Method for improving toughness of power distribution network based on active and reactive collaborative optimization under extreme disasters

Abstract

The invention discloses a power distribution network toughness improving method for active and reactive collaborative optimization under extreme disasters, and relates to the technical field of power system optimization scheduling. The method specifically comprises the following steps: firstly, in a first stage, predicting renewable energy power generation and load requirements in a next time window, and optimizing a remote control switch, a capacitor bank and an energy storage charging / discharging control strategy on a long-time scale; then, in the second stage, according to the latest accurate prediction information and the decision of the first stage, the output of the distributed resources and the static reactive power compensator is optimized on a short time scale so as to compensate for the deviation caused by the uncertainty in the decision of the first stage; and finally, as time goes on, the prediction time window continuously rolls forwards, and cooperative optimization is carried out on the active and reactive equipment through cooperation of the two stages, so that the decision is always based on the latest prediction information. According to the invention, a two-stage active power distribution network scheduling strategy considering the equipment response capability difference is provided, and the recovery capability and toughness of the power distribution system are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of power system optimal dispatch, and specifically to a method for improving the resilience of a distribution network with coordinated active and reactive power optimization under extreme disasters. Background Technique

[0002] In recent years, large-scale and long-duration power outages caused by high-impact and low-probability extreme events have occurred repeatedly, threatening personal and people's property safety. Compared with the transmission network, the active distribution network has a lower safety protection standard in planning and design, is more vulnerable to extreme disasters, and the active distribution network has become an important part of building a new power system. Therefore, it is of great practical significance to study the strategy for improving the resilience of the active distribution network.

[0003] Extreme events may lead to distribution network failures and interruptions of the upper-level power supply. In this case, by isolating the fault area to form a self-sufficient island microgrid and optimizing the dispatch of distributed energy resources (DER) therein, the power outage scope can be minimized, the power outage time can be shortened, and critical loads can be restored preferentially, thereby effectively improving the resilience of the system. The literature (Peng Hanmei, Liu Ziwei, Tan Mao, etc. A collaborative method for active distribution network reconfiguration and component repair for resilience improvement [J]. Power System Protection and Control, 2022, 50(17): 35-44.) proposed a collaborative strategy for island division and fault component repair for resilience improvement. With the gradual repair of the fault components, the dynamic division of the island microgrid can improve the restoration effect. The literature (Pang Kaiyuan, Wang Chongyu, Wen Fushuan, etc. Flexible island division and real-time dispatch strategy for active distribution network [J]. Automation of Electric Power Systems, 2022, 46(22): 13-24.) further proposed a real-time dispatch strategy for island division of the active distribution network and constructed a rolling optimization model for the real-time operation of the island.

[0004] Existing island restoration methods focus on achieving load restoration by dispatching DERs within the microgrid, while neglecting the scheduling optimization of reactive power compensators (RPCs) during the restoration process. In the distribution network, due to a higher R / X ratio compared to the transmission network, ignoring the reactive power distribution may exacerbate the node voltage drop, thus violating the voltage constraint and leading to additional load shedding. Therefore, to further enhance the restoration ability of the islanded microgrid and ensure operational safety, active-reactive coordinated optimization is required during the restoration process. The literature (Kou Lingfeng, Wu Ming, Li Yang, et al. Active distribution network distributed active and reactive optimization control method [J]. Proceedings of the CSEE, 2020, 40(06): 1856-1865.) established an active-reactive coordinated optimization model to coordinately control DERs, RPCs, energy storage, and on-load tap-changing transformers, etc., and optimize the operation of the active distribution network. The literature (Lin W, Zhu J, Yuan Y, et al. Robust optimization for island partition of distribution system considering load forecasting error [J]. IEEE Access, 2019, 7: 64247–64255.) adjusts the output of distributed generation and static var compensators simultaneously during post-disaster restoration and combines it with the islanded microgrid partition to reduce the load shedding cost. However, existing studies do not consider the differences in the response speeds of devices during the coordinated optimization process. For example, remote control switches and capacitor banks are mechanical devices with relatively slow response speeds and are difficult to adjust quickly in the face of power fluctuations.

[0005] Aiming at the deficiencies of existing studies, the present invention proposes a two-stage resilience improvement strategy for the distribution network with coordinated scheduling of active and reactive devices during the post-disaster restoration stage. This restoration strategy takes into account the dynamic partitioning of the islanded microgrid during the repair process of the faulty line, the differences in the response speeds of different devices, and the uncertainties of renewable energy generation output and load demand. Its main goal is to quickly restore the critical loads of the active distribution network through the coordinated action of the source-network-load-storage after an extreme disaster event. By rolling the solution within the set prediction time window, not only can the solution efficiency be improved, but also the adverse impact of prediction errors on the optimization decision can be reduced by using the information of the latest prediction time window. Summary of the Invention

[0006] In order to coordinately dispatch active and reactive devices with different response speeds and quickly restore the critical loads of the active distribution network after an extreme disaster, the present invention proposes a method for improving the resilience of the distribution network with active-reactive coordinated optimization under extreme disasters considering uncertainties.

[0007] The present invention is implemented through the following technical scheme: a method for improving the resilience of distribution networks by collaboratively optimizing active and reactive power under extreme disasters. First, the output of wind turbines and the load demand interval are predicted within a set prediction window, and the number of switching groups of capacitor groups, the working state of remote control switches, and the charging and discharging state of energy storage are solved in the first stage robust optimization model on a long time scale (set as 1 hour in the present invention), and only the optimization decision of the previous hour is executed. Then, based on the latest prediction information and the decision results of the first stage, the optimization is performed in the second stage period, and the output control strategy of gas turbines, energy storage, wind turbines, and static VAR compensators is obtained on a short time scale. Due to the immediacy of the prediction, the prediction data at the next moment is quite accurate and can be considered as a precise point prediction, so the second stage is a deterministic optimization. This stage aims to compensate for the errors that may be caused by the uncertainty interval in the first stage decision. Finally, with the passage of time and the advancement of post-disaster repair work, the damaged lines will be gradually repaired, and the prediction window will continue to roll forward to ensure that the decision is always based on the latest prediction information. The specific scheme includes the following steps:

[0008] Phase 1: In the first phase, a long-time scale robust optimization model is established, as follows:

[0009] The uncertainty interval is used to characterize the fluctuation range of wind turbine output and load demand in the next prediction window. A three-layer robust optimization model is established with the goal of minimizing weighted load shedding, including power flow constraints, radial topology constraints, gas turbine constraints, wind turbine constraints, energy storage constraints, capacitor group constraints, static VAR compensator constraints and load constraints. The model decides the number of capacitor groups switched on and off, the working state of the remote control switch and the charging and discharging state of the energy storage on a long time scale.

[0010] S1: Objective function:

[0011] For the post-disaster recovery phase of the resilient distribution network, the primary goal is to minimize the amount of load shedding. To ensure the continuous power supply of important loads, this model also considers the weight level of the load. It should be noted that the voltage limit caused by reactive power shortage will also be reflected in the load abandonment. In view of the uncertainty of load demand and wind turbine output, in order to ensure that the scheduling decision is applicable to all possible scenarios, the proposed first-stage uncertainty optimization problem can be expressed as a three-layer robust optimization model, striving to minimize the total load shedding in the worst scenario within the prediction time window. The objective function is as follows:

[0012]

[0013] Where: X is a decision vector composed of the states of remote control switches in the line, the charge and discharge states of energy storage, the switching groups of capacitor banks, and their output reactive power; Y is the output variable of continuously adjustable equipment; R and L are the sets of uncertainties of wind turbine output and load demand respectively; N is the set of all nodes, and T is the prediction time window. Y ∈ Ω(X, r, l) represents the feasible region of Y given a set of (X, r, l). ω j is the node load weight, and is the load shedding amount at node j in period t.

[0014] S2: Constraint conditions, including power flow constraints, radial topology constraints, gas turbine constraints, wind turbine constraints, energy storage constraints, capacitor bank constraints, static var compensator constraints, and load constraints, are as follows:

[0015] S2-1: Power flow constraints

[0016] When a large number of discrete variables are involved, the complexity of power flow calculation will increase significantly. Therefore, the present invention introduces a linearized Dist-Flow power flow model applicable to radial network topologies to improve the calculation efficiency. And a state variable c representing the line break is introduced into the model ij , and it is relaxed by the big M method, so that the model can be applicable to complex distribution networks with variable topologies. The linearized Dist-Flow power flow model is as follows:

[0017]

[0018] U j min ≤U j,t ≤U j max , j ∈ N\N G (5)

[0019] U j,t =U 0 , j ∈ N G (6)

[0020] Where: φ(j) and δ(j) represent the sets of the parent node and child node of node j respectively, P ij,t represents the active power flowing from node i to node j in period t, Q ij,t represents the reactive power flowing from node i to node j in period t, P js,t represents the active power flowing from node j to node s in period t, Q js,t represents the reactive power flowing from node j to node s in period t, N G is the set of gas turbines, ε is the set of lines, and respectively represent the active power output and predicted active load of the nodal gas turbine, energy storage, and wind turbine at node j during period t, and respectively represent the reactive power output and predicted reactive load of the nodal gas turbine, wind turbine, capacitor bank, and static var compensator at node j during period t, U 0 is the reference node voltage (in this invention, the node where the gas turbine is located is set as the reference node), U i,t represents the voltage of node i during period t, U j,t represents the voltage of node j during period t, U j min and U j max respectively represent the minimum and maximum voltage values of node j, c ij,t represents the open - circuit state of line ij during period t, M represents a very large constant, r ij and x ij are the resistance and reactance of line ij, where Equation (4) is the branch capacity constraint and Equation (5) is the node voltage upper and lower limit constraint.

[0021] S2 - 2: Radial Topology Constraint

[0022] During the restoration process, the distribution network should always maintain its radial topology. To meet the radial topology, it is necessary to simultaneously satisfy sub - graph connectivity and the relationship between the number of nodes and edges, which can be expressed as the following constraints:

[0023]

[0024]

[0025] W j ≥1, j ∈ N G (10)

[0026] ∑ ij∈ε c ij =|N| - |N G | (11)

[0027] In the formula: F ij represents the virtual power flow on line ij in the virtual network, F js represents the virtual power flow on line js in the virtual network, the load of each virtual node is 1, and W j is the power generated by the source node in the virtual network.

[0028] S2 - 3: Gas Turbine Constraint

[0029]

[0030] In the formula: Equations (12) - (14) are the output constraints of the gas turbine. and are the minimum and maximum active power outputs of the gas turbine at node j, respectively. and are the minimum and maximum reactive power outputs of the gas turbine at node j, respectively. is the rated capacity of the gas turbine at node j.

[0031] S2-4: Wind Turbine Constraints

[0032]

[0033] In the formula: Equations (15)-(16) are the output constraints of the wind turbine, r j,t is the predicted output of the wind turbine at node j at time period t, is the rated capacity of the wind turbine at node j.

[0034] S2-5: Energy Storage Constraints

[0035]

[0036]

[0037] In the formula: Equations (17)-(20) are the charge and discharge power constraints of the energy storage, and Equation (21) defines the remaining capacity constraints of the energy storage device at each time period during the scheduling, preventing overcharging and over-discharging of the energy storage and prolonging the life of the energy storage. and represent the discharge and charge states of the energy storage at node j at time period t, respectively. When or has a value of 1, it means that the energy storage is discharging or charging. is the maximum charge and discharge power of the energy storage at node j. and are the discharge and charge powers of the energy storage at node j at time period t, respectively. and are the minimum and maximum capacities (kW / h) allowed during the operation of the energy storage at node j. E s (0) is the initial capacity of the energy storage, and α is the charge and discharge efficiency of the energy storage.

[0038] S2-6: Capacitor Bank Constraints

[0039]

[0040] In the formula: Equations (22)-(23) constrain the number of switching groups of the capacitor bank. Considering the short prediction time window, the number of switching times of the capacitor bank within a cycle is not restricted. is the number of switching groups of the capacitor bank connected to node j at time period t, which is an integer variable. The reactive power switched in a capacitor bank connected to node j The maximum number of switched-in capacitor banks connected to node j

[0041] S2-7: Static var compensator constraint

[0042] In the process of optimizing the dispatch of the distribution network, to facilitate calculation and improve the operability of the model, the model of the static var compensator is usually simplified. The simplified static var compensator model can be expressed as follows:

[0043]

[0044] Where: and are the upper and lower limits of the reactive power output by the static var compensator connected to node j, respectively.

[0045] S2-8: Load constraint

[0046] In view of the development trend of the active distribution network, the present invention regards the load as a flexible load, which can perform load shedding operations according to the agreement with users in the event of extreme events. Therefore, the present invention sets the following load constraints:

[0047]

[0048] Where: l j,t is the predicted load demand at node j in period t; μ is the proportional coefficient of active load to reactive load.

[0049] S3: Uncertainty sets of wind turbine output and load demand

[0050] With the increasing penetration of renewable energy in the distribution network, the randomness of its power generation cannot be ignored in the optimal dispatch of the islanded microgrid. At the same time, the uncertainty of load forecasting also needs to be fully considered in the model. Therefore, the present invention considers the uncertainty of wind turbine output and load demand and describes them as the following polyhedral uncertainty sets:

[0051]

[0052] Where: and represent the predicted output, upper deviation limit and lower deviation limit of the wind turbine at node j at time t, respectively, and represent the predicted demand, upper deviation limit and lower deviation limit of the load at node j at time t; by introducing variables and to control the output of the wind turbine at node j at time t within the interval Inside; introduce variables and to control the demand of the load at node j at time t within the interval Inside, Π w and Π l are the uncertainty adjustment parameters of the wind turbine and the load respectively.

[0053] Stage 2: Establishment of a short - time - scale optimization model during the second - stage time period:

[0054] Solve the first - stage model to obtain the switching times of the capacitor bank within the time window The working state c of the remotely controlled switch ij and the charge - discharge state of the energy storage and the control strategy, and execute the strategy of the previous hour, then enter the second stage. In this stage, according to the latest predicted renewable energy generation and load demand, the output of the gas turbine, wind turbine, energy storage, and static var compensator is optimized and scheduled on a short - time scale. Due to the immediacy of the prediction, the predicted renewable energy generation and load demand for the next moment can be regarded as highly accurate point predictions. Therefore, the constructed second - stage model is a deterministic model. The following is the mathematical formulation of the second - stage model:

[0055]

[0056] The present invention proposes a two - stage rolling optimization framework, as Figure 1 shown, and the specific process is as follows:

[0057] First, the present invention predicts the output of the wind turbine and the load demand interval within the set prediction time window, uses the column - and - constraint generation algorithm to solve S1, obtains the control strategies of the remotely controlled switch, capacitor bank, and energy storage, and only executes the optimization decisions of the previous hour. Then, based on the latest prediction information and the first - stage decision results, optimize within the S2 time period to obtain the output control strategies of the gas turbine, energy storage, wind turbine, and static var compensator. As time goes by, the prediction time window rolls forward continuously to ensure that the decision is always based on the latest prediction information. The specific process is as Figure 2 shown.

[0058] When solving the robust optimization model, due to the advantages of the column - and - constraint generation algorithm in terms of optimality and efficiency, it is widely used in solving the robust optimization model. The present invention uses the column - and - constraint generation algorithm, decomposes the original two - stage robust optimization problem into a master problem and a sub - problem, and solves them alternately to obtain the control strategies of the remotely controlled switch, capacitor bank, and energy storage under the worst - case scenario. Description of the Drawings

[0059] Figure 1 This is the framework diagram of the two-stage resilience improvement strategy of the present invention.

[0060] Figure 2 This is the flowchart of the two-stage resilience improvement strategy after a disaster of the present invention.

[0061] Figure 3 This is the improved IEEE-33 node system diagram used in the case study analysis of the present invention.

[0062] Figure 4 This is the predicted curve graph of the output of the wind turbine used in the case study analysis of the present invention.

[0063] Figure 5 This is the predicted curve graph of the load demand used in the case study analysis of the present invention.

[0064] Figure 6 This is the diagram of the division of the islanded microgrid in each time period in the first stage of the case study analysis of the present invention.

[0065] Figure 7 This is the accurate point prediction graph of the output of the wind turbine used in the case study analysis of the present invention.

[0066] Figure 8 This is the output graph after the second-stage optimization of the static var compensator and capacitor bank in the case study analysis of the present invention.

[0067] Figure 9 This is the graph of the two-stage load restoration result in the case study analysis of the present invention.

[0068] Figure 10 This is the comparison graph of the influence result of reactive power on the restoration scheme in the case study analysis of the present invention.

[0069] Figure 11 This is the node voltage distribution graph at each moment in the case study analysis of the present invention. Specific implementation manner

[0070] The following further illustrates the present invention in conjunction with specific examples.

[0071] A two-stage distribution network resilience improvement method considering uncertainty of active and reactive power coordination under extreme disasters provided by the present invention, the flowchart is as Figure 2 shown, and it is applied to Figure 3 the improved IEEE-33 node system shown.

[0072] Take the loads in the standard IEEE - 33 - bus system as peak loads, and set the allowable range of node voltages to 0.95 - 1.05 p.u. For the convenience of simulation analysis, the parameters of all gas turbines, wind turbines, energy storage, capacitor banks, and static var compensators in the system are the same. The compensation power of the static var compensator is [-200, 600] kVar. There are 6 unit capacitors in each capacitor bank, and each has a power of 40 kVar. The rated power of the wind turbine is 200 kW, and the rated capacity is 300 kVA. The uncertainty adjustment parameters Π w and Π l are set to 4. The remaining parameters are shown in Table 1 - Table 2. The loads are divided into three levels according to their importance, and the specific weight settings are shown in Table 3. This invention assumes that after an extreme event occurs, the distribution system is completely disconnected from the superior power grid, and it takes 4 hours to repair the substation. Assume the affected period is from 21:00 to 1:00 at night. During this period, the maintenance and rescue team conducts operations to repair the faulty lines, and the recovery time of the faulty lines is shown in Table 4. Assume the output prediction deviation coefficient of the wind turbine is set to 0.1, the load prediction deviation coefficient is set to 0.05, and the load interval prediction and wind turbine interval prediction during the affected period are as Figure 4 and Figure 5 shown, and the proportional coefficient μ of the active load to the reactive load is set to 0.8.

[0073] Table 1 Gas Turbine Parameters

[0074]

[0075] Table 2 Energy Storage Parameters

[0076]

[0077]

[0078] Table 3 Load Weights of Each Node

[0079]

[0080] Table 4 Faulty Line Recovery Time Table

[0081]

[0082] Build a mathematical simulation model through MATLAB, solve it using the Gurobi solver, and then analyze the strategy proposed in this invention. When analyzing the two - stage resilience improvement strategy of the distribution network, first deeply explore the load - shedding results of the coordinated scheduling of active and reactive power equipment considering uncertainty. Subsequently, further analyze the specific impact of the optimal allocation of reactive power during the recovery process on reducing the load - shedding amount. The simulation results of this invention example are as follows:

[0083] ① Analysis of load shedding results of coordinated dispatch of active and reactive equipment considering uncertainty under extreme disasters

[0084] Phase 1: Based on the interval prediction data within the prediction window, the number of capacitor groups to be switched, the working state of the remote control switch, and the charging and discharging state of the energy storage are determined on a long-term scale. As the fault line is gradually repaired, the line state changes. By optimizing the remote control switch state, three isolated microgrids are dynamically formed, such as Figure 6 After solving the three-layer robust optimization model of stage 1, not only the optimal solution of the variables on a long time scale can be obtained, but also the output of the equipment that can be continuously adjusted on a short time scale under the worst scenario can be obtained.

[0085] Phase 2: After the decision is made in the first phase, the optimization decision is implemented in the first hour of the time window. Then, the second phase begins. In this phase, based on the accurate point prediction of the next moment, the decision can continuously adjust the output of the equipment on a short time scale. The optimization is performed every 20 minutes. Each wind turbine accurately predicts the output of the equipment. Figure 7 As shown, the precise load prediction is not shown here due to space limitations. Figure 8 The control strategy of the capacitor bank and the static VAR compensator is shown in Figure 1. The output of the capacitor bank is the optimization result of stage 1, while the output of the static VAR compensator is the optimization result of stage 2. The two cooperate with each other on long and short time scales, dynamically adjusting their reactive power output according to load demand, which can reduce the additional load loss caused by voltage exceeding the limit and play a supporting role for the isolated island microgrid.

[0086] Figure 9 The worst-case scenario in the first phase and the load recovery at each moment after the second phase scheduling are shown. The total weighted load shedding of the robust recovery strategy in the worst-case scenario in the first phase is 19899.9kW, and the total weighted load shedding after the second phase optimized scheduling is 17397.3kW. By comparison, it can be seen that after the second phase optimized scheduling, the weighted load shedding is reduced by 12.6%, which shows that the readjustment of DERs on a short time scale in the second phase can effectively compensate for the prediction error in the first phase, thereby further improving the recovery performance.

[0087] ②The impact of optimal reactive power allocation on post-disaster recovery process

[0088] This paper studies the impact of optimal allocation of reactive power on the resilience of distribution networks by comparing dispatching with or without RPCs. Figure 10As shown, the total weighted load shedding amount at each moment for the coordinated dispatch of DERs and RPCs (Scenario 1) is 17,397.3 kW, and the total weighted load shedding amount at each moment for the dispatch of only DERs (Scenario 2) is 19,799.5 kW. The weighted load shedding amount in Scenario 2 is 13.8% higher than that in Scenario 1. The node voltage distribution at each moment for Scenario 1 and Scenario 2 is as Figure 11 shown. It can be seen that the voltage fluctuation amplitude of Scenario 1 is smaller, its node voltage deviation is less than that of Scenario 2, and it has a stronger support ability for the islanded microgrid.

[0089] Thus, through the coordinated dispatch of DERs and RPCs, reactive power support can be provided, the additional load shedding caused by voltage over-limit can be reduced, and the node voltage distribution can be improved. It should be noted that the difference between the two scenarios is more obvious in the first 7 moments. Digging deeper into the reason: in the first 7 moments, the system load demand is at a relatively high level, while the output of the wind turbines is relatively small. Therefore, in this stage, the gas turbine and the wind turbines mainly output active power to restore the load to the maximum extent, and the insufficient reactive power of the system leads to an increase in the load shedding amount. As the load demand decreases and the output of the wind turbines increases, the gas turbine and the wind turbines are capable of outputting more reactive power to meet the system's demand for reactive power, so the restoration effects of Scenario 1 and Scenario 2 gradually tend to be the same.

[0090] The scope of protection claimed by the present invention is not limited to the above specific embodiments. Moreover, for those skilled in the art, the present invention can have various deformations and modifications. Any modification, improvement, and equivalent replacement made within the concept and principle of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for improving the resilience of a distribution network by collaboratively optimizing active and reactive power under extreme disasters, characterized in that: The following steps are involved: Phase 1: The first phase is to establish a long-term robust optimization model: uncertainty intervals are used to characterize the fluctuation range of wind turbine generators and load demand in the next forecast window, and a robust optimization model is established with the goal of minimizing weighted load shedding, including power flow constraints, radial topology constraints, gas turbine constraints, wind turbine constraints, energy storage constraints, capacitor bank constraints, static VAR compensator constraints, and load constraints. The number of capacitor bank switching groups, the working state of the remote control switch, and the charging and discharging state of the energy storage are determined on a long-term basis; Phase 2: Establishment of short-time-scale optimization model during the second phase: Based on the latest forecast information and combined with the decision results obtained in the first phase, a deterministic optimization model is established with the goal of minimizing weighted load shedding. The output of the gas turbine, energy storage, wind turbine and static VAR compensator at the next moment is finely optimized on a short-time scale to compensate for the errors that may be caused by the uncertainty interval in the first phase decision.

2. The method for improving the resilience of a distribution network by collaboratively optimizing active and reactive power under extreme disasters according to claim 1 is characterized in that: The specific steps of the first phase are as follows: S1: Objective function: Where: X is the decision vector composed of the state of the remote control switch in the line, the charge and discharge state of the energy storage, the number of capacitor groups switched on and off and their output reactive power; Y is the continuously adjustable equipment output variable, R and L are the uncertainty sets of the wind turbine output and load demand, respectively, N is the set of all nodes, T is the prediction time window, Y∈Ω(X,r,l) represents the feasible domain for a given set (X,r,l), ω j is the node load weight, is the load shedding amount of node j in period t; S2: Constraints S2-1: Power flow constraints: U j min ≤U j,t ≤U j max ,j∈N\N G IN j,t =U 0 ,j∈N G Where: φ(j) and δ(j) represent the parent node and child node set of node j respectively, P ij,t represents the active power from node i to node j during period t, Q ij,t represents the reactive power from node i to node j during period t, P js,t represents the active power from node j to node s during period t, Q js,t represents the reactive power from node j to node s during period t, N G is the set of gas turbines, ε is the set of lines, and They represent the active power output and predicted active power load of the gas turbine, energy storage, and wind turbine at node j during period t, respectively. and Respectively represent the reactive output and predicted reactive load of the gas turbine, wind turbine, capacitor bank and static VAR compensator at node j in period t, U 0 is the reference node voltage, U i,t represents the voltage of node i during period t, U j,t represents the voltage of node j during period t, U j min and U j max They represent the minimum and maximum voltage of node j, respectively, and c ij,t represents the breaking state of line ij during period t, M represents a constant, r ij and x ij is the resistance and reactance of line ij; S2-2: Radial topological constraints: IN j ≥1,j∈N G ∑ ij∈ε c ij =|N|-|N G | Where: F ij represents the virtual power flow on line ij in the virtual network, F js represents the virtual power flow on line js in the virtual network, c ij Represents the disconnection state of line ij, W j is the power emitted by the source node in the virtual network; S2-3: Gas Turbine Constraints: Where: and are the minimum and maximum active output of the gas turbine at node j, and are the minimum and maximum reactive power outputs of the gas turbine at node j, is the rated capacity of the gas turbine at node j; S2-4: Wind turbine constraints: In the formula, r j,t is the predicted output of node j in period t, is the rated capacity of the wind turbine at node j; S2-5: Energy storage constraints: Where: and Represent the discharge and charge states of node j in period t, respectively. is the maximum charge and discharge power of node j, and are the discharge and charge powers of node j in period t, and is the minimum and maximum capacity allowed for node j during operation, E s (0) is the initial capacity of energy storage, α is the charging and discharging efficiency of energy storage; S2-6: Capacitor bank constraints: Where: is the number of capacitor groups switched at node j during period t, is the reactive power of a group of capacitors connected to node j, is the maximum number of capacitor banks connected to node j; S2-7: Static VAR compensator constraints: Where: and are the upper and lower limits of the reactive power emitted by the static VAR compensator connected to node j respectively; S2-8: Load constraints: Where: l j,t is the load demand predicted by node j in period t; μ is the ratio coefficient between active load and reactive load; S3: Uncertainty set of wind turbine output and load demand: in: and They represent the predicted output, upper and lower limits of the deviation of the wind turbine at node j at time t, respectively. and Represent the predicted demand, upper limit and lower limit of the load at node j at time t respectively; by introducing the variable and To control the output of the wind turbine at node j at time t within the interval Introducing variables and To control the load demand at node j at time t in the interval Inside, Π w and Π l are the uncertainty adjustment parameters of wind turbine and load respectively.

3. The method for improving the resilience of a distribution network by collaboratively optimizing active and reactive power under extreme disasters according to claim 2 is characterized in that: In the solution stage 1, the control strategy for the number of capacitor groups switched, the working state of the remote control switch, and the charging and discharging state of the energy storage is obtained within the time window, and the strategy of this stage is executed, and then the second stage is entered; in this stage, according to the latest predicted wind turbine power generation and load demand, the output of the gas turbine, wind turbine, energy storage and static VAR compensator at the next moment is optimized on a short time scale. The mathematical expression of the second stage model is:

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