A two-stage planning method and device for active power distribution network considering cyber attacks

Abstract

The application provides a kind of active power distribution network two-stage planning method and device considering network attack, comprising: according to the importance degree of node, corresponding penalty cost coefficient is given, and target function is established;According to the budget of pre-set, the first-order planning of line reinforcement and remote control switch deployment is carried out to the target function, and the first-order planning decision constraint is constructed;According to the line fault and the propagation of line fault under attack scene, the second-order planning of defense strategy is carried out to the target function based on the first-order planning decision constraint, and the second-order planning decision constraint is obtained;According to the first-order planning decision constraint and the second-order planning decision constraint, the target function is solved, and the optimal defense strategy corresponding to the worst attack scene and the optimal planning strategy vector are obtained, so as to regulate and control the active power distribution network according to the optimal defense strategy and the optimal planning strategy vector;The application can improve the power distribution planning flexibility of active power distribution network under limited budget.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of active power distribution network system planning, and particularly relates to a two-stage planning method and device for active power distribution network considering network attacks. BACKGROUND

[0002] Serious power outage accidents and corresponding economic losses caused by high-impact low-frequency events such as extreme weather and network information attacks have triggered widespread attention to the construction of resilient power systems. Compared with traditional transmission systems, active power distribution network systems are generally more vulnerable to high-impact low-frequency events, which makes the planning and design scheme for the purpose of enhancing the resilience of the power distribution network system in the power distribution network system more important. Line reinforcement and remote control sectionalizing switch deployment have been verified as two effective measures to enhance the resilience of the power distribution network system in the active power distribution network. Due to budget constraints, all lines in the active power distribution network cannot be reinforced and bilateral remote control switches cannot be installed in each line. Unlike line reinforcement, which usually requires cost / benefit analysis, the optimal deployment of remote control switches is considered a rather complex problem.

[0003] However, the propagation after potential line faults, such as tie-line faults, is not fully considered, so the degradation of the performance of the power distribution network system is not accurately evaluated, and the reinforcement scheme of the power distribution network system is based on the performance evaluation of the power distribution network system, and the impact of the budget on the planning of the power distribution network system is also not considered, resulting in that the planning scheme is not suitable for actual conditions and has low practicability.

[0004] Therefore, how to propose a power distribution network planning scheme under limited budget to improve the resilience of the active power distribution network is a technical problem to be solved by the technical personnel in the field. SUMMARY

[0005] The present application aims at the deficiencies of the above-mentioned prior art, and provides a two-stage planning method and device for active power distribution network considering network attacks, which can improve the resilience of the power distribution planning of the active power distribution network under limited budget.

[0006] In a first aspect, the present application provides a two-stage planning method for active power distribution network considering network attacks, comprising:

[0007] According to the importance of the nodes, corresponding penalty cost coefficients are given, and a target function is established by taking the defense strategy as an operating variable, taking the attack scenario as an uncertainty variable and taking the planning decision vector as a planning variable;

[0008] According to the preset budget, a first-order planning of line reinforcement and remote control switch deployment is performed on the target function, and a first-order planning decision constraint is constructed;

[0009] According to the line fault under the attack scene and the propagation of the line fault, the second-order programming of the defense combat strategy is carried out on the target function based on the first-order programming decision constraint, and the second-order programming decision constraint is obtained.

[0010] According to the first-order programming decision constraint and the second-order programming decision constraint, the target function is solved, and the optimal defense combat strategy and the optimal planning strategy vector corresponding to the worst attack scene are obtained, so that the active power distribution network is regulated according to the optimal defense combat strategy and the optimal planning strategy vector.

[0011] The application gives a penalty cost coefficient to the node, measures the fault node, and constructs a target function through operating variables, uncertainty variables and planning variables. For the three variables, the application uses line fault and line fault propagation to construct a first-order programming decision constraint under the budget, and constructs a second-order programming decision constraint under the first-order programming decision constraint, so that the propagation after the potential line fault can be fully considered based on the actual budget, the values of the three variables can be accurately calculated, and then the power distribution network planning is planned based on the three solving results, thereby improving the flexibility of the power distribution network planning.

[0012] Further, the corresponding penalty cost coefficient is given according to the node importance, and a target function is established with the defense combat strategy as the operating variable, the attack scene as the uncertainty variable and the planning decision vector as the planning variable, including:

[0013] According to the corresponding penalty cost coefficient given according to the node importance, the product of the fault duration and the penalty cost coefficient of the node is accumulated after the fault occurs, and the total penalty cost is obtained. According to the order of the defense combat strategy as the operating variable, the attack scene as the uncertainty variable and the planning decision vector as the planning variable, a target function with a corresponding min-max-min structure is established for the total penalty cost.

[0014] The application takes the total penalty cost of the penalty cost coefficient of each node after the fault as the target, and separately obtains the three variables with a min-max-min structure, which can guarantee that the fault cost after the fault is the lowest, and is more suitable for actual power distribution network planning and has stronger practicability.

[0015] Further, according to the line fault under the attack scene and the propagation of the line fault, the second-order programming of the defense combat strategy is carried out on the target function based on the first-order programming decision constraint, and the second-order programming decision constraint is obtained, including:

[0016] Based on the first-order planning decision constraint, if a line fault occurs in an attack scenario, then according to the two end nodes directly affected by the line fault and the indirect propagation of the fault state through the connected line, a fault propagation constraint is established, the minimum power outage area divided by the tie line and the switch deployment position is obtained, and a second-order planning of the defense strategy is performed on the target function according to the minimum power outage area, and a second-order planning decision constraint is obtained.

[0017] The present application simultaneously considers the deployment of bilateral switches and the propagation of tie line faults when designing power distribution network planning problems, can quickly obtain the minimum power outage area divided by the tie line and the switch deployment position under the complex operation constraints of the power distribution network system, and thus can accurately obtain the power distribution network planning scheme, thereby improving the flexibility of power distribution network planning.

[0018] In a second aspect, the present application provides an active power distribution network two-stage planning device considering network attacks, comprising: a target function construction module, a first-order planning module, a second-order planning module and a solution module; wherein,

[0019] The target function construction module is configured to assign a corresponding penalty cost coefficient according to the node importance, and establish a target function by taking the defense strategy as an operating variable, the attack scenario as an uncertain variable and the planning decision vector as a planning variable.

[0020] The first-order planning module is configured to perform a first-order planning of line reinforcement and remote switch deployment on the target function according to a preset budget, and construct a first-order planning decision constraint.

[0021] The second-order planning module is configured to perform a second-order planning of the defense strategy on the target function according to the line fault in the attack scenario and the propagation of the line fault, based on the first-order planning decision constraint, and obtain a second-order planning decision constraint.

[0022] The solution module is configured to solve the target function according to the first-order planning decision constraint and the second-order planning decision constraint, obtain an optimal defense strategy and an optimal planning strategy vector corresponding to the worst attack scenario, and regulate and control the active power distribution network according to the optimal defense strategy and the optimal planning strategy vector. BRIEF DESCRIPTION OF DRAWINGS

[0023] Figure 1 is a flowchart of a two-stage planning method of an active power distribution network considering network attacks provided by the present embodiment;

[0024] Figure 2 is a schematic diagram of deploying bilateral remote switches in a line;

[0025] Figure 3is a schematic diagram of two fault propagation modes provided by the embodiment;

[0026] Figure 4 is a schematic diagram of the topology structure of the IEEE 33-node distribution network system provided by the embodiment;

[0027] Figure 5 is a schematic diagram of fault identification and reconstruction of different budgets provided by the embodiment;

[0028] Figure 6 is a schematic diagram of fault detection results of a lower budget provided by the embodiment;

[0029] Figure 7 is a schematic diagram of fault detection results of a higher budget provided by the embodiment;

[0030] Figure 8 is a schematic diagram of the structure of a two-stage planning device for active distribution networks considering network attacks provided by the embodiment. DETAILED DESCRIPTION

[0031] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0032] It is worth noting that the purpose of the present application is to solve the problem that factors are not fully considered in the planning modeling of the resilience improvement of active distribution networks under high-impact low-frequency events such as network attacks, and to propose a two-stage robust planning model considering random tie-line faults and related fault propagation for improving the resilience of active distribution networks. The first stage involves the decision of line reinforcement and remote switch deployment, and the second stage applies the worst-case scenario to determine the defensive operation in the active distribution network. In order to better illustrate the technical solutions of the present application, the following embodiments will be described in detail.

[0033] Embodiment 1

[0034] Referring to Figure 1 is a schematic diagram of the flow of a two-stage planning method for active distribution networks considering network attacks provided by the embodiment, comprising steps S11-S14, specifically:

[0035] Step S11, according to the node importance degree, a corresponding penalty cost coefficient is given, and a defense strategy is taken as an operation variable, an attack scenario is taken as an uncertainty variable, and a planning decision vector is taken as a planning variable, and a target function is established.

[0036] In some embodiments, a corresponding penalty cost coefficient is assigned according to the node importance, and a target function is established by taking the defense combat strategy as an operation variable, the attack scene as an uncertainty variable, and a planning decision vector as a planning variable, including: a corresponding penalty cost coefficient is assigned according to the node importance, and the product of the cumulative fault duration and the penalty cost coefficient of the node is obtained after the fault occurs, to obtain a total penalty cost; and the total penalty cost is used to establish a target function with a corresponding min-max-min structure in the order of the defense combat strategy as an operation variable, the attack scene as an uncertainty variable, and the planning decision vector as a planning variable.

[0037] It is worth noting that the expected energy not served (EENS) is usually used as a quantitative standard for evaluating the performance of a power distribution network system. In the present embodiment, different penalty cost coefficients are assigned to each node in the power distribution network system according to the importance of the node. When the power distribution network system is attacked, line faults can cause some nodes to lose load. The load shedding amount of a node multiplied by the fault duration and the penalty cost coefficient of the node gives the fault cost of the node. The fault costs of the nodes that lose load after the fault of the power distribution network system are added to obtain the total penalty cost of the power distribution network system, so as to evaluate the consequences of power outage.

[0038] In some embodiments, the target function with a min-max-min structure is represented as:

[0039]

[0040] wherein Z, U and Y represent the set of planning variables, uncertainty variables and operation variables, respectively; is the penalty cost coefficient of node i; is the load shedding amount of node i at time t; and Δt is the fault duration. The above variables will be iteratively calculated in the two-stage robust optimization model to obtain the final planning scheme.

[0041] In some embodiments, the expected energy not served (EENS) can be used as a quantitative index for evaluating the performance of a power distribution network system, and different weights are assigned to each node load to evaluate the consequences of power outage, so as to establish a target function.

[0042] In step S12, a first-order planning of line reinforcement and remote switch deployment is performed on the target function according to a preset budget, and a first-order planning decision constraint is constructed.

[0043] In some embodiments, a first-order programming of line reinforcement and remote switch deployment of the objective function is performed according to a preset budget, and first-order programming decision constraints are constructed, including: setting K remote switches in the line, and reinforcing the line and deploying at least one switch on any line, establishing budget constraints, candidate planning position constraints of the remote switch, line reinforcement constraints and at least one switch deployment constraint on any line according to the investment cost of deploying the remote switch and the line reinforcement, to obtain the first-order programming decision constraints; wherein K is a positive integer.

[0044] In some embodiments, the planning scheme of line reinforcement and remote switch deployment in the active power distribution network is designed to obtain the first-order programming decision constraints, including steps S12.1-S12.4, which are specifically:

[0045] Step S12.1: The power supply company sets a limited budget for the power distribution network system, and controls it by budget constraints, which can be expressed as:

[0046]

[0047] In the formula, C Inv represents the total investment cost; C DG represents the installation cost of the distributed generator set; C RCS represents the investment cost of the remote switch; C H represents the investment cost of the line reinforcement; and C represents the upper limit of the investment budget.

[0048] In some embodiments, K can be 2, which can ensure that the double switch in the line has better performance than the single switch in the extreme event; or K can be 1 to meet the lower budget; or K can be 3, or K can be 4, or other more number of remote switches to meet the higher budget, and to achieve faster and more secure defense in the event of an extreme event, so as to realize higher flexibility of the active power distribution network.

[0049] Step S12.2: In this embodiment, two remote switches are set in the line, and the candidate planning position constraints can be expressed as:

[0050]

[0051] In the formula, c RCS represents the unit cost of the remote switch; and represents a 0 / 1 variable of whether to deploy a switch, which is 1 if the sending / receiving end of the line ij deploys a remote switch, otherwise 0.

[0052] Step S12.3: Reinforce the conventional line / interconnection line in the power distribution network system, and the line reinforcement constraint can be expressed as:

[0053]

[0054] wherein, denotes the line reinforcement cost per unit distance; l ij denotes the length of line ij; denotes a 0 / 1 variable indicating whether the line is reinforced, 1 if line ij is reinforced, otherwise 0.

[0055] Step S12.4: At least one switch needs to be deployed on any tie line in the distribution system to maintain the radial operation of the distribution network, and the line reinforcement constraint and the constraint of deploying at least one switch on any line can be expressed as:

[0056]

[0057] In some embodiments, referring to Figure 2 is a schematic diagram provided by the embodiment for deploying double bilateral remote control switches in the line, according to Figure 2 The upper half of the figure shows that when the line LS2 fails, when only one switch is deployed on the line, the load of node 1 can be normally restored, but the load of node 2 cannot be restored until the fault is repaired, which will increase the EENS of the distribution system and reduce the power supply reliability of the distribution system; and when two sectional switches are installed on the line, the load of node 2 can be supplied by the distributed power supply linked on the right. The lower half of the figure shows that when the tie line and the normal line fail, if there is only one switch on the tie line, nodes 3 and 4 cannot be restored to power supply, but if the remote control switch is deployed on both sides, nodes 3 and 4 can be normally powered. As can be seen, the bilateral remote control switch is beneficial to reduce the area of fault propagation and can restore more normal node loads, so the deployment of the bilateral remote control switch is superior to the unilateral deployment. Figure 2

[0058] Step S13, according to the line failure and the propagation of the line failure under the attack scenario, a second-order programming of the objective function is performed based on a first-order programming decision constraint to obtain a second-order programming decision constraint.

[0059] It is worth noting that in the second stage, the active distribution system will follow the corresponding operation constraints to mitigate the harmful effects of the high-impact low-frequency event attack strategy, such as power flow adjustment and microgrid formation, and the feasible region of the operation of the distribution system is described by a second-order programming constraint.

[0060] ​In some embodiments, according to the line fault and the propagation of the line fault under the attack scenario, the second-order programming of the defense strategy of the target function is obtained based on the first-order programming decision constraint, and the second-order programming decision constraint is obtained, including: based on the first-order programming decision constraint, if the line fault occurs under the attack scenario, then according to the two end nodes directly affected by the line fault and the indirect propagation of the fault state through the connected line, the fault propagation constraint is established, the minimum power outage area divided according to the deployment position of the tie line and the switch is obtained, and the second-order programming of the defense strategy of the target function is obtained according to the minimum power outage area. The second-order programming decision constraint is obtained.

[0061] In some embodiments, the planned island in the active power distribution network is to adjust the network topology by operating the remote switch and restore the node load not affected by the fault. Considering the uncertainty of the deployment position of the tie line and the switch, the present example realizes a fast detection mechanism for identifying the minimum power outage area through the fault propagation constraint.

[0062] In some embodiments, when the remote switch is deployed on a certain line, the switch operating state of the sending end or the receiving end of the line can be opened, that is, or or

[0063] In some embodiments, the fault propagation constraint corresponding to the minimum power outage area is represented as:

[0064]

[0065] Wherein, 0 / 1 variable representing the open state of the switch, open is 1 and closed is 0.

[0066] In some embodiments, the fault propagation constraint for identifying the minimum power outage area can be represented as:

[0067]

[0068] Wherein, represents 1 if the fault can be directly propagated to node i when the regular line or tie line ij fails, otherwise 0; represents the number of lines connected to node i; h i,t,1 represents 0 if node i is identified as a fault after the first detection, otherwise 1; T is the total duration of the fault duration;

[0069]

[0070] is 0 when the regular line RL and the tie line TL ij are in the outage state at time t, otherwise 1; taking the regular line (RL) as an example, only when the line ij is out of service​ and the switch deployed on line ij close to node i is opened ,

[0071]

[0072] h i,t,p is 0 if node i is identified as faulty after the pth detection at time t, otherwise 1; is 1 if faulty node j can indirectly propagate the fault to node i, otherwise 0; denotes the number of lines connected to node i.

[0073] It is worth mentioning that the fault propagation constraints include three constraints, the first two constraints indicate that any faulty node j connected to normal node i can indirectly propagate the fault through the connected line; the third constraint ensures that once node i is confirmed as a faulty node in a certain detection, this fault state will be inherited in the subsequent detection.

[0074] In some embodiments, referring to Figure 3 is a schematic diagram of two fault propagation modes provided by the embodiments, including: direct fault propagation (Direct propagation), which directly affects the nodes at both ends of the attacked line after the line fails, causing the nodes to shed load; and indirect fault propagation (Indirect propagation), which propagates from the faulty node to the external nodes. Figure 2 In Fig. 3, since line 23 fails due to a low-frequency high-impact event such as a network attack, and no sectional switch is deployed, nodes 2 and 3 are directly affected and shed load, becoming faulty nodes, which belongs to direct fault propagation. Because no sectional switch is deployed in line 34 and line 36, nodes 4 and 6 are also affected by the fault, which belongs to indirect fault propagation.

[0075] In some embodiments, the fault propagation constraints can also include:

[0076]

[0077] wherein, denotes the maximum number of detections; the two constraints in the formula indicate that the indirect fault propagation of line ij to node i in the pth detection is valid only when node i is confirmed as faulty in the (p-1)th detection, and the remote control switch deployed on line ij is not opened.

[0078] In some embodiments, the second-order programming of the defense strategy of the target function according to the minimum power outage area obtains the second-order programming decision constraint by: combining the fault propagation constraint corresponding to the minimum power outage area with at least one of the load reduction constraint of the fault node, the line operation state constraint, the node safety margin constraint, the output limit constraint of the substation and the distributed power corresponding to the line, the active and reactive power constraint of the line energization, the linear power flow equation constraint, the active and reactive power constraint of the node, the operation time interval constraint of the switch, the load constraint of the normal node of the microgrid formed in the degradation period, the connection constraint of the radial operation distribution network and the radial operation constraint, performing the second-order programming of the defense strategy of the target function, and obtaining the joint constraint, and taking the joint constraint as the second-order programming decision constraint.

[0079] It is worth noting that after the node fails, the load thereof will be reduced, and the load of the normal node can continuously change without exceeding the local demand.

[0080] In some embodiments, the load reduction constraint of the fault node is expressed as:

[0081]

[0082] wherein, P i L represents the total load demand of the node i; represents the load reduction of the node i at time t.

[0083] In some embodiments, if there is at least one disconnected switch on the line ij , the line is out of service (w ij,t = 0).

[0084] In some embodiments, the line operation state constraint is expressed as:

[0085]

[0086] wherein, w ij,t represents 1 if the line ij is energized at time t, otherwise 0.

[0087] In some embodiments, the voltage per unit of each node must satisfy the node safety margin constraint, and the node safety margin constraint is expressed as:

[0088]

[0089] wherein, , represents the voltage safety margin of the node i.

[0090] In some embodiments, power can only be generated at normal nodes, and the output limits of substations and distributed power sources are correspondingly set, and the output limit constraints of substations and distributed power sources are respectively represented as:

[0091]

[0092]

[0093] wherein, Pi, qitdenotes the active and reactive power generated by the power source at node i at time t; Pi, qitdenotes the active and reactive capacity of substation i; Pi, qitdenotes the active and reactive capacity of distributed power source at node i.

[0094] In some embodiments, when the line is energized, the active and reactive power thereof should not exceed the specified line capacity limit, and the active and reactive power constraints of the line energized are represented as:

[0095]

[0096] wherein, w ij,t denotes 1 if line ij is energized at time t, otherwise 0; P ij,t , Q ij,t denotes the active and reactive power on line ij at time t; denotes the maximum allowed capacity of active and reactive power of line ij.

[0097] In some embodiments, the verified linearized power flow equation is applied to the radial operation of the distribution network system and used to solve the load restoration problem, and the linear power flow equation constraint is represented as:

[0098]

[0099] wherein, denotes the upstream and downstream of node i, respectively.

[0100] In some embodiments, when line ij is energized, the voltage limit between the two nodes remains unchanged, and the active and reactive loads on each node are set to be reduced at an equal proportion, and the active and reactive constraints of the nodes are represented as:

[0101]

[0102] wherein, w ij,t denotes 1 if line ij is energized at time t, otherwise 0; r ij , x ij denotes the resistance and reactance of line ij.

[0103] In some embodiments, frequent switching operation can shorten the service life of the remote control switch and can cause high inrush voltage, so the running time interval of the switch is limited, and the running time interval constraint of the switch is represented as:

[0104]

[0105] wherein, indicates that the switch at the sending and receiving end of the line ij operates at t+1 time, and is 1, otherwise 0; t0,t e indicates the time point of the start and end of the fault event.

[0106] In some embodiments, in the degradation period, the load of the normal node is restored in time by forming a micro-grid, the node containing a substation or a distributed power supply is defined as a root node, and the distribution boundary needs to meet the load constraint of the normal node restored by the micro-grid formed in the degradation period, and is represented as:

[0107]

[0108] wherein, ξ i,t indicates that node i is a root node at t time, and is 1, otherwise 0.

[0109] In some embodiments, in the radial operation distribution network considering fault propagation, the connection constraint should be applied only to the normal node and the line connected thereto, therefore, the connection constraint of the radial operation distribution network is represented as:

[0110]

[0111]

[0112] wherein, F ij,t indicates the power flow on the line ij at t time.

[0113] In some embodiments, the distribution network system is constrained to meet the radial operation, therefore, the radial operation constraint is:

[0114]

[0115] wherein, the number of energized lines is equal to the number of nodes minus the number of micro-grids.

[0116] Step S14, according to the first-order planning decision constraint and the second-order planning decision constraint, the target function is solved, and the optimal defense combat strategy and the optimal planning strategy vector corresponding to the worst attack scene are obtained, so as to regulate and control the active distribution network according to the optimal defense combat strategy and the optimal planning strategy vector.

[0117] It is worth mentioning that the two-stage planning problem is decomposed into a master problem (MP) and a subproblem (SP), and a suitable algorithm is selected to solve the model.

[0118] In some embodiments, the target function is solved according to the first-order planning decision constraint and the second-order planning decision constraint to obtain an optimal defense combat strategy corresponding to the worst attack scenario and an optimal planning strategy vector, including: decomposing the target function into a master problem and a subproblem, according to the first-order planning decision constraint and the second-order planning decision constraint, in the master problem, given the worst attack scenario and given the optimal defense combat strategy, obtaining the optimal planning decision vector, substituting the optimal planning decision vector into the subproblem, and solving the worst attack scenario and the optimal defense combat strategy.

[0119] In some embodiments, the solution of the target function includes steps S14.1-S14.3, specifically:

[0120] Step 4.1: In the master problem , the current optimal planning decision vector z* is calculated using the given worst attack scenario u* and the given optimal defense combat strategy y*, and the C&CG algorithm is used for solving.

[0121] Step 4.2: In the solution of the subproblem , the values of u* and y* for the optimal planning decision vector z* will be found. Since there are binary variables in the min problem, the problem is non-convex and does not satisfy strong duality, so the Nested C&CG algorithm is used for solving.

[0122] Step 4.3: The optimization problem in the two-stage robust planning model of the active power distribution network constructed in this embodiment is a mixed integer linear programming (MILP) problem, which can be quickly and effectively solved by using a commercial solver (such as Gurobi).

[0123] This embodiment gives a penalty cost coefficient to the node, measures the fault node, and constructs a target function through operation variables, uncertainty variables and planning variables. For the three variables, the invention uses line fault and line fault propagation to construct a first-order planning decision constraint under the budget, and constructs a second-order planning decision constraint under the first-order planning decision constraint, so that based on the actual budget, the propagation after the potential line fault can be fully considered, the values of the three variables can be accurately calculated, and then the power distribution network planning is planned based on the three solving results, thereby improving the flexibility of the power distribution network planning.

[0124] Embodiment 2

[0125] To verify the effectiveness and superiority of the method proposed in this embodiment 1, simulation is performed on the improved IEEE 33-node distribution network system, and the topological structure thereof is shown in Figure 4 , which is a topological structure diagram of the IEEE 33-node distribution network system provided in this embodiment. To evaluate the maximum expected unserved energy of the distribution network system under high-impact low-frequency time events such as network attacks, this embodiment assumes that each successful attack will directly cause a line fault; and after reinforcement of the line, it will no longer be affected by the original fault. After the degradation period of the distribution network system ends, it will enter the recovery and maintenance period, in which the average service repair time of the node load is 2 hours. Nodes 16, 19, 24, 29 and 33 are regarded as critical loads in the distribution network system, and the load demand of each node is shown in Table 1. Three energy storage devices are installed at nodes 18, 22 and 25 as distributed energy sources, with active capacities of 80kW, 120kW and 300kW respectively. All simulations can be solved by the commercial solver Gurobi.

[0126] Table 1 Location and demand of critical load

[0127]

[0128] To verify the effectiveness of the planning method proposed in embodiment 1, two distribution network planning scheme examples with budgets of 200,000 dollars and 500,000 dollars are set respectively, and the fault identification and reconstruction of the distribution network system after the occurrence of high-impact low-frequency events such as network attacks are studied, as shown in Figure 5 , which is a schematic diagram of fault identification and reconstruction provided in this embodiment with different budgets.

[0129] In this embodiment, two fault scenarios are considered, namely line faults caused by extreme weather and line faults under network multi-target attacks, and it is assumed that the consequences of the faults caused by the two scenarios are the same.

[0130] When a large number of lines fail, the substation will temporarily be unable to supply power to the users on the nodes. Therefore, the active distribution network will generate a planned island to restore the load of the critical nodes, especially those with high load demand, such as node 24, to reduce the EENS of the distribution network system.

[0131] Example 1: When the budget is $200,000, the planning and design will focus on reinforcing the lines near the important load nodes and installing sectional switches. After the fault occurs, the distribution network system is reconfigured to form microgrid MG-1 to restore the key loads of nodes 24 and 29 and microgrid MG-2 to restore the key loads of node 19. When lines 23-24, 28-29 and 32-33 fail, the deployment of sectional switches on both sides of nodes 24 and 29 enables the formation of MG-1 island. When lines 2-19 and 12-22 fail, the deployment of sectional switches on both sides of node 19 and the deployment of double-sided remote-controlled switches on tie line 12-22 enable the formation of MG-2 island.

[0132] Example 2: When the budget is $500,000, compared with Example 1, the load of key node 33 can be restored, thanks to the reinforcement of lines 31-32 and 32-33, which are not affected by the faults in Example 1, and the deployment of double-sided sectional switches on tie line 18-33, which can isolate faults.

[0133] Referring to Figure 6 and Figure 7 , which are a fault detection result diagram under a lower budget and a fault detection result diagram under a higher budget provided by the embodiment, respectively, the fault detection method proposed in Example 1 is applied to obtain Figure 5 the node fault detection results under two different budgets, that is, the entire process of detecting the node state at the end of the degradation phase of the distribution network system. As can be seen from Figure 6 and Figure 7 , under the budgets of $200,000 and $500,000, the node states of the distribution network system at the third round of detection are the same as the detection results of the last round, verifying the accuracy and effectiveness of the method. By comparing the node state recognition results of Figure 6 and Figure 7 with the intuitive fault area shown in Figure 5 , it can be found that the fault detection method proposed in Example 1 can accurately detect the health states of all nodes.

[0134] The two-stage robust planning method designed in the application aims to enhance the resistance of active distribution networks to high-impact low-frequency events such as network attacks. Conventional line reinforcement, tie line reinforcement and deployment of remote-controlled sectional switches are used as three investment options for distribution network planning in the application. Firstly, the minimum failure region search algorithm is used to model the outage failure propagation of conventional lines and tie lines in detail and linearize the operating constraints. Secondly, the Nested C&CG algorithm is used to solve the two-stage robust optimization model designed in the application. The calculation results show that the active distribution network resilience improvement planning model proposed in the application can quickly form a microgrid after a line failure occurs by deploying and reinforcing conventional lines and tie lines, restore critical node loads, and effectively reduce the penalty cost of the distribution network system.

[0135] Embodiment 3

[0136] Reference Figure 8 Fig. 1 is a structural schematic diagram of a two-stage planning device for active distribution networks considering network attacks provided by the application, which comprises a target function construction module 31, a first-order planning module 32, a second-order planning module 33 and a solution module 34.

[0137] In some embodiments, the target function construction module 31 outputs a target function according to the penalty cost coefficient of the input node, and transmits the target function to the first-order planning module 32 and the solution module 34; after receiving the target function, the first-order planning module 32 outputs a first-order planning decision constraint, and transmits the first-order planning decision constraint to the second-order planning module 33 and the solution module 34; after inputting the first-order planning decision constraint, the second-order planning module 33 outputs a second-order planning decision constraint to the solution module 34; after receiving the target function, the first-order planning decision constraint and the second-order planning decision constraint, the solution module 34 outputs a planning scheme; the planning scheme comprises an optimal defense strategy corresponding to the worst attack scenario and an optimal planning strategy vector.

[0138] The target function construction module 31 is configured to assign a corresponding penalty cost coefficient according to the node importance, and establish a target function by taking the defense strategy as an operating variable, the attack scenario as an uncertainty variable and the planning decision vector as a planning variable.

[0139] In some embodiments, the target function is established by assigning a corresponding penalty cost coefficient according to the node importance, and taking the defense strategy as an operating variable, the attack scenario as an uncertainty variable and the planning decision vector as a planning variable, which comprises: assigning a corresponding penalty cost coefficient according to the node importance, accumulating the product of the fault duration and the penalty cost coefficient of the node after the fault occurs to obtain the total penalty cost, and establishing a target function with a corresponding min-max-min structure for the total penalty cost in the order of the defense strategy as an operating variable, the attack scenario as an uncertainty variable and the planning decision vector as a planning variable.

[0140] In some embodiments, the objective function of the min-max-min structure is represented as:

[0141]

[0142] wherein Z, U and Y represent the set of planning variables, uncertainty variables and operation variables, respectively; is the penalty cost coefficient of node i; is the load shedding amount of node i at time t; and Δt is the duration of the fault.

[0143] A first-order planning module 32 is configured to perform first-order planning of the target function according to a preset budget, and to construct first-order planning decision constraints.

[0144] In some embodiments, the first-order planning of the target function according to the preset budget includes: setting K remote control switches in the line, and reinforcing the line and deploying at least one switch on any line, establishing budget constraints, candidate planning location constraints of the remote control switches, line reinforcement constraints and constraints of deploying at least one switch on any line according to the investment cost of deploying the remote control switches and reinforcing the line, to obtain the first-order planning decision constraints; wherein K is a positive integer.

[0145] A second-order planning module 33 is configured to perform second-order planning of the target function according to the line fault and the propagation of the line fault under the attack scenario, based on the first-order planning decision constraints, to obtain second-order planning decision constraints.

[0146] In some embodiments, the second-order planning of the target function according to the line fault and the propagation of the line fault under the attack scenario, based on the first-order planning decision constraints, to obtain the second-order planning decision constraints includes: based on the first-order planning decision constraints, if a line fault occurs under the attack scenario, then according to the two end nodes directly affected by the line fault and the indirect propagation of the fault state through the connected line, establishing a fault propagation constraint, obtaining the minimum power outage area divided according to the location of the tie line and the switch deployment, and according to the minimum power outage area, performing the second-order planning of the target function according to the defense combat strategy, to obtain the second-order planning decision constraints.

[0147] In some embodiments, the fault propagation constraint corresponding to the minimum power outage area is represented as:

[0148]

[0149] wherein xij represents a 0 / 1 variable of the open / close state of the switch, 1 for open and 0 for closed;

[0150]

[0151] wherein, denotes 1 if the regular line or tie-line ij can directly propagate the fault to node i, otherwise 0; denotes the number of lines connected to node i;h i,t,1 denotes 0 if node i is identified as fault after the 1st detection, otherwise 1; T is the total duration of the fault;

[0152]

[0153] denotes 0 if the regular line RL and tie-line TL ij are in outage at time t, otherwise 1;

[0154]

[0155] h i,t,p denotes 0 if node i is identified as fault after the pth detection at time t, otherwise 1; denotes 1 if the fault node j can indirectly propagate the fault to node i, otherwise 0; denotes the number of lines connected to node i;

[0156]

[0157] wherein, denotes the maximum number of detections. The two constraints in the formula indicate that the indirect fault propagation of line ij to node i in the pth detection is valid only when node i is confirmed as fault in the (p-1)th detection, and the remote-controlled switch deployed on line ij is not opened.

[0158] In some embodiments, according to the minimum outage area, the second-order programming of the defense strategy for the objective function is performed to obtain the second-order programming decision constraint, including: combining the fault propagation constraint corresponding to the minimum outage area with at least one of the load reduction constraint of the fault node, the line operation state constraint, the node safety margin constraint, the output limit constraint of the substation and the distributed power, the active and reactive power constraint of the line energization, the linear power flow equation constraint, the active and reactive power constraint of the node, the operation time interval constraint of the switch, the load constraint of the normal node of the microgrid formed in the degradation period, the connection constraint of the radial operation distribution network and the radial operation constraint, and performing the second-order programming of the defense strategy for the objective function to obtain the joint constraint, and taking the joint constraint as the second-order programming decision constraint.

[0159] In some embodiments, the load reduction constraint of the fault node is expressed as:

[0160]

[0161] where P i L denotes the total load demand of node i; denotes the shed load of node i at time t.

[0162] In some embodiments, the line operation state constraints are represented as:

[0163]

[0164] where w ij,t denotes 1 if line ij is energized at time t, otherwise 0.

[0165] In some embodiments, the node security margin constraints are represented as:

[0166]

[0167] where, , denotes the voltage security margin of node i.

[0168] In some embodiments, the power output limit constraints corresponding to substations and distributed power sources are represented as:

[0169]

[0170]

[0171] where, denotes the active and reactive power generated by the power source at node i at time t; denotes the active and reactive capacity of substation i; denotes the active and reactive capacity of the distributed power source at node i.

[0172] In some embodiments, the active and reactive power constraints for line energization are represented as:

[0173]

[0174] where w ij,t denotes 1 if line ij is energized at time t, otherwise 0; P ij,t ,Q ij,t denotes the active and reactive power on line ij at time t; denotes the maximum allowed capacity of active and reactive power for line ij.

[0175] In some embodiments, the linear power flow equation constraints are represented as:

[0176]

[0177] where, and represent the upstream and downstream of node i, respectively.

[0178] In some embodiments, the active and reactive power constraints of nodes are represented as:

[0179]

[0180] where, w ij,t is 1 if line ij is energized at time t, otherwise 0; r ij , x ij represent the resistance and reactance of line ij.

[0181] In some embodiments, the operation time interval constraints of switches are represented as:

[0182]

[0183] where, is 1 if the sending or receiving end of line ij is operated at time t+1, otherwise 0; t0,t e represent the time points of the start and end of fault events.

[0184] In some embodiments, the load constraints of normal nodes restored by microgrids in the degradation period are represented as:

[0185]

[0186] where, ξ i,t is 1 if node i is a root node at time t, otherwise 0.

[0187] In some embodiments, the connection constraints of radial operation distribution networks are represented as:

[0188]

[0189]

[0190] where, F ij,t represents the power flow on line ij at time t.

[0191] In some embodiments, the radial operation constraints are:

[0192]

[0193] where, the number of energized lines is equal to the number of nodes minus the number of microgrids.

[0194] The solving module 34 is configured to solve the target function according to the first-order programming decision constraint and the second-order programming decision constraint, and obtain the optimal defense combat strategy and the optimal programming strategy vector corresponding to the worst attack scenario, so as to regulate and control the active power distribution network according to the optimal defense combat strategy and the optimal programming strategy vector.

[0195] In some embodiments, the solving of the target function according to the first-order programming decision constraint and the second-order programming decision constraint to obtain the optimal defense combat strategy and the optimal programming strategy vector corresponding to the worst attack scenario comprises: decomposing the target function into a main problem and a sub-problem, obtaining the optimal programming decision vector in the main problem under the given worst attack scenario and the given optimal defense combat strategy according to the first-order programming decision constraint and the second-order programming decision constraint, and substituting the optimal programming decision vector into the sub-problem to solve the worst attack scenario and the optimal defense combat strategy.

[0196] In this embodiment, the target function module 31 is configured to give a penalty cost coefficient to the node, measure the fault node, and construct the target function through the operation variable, the uncertainty variable and the programming variable. For the three variables, the first-order programming module 32 is configured to construct the first-order programming decision constraint according to the line fault and the propagation of the line fault under the budget, and construct the second-order programming decision constraint through the second-order programming module 33 under the first-order programming decision constraint, so that the propagation after the potential line fault can be fully considered based on the actual budget, the values of the three variables can be accurately calculated through the solving module 34, and then the power distribution network planning is planned based on the three solving results, thereby improving the flexibility of the power distribution network planning.

[0197] Those skilled in the art will understand that the embodiments of the present application can also provide a computer program product. Therefore, the present application can adopt a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer usable storage media (including but not limited to disk memory, CD-ROM, optical memory, etc.) containing computer usable program code.

[0198] The present application is described with reference to flowcharts and / or block diagrams according to the methods, devices (apparatuses), and computer program products of the embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of the flows and / or blocks in the flowcharts and / or block diagrams can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices produce a device that implements the functions described in the flowcharts and / or block diagrams. Figure 1 one flow or multiple flows and / or blocksFigure 1 means for performing the function specified in the block or blocks.

[0199] These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the flow Figure 1 flow or flows and / or blocks Figure 1 means for performing the function specified in the block or blocks.

[0200] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the flow Figure 1 flow or flows and / or blocks Figure 1 steps of means for performing the function specified in the block or blocks.

[0201] The above description is only preferred embodiments of the present application, it should be pointed out that, for those skilled in the art, without departing from the technical principles of the present application, a number of improvements and modifications can also be made, these improvements and modifications should be considered as the protection scope of the present application.

Claims

1. A two-stage planning method for active distribution networks considering network attacks, characterized in that, include: Based on the importance of nodes, corresponding penalty cost coefficients are assigned, and an objective function is established using defensive combat strategy as the operational variable, attack scenario as the uncertainty variable, and planning decision vector as the planning variable. Based on the preset budget, a first-order programming approach is used to implement line reinforcement and remote control switch deployment for the objective function, and first-order programming decision constraints are constructed as follows: K remote control switches are set up in the line, and the line is reinforced and at least one switch is deployed on any line. Based on the investment cost of deploying the remote control switches and reinforcing the line, budget constraints, candidate planning location constraints of the remote control switches, line reinforcement constraints, and constraints of deploying at least one switch on any line are established to obtain first-order planning decision constraints; where K is a positive integer. Based on the line faults in the attack scenario and their propagation, and based on the first-order planning decision constraints, a second-order planning process for the defensive combat strategy is performed on the objective function to obtain the second-order planning decision constraints, specifically: Based on the first-order planning decision constraints, if a line fault occurs in an attack scenario, a fault propagation constraint is established based on the two ends of the line fault directly affected and the fault state indirectly propagated through the connecting line. The minimum power outage area is obtained by dividing the connection line and the switch deployment location. Based on the minimum power outage area, a second-order planning of the defensive combat strategy is performed on the objective function to obtain the second-order planning decision constraints. Based on the first-order planning decision constraints and the second-order planning decision constraints, the objective function is solved to obtain the optimal defense strategy and the optimal planning strategy vector corresponding to the worst attack scenario, so as to regulate the active power distribution network according to the optimal defense strategy and the optimal planning strategy vector. The step of solving the objective function based on the first-order and second-order planning decision constraints to obtain the optimal defense strategy and optimal planning strategy vector corresponding to the worst-case attack scenario includes: The objective function is decomposed into a main problem and sub-problems. Based on the first-order and second-order planning decision constraints, in the main problem, under the given worst-case attack scenario and the given optimal defense strategy, the optimal planning decision vector is obtained. The optimal planning decision vector is then substituted into the sub-problems to solve for the worst-case attack scenario and the optimal defense strategy.

2. The two-stage planning method for active distribution networks as described in claim 1, characterized in that, The process involves assigning corresponding penalty cost coefficients based on node importance, and establishing an objective function using defensive combat strategy as the operational variable, attack scenario as the uncertainty variable, and planning decision vector as the planning variable. This function includes: The node is assigned a corresponding penalty cost coefficient based on its importance. After a failure occurs, the total penalty cost is obtained by multiplying the cumulative failure duration by the node's penalty cost coefficient. The objective function with a corresponding min-max-min structure is established for the total penalty cost, following the order of defensive combat strategy as the operational variable, attack scenario as the uncertainty variable, and planning decision vector as the planning variable.

3. The two-stage planning method for active power distribution networks as described in claim 2, characterized in that, The objective function of the min-max-min structure is expressed as: Where Z, U, and Y represent the sets of planning variables, uncertainty variables, and operational variables, respectively; Let be the penalty cost coefficient for node i; Δt represents the load shedding amount of node i at time t; Δt represents the fault duration; T represents the total duration of the fault; and N represents the total number of nodes.

4. The two-stage planning method for active distribution networks as described in claim 1, characterized in that, The fault propagation constraint corresponding to the minimum power outage area is expressed as follows: Among them, the four parameters represent the 0 / 1 variables of the switch's on / off state, with 1 for on and 0 for off; This is a 0 / 1 variable indicating whether a switch is deployed on a regular line ij. It is 1 if a remote control switch is deployed at the transmitting / receiving end of line ij, and 0 otherwise. This is a 0 / 1 variable indicating whether a switch is deployed on the tie line ij. It is 1 if a remote control switch is deployed at the transmitting / receiving end of the tie line ij, and 0 otherwise. A 0 / 1 variable representing the on / off state of a regular circuit switch, with 1 for on and 0 for off; The variable represents the open / closed state of the tie line switch, with 1 for open and 0 for closed; L represents the set of branches. in, The value is 1 if a fault occurs in the regular line or tie line ij and can propagate directly to node i; otherwise, it is 0. The value is 1 if a fault occurs on the regular line ij and can be directly propagated to node i, otherwise it is 0. The value is 1 if a fault occurs in the connection line ij and can propagate directly to node i, otherwise it is 0. h represents the number of lines connected to node i; i,t,1 0 indicates that node i is identified as faulty after the first detection, and 1 otherwise; T is the total duration of the fault. If line ij in the conventional line RL and the connecting line TL is out of service at time t, the value is 0; otherwise, the value is 1. h i,t,p A value of 0 indicates that node i is identified as faulty after the p-th detection at time t, and a value of 1 otherwise. In a conventional RL line, a value of 1 indicates that if the fault profile can be propagated to node i when deployed on line ij near node j, the value of 0 indicates otherwise. A value of 1 indicates that the fault profile can be propagated to node i if the connection line TL is deployed on the side of line ij closer to node j, otherwise a value of 0 indicates that the connection line TL is deployed on the side of line ij closer to node j. M represents the number of lines connected to node i; M represents a constant. in, This represents the maximum number of detections; two fault propagation constraints are used to indicate that indirect fault propagation from line ij to node i is valid in the p-th detection, only if node i is confirmed as faulty in the (p-1)-th detection and the remote control switch deployed on line ij is not turned on; h i,t,p-1 A value of 0 indicates that node i is identified as faulty after the (p-1)th detection at time t, and a value of 1 otherwise. In a conventional RL line, a value of 1 indicates that if the fault profile can be propagated to node j on the side of line ij closer to node i, the value of 0 indicates that the fault profile can be propagated to node j otherwise. The value is 1 if the fault profile deployed on the line ij in the tie line TL is close to node i and can propagate to node j, otherwise it is 0.

5. The two-stage planning method for active power distribution networks as described in claim 4, characterized in that, The step of performing second-order programming of the defensive combat strategy on the objective function based on the minimum power outage area, and obtaining the second-order programming decision constraints, includes: The fault propagation constraint corresponding to the minimum power outage area is combined with at least one of the following constraints: load reduction constraint of the fault node, line operation status constraint, node safety margin constraint, output limit constraint of substation and distributed power source, active and reactive power constraint of line energization, linear power flow equation constraint, active and reactive power constraint of node, operating time interval constraint of switch, load constraint of microgrid node returning to normal during degradation period, connection constraint of radial distribution network and radial operation constraint. The resulting joint constraint is used as the second-order programming decision constraint for the objective function.

6. The two-stage planning method for active power distribution networks as described in claim 5, characterized in that, The load reduction constraint of the faulty node is expressed as: Among them, P i L This represents the total load demand of node i; This represents the load shedding at node i at time t; A value of 0 indicates that node i is identified as faulty after the maximum number of checks at time t, and a value of 1 otherwise; N represents the total number of nodes. The line operation status constraints are represented as follows: Among them, w ij,t This means that if line ij is energized at time t, the value is 1; otherwise, it is 0. The node safety margin constraint is expressed as: in, , This represents the voltage safety margin at node i; The output constraints for substations and distributed generation are expressed as follows: in, This represents the active and reactive power generated by the power source at node i at time t; This represents the active and reactive power capacity of substation i; N represents the active and reactive power capacity of the distributed power source at node i; Sub Represents the set of substation nodes; N\N Sub Represents all elements in set N that do not belong to set N. Sub The set consisting of the elements; The active and reactive power constraints of a energized line are expressed as follows: Among them, w ij,t The value of P indicates that line ij is 1 if it is energized at time t, and 0 otherwise; ij,t Q ij,t This represents the active and reactive power on line ij at time t; This indicates the maximum permissible capacity of active and reactive power for line ij. The constraints of the linear power flow equations are expressed as follows: in, Let i represent the upstream and downstream of node i, respectively. This represents the total reactive power load demand of node i; The active and reactive power constraints of a node are represented as follows: Among them, w ij,t The value of r indicates that line ij is 1 if it is energized at time t, and 0 otherwise; ij ,x ij V represents the resistance and reactance of line ij; i,t V represents the voltage value at node i at time t; j,t Vj represents the voltage value of node j at time t; V0 represents the voltage value of the reference node. The operating time interval constraint of the switch is expressed as: in, This indicates that the switch at the transmitting and receiving ends of line ij is 1 if it operates at time t+1, and 0 otherwise; t0, t e Indicates the start and end times of the fault event; The load constraints of nodes in a microgrid that have recovered from degradation are expressed as follows: Where, ξ i,t The value is 1 if node i is the root node at time t, and 0 otherwise. The connection constraints of a radially operating distribution network are expressed as follows: Among them, F ij,t h represents the power flow on line ij at time t; i,t This indicates the node's fault status; 0 indicates a fault, and 1 indicates otherwise. The radial running constraints are: The number of power lines is equal to the number of nodes minus the number of microgrids.

7. A two-stage planning device for active power distribution networks that takes into account network attacks, characterized in that, include: Construct a target function module, a first-order programming module, a second-order programming module, and a solution module; among them, The objective function construction module is used to assign corresponding penalty cost coefficients according to the importance of nodes, and to establish an objective function with defensive combat strategy as the operational variable, attack scenario as the uncertainty variable, and planning decision vector as the planning variable. The first-order planning module is used to perform first-order planning for line reinforcement and remote control switch deployment based on a preset budget, and to construct first-order planning decision constraints, specifically: K remote control switches are set up in the line, and the line is reinforced and at least one switch is deployed on any line. Based on the investment cost of deploying the remote control switches and reinforcing the line, budget constraints, candidate planning location constraints of the remote control switches, line reinforcement constraints, and constraints of deploying at least one switch on any line are established to obtain first-order planning decision constraints; where K is a positive integer. The second-order planning module is used to perform second-order planning of the defensive combat strategy on the objective function based on the line faults in the attack scenario and the propagation of the line faults, and on the basis of the first-order planning decision constraints, to obtain the second-order planning decision constraints, specifically: Based on the first-order planning decision constraints, if a line fault occurs in an attack scenario, a fault propagation constraint is established based on the two ends of the line fault directly affected and the fault state indirectly propagated through the connecting line. The minimum power outage area is obtained by dividing the connection line and the switch deployment location. Based on the minimum power outage area, a second-order planning of the defensive combat strategy is performed on the objective function to obtain the second-order planning decision constraints. The solution module is used to solve the objective function according to the first-order planning decision constraints and the second-order planning decision constraints to obtain the optimal defense strategy and the optimal planning strategy vector corresponding to the worst attack scenario, so as to regulate the active power distribution network according to the optimal defense strategy and the optimal planning strategy vector. The step of solving the objective function based on the first-order and second-order planning decision constraints to obtain the optimal defense strategy and optimal planning strategy vector corresponding to the worst-case attack scenario includes: The objective function is decomposed into a main problem and sub-problems. Based on the first-order and second-order planning decision constraints, in the main problem, under the given worst-case attack scenario and the given optimal defense strategy, the optimal planning decision vector is obtained. The optimal planning decision vector is then substituted into the sub-problems to solve for the worst-case attack scenario and the optimal defense strategy.

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