Load replacement attack defense method and device based on topology switching and power flow regulation

Abstract

The present application belongs to the field of electric digital data processing, and particularly relates to a load replacement attack defense method and device based on topology switching and power flow regulation. The defense method solves the optimal joint deployment strategy by constructing a double-layer Stackelberg game model for cooperatively defending the load replacement attack by integrating intelligent soft switches and remote control switches, wherein the upper defense model plans to comprehensively consider the constraint conditions such as voltage regulation, power flow balance, radial network structure and continuity, so as to minimize the equipment investment-operation cost and voltage out-of-limit index; in the lower attack model, the optimal attack strategy of the resource-limited attacker is generated under the given defense strategy of the defender to maximize the voltage deviation. The problems that the traditional topology switching-based defense method has response lag, limited regulation capacity, and the mitigation strategy of deploying only intelligent soft switches faces high deployment cost and poor defense effect are solved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of digital data processing, and particularly relates to a load replacement attack defense method and device based on topology switching and power flow regulation. BACKGROUND

[0002] With the acceleration of the digitalization process of new power systems, a high proportion of Internet of Things devices are widely connected, which has become a potential entry point for network attacks, leading to serious network security challenges for power systems.

[0003] LAAs is the English abbreviation of Load Altering Attacks, which is translated into Chinese as load replacement attacks. Load replacement attacks are a typical form of network attacks in power systems. Such attacks can cause cascading voltage instability and line overload by manipulating Remote-Controllable Loads, which is the English name for Remote-Controllable Loads, and the English abbreviation is RCLs. Therefore, it is of great significance to study defense methods against load replacement attacks to eliminate the impact of attacks and ensure the safe and stable operation of power systems.

[0004] SOPs is the English abbreviation of Soft Open Points, which is translated into Chinese as intelligent soft switch. Intelligent soft switches are composed of devices such as back-to-back voltage source converters and are widely used in distribution networks to improve system flexibility and reliability. Intelligent soft switches can precisely regulate power flow, provide voltage support, and provide reactive power compensation between feeders by controlling active power flow between connected feeders under normal operating conditions and absorbing or providing reactive power at their interface terminals, effectively solving problems such as power fluctuations, local overloads, and voltage quality caused by the connection of distributed energy sources.

[0005] RCSs is the English abbreviation of Remote Controlled Switches, which is translated into Chinese as remote control switch. Remote control switches are a kind of hard switch device that can be opened and closed by remote operation. Through fast topology switching, fast fault isolation and service recovery after network attacks can be achieved, so they are widely used in distribution networks. Compared with sectional switches and tie switches, which usually require manual intervention and have slow recovery time, remote control switches have fast response capability and can be remotely operated, greatly reducing the existence time of risks and enabling the system to recover to steady state as soon as possible.

[0006] Traditional topology reconfiguration defense methods based on sectionalizing switches and tie switches have problems of response lag, limited adjustment capacity, etc. Attack impact mitigation strategies considering only the deployment of intelligent soft switches face problems of excessive investment cost and poor defense effect. For example, Chinese patent document CN110783911A discloses a method for configuring soft intelligent switches in a medium and low voltage distribution network, which comprises the following steps: step S1: obtaining distribution network resilience process information to generate distribution network resilience quantification information; step S2: establishing a distribution network attack fault model according to the obtained spatiotemporal characteristic information of the disaster attack on the distribution network; step S3: establishing an SNOP optimization configuration model according to the distribution network resilience quantification information and the distribution network attack fault model; and step S4: solving the SNOP optimization configuration model. However, only intelligent soft switches are deployed, which leads to problems of high cost and inflexible response when dealing with network attacks. SUMMARY

[0007] The present application aims to provide a load replacement attack defense method based on topology switching and power flow regulation, to solve the problems of response lag, limited adjustment capacity of the defense method based on traditional topology switching, and high deployment cost and poor defense effect of the mitigation strategy considering only the deployment of intelligent soft switches. The defense method solves the optimal joint deployment strategy by constructing a double-layer Stackelberg game model for collaborative defense of load replacement attacks by intelligent soft switches and remote control switches, wherein the upper layer plans to comprehensively consider voltage regulation, power flow balance, radial network structure, continuity and other constraint conditions to minimize device investment and operation and maintenance cost and voltage out-of-limit index; and in the lower layer, the optimal attack strategy of the resource-limited attacker is simulated under the given defense strategy of the defender to maximize the voltage deviation.

[0008] The present application also discloses a device loaded with the load replacement attack defense method based on topology switching and power flow regulation.

[0009] To solve the above problems, the present application provides a load replacement attack defense method based on topology switching and power flow regulation, which comprises:

[0010] S1, constructing a load replacement attack model based on a power flow model of a distribution network;

[0011] S2, constructing a double-layer game model of a defender and an attacker based on the load replacement attack model constructed in step S1, wherein the upper layer is a defense model and the lower layer is an attack model, and the defense model is a collaborative defense model integrating intelligent soft switches and remote control switches;

[0012] S3, simplifying and equivalently converting the double-layer game model constructed in step S2 by model linear equivalence and second-order cone method;

[0013] S4, by Karush-Kuhn-Tucker condition, the double-layer game model after simplification and equivalent conversion in step S3 is converted into a single-layer model, and the single-layer optimization problem of the single-layer model is solved to obtain the optimal planning deployment method.

[0014] Preferably, in the step S1, a linearized power distribution system power flow model is used to approximate the power flow of the power distribution system, and the power flow equation under the model is as follows:

[0015] (1)

[0016] (2)

[0017] (3)

[0018] Formula (1) describes the node power conservation relationship; wherein, represents the branch set, represents the node set, represents the node active power flowing to the node , represents the active power flowing to the node active power flowing to the node , represents the active load demand of the node , formula (1) ensures that the active power input minus the output at the node is equal to the node load; formula (2) is the reactive expression of the power conservation relationship, wherein, represents the reactive power flowing to the node reactive power flowing to the node , represents the reactive power flowing to the node reactive power flowing to the node , represents the reactive load demand of the node ; in formula (3) , respectively represent the voltage amplitude of the node and , , are respectively the resistance and reactance parameters of the branch;

[0019] The constructed load substitution attack model is described as:

[0020] (4)

[0021] (5)

[0022] Wherein, in formulas (4) (5) a set of LA attack nodes selected by the attacker, a load perturbation variable injected by the attacker at the current node.

[0023] Preferably, the double-layer game model of the defender and the attacker in step S2, the upper-layer defense model, the defender resists the LA attack by deploying SOPs and RCSs, so that the system voltage is kept within the safe range; the lower-layer attack model, the attacker decides the load perturbation value to maximize the voltage deviation under the resource constraint according to the deployment strategy of the upper layer.

[0024] Further preferably, the objective function of the upper-layer defense model is:

[0025] (6)

[0026] (7)

[0027] wherein, minimizes the value of the objective function, which consists of four parts, specifically including the total deployment cost of the SOP , the total deployment cost of the RCS , the SOP power loss cost , and the total amount of voltage out-of-bound , wherein and are weight coefficients for determining the SOP loss weight coefficient and the total amount of voltage out-of-bound, respectively; specifically, and are the unit capacity cost of the SOP device and the capacity size of the single-sided VSC thereof, and are the fixed cost of the SOP installation and the binary variable of whether to deploy the SOP at the current position, wherein represents a set of all candidate SOP installation positions; and are the cost of a single RCS and the binary variable of whether to deploy the RCS at the current branch; and are the unit cost of active power loss and the active power loss of the SOP; is the total voltage deviation exceeding the upper voltage limit and the lower voltage limit , and the specific rules are: if ≥ , then is counted in the total amount, otherwise it is 0; conversely, if ≥ , then is counted in the total amount, otherwise it is 0.

[0028] The objective function of the lower-layer attack model is:

[0029] (8)

[0030] where, and represent the optimal active and reactive power injection at the node , respectively, and

[0031] Further preferably, the constraint conditions of the upper-layer defense model include:

[0032] The active power balance equation, the reactive power balance equation and the voltage drop constraint, see equations (9)-(11):

[0033] (9)

[0034] (10)

[0035] (11)

[0036] where, equations (9)(10) are further modified based on equations (4)(5), introducing the active power injection and the reactive power injection of the intelligent soft switch at the node , denoting that the branch i to j is connected.

[0037] The line capacity limit constraint is as follows:

[0038] (12)

[0039] where, is the rated apparent power of the branch; equation (12) is used to prevent overload risk and system instability, while ensuring the open state of the branch;

[0040] The SOP operation related constraints are as follows:

[0041] (13)

[0042] (14)

[0043] (15)

[0044] (16)

[0045] (17)

[0046] wherein, equation (13) is the power balance constraint between the two nodes connected by the SOP after replacing the tie switch. wherein and is the active power between the two nodes connected by the SOP device, and is the active power loss of the two voltage source converters (VSCs) at the ends of the SOP, the calculation method of which is shown in equation (14). wherein is the power loss factor of the SOP, which is a constant. Equation (15) specifies the capacity constraint condition of the SOP, wherein is the reactive power between the two nodes connected by the SOP device, is the capacity of the SOP at node i. Equation (16) describes the reactive power operating limit of the two sets of VSCs, wherein is the lower and upper limit coefficient of the reactive power regulation ratio, which ensures that the reactive power of the SOP is adjusted within the effective range. Equation (17) is added to determine whether to deploy the SOP at the current location and determine the capacity size of the deployed SOP , represents the deployment set of the candidate SOP, represents the set of nodes connected to the current location of the SOP.

[0047] The radial topology and the spatial exclusion constraint are as follows:

[0048] (18)

[0049] (19)

[0050] (20)

[0051] (21)

[0052] (22)

[0053] (23)

[0054] (24)

[0055] (25)

[0056] (26)

[0057] wherein, n in equation (18) is the total number of nodes in the power distribution network, which ensures that the total number of connected edges in the radial structure is n-1, wherein characterizing the connectivity state of a branch; equation (19) guarantees the root node has no upstream parent node connection; equation (20) ensures the non-root node has and only has one parent node, where if is 1, it indicates that node is the parent node of node , otherwise is 0; equation (21) indicates that a branch can only choose one direction as the "parent-child relationship"; equation (22) limits and are both binary variables; equation (23) guarantees that RSC and SOP cannot be installed in the same branch at the same time, and are binary variables representing the deployment state of RSC and SOP. If branch , is installed with RCS, equals 1, otherwise equals 0. Similarly, if branch , is installed with SOP, equals 1, otherwise equals 0. Equation guarantees that the branch installed with SOP must remain disconnected; equations (25) (26) collectively guarantee that only the position deployed with RCS can switch the connection state and the branch remains closed if it is not installed with RCS.

[0058] The constraint conditions of the lower-layer attack model include:

[0059] The attacker needs to consider the power constraint and the parent-child balance constraint of the voltage when attacking, as follows:

[0060] (27)

[0061] (28)

[0062] (29)

[0063] (30)

[0064] (31)

[0065] wherein, the specific explanations of equations (27)-(29) can be found in equations (9)-(11); equations (30) (31) guarantee that the power flow is zero when the branch is disconnected, is the maximum capacity limit of branch power transmission;

[0066] Finally, considering the characteristics of the load substitution attack, the following constraints are introduced:

[0067] (32)

[0068] (33)

[0069] (34)

[0070] (35)

[0071] (36)

[0072] wherein formula (32) (33) ensures that the attack amplitude of a single node does not exceed a fixed proportion of the load value of the node itself , is a proportionality coefficient; formula (34) ensures that the load of a non-attack node cannot be modified; formula (35) (36) indicates that the total active and reactive disturbance of the attacker in the entire network is limited by the total amount of attack resources, wherein is the total resource limit of the attacker on the active power attack, is the total resource limit of the attacker on the reactive power attack.

[0073] Preferably, step S3 is specifically:

[0074] S31, using variables replace the variables in formula (7) (8) (11) (29) as follows;

[0075] (37)

[0076] (38)

[0077] (39)

[0078] wherein, denotes the voltage square of node i, denotes the voltage square of node j.

[0079] S32, using the linearization technique based on large M, equivalent linearization is performed on formula (38) as follows:

[0080] (40)

[0081] (41)

[0082] Formula (40) (41) jointly constrain only when the branch is connected =1, a voltage drop relationship is applied, =0, no voltage drop relationship is applied, wherein is a larger constant.

[0083] S33, using a second-order cone method, formula (12), (14) is converted into a second-order cone form, the converted second-order cone form is shown in formula (42), (43);

[0084] (42)

[0085] (43).

[0086] Preferably, step S4 is specifically:

[0087] Using Karush-Kuhn-Tucker condition to linearize the constraint condition of the attack model of the double-layer game model simplified and equivalently converted through step S3, the double-layer model is converted into a single-layer model, the double-layer optimization problem of the double-layer game model is converted into a single-layer optimization problem that can be solved by the single-layer model, and the single-layer optimization problem of the single-layer model is solved to obtain the optimal planning deployment method.

[0088] Further preferably, using Karush-Kuhn-Tucker condition to linearize the constraint condition of the lower attack model of the double-layer game model simplified and equivalently converted through step S3, the double-layer model is converted into a single-layer model, the double-layer optimization problem of the double-layer game model is converted into a single-layer optimization problem that can be solved by the single-layer model, including:

[0089] The complementary relaxation condition in the KKT condition is linearized by the big M method, and the linearized form is shown in formula (44)-(52).

[0090] (44)

[0091] (45)

[0092] (46)

[0093] (47)

[0094] (48)

[0095] (49)

[0096] (50)

[0097] (51)

[0098] (52)

[0099] Equations (44)-(52) introduce Lagrange multipliers in equation (51) for the dual variables of the lower level optimization. Where, are Lagrange multipliers for inequalities (30) and (31), are Lagrange multipliers for inequalities (32) and (33), are Lagrange multipliers for inequalities (35) and (36), are Lagrange multipliers for inequalities (40) and (41).

[0100] Meanwhile, binary variables in equation (52) are introduced as a big-M method linearization of the complementary slackness condition, which constrains that when one side condition is activated, the other side condition is forced to be off, and M refers to a sufficiently large positive number.

[0101] The gradient condition in KKT conditions, as follows:

[0102] (53)

[0103] (54)

[0104] (55)

[0105] (56)

[0106] (57)

[0107] Equation (53) is the gradient condition for the node voltage, where and represent the child branch, i.e., the directly connected downstream branch, and the father branch, i.e., the directly connected upstream branch, of node respectively; equations (54) and (55) are gradients for active and reactive power, respectively, where and are Lagrange multipliers for power balance equations (27) and (28), represent the index of the power balance equation with the current branch as the inflow branch and the index of the power balance equation with the current branch as the outflow branch; equations (56) and (57) are the gradient conditions for the perturbation variables and ; denotes that branch is an upstream branch of node i; denotes that branch Index of the power balance equation for the outgoing branch; Index of the power balance equation for the outgoing branch Index of the power balance equation for the outgoing branch; Index of the power balance equation for the outgoing branch Index of the power balance equation for the outgoing branch Index of the power balance equation for the outgoing branch.

[0108] The objective function of the single-level optimization problem can be finally described as:

[0109]

[0110] The constraint conditions of the single-level optimization problem include:

[0111] Upper constraints: equations (9)-(10), (13), (15)-(26), (40)-(43)

[0112] Lower original feasibility conditions: equations (27)-(28), (30)-(36), (40), (41)

[0113] Complementary slackness and Lagrange multiplier non-negativity: equations (44)-(52)

[0114] Gradient conditions: equations (53)-(57).

[0115] In another aspect of the present application, there is provided a device for implementing the load replacement attack defense method based on topology switching and power flow regulation, comprising:

[0116] a processor; and a memory having a computer program stored thereon and executable on the processor;

[0117] wherein the computer program, when executed by the processor, implements the load replacement attack defense method based on topology switching and power flow regulation.

[0118] In another aspect of the present application, there is also provided a machine-readable storage medium having executable instructions stored thereon, which, when executed, cause the machine to perform the load replacement attack defense method based on topology switching and power flow regulation as described above.

[0119] Compared with the prior art, the present application has the following beneficial effects:

[0120] Compared with the prior art, the present application has the following beneficial effects:

[0121] (1) The attack defense of the present application is based on topology switching and load replacement attack of power flow regulation, the power flow regulation / voltage support capacity of intelligent soft switch SOPs is cooperatively planned with the fast topology switching capacity of remote control switch RCSs, the problems of response lag and weak regulation capacity caused by manual intervention in topology switching through sectionalizing switch and tie switch are overcome, and the limitations of high cost and poor defense effect caused by relying on SOPs only are overcome.

[0122] (2) The present application constructs a double-layer Stackelberg game of defender-attacker: the upper layer takes the device cost and voltage out-of-limit as the comprehensive target, the lower layer maximizes the voltage deviation under resource constraints, and the optimal confrontation of the resource-constrained attacker is explicitly depicted, so that the obtained deployment is more robust.

[0123] (3) The present application uses a linearized power flow model LinDistFlow to replace the traditional nonlinear power flow equation, which significantly reduces the computational complexity of optimization solution while considering the modeling accuracy; and the behavior of the attacker is included in the model, which is constructed as a convex optimization problem, so as to ensure that the attack modeling can truly reflect the optimal strategy of the attacker.

[0124] (4) The present application converts the mixed integer nonlinear double-layer problem into a single-layer solvable model through variable substitution, equivalent linearization based on large M, second-order cone transformation and KKT condition, and finally gives the optimal joint deployment position and quantity of intelligent soft switch and remote control switch.

[0125] (5) The present application is solved on the existing general optimization solver CPLEX, and simulation experiments are carried out based on IEEE 69 node system. Comparative analysis is carried out under five typical operating conditions, and the results show that the optimization scheme can significantly reduce the voltage out-of-limit risk caused by load replacement attack LAA, and effectively eliminate the influence of the attack on voltage operation. Further experimental results show that the method has stable and excellent protection performance in a wide range of load fluctuations, verifying its strong applicability and engineering value. BRIEF DESCRIPTION OF DRAWINGS

[0126] Figure 1 is an interaction schematic diagram between the defender and the attacker of the method of the present application;

[0127] Figure 2 is a data flow processing schematic diagram of the method of the present application;

[0128] Figure 3 is a comparison and analysis graph of multiple defense strategies under the IEEE69 node test system of embodiment 4 of the present application;

[0129] Figure 4The effectiveness verification chart of the joint planning and deployment strategy of the SOPs and the RCSs in the embodiment 5 of the present application;

[0130] Figure 5 The adaptability verification chart of the joint planning and deployment strategy of the SOPs and the RCSs in the embodiment 6 of the present application. DETAILED DESCRIPTION

[0131] In order to better illustrate the technical solutions, design ideas and actual effects of the present application, in the following content, the embodiments will be described in detail in combination with the drawings and specific embodiments. These embodiments are intended to help understand the present application, and are not used to limit the protection scope of the present application. For those skilled in the art, without departing from the spirit and core idea of the present application, various adjustments, modifications or equivalent replacements can be made to these embodiments, and these shall be considered to fall within the scope of the present application.

[0132] Embodiment 1

[0133] The present application provides a load replacement attack defense method based on topology switching and power flow regulation, as shown in Figure 1 , 2 , the method comprises:

[0134] S1, based on the power flow model of the distribution network, a load replacement attack model is constructed;

[0135] The distribution system model used in the present research can be abstracted as a directed connected graph , wherein represents a node / bus set, represents a branch set. The node set represents the bus number in the system, represents the branch number.

[0136] Further, in order to balance the modeling accuracy and computational complexity, the linearized distribution system power flow model, namely LinDistFlow, is used to approximate the power flow of the distribution system. The LinDistFlow model simplifies the traditional branch power flow model, and by ignoring the active and reactive power loss in the branch, the model has higher computational efficiency, and is widely used in distribution network modeling, distributed energy analysis and control strategy research. The power flow equation under this model is as follows:

[0137] (1)

[0138] (2)

[0139] (3)

[0140] Equation (1) describes the node power conservation relationship; where, denotes the set of branches, denotes the set of nodes, denotes node active power flowing to node , denotes node active power flowing to node , denotes node active load demand; Equation (1) ensures that the active power input minus output at a node equals the node load; Equation (2) is the reactive power expression for the power conservation relationship, where, denotes node reactive power flowing to node , denotes node reactive power flowing to node , denotes node reactive load demand; the voltage drop equation, Equation (3), is , denotes the voltage magnitude of node and , , are the resistance and reactance parameters of the branch, respectively;

[0141] In a distribution system, topology switching is widely used to optimize power flow distribution, reduce network loss, and restore power supply by changing the states of tie switches and sectionalizing switches, especially in abnormal situations such as faults or cyber attacks. At the same time, the distribution system usually has a tree-like radial structure during the process of topology switching, i.e., from the root node, all other nodes can be reached through a unique non-repeating branch path. Therefore, the connectivity of the distribution network after reconstruction needs to be considered, and there is no island and loop network, and the specific constraints are as follows:

[0142] (4)

[0143] (5)

[0144] (6)

[0145] (7)

[0146] (8)

[0147] wherein Equation (4) n is the total number of nodes of the distribution network, which ensures that the total number of connected edges of the radial structure is wherein characterizes the connectivity state of a branch; equation (5) guarantees that the root node has no upstream parent node connection; equation (6) ensures that the non-root node has and only has one parent node, wherein if is 1, it indicates that the node is the parent node of the node , otherwise is 0; equation (7) indicates that a branch can only select one direction as the parent-child relationship; equation (8) limits and to be binary variables;

[0148] The intelligent soft switch is composed of two back-to-back VSCs, and the operation constraint conditions thereof can be expressed as follows:

[0149] (9)

[0150] (10)

[0151] (11)

[0152] (12)

[0153] (13)

[0154] (14)

[0155] (15)

[0156] Equation (9) is a power balance constraint between the two nodes connected by the SOP after replacing the tie switch. Wherein and are the active power between the two bus nodes connected by the SOP device, and are the active power losses of the two voltage source converters (VSCs) at the ends of the SOP, and the calculation method of the losses is shown in equations (10) and (11). Wherein is the power loss factor of the SOP, which is a constant. Equations (12) and (13) specify the capacity constraint conditions of the SOP, wherein and are the reactive power connected between the two bus nodes by the SOP device, and are the apparent power rating capacity of the SOP at nodes i and j. Equations (14) and (15) describe the reactive power operation limits of the two groups of VSCs, wherein are the lower and upper limit coefficients of the reactive power regulation ratio, which ensure the reactive power of the SOP to be regulated in an effective range.

[0157] Considering the exclusivity of the intelligent soft switch and the remote control switch in the deployment location, i.e., not allowing both to be installed at the same location at the same time, the following constraint is introduced:

[0158] (16)

[0159] (17)

[0160] (18)

[0161] (19)

[0162] Formula (16) ensures that the RSC and the SOP cannot be installed at the same branch at the same time, and are binary variables representing the deployment states of the RSC and the SOP. If the branch , ) is installed with the RCS, equals 1, otherwise equals 0. Similarly, if the branch , ) is installed with the SOP, equals 1, otherwise equals 0. Formula (17) ensures that the branch installed with the SOP must remain open; formulas (18) and (19) collectively ensure that only the location deployed with the RCS can switch the connection state and that the branch remains closed if the RCS is not installed.

[0163] In a load replacement attack, an attacker can use such vulnerabilities to turn a group of devices into zombie devices and destroy system stability by frequently starting and stopping and increasing or weakening the load of the current device. Based on this, when the system is subjected to such attacks, the load replacement attack model is constructed based on the original linearized power distribution flow model, and formulas (1) and (2) can be re-described as:

[0164] (20)

[0165] (21)

[0166] wherein, in formulas (20) and (21) represents the LA attack node set selected by the attacker, is the load disturbance variable injected by the attacker at the current node.

[0167] In the load replacement attack, the attacker controls the active and reactive load changes of the node by controlling the remote controllable load. According to formula (3), the influence of the node load disturbance on the voltage can be obtained.

[0168] S2, based on the load replacement attack model constructed in step S1, a double-layer game model of a defender and an attacker is constructed, wherein the upper layer is a defense model, and the lower layer is an attack model, and the defense model is a cooperative defense model of a fusion intelligent soft switch and a remote control switch;

[0169] In a more specific technical solution, in S2, the interaction relationship between the defender and the attacker is described as a double-layer optimization problem by using a Stackelberg game framework by using the following logic:

[0170] The purpose of the attacker is to maximize the voltage deviation of the system to cause the voltage to exceed the boundary. The purpose of the defender is to minimize the influence of the attack on the voltage deviation. Therefore, a double-layer game model is used to identify the most destructive attack strategy under the joint defense strategy to make the system stable within the safe range.

[0171] In the double-layer game model, the upper layer is a defense model, and the defender deploys SOPs and RCSs to resist the LA attack, so that the system voltage remains within the safe range. The lower layer is an attack model, and the attacker decides the load disturbance value to maximize the voltage deviation according to the deployment strategy of the upper layer under the resource constraint. According to the interaction relationship between the two, a Stackelberg game model is constructed.

[0172] The objective function of the upper-layer defense model is:

[0173] (22)

[0174] (23)

[0175] wherein, means minimizing the value of the objective function, and the objective function is composed of four parts, specifically including the total deployment cost of the SOP , the total deployment cost of the RCS , the SOP power loss cost , and the total amount of voltage exceeding the boundary , wherein and are weight coefficients for determining the SOP loss weight coefficient and the total amount of voltage exceeding the boundary, respectively. Specifically, and are the unit capacity cost of the SOP device and the capacity size of the single-sided VSC thereof, and are the fixed cost of the SOP installation and whether it is currently Binary variables for the deployment of SOPs at locations, where is the set of installation locations for all candidate SOPs; and are the cost of a single RCS and a binary variable for whether to deploy RCS at the current branch, respectively; and are the unit cost of active power loss and the active power loss of a SOP; and are the total voltage deviation below the lower voltage bound, with the specific rule that if ≥ , then is counted in the total, otherwise it is set to 0; conversely, if ≥ , then is counted in the total, otherwise it is set to 0.

[0176] The constraints of the upper defense model include:

[0177] The active power balance equation, the reactive power balance equation, and the voltage drop constraint are shown in equations (24)-(26):

[0178] (24)

[0179] (25)

[0180] (26)

[0181] where equations (24) and (25) are further modified based on equations (20) and (21), introducing the active power injection and the reactive power injection of the intelligent soft switch at node , represent the optimal active disturbance and the optimal reactive disturbance of the attacker at node , respectively. indicates that branch i to j is connected.

[0182] The line capacity limit constraint is as follows:

[0183] (27)

[0184] where is the rated apparent power of the branch; equation (27) is used to prevent overload risk and system instability, while ensuring the open state of the branch;

[0185] The SOP operation-related constraints are as follows:

[0186] (28)

[0187] (29)

[0188] (30)

[0189] (31)

[0190] (32)

[0191] wherein equation (28) is the power balance constraint between the two nodes connected by the SOP after replacing the tie switch. wherein and are the active power between the two nodes connected by the SOP device, and are the active power losses of the two voltage source converters (VSCs) at the ends of the SOP, whose calculation method is shown in equation (29). wherein is the power loss factor of the SOP, which is a constant. Equation (30) specifies the capacity constraint condition of the SOP, wherein is the reactive power between the two bus nodes connected by the SOP device, is the capacity of the SOP at node i. Equation (31) describes the reactive power operating limit of the two groups of VSCs, wherein are the lower and upper limit coefficients of the reactive power regulation ratio, which ensure that the reactive power of the SOP is adjusted within the effective range. Equation (32) is added to determine whether to deploy the SOP at the current location and to determine the capacity size of the deployed SOP , , represents the deployment set of the candidate SOP, represents the node set connected to the current location of the SOP.

[0192] The radial topology and the spatial exclusion constraint are as follows:

[0193] (33)

[0194] (34)

[0195] (35)

[0196] (36)

[0197] (37)

[0198] (38)

[0199] (39)

[0200] (40)

[0201] (41)

[0202] In formula (33), n represents the total number of distribution network nodes, ensuring that the total number of connected edges in the radial structure is n-1. Characterizes the connectivity state of the branch; Formula (34) guarantees the root node There is no upstream parent node connection; Equation (35) ensures that the non-root node... It has one and only one parent node, where if A value of 1 indicates that the node It is a node The parent node, otherwise =0; Formula (36) means that a branch can only choose one direction as the parent-child relationship; Formula (37) restricts and All are binary variables; formula (38) ensures that RSC and SOP cannot be installed on the same branch at the same time. and Both are binary variables representing the deployment status of RSC and SOP. If the branch ( , RCS was installed. It equals 1 if the branch is 1, otherwise it equals 0. Similarly, if the branch ( , SOP has been installed. It equals 1 if it is true, otherwise it equals 0. (Formula) Ensure that the branch where the SOP is installed must remain disconnected; formulas (40) and (41) together ensure that the connection state can only be switched at the location where the RCS is deployed, and on other branches besides the candidate SOP location ( If RCS is not installed, the branch remains closed.

[0203] In the upper-level optimization formulas (22)-(41), the defender aims to minimize the operating cost of investing in smart soft switches for defense equipment and the voltage overrun index.

[0204] The objective of the lower-level attack model is:

[0205] (42)

[0206] in, These represent the attacker's position on the node. The optimal active power disturbance and the optimal reactive power disturbance at the location. Vnom is the nominal voltage value of the system, Vmax(i) is the voltage amplitude of node i, N is the set of nodes, Pd(i) and Qd(i) are the active and reactive disturbance variables injected by the attacker at the current node i.

[0207] The constraints of the lower-layer attack model include:

[0208] The attacker needs to consider the power constraints and the parent-child balance constraints of the voltage when attacking, as follows:

[0209] (43)

[0210] (44)

[0211] (45)

[0212] (46)

[0213] (47)

[0214] wherein the specific explanations of formulas (43)-(45) can be seen in formulas (24)-(26); formulas (46) and (47) ensure that the power flow is zero when the branch is disconnected, is the maximum capacity limit of the branch power transmission.

[0215] Finally, considering the characteristics of the load replacement attack, the following constraints are introduced:

[0216] (48)

[0217] (49)

[0218] (50)

[0219] (51)

[0220] (52)

[0221] wherein formulas (48) and (49) ensure that the attack amplitude of a single node does not exceed a fixed proportion of the load value of the node itself , is a proportionality coefficient; formula (50) ensures that the load of the non-attack node cannot be modified; formulas (51) and (52) represent that the total amount of active and reactive disturbances of the attacker in the whole network is limited by the total amount of attack resources, wherein is the total resource limit of the attacker on the active power attack, Total resource limit of the attacker on the reactive power attack.

[0222] To more clearly show the game relationship between the defender and the attacker, Figure 1 and Figure 2 The data flow processing diagram of the adopted Stackelberg game structure and the attack and defense method of the load replacement attack based on the intelligent soft switch and the remote control switch are clearly shown. Specifically, Figure 1 It is shown that the defender, that is, the system planner, is the leader of the game, and the core goal is to eliminate the system out-of-limit according to the attack strategy of the attacker, and jointly deploy the least-cost SOPs and RCSs. The attacker, as a follower in the game, aims to select the optimal attack resource allocation under the known defense deployment scheme and attack resource constraints, and finally maximize the voltage deviation of the system.

[0223] S3, simplifying and equivalently converting the double-layer game model constructed in step S2 through model linear equivalence and second-order cone method;

[0224] The double-layer optimization problem of the above double-layer model is actually a mixed integer nonlinear problem, that is, MINLP, which is difficult to solve directly. The problem is converted into a mixed integer quadratic cone programming problem, that is, MISOCP, which can significantly improve the solving efficiency.

[0225] Specifically includes:

[0226] S31, in the proposed model, the variable In formula (23) (26) (42) (45), the variable is replaced by

[0227] (53)

[0228] (54)

[0229] (55)

[0230] Wherein, represents the voltage square of node i, represents the voltage square of node j.

[0231] Although formula (54) has been replaced by a linear expression, the equation is a constraint with specified conditions, that is, only when the branch , ) is operable and valid only when closed, otherwise it is not required to be satisfied. This means that it only solves the nonlinearity of the formula, but does not solve the limitation that the voltage drop formula is only applicable to closed branches. In order to linearize it equivalently, a large M-based linearization technique is used.

[0232] S32, using a large M-based linearization technique, the formula (54) is linearized equivalently as follows:

[0233] (56)

[0234] (57)

[0235] The formula (56) (57) represents the voltage drop relationship of the branch in the connected state, but this constraint only holds when the branch is connected, that is =1, if the branch is disconnected, that is =0, then the equation does not have to be satisfied, where is a large constant.

[0236] S33, using the second-order cone method formula, (27), (29) is converted into a second-order cone form, and the converted second-order cone form is shown in formula (58), (59):

[0237] (58)

[0238] (59);

[0239] S4, by Karush-Kuhn-Tucker condition, the double-layer game model simplified and equivalently converted by step S3 is converted into a single-layer model, and the single-layer optimization problem of the single-layer model is solved to obtain the optimal planning deployment method.

[0240] Specifically, using the Karush-Kuhn-Tucker condition to linearize the constraint condition of the attack model of the double-layer game model simplified and equivalently converted by step S3, the double-layer model is converted into a single-layer model, the double-layer optimization problem of the double-layer game model is converted into a single-layer optimization problem that can be solved by the single-layer model, and the single-layer optimization problem of the single-layer model is solved to obtain the optimal planning deployment method.

[0241] In order to solve the double-layer optimization problem of the above double-layer model, and considering that the lower optimization problem is a linear convex problem, the lower optimization problem is equivalently replaced by Karush-Kuhn-Tucker, that is, KKT condition. Since the lower optimization problem is a convex problem, the above replacement is equivalent.

[0242] By KKT conditions, the above double-layer model can be converted into a single-layer model:

[0243] Because of the bilinear term involving decision variables and Lagrange multipliers in the complementary slackness condition of KKT conditions, the present application adopts a big M method to linearize the expression of the complementary slackness condition in KKT conditions, and the linearized form is shown in formulas (60)-(68).

[0244] (60)

[0245] (61)

[0246] (62)

[0247] (63)

[0248] (64)

[0249] (65)

[0250] (66)

[0251] (67)

[0252] (68)

[0253] Formulas (60)-(68) introduce the Lagrange multipliers in formula (67) to describe the dual variables of the lower optimization. Among them, is the Lagrange multiplier of inequality formulas (46) and (47), is the Lagrange multiplier of inequality formulas (48) and (49), is the Lagrange multiplier of inequality formulas (51) and (52), is the Lagrange multiplier corresponding to inequality formulas (56) and (57).

[0254] At the same time, the binary variable in formula (68) is introduced as a big M method to linearize the complementary slackness condition. The big M method restricts that when one side condition is activated, the other side condition is forced to be closed, and M refers to a large enough positive number.

[0255] The gradient condition in KKT conditions is as follows:

[0256] (69)

[0257] (70)

[0258] (71)

[0259] (72)

[0260] (73)

[0261] Equation (69) is the gradient condition for the node voltage, where and represent the child branch, i.e., the directly connected downstream branch, and the father branch, i.e., the directly connected upstream branch, of node Equations (70) and (71) are the gradients for active and reactive power, respectively, where and are the Lagrange multipliers corresponding to the power balance equations (43) and (44), and represent the index of the power balance equation with the current branch as the inflow branch and the index of the power balance equation with the current branch as the outflow branch, respectively. Equations (72) and (73) are the gradient conditions for the perturbation variables and is the upstream branch of node i; is the index of the power balance equation with the current branch as the outflow branch; is the index of the power balance equation with the current branch as the inflow branch; are the power-related parameters, is the downstream branch of node i.

[0262] The above bi-level model is transformed into a single-level model through a series of equivalences and second-order cone and KKT transformations, which converts the bi-level optimization problem of the bi-level model into a single-level optimization problem that can be solved. The objective function of the single-level optimization problem is described as:

[0263]

[0264] The constraint conditions of the single-level optimization problem include:

[0265] Upper constraints: (24)-(25), (28), (30)-(41), (56)-(59)

[0266] Lower original feasibility conditions: (43)-(44), (46)-(52), (56), (57)

[0267] Complementary slackness and non-negativity of Lagrange multipliers: (60)-(68)

[0268] ​Gradient conditions: (69)-(73)

[0269] The above model is solved using existing commercial solver CPLEX to obtain the optimal planning deployment strategy of intelligent soft switches SOPs and remote control switches RCSs.

[0270] Embodiment 2

[0271] The embodiment provides a device for implementing the load replacement attack defense method based on topology switching and power flow regulation.

[0272] a processor; and

[0273] a memory having stored thereon a computer program executable on the processor;

[0274] When the computer program is executed by the processor, the load replacement attack defense method based on topology switching and power flow regulation is implemented.

[0275] Embodiment 3

[0276] The embodiment also provides a machine-readable storage medium having stored executable instructions, which when executed cause the machine to perform the load replacement attack defense method based on topology switching and power flow regulation.

[0277] Specifically, a system or device equipped with a readable storage medium can be provided, the readable storage medium stores software program codes implementing the functions of any of the above embodiments, and the computer or processor of the system or device reads and executes the instructions stored in the readable storage medium.

[0278] In this case, the program codes read from the readable medium can themselves implement the functions of any of the above embodiments, and thus the machine-readable codes and the readable storage medium storing the machine-readable codes constitute a part of the present specification.

[0279] Embodiments of the readable storage medium include floppy disks, hard disks, magneto-optical disks, optical disks (such as CD-ROMs, CD-Rs, CD-RWs, DVD-ROMs, DVD-RAMs, DVD-RWs, DVD-RWs), magnetic tapes, non-volatile memory cards, and ROMs. Alternatively, the program codes can be downloaded from a server computer or the cloud over a communication network.

[0280] Embodiment 4

[0281] In embodiment 4, in order to verify the effectiveness and superiority of the proposed method, five typical working conditions are designed to evaluate the voltage response performance of the distribution network when subjected to LA attacks under different defense strategy deployments, as shown in Figure 3 ​

[0282] 1. No defense and no LA attack: In the case of no deployment of any defense devices, including intelligent soft open points (SOPs) and remote control switches (RCSs), and no attack, the system is in a normal operating state to characterize the voltage distribution.

[0283] 2. LA attack under no defense: Refers to the voltage distribution state of the power distribution network after being subjected to an LA attack under the condition of no deployment of any defense devices, to evaluate the vulnerability and voltage deviation degree of the system when facing the LA attack.

[0284] 3. LA attack under only deployment of SOPs: This strategy improves the system voltage condition by optimizing the deployment location of SOPs. As can be seen from Table 3, although there is a certain alleviating effect compared with the no defense working condition, voltage out-of-bounds still occurs in the system edge area such as nodes 60 to 65, among which the voltage of node 64 is 0.9391 p.u., indicating that although the deployment of SOPs has adjusting ability, its protection range is limited and cannot fully guarantee the stability of the system voltage. Figure 3

[0285] 4. LA attack under only deployment of RCSs: This strategy realizes fast topology switching and fault isolation through RCSs, and the voltage of some nodes is slightly improved, but the overall adjusting ability is still limited. As can be seen from Table 4, the voltages of nodes 58 to 63 are lower than 0.95 p.u., and the alleviating LA attack ability is worse than the only SOP strategy. Figure 3

[0286] 5. Joint deployment of SOPs and RCSs to cope with attack: The joint deployment strategy combines the voltage adjusting function of SOPs and the network reconstruction ability of RCSs to achieve the optimal protection effect. As can be seen from Table 5, the node voltage is maintained at a high level, and most of the nodes are stabilized above 0.96 p.u., except that the voltage of node 61 is 0.9484 p.u., and there is no out-of-bounds, and the cooperative control effect is significantly better than the single device deployment. Figure 3

[0287] Figure 3 The protection effects of the system under the above five strategies are shown. As can be seen, the "only deployment of SOPs" and "only deployment of RCSs" strategies can alleviate the influence of LA attack to a certain extent, but there is still a risk of voltage out-of-bounds, especially in the system edge nodes. The strategy of joint deployment of SOPs and RCSs has the best performance in voltage control ability, out-of-bounds suppression range and global stability, and can comprehensively suppress voltage deviation, which has a significant protection advantage.

[0288] In summary, the joint deployment strategy has better comprehensive performance in improving system stability and resisting attacks.

[0289] Example 5 ​​​

[0290] The present application is based on the YALMIP modeling platform for optimization modeling under the MATLAB R2021a environment, and CPLEX is used as the solver for mixed integer second order cone programming (MISOCP) problems. The simulation test is based on the IEEE69 node distribution system, and the specific parameter configuration and attack scene modeling are as follows: based on MATPOWERCASE69, the load of part of the nodes is modified, among which node 27 is enlarged by 4 times, node 35 and 69 are enlarged by 5 times, node 46 and 50 are enlarged by 2 times, and node 52 is enlarged by 10 times. At the same time, considering the electrical distance additional branch (15, 46), (11, 43), (13, 21), (27, 65) and (50, 59) as a whole, a total of 5 lines are selected as the candidate deployment position of the intelligent soft switch SOP; the edge nodes 27, 35, 46, 50, 52, 65, 67, 69 are selected as the attack target nodes, and the load replacement attack LAA is simulated. The upper limit of the total power disturbance is set to 10% of the total load of the target node, and the single node disturbance amplitude ratio is limited to 0.5. In terms of operation constraints, the upper and lower limits of the node voltage are set to 1.05 p.u. and 0.95 p.u.; the capacity of SOP is set to 800kW, the power loss factor = 0.02, and the reactive power regulation ability range is [-0.8, 0.8]; the unit capacity cost of SOP is $100 / kW, the fixed installation cost is $100,000, and the operation cost is $0.08 / kWh. The fixed cost of a single remote control switch RCS is $9,071. In addition, the large constant used in the complementary condition is set to M=10 5 .

[0291] As Figure 4 shown, the present embodiment verifies the effectiveness of the proposed collaborative defense mechanism based on intelligent soft switches SOPs and remote control switches RCSs in coping with load replacement attacks. It should be noted that when the load level is too high, it may lead to no feasible solution for the system, so the total load range set in the experiment is 93% to 107% of the given load in the MATPOWER standard test case, among which 100% is the standard load level. Specifically, Figure 4 the voltage out-of-limit index of the system under different defense deployment strategies and the corresponding minimum planning deployment total cost are shown, aiming to comprehensively evaluate the performance of the defense strategy from the two dimensions of voltage stability and economy. The following three typical strategies are compared:

[0292] 1. Only deploy SOPs: under this strategy, the voltage out-of-limit index of the system is lower than that under the LA attack There is a significant decrease, indicating that SOP has certain ability in power flow regulation and voltage support. However, the data shows that it still cannot completely eliminate the risk of voltage out-of-limit at all load levels, and the total load is in the range of 93% to 107% from 0.0297 p.u. to 0.1949 p.u., which indicates that there is still a certain security risk in this strategy. In addition, the deployment cost of SOP is stable at about $900,000, which is not economical.

[0293] 2, only deploy RCSs: This strategy realizes the rapid reconstruction of network structure by remote switching of distribution network branches, and has certain attack mitigation ability, but the experimental results show that its voltage regulation effect is limited. In the full load range, the system voltage out-of-limit index is always greater than 0.1 p.u., and at high load levels such as 107%, it reaches 0.2950 p.u., and the system still has obvious voltage out-of-limit phenomenon, which cannot meet the stable operation requirements of power system. Therefore, RCS alone is not suitable as the main defense line, but only as a supporting auxiliary mechanism.

[0294] 3, joint deployment of SOPs and RCSs: This strategy combines the power flow regulation ability of SOP and the rapid reconstruction advantage of RCS, and can effectively resist the impact of LA attack at full load levels. Experimental data show that the voltage out-of-limit index of the joint deployment scheme at 93%-107% total load level is almost zero, far lower than other strategies, showing high defense robustness. At the same time, the deployment cost of this strategy is much lower than that of the SOP-only deployment scheme, and the economy is significantly improved.

[0295] In summary, the joint deployment of SOPs and RCSs achieves a good balance between performance and cost, and exhibits superior LA attack mitigation ability and voltage stability guarantee effect at 93%-107% wide load level, verifying the practical application value of this method.

[0296] Example 6

[0297] The relevant parameters are the same as in Example 5.

[0298] This example further explores that the optimal planning and deployment strategy in the joint planning and deployment of intelligent soft-switching SOPs and remote control switches RCSs attack mitigation method depends on the current load value. It should be pointed out that different load scenarios will lead attackers to adopt different attack strategies, thus changing the resource requirements of the defense deployment. Therefore, in some scenarios, additional SOPs or RCSs may need to be deployed to ensure protection effectiveness. To systematically evaluate the adaptability of the strategy, experiments construct different operating scenarios between the total load range of 93% to 107%. The construction method is as follows: the active and reactive load disturbance range of each node is set to ± 50% of its own load value, and 100 sample data sets are randomly generated on this basis to test the applicability and stability of the current deployment scheme under wide load changes. As shown in FIG. 6, Figure 5 , the horizontal axis of the figure represents the change of the overall load of the system from 93% to 107%, reflecting the total load level; the vertical axis represents the load state percentage at the decision-making moment, reflecting the fluctuation of the system load under dynamic scheduling scenarios. The color in the figure represents the voltage out-of-bounds index of the system , the higher the value, the more serious the system voltage out-of-bounds situation, and the value is the average value of the obtained under the total load of 100 sample data sets. As can be seen from the figure, within the range of all the total loads covered, the system voltage out-of-bounds index always remains at a low level, although the color is relatively deep in the range of 93%-96% of the total load, but the out-of-bounds index all do not exceed 0.074 p.u., far below the common risk threshold, indicating that the system has a certain redundancy and regulation margin. The results also fully illustrate that the current joint deployment strategy still has good voltage regulation ability when dealing with large-scale load fluctuations. Especially in the scenario where the current decision-making load is low and the total load is high, the system shows stronger voltage control stability and defense robustness.

[0299] In summary, the application proposes a collaborative defense method for load replacement attack LAA of power distribution network, which fully combines the deployment and regulation advantages of intelligent soft switch SOPs and remote control switch RCSs. By modeling the interaction between the defender and the attacker as a double-layer Stackelberg game optimization problem, the application systematically solves the outstanding problems of response lag, insufficient regulation capacity and high cost in the existing defense strategy. Through model linear equivalent conversion and KKT condition introduction, the original mixed integer nonlinear programming (MINLP) problem is successfully converted into a mixed integer quadratic cone programming (MISOCP) problem, which significantly improves the calculation efficiency and solvability. Simulation results show that this method not only can realize the overall stability guarantee of system voltage under various attack and load scenarios, but also has more advantages in deployment cost control compared with traditional single defense strategy. In addition, through the comparison and verification of multiple examples, the joint deployment strategy realizes a good balance between performance improvement and cost optimization, and exhibits high stability, economy and adaptability, providing an efficient and feasible defense scheme for smart distribution network in the face of network security threats.

Claims

1. A load replacement attack defense method based on topology switching and power flow regulation, characterized in that, The method comprises: S1, constructing a load replacement attack model based on a linearized power distribution system power flow model of a power distribution network; S2, constructing a double-layer game model of a defender and an attacker based on the load replacement attack model constructed in step S1, wherein the upper layer is a defense model and the lower layer is an attack model, and the defense model is a collaborative defense model fusing an intelligent soft switch and a remote control switch; S3, simplifying and equivalently converting the double-layer game model constructed in step S2 through model linear equivalence and a second-order cone method; S4, converting the double-layer game model after simplification and equivalent conversion in step S3 into a single-layer model through a Karush-Kuhn-Tucker condition, and solving a single-layer optimization problem of the single-layer model to obtain an optimal planning deployment method; The objective function of the upper-layer defense model in step S2 is: （6） （7） wherein, is to minimize the value of the objective function, which consists of four parts, including the total deployment cost of SOP , the total deployment cost of RCS , the SOP power loss cost , and the total amount of voltage out-of-bound , wherein and are the weight coefficients of the SOP loss and the total amount of voltage out-of-bound, respectively; in particular, and are the unit capacity cost of SOP equipment and the capacity size of its single-sided VSC, respectively, and are the fixed cost of SOP installation and the binary variable of whether to deploy SOP at the current location, wherein represents the set of all candidate SOP installation locations; and are the cost of a single RCS and the binary variable of whether to deploy RCS at the current branch, respectively; and are the unit cost of active power loss and the active loss of SOP; represents the set of branches, represents the set of nodes; is the total voltage deviation that exceeds the upper voltage limit and is below the lower voltage limit , and the specific rules are: if ≥ , then is counted in the total amount, otherwise it is 0; conversely, if ≥ , then is counted in the total amount, otherwise it is 0; The objective function of the lower-layer attack model is: （8） wherein, respectively represent the optimal active disturbance amount and the optimal reactive disturbance amount of the attacker at the node , is the system nominal voltage value; Step S4 is specifically: linearizing the constraint condition of the attack model of the double-layer game model after simplification and equivalent conversion in step S3 using a Karush-Kuhn-Tucker condition, converting the double-layer model into a single-layer model, completing the conversion of the double-layer optimization problem of the double-layer game model into a single-layer optimization problem that can be solved by the single-layer model, and solving the single-layer optimization problem of the single-layer model to obtain the optimal planning deployment method; wherein the complementary slackness condition in the Karush-Kuhn-Tucker condition is linearly expressed by a large M method.

2. The method of defense of claim 1, wherein, In step S1, a linearized power distribution system power flow model is used to approximately describe the power flow of the power distribution system, and the power flow equation under this model is as follows: （1） （2） （3） Formula (1) describes the nodal power conservation relationship; where, Represents the set of branches. Represents a set of nodes. Represents a node Flow to Node active power, Represents a node Flow to Node active power, Represents a node The active load demand; Formula (2) is the reactive power expression of the power conservation relationship, where, Represents a node Flow to Node reactive power, Represents a node Flow to Node reactive power, Represents a node The reactive load demand; in formula (3) , Representing nodes respectively and voltage amplitude, , These are the resistance and reactance parameters of the branch, respectively; The constructed load replacement attack model is described as: （4） （5） wherein the formulas (4) (5) in represents the set of LA attack nodes selected by the attacker, is the load disturbance variable injected by the attacker at the current node.

3. The method of defense of claim 2, wherein, The constraint conditions of the upper-layer defense model include: The active power balance equation, the reactive power balance equation and the voltage drop constraint are shown in formulas (9)-(11): （9） （10） （11） wherein the equations (9) (10) introduce the intelligent soft switching at the node of the active power injection and the reactive power injection , denotes that the branch i to j is connected. The line capacity constraint is as follows: （12） wherein, Pn is the rated apparent power of the branch; equation (12) is used to prevent the risk of overload and system instability while ensuring the open state of the branch; The SOP operation related constraint is as follows: （13） （14） （15） （16） （17） Among them, formula (13) is the power balance constraint between the two nodes connected by SOP after the replacement of the tie switch; and The active power between the two nodes connected to the SOP device. and The active power loss of the two voltage source converters VSC at both ends of SOP is calculated using formula (14); where... The power loss factor of the SOP is a constant; formula (15) specifies the capacity constraint condition of the SOP, where The reactive power of the SOP device connected between the two bus nodes. The capacity of a single VSC in the SOP device is given; formula (16) describes the reactive power operating limits of the two VSCs, where... The lower and upper limits of the reactive power regulation ratio are set to ensure that the reactive power of the SOP is regulated within the effective range; formula (17) is added. To decide whether to deploy an SOP at the current location and to determine the size of the SOP to be deployed. , The set of deployments representing candidate SOPs. Indicates the position relative to the current SOP. A connected set of nodes; The radial topology and spatial mutual exclusion constraint is as follows: （18） （19） （20） （21） （22） （23） （24） （25） （26） where n is the total number of nodes in the distribution network, which guarantees the total number of connections in the radial structure is n-1, and characterizes the connectivity state of a branch; formula (19) guarantees that the root node has no upstream parent node connection; formula (20) ensures that the non-root node has and only has one parent node, where if is 1, it indicates that node is the parent node of node , otherwise is 0; formula (21) indicates that only one direction of a branch can be selected as the "parent-child relationship"; formula (22) limits and are both binary variables; formula (23) guarantees that RSC and SOP cannot be installed in the same branch at the same time, and are binary variables representing the deployment state of RSC and SOP; if branch , is installed with RCS, is equal to 1, otherwise it is equal to 0; similarly, if branch , is installed with SOP, is equal to 1, otherwise it is equal to 0; formula guarantees that the branch installed with SOP must remain disconnected; formulas (25) and (26) jointly guarantee that only the position deployed with RCS can switch the connection state and that the branch remains closed if it is not installed with RCS.

4. The method of defense of claim 3, wherein, The constraint conditions of the lower-layer attack model include: The attacker needs to consider the power constraint and the parent-child balance constraint of the voltage when attacking, as follows: （27） （28） （29） （30） （31） wherein equations (30) and (31) ensure that the power flow is zero at the branch disconnection, is the maximum capacity limit of the branch power transfer; Finally, considering the characteristics of the load replacement attack, the following constraint is introduced: （32） （33） （34） （35） （36） Wherein, the formula (32) (33) ensures that the attack amplitude of a single node does not exceed the fixed proportion of the load value of the node itself , is a proportional coefficient; the formula (34) ensures that the load of the non-attack node cannot be modified; the formula (35) (36) represents that the total active and reactive disturbance of the attacker in the whole network is limited by the total amount of attack resources, wherein is the total resource limit of the attacker on the active power attack, is the total resource limit of the attacker on the reactive power attack.

5. The method of defense of claim 4, wherein, Step S3 is specifically: S31, using variables Substitute variables in equations (7) (8) (11) (29) As follows; （37） （38） （39） wherein, V2i represents the voltage square at node i, V2j represents the voltage square at node j; S32, equivalently linearizing formula (38) using a linearization technology based on a large M, as follows: （40） （41） Equations (40) and (41) together constrain the voltage drop relationship to apply only when the branch is connected, i.e. = 1, and not to apply when the branch is not connected, i.e. = 0, where is a large constant; S33, converting formulas (12) and (14) into a second-order cone form using a second-order cone method, and the converted second-order cone form is shown in formulas (42) and (43); （42） （43）。 6. The method of defense of claim 5, wherein, The use of the Karush-Kuhn-Tucker condition to linearize the constraint condition of the lower-layer attack model of the double-layer game model after simplification and equivalent conversion in step S3, converting the double-layer model into a single-layer model, completing the conversion of the double-layer optimization problem of the double-layer game model into a single-layer optimization problem that can be solved by the single-layer model, includes: The complementary slackness condition in the Karush-Kuhn-Tucker condition is linearly expressed by a large M method, and the linearized form is shown in formulas (44)-(52): （44） （45） （46） （47） （48） （49） （50） （51） （52） Equations (44) - (52) introduce Lagrange multipliers in equation (51) for the dual variables of the lower level optimization; where, are Lagrange multipliers for inequalities equations (30) and (31), are Lagrange multipliers for inequalities equations (32) and (33), are Lagrange multipliers for inequalities equations (35) and (36), are Lagrange multipliers corresponding to inequalities equations (40) (41); At the same time, the binary variable introduced in equation (52) is used as a linearization of the complementary slackness condition by the big-M method, which constrains that when one side condition is activated, the other side condition is forced to be off, and M refers to a sufficiently large positive number; The gradient condition in the KKT conditions, as follows: （53） （54） （55） （56） （57） Equation (53) is the gradient condition for the node voltage, where and represent the child branches, i.e., the directly connected downstream branches, and the father branches, i.e., the directly connected upstream branches, of the node Equations (54) and (55) are the gradients for the active and reactive power, respectively, where and are the Lagrange multipliers corresponding to the power balance equations (27) and (28), and represent the index of the power balance equation for the incoming branch and the index of the power balance equation for the outgoing branch, respectively, with the current branch and are the gradient conditions for the perturbed variables and indicates that the branch is an upstream branch of the node i; indicates the index of the power balance equation for the outgoing branch; indicates the index of the power balance equation for the incoming branch; are the power-dependent parameters, and indicates that the branch is a downstream branch of the node i; The objective function of the single-level optimization problem can be finally described as: The constraint conditions of the single-level optimization problem include: Upper-level constraints: equations (9)-(10), (13), (15)-(26), (40)-(43) Lower-level original feasibility conditions: equations (27)-(28), (30)-(36), (40), (41) Complementary slackness and non-negativity of Lagrange multipliers: equations (44)-(52) Gradient condition: equations (53)-(57).

7. An apparatus for implementing a load substitution attack defense method based on topology switching and power flow regulation, characterized in that, The apparatus comprises: at least one processor; and a memory storing instructions that, when executed by the at least one processor, cause the at least one processor to perform the load substitution attack defense method based on topology switching and power flow regulation according to any one of claims 1 to 6.

8. A machine-readable storage medium, characterized in that, The machine-readable storage medium has stored executable instructions that, when executed, cause the machine to perform the load substitution attack defense method based on topology switching and power flow regulation according to any one of claims 1 to 6.

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