintenance personnel scheduling model By building a maintenance personnel model, we can obtain the fault repair time under scenario s. And on this basis, adjust the network topology and restore the load together with the distributed power generation; (2) Energy supply path model The single-object network flow method is used to model the energy supply path: Formula (7) indicates that the number of closed switches is equal to the total number of cells minus the number of substations; Formula (8) indicates that each cell can be connected to the substation; Formula (9) ensures that in each scenario s, the switch between cells m and n is closed at most once. If the intelligent switch between cells m and n is closed, that is, At this time must be 0; Formula (10) indicates that if there is an ordinary switch between two m and n cells with independent power sources, they cannot be closed to form an energy supply path; Formula (11) indicates that the switch investment cost before the disaster and the power outage loss during the disaster and post-disaster stages are controlled at a certain value, and the coupling constraints of pre-disaster planning, pre-disaster prevention, and disaster and post-disaster stages are established; Where: F mn,s is the virtual power flow of the energy supply path between cells m and n in scenario s; R cb represents the maximum value of the sum of the investment cost and power outage loss in the three stages; M is a constant with a large value, which is used for model linearization; x t n It is a 0-1 variable, indicating whether node n is a root node; (3) Load recovery time model When the fault in the cell is repaired but the upstream substation is not repaired, for the cell containing the distributed generation, the distributed generation supplies power to the load in the cell, as shown in formula (12): For cells that do not contain distributed generation, the power supply restoration time is equal to the restoration time of the upstream substation, as shown in formula (13); for cells with internal fault components, the power supply is restored after the fault inside the cell is repaired, as shown in formula (14): (4) Safety operation constraints The linearized distribution network flow model is adopted, including the following constraints: Equation (15) represents the active power and reactive power balance equation in the line; Equation (16) is the line voltage drop equation; Equation (17) represents that the active and reactive output of distributed power sources will be constrained by whether the distributed power sources are black started; Equation (18) represents the active and reactive output of the upstream substation; Equation (19) represents the upper and lower limit constraints of the flow borne by the line; Equation (20) represents the upper and lower limit constraints of the voltage of the node; Where: P i,j,s is the active power of line ij in scenario s; Q i,j,s is the reactive power of line ij in scenario s; is the active power of the distributed generation at node i in scenario s; is the reactive power of the distributed generation at node i in scenario s; is the power factor of the load; U i,s is the voltage amplitude of node i in scenario s; is the lower limit of the voltage amplitude at node i; is the upper limit of the voltage amplitude at node i; R ij is the resistance of line ij; X ij is the reactance of line ij; U0 is the reference voltage; is the non-switching line between nodes i and j in scenario s; is the active transmission capacity of line ij; is the reactive transmission capacity of line ij; S3. Solution Algorithm The objective function of formula (1) is simplified to the form of formula (21), the constraint condition is simplified to the form of formula (22), and the unexpected constraint is simplified to the form of formula (23): Where: z 1 It is a variable in the pre-disaster planning stage; are the relevant variables of the pre-disaster prevention stage under scenario s; is a relevant variable in the emergency response and post-disaster recovery stages; u T , and is the coefficient vector of the objective function; d s is the coefficient vector of the constraint conditions; U, V s and W s is the coefficient matrix of the constraints; is the decision variable in the pre-disaster prevention phase under scenario s; is the decision variable in the pre-disaster prevention stage under scenario s′; scenarios s and s′ are different fault scenarios under the same disaster intensity, both belonging to the scenario set S′; The model is reconstructed using the step-by-step hedging algorithm, as shown in equations (24) and (25): Where: and is the μth iteration about and The iterative Lagrange multiplier vector of is shown in formula (26); η is the penalty coefficient; represents the 2-norm; and is the μth iteration of the stepwise hedging algorithm. and Perform weighted average, as shown in equation (27) and equation (28); 2. The intelligent switch planning method considering multi-stage coordination before, during and after a disaster and disaster uncertainty according to claim 1 is characterized in that: By black-starting distributed power sources during disasters to form microgrids, repairing faults after disasters and taking network reconstruction and recovery measures, the power supply to loads can be quickly restored.

3. The intelligent switch planning method considering multi-stage coordination before, during and after a disaster and disaster uncertainty according to claim 2 is characterized in that: Using unexpected constraints to configure decision variables for smart switches Modeling is performed, and the unexpected constraints are as shown in formula (29), which represents the decision variables in the pre-disaster prevention stage It is only related to the realization of disaster intensity in the prevention phase, and has nothing to do with the realization of post-disaster failure uncertainty; Where: IU s represents the fault scenario s under the disaster intensity IU, IU s' represents the fault scenario s′ under the disaster intensity IU; S′(IU) represents the set of scenarios where the disaster intensity is IU; It indicates the configuration of the intelligent switch under the fault scenario s in the disaster intensity IU.

4. The intelligent switch planning method considering multi-stage coordination before, during and after a disaster and disaster uncertainty according to claim 3 is characterized in that: The cellular model is used to model the load recovery time. During the disaster stage, the cells without faults and with DG in the area are denoted as N A , the distributed generation recovers the load in the area through black start, as shown in formula (30); formula (31) indicates that the recovery time of the cell without fault and equipped with DG is equal to the DG black start time; formula (32) indicates that the recovery time of the load in the cell is equal to the recovery time of the cell. Considering the existence of controllable load, there may be T c Delayed recovery, T c To delay the recovery time; Where: K represents the black start variable of DG on node i in scenario s. Its value is 1, indicating that DG performs black start, and its value is 0, indicating that DG does not perform black start. dg Represents the number of DGs with black start capability in the distribution network; N B represents the set of cells with faults and DG in the area, represents the recovery time of cell m in scene s.

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