Multi-stage power supply recovery method for power distribution system containing reconfigurable soft switch to cope with network-physical collaborative threat

Abstract

The invention discloses a multi-stage power supply recovery method for a power distribution system containing a reconfigurable soft switch to cope with a network-physical collaborative threat, and the method comprises the steps: 1, building a network-physical collaborative threat model, so as to analyze the influence characteristics of the network-physical collaborative threat model on the power distribution system; 2, establishing a reconfigurable soft switch mathematical model; 3, establishing a multi-stage power supply recovery model of the power distribution system containing the reconfigurable soft switch under the network-physical collaborative threat; and 4, converting the multi-stage power supply recovery model of the power distribution system containing the reconfigurable soft switch under the network-physical cooperative threat into a mixed integer second-order cone programming constraint, and then performing solution to obtain a power distribution system operation scheme containing reconfigurable soft switch action and a remote controllable switch. According to the invention, the operation of the remote controllable switch and the reconfigurable soft switch is coordinated, so that the flexible regulation and control capability and the load recovery level of the system under extreme conditions can be improved.

Description

Technical Field

[0001] This invention belongs to the field of power distribution system operation optimization, specifically a multi-stage power supply restoration method for power distribution systems containing reconfigurable soft switches to cope with network-physical collaborative threats. Background Technology

[0002] In recent years, power systems have faced increasingly frequent natural disasters and cyberattacks, leading to frequent large-scale power outages and seriously threatening the safe and stable operation of the power system. With the deep integration of the information and physical layers of the power distribution system, the attack methods it faces are becoming increasingly complex, and cyber-physical threats are gradually becoming a major threat to the operation of power distribution systems. Compared to single-type attacks, cyber-physical threats, through the combined effect of cyberattacks and physical damage, cause more severe impacts on the power distribution system.

[0003] After a power distribution system is attacked, faults on its lines may propagate along closed circuits. In this case, the power distribution system often exhibits phased evolutionary characteristics (degradation, isolation, and recovery), necessitating research on the multi-stage recovery process. However, current research on power system recovery strategies after being subjected to cyber-physical threats typically focuses on the power restoration phase within the entire recovery process after an attack, neglecting research on the multi-stage recovery process for addressing cyber-physical threats. This further leads to imbalances in resource allocation and a decline in overall recovery efficiency. Summary of the Invention

[0004] This invention addresses the shortcomings of existing technologies by proposing a multi-stage power supply restoration method for power distribution systems containing reconfigurable soft switches to cope with cyber-physical threats. The aim is to coordinate reconfigurable soft switches, controllable switches, and other equipment to resist cyber-physical threats, achieve effective recovery under cyber-physical threats, and improve the system's flexible control capability and load recovery level under extreme conditions.

[0005] To achieve the above-mentioned objectives, the present invention adopts the following technical solution: The present invention provides a multi-stage power supply restoration method for a power distribution system containing a reconfigurable soft switch to cope with cyber-physical cooperative threats, characterized by the following steps: Step 1: Construct the constraints of a multi-stage power supply recovery model for a power distribution system with reconfigurable soft switches to cope with cyber-physical threats; Step 2: Construct the objective function of a multi-stage power supply recovery model for a power distribution system with reconfigurable soft switches to address cyber-physical threats. ; Step 3: The multi-stage power supply recovery model of the power distribution system with reconfigurable soft switches to cope with cyber-physical collaborative threats is transformed into a mixed integer second-order cone programming constraint and then solved to obtain the operation scheme of the power distribution system including the action of the reconfigurable soft switch R-SOP and the actions of all switches.

[0006] The multi-stage power restoration method for power distribution systems with reconfigurable soft switches to cope with cyber-physical threats, as described in this invention, is also characterized in that step 1 includes the following steps: Step 1.1: Obtain the quantitative constraints of network-physical cooperative threats from equations (1) to (7): (1) (2) (3) (4) (5) (6) (7) In equations (1)-(7), represent Time Node The amount of load tampering; This represents the extent of load tampering; The total number of moments; Represents the power transfer distribution factor matrix; Represents the attack vector for power flow measurement; Represents the attack vector for load measurement; Represents the set of all nodes in the power distribution system; for Time Node The active power consumed by the load; represent Time Node The 0-1 integer variables corresponding to the load nodes; represent Time Node With nodes Branch roads between The corresponding 0-1 integer variable; The set number of attackable resources; represent Time Branch Transmission power tampering amount; Representative branch road A 0-1 integer variable indicating whether the target has been subjected to a physical attack; Represents physical attack resources; represent Time Branch A 0-1 integer variable indicating whether the network is connected; Step 1.2: Obtain the constraints of the reconfigurable soft switch R-SOP from equations (8) to (17): (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) In equations (8)-(17), , These represent the set of nodes connected to the voltage source converter and the set of all tie switches, respectively. This refers to the number of voltage source converters; Indicates the first A voltage source converter in Whether the node is connected to the voltage source converter at any time Connected; express Nodes that are always connected to the voltage source converter The status of all connected interconnecting switches; express Nodes that are always connected to the voltage source converter The status of all connected interconnecting switches; express Nodes that are always connected to the voltage source converter The status of all connected interconnecting switches; represent Nodes that are always connected to the voltage source converter The maximum apparent power transmitted across all connected feeders; For the first The capacity of the voltage source converter; , , Represent Time Node The active power, reactive power, and DC-side power transmitted by all connected voltage source converters; represent Time Node Active power losses on all connected voltage source converters; This is the loss coefficient; represent Time of the first Status of each contact switch; represent Nodes that are always connected to the voltage source converter The voltage; represent Nodes that are always connected to the voltage source converter The port open state of the reconfigurable intelligent soft switch R-SOP; The reference voltage for the power distribution system is M; M is a constant. Step 1.3: Construct the switching action constraints and fault state propagation constraints for the degradation stage using equations (18)-(20): (18) (19) (20) In equations (18)-(20), Represents the degeneration stage Time Node A 0-1 integer variable indicating whether it is in a fault state; Represents the degeneration stage Time Node A 0-1 integer variable indicating whether it is in a fault state; Represents the stage of degradation Timetable A 0-1 variable indicating whether the network is connected; Step 1.4: Construct the switching action constraints and fault state propagation constraints for the fault isolation stage using equations (21)-(24): (twenty one) (twenty two) (twenty three) (twenty four) In equations (21)-(24), Represents the fault isolation phase Time Node A 0-1 integer variable indicating whether it is in a fault state; Represents the fault isolation phase Time Node A 0-1 integer variable indicating whether it is in a fault state; Represents the fault isolation phase Timetable A 0-1 variable indicating whether the network is connected; Step 1.5: Construct the switching action constraints and fault state propagation constraints for the power supply restoration phase using equations (25) and (26): (25) (26) In equations (25)-(26), Represents the power restoration phase Time Node A 0-1 integer variable indicating whether it is in a fault state; Represents the power restoration phase Time Node A 0-1 integer variable indicating whether it is in a fault state; Represents the power restoration phase Timetable A 0-1 variable indicating whether the network is connected; Representative Line Whether to configure the 0-1 variable of the switch; Step 1.6: Construct the virtual power flow constraints for the power distribution system reconfiguration during the power supply restoration phase using equations (27)-(30): (27) (28) (29) (30) In equations (27)-(30), yes Time Branch The virtual trend; yes Time Node The current generated by the virtual power source; It is a node Virtual demand; The number of nodes in the power distribution system; Step 1.7: Construct multi-stage power flow constraints for a power distribution system with reconfigurable soft-switching R-SOP to cope with network-physical cooperative threats using equations (31)-(41): (31) (32) (33) (34) (35) (36) (37) (38) (39) (40) (41) (42) (43) (44) In equations (31)-(44), and They are respectively Phase 2 Timetable The active and reactive power transmitted upstream; and The lines are respectively Resistance and reactance; and They are respectively Phase 2 Time Node The injected active and reactive power; for Phase 2 Time Node Active load reduction for Phase 2 Time Node The amount of reactive load reduction; for Phase 2 Time Node voltage, for Phase 2 Time Line The current transmitted upwards; , They are respectively Time Node Photovoltaic active power output and The reduction in active power generation from photovoltaic power during the current phase; for Time Node Photovoltaic reactive power output; for Time Node The reactive power consumed by the load; and for Phase 2 Time Node The active and reactive power injected at R-SOP; for Phase 2 Time Node Active power injected by DG; and For the line The maximum transmitted active and reactive power; and These represent the maximum and minimum values ​​of the node voltage; This represents the upper limit of branch current in the power distribution system. and The maximum and minimum active power injected into DG; When c=1, The stage represents the degradation stage; when c=2, The stage represents the fault isolation stage; when c=3, The term "phase" indicates the power restoration phase.

[0007] Furthermore, in step 2, the objective function is constructed using equations (45) and (46). : (45) (46) In equations (45)-(46), Indicates the moment when the switch is activated to isolate a fault; Indicates the moment when the switch is activated to restore power; Indicates the moment when the maintenance personnel began the operation; This represents the amount of load reduced during the degradation phase; This represents the amount of workload reduced during the isolation phase; This represents the amount of load reduction during the recovery phase.

[0008] Furthermore, step 3 includes the following steps: Step 3.1: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require and Replace them with two linear variables respectively and And the big-M method is used to relax equations (31)-(34) and (39)-(40), so that the transformed linear constraints can be obtained using equations (47)-(52): (47) (48) (49) (50) (51) (52) In equations (47)-(52), and respectively Phase 2 Time Node The square of the voltage at the point, Phase 2 Time Node To the node Branch road The square of the current; Step 3.2: Use equation (53) to transform equation (50) into a second-order cone constraint: (53) In equation (53), T represents transpose; Step 3.3: Use equation (54) to transform equation (12) into a rotating cone constraint: (54).

[0009] The present invention provides an electronic device, including a memory and a processor, characterized in that the memory is used to store a program supporting the processor in executing the power restoration method, and the processor is configured to execute the program stored in the memory.

[0010] The present invention provides a computer-readable storage medium storing a computer program, characterized in that the computer program, when executed by a processor, performs the steps of the power restoration method.

[0011] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention establishes a cyber-physical collaborative threat quantification model to deeply analyze its impact characteristics on power distribution systems. By analyzing the phased evolution characteristics (degradation, isolation, and recovery) exhibited by power distribution systems, it provides a scientific basis for power distribution system defense strategies and offers technical support for improving the security and resilience of power distribution systems.

[0012] 2. This invention proposes a multi-stage power supply restoration method for power distribution systems with reconfigurable soft switches to cope with cyber-physical threats. This method systematically models and analyzes the evolutionary characteristics of the power distribution system during the multi-stage processes of degradation, isolation, and recovery. It innovatively introduces a partitioned, flexibly switchable Redirect Switching Operator (R-SOP) to achieve dynamic switching of operating modes and efficient utilization of port capacity. By further coordinating the operation of Remote Controllable Switches (RCS), load measurement protection, and R-SOPs, the scope of fault impact is effectively reduced, the power supply guarantee level of critical loads is improved, and the rapid response and overall recovery capability of the power distribution system against cyber-physical threats is significantly enhanced. Attached Figure Description

[0013] Figure 1 A diagram illustrating the principles of load redistribution attacks and cyber-physical collaborative threats; Figure 2 For the modified IEEE 33-node power distribution system; Figure 3 To restore the topology of the power distribution system in multiple stages; Figure 4 This is a schematic diagram illustrating the recovery rate at each stage. Figure 5 A comparison chart of feeder port capacity at different time periods; Figure 6 This is a comparison chart showing the recovery status of the cases. Detailed Implementation

[0014] In this embodiment, a multi-stage power supply restoration method for a power distribution system containing a reconfigurable soft switch to cope with cyber-physical collaborative threats is described, with the following specific steps: Step 1: Constraints for constructing a multi-stage power supply recovery model for a power distribution system with reconfigurable soft switches to cope with cyber-physical threats: Step 1-1: Obtain the quantitative constraints of network-physical cooperative threats from equations (1) to (7): (1) (2) (3) (4) (5) (6) (7) In equations (1)-(7), represent Time Node The amount of load tampering; This represents the extent of load tampering, and is between 0 and 1. The total number of moments; Represents the power transfer distribution factor matrix; Represents the attack vector for power flow measurement; Represents the attack vector for load measurement; Represents the set of all nodes in the power distribution system; for Time Node The active power consumed by the load; represent Time Node The 0-1 integer variables corresponding to the load nodes; represent Time Node With nodes Branch roads between The corresponding 0-1 integer variable; The set number of attackable resources; represent Time Branch Transmission power tampering amount; Representative branch road A 0-1 integer variable indicating whether the target has been subjected to a physical attack; Represents physical attack resources; represent Time Branch A 0-1 integer variable indicating whether the network is connected.

[0015] Step 1-2: Obtain the constraints of the reconfigurable soft switch R-SOP from equations (8) to (17): (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) In equations (8)-(17), , These represent the set of nodes connected to the voltage source converter and the set of all tie switches, respectively. This refers to the number of voltage source converters; Indicates the first A voltage source converter in Whether the node is connected to the voltage source converter at any time Connected; express Nodes that are always connected to the voltage source converter The status of all connected interconnecting switches; express Nodes that are always connected to the voltage source converter The status of all connected interconnecting switches; express Nodes that are always connected to the voltage source converter The status of all connected interconnecting switches; represent Nodes that are always connected to the voltage source converter The maximum apparent power transmitted across all connected feeders; For the first The capacity of the voltage source converter; , , Represent Time Node The active power, reactive power, and DC-side power transmitted by all connected voltage source converters; represent Time Node Active power losses on all connected voltage source converters; This is the loss coefficient; represent Time of the first Status of each contact switch; represent Nodes that are always connected to the voltage source converter The voltage; represent Nodes that are always connected to the voltage source converter The port open state of the reconfigurable intelligent soft switch R-SOP; is the reference voltage of the power distribution system; M is a constant.

[0016] Steps 1-3: Construct the switching action constraints and fault state propagation constraints for the degradation stage using equations (18)-(20): (18) (19) (20) In equations (18)-(20), Represents the degeneration stage Time Node A 0-1 integer variable indicating whether it is in a fault state; Represents the degeneration stage Time Node A 0-1 integer variable indicating whether it is in a fault state; Represents the stage of degradation Timetable A 0-1 variable indicating whether the network is connected.

[0017] Steps 1-4: Construct the switching action constraints and fault state propagation constraints for the fault isolation stage using equations (21)-(24). (twenty one) (twenty two) (twenty three) (twenty four) In equations (21)-(24), Represents the fault isolation phase Time Node A 0-1 integer variable indicating whether it is in a fault state; Represents the fault isolation phase Time Node A 0-1 integer variable indicating whether it is in a fault state; Represents the fault isolation phase Timetable A 0-1 variable indicating whether the network is connected.

[0018] Steps 1-5: Construct the switching action constraints and fault state propagation constraints for the power supply restoration phase using equations (25)-(26). (25) (26) In equations (25)-(26), Represents the power restoration phase Time Node A 0-1 integer variable indicating whether it is in a fault state; Represents the power restoration phase Time Node A 0-1 integer variable indicating whether it is in a fault state; Represents the power restoration phase Timetable A 0-1 variable indicating whether the network is connected; Representative Line Whether to configure the 0-1 variable of the switch.

[0019] Steps 1-6: Construct virtual power flow constraints for power distribution system reconfiguration during the power supply restoration phase using equations (27)-(30): (27) (28) (29) (30) In equations (27)-(30), yes Time Branch The virtual trend; yes Time Node The current generated by the virtual power source; It is a node Virtual demand; This represents the number of nodes in the power distribution system.

[0020] Steps 1-7: Construct a multi-stage power flow constraint for a power distribution system with reconfigurable soft switches to cope with network-physical cooperative threats using equations (31)-(44): (31) (32) (33) (34) (35) (36) (37) (38) (39) (40) (41) (42) (43) (44) In equations (31)-(44), and They are respectively Phase 2 Timetable The active and reactive power transmitted upstream; and The lines are respectively Resistance and reactance; and They are respectively Phase 2 Time Node The injected active and reactive power; for Phase 2 Time Node Active load reduction for Phase 2 Time Node The amount of reactive load reduction; for Phase 2 Time Node voltage, for Phase 2 Time Line The current transmitted upwards; , They are respectively Time Node Photovoltaic active power output and The amount of active power reduction during the phase; for Time Node Photovoltaic reactive power output; for Time Node The reactive power consumed by the load; and for Phase 2 Time Node The active and reactive power injected at R-SOP; for Phase 2 Time Node Active power injected by DG; and For the line The maximum transmitted active and reactive power; and These represent the maximum and minimum values ​​of the node voltage; This represents the upper limit of branch current in the power distribution system. and The maximum and minimum active power injected into DG.

[0021] Step 2: Construct the objective function of a multi-stage power supply recovery model for a power distribution system with reconfigurable soft switches to cope with cyber-physical threats using equations (45)-(46). : (45) (46) In equations (45)-(46), Indicates the moment when the switch is activated to isolate a fault; Indicates the moment when the switch is activated to restore power; Indicates the moment when the maintenance personnel began the operation; This represents the amount of load reduced during the degradation phase; This represents the amount of workload reduced during the isolation phase; This represents the amount of load reduction during the recovery phase.

[0022] Step 3: Transform the multi-stage power supply recovery model of the power distribution system containing reconfigurable soft switches to cope with cyber-physical collaborative threats into a mixed integer second-order cone programming constraint and then solve it to obtain the operation scheme of the power distribution system including the action of reconfigurable soft switches R-SOP and the action of controllable switches.

[0023] Step 3-1: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require and Replace them with two linear variables respectively and The big-M method is used to relax equations (31)-(34) and (39)-(40) to transform them into linear constraints, and then the transformed constraints are constructed using equations (47)-(52): (47) (48) (49) (50) (51) (52) In equations (47)-(52), and Separate stages Time Node Square of voltage, stage Time Node To the node Branch road The square of the current.

[0024] Step 3-2: Use equation (53) to transform equation (50) into a second-order cone constraint: (53) In equation (53), T represents transpose.

[0025] Step 3-3: Use equation (54) to transform equation (12) into a rotating cone constraint: (54) Using the above method, the multi-stage power supply recovery model of the power distribution system containing reconfigurable soft switches to cope with cyber-physical collaborative threats is transformed into a mixed integer second-order cone programming constraint and then solved to obtain the operation scheme of the power distribution system including the action of reconfigurable soft switches R-SOP and the action of controllable switches.

[0026] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described method, and the processor is configured to execute the program stored in the memory.

[0027] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.

[0028] To enable those skilled in the art to better understand the present invention, the numerical example analysis includes the following components: I. Example Description and Simulation Result Analysis: like Figure 2In the test system shown, the photovoltaic (PV) nodes are 7, 30, 19, 21, 27, and 15. Lines 2-3, 8-9, 15-16, and 3-23 in the test system are subject to Type I physical attacks, while lines 4-5 and 12-13 are subject to Type II physical attacks. Simulation results from the DAD model show that load data measurement protection devices are deployed at nodes 3, 14, 17, 24, 31, and 33. Due to the deployment of these protection devices, attackers cannot choose the optimal load data for their attack and can only tamper with the load data at nodes 23, 25, 10, 11, 16, and 18. The system reference voltage is 12.66 kV, with a voltage safety range of 0.95-1.05 pu. A distributed generator (DG) with a maximum output of 0.3 MW is connected at node 11. To expand the scope of the R-SOP, this invention employs a six-feeder, four-converter R-SOP connected to nodes 33, 9, 12, 15, 18, and 22, with a total capacity of 1.5MW. The capacities of the four converters are set according to the golden ratio. The fault is assumed to occur at 9:00 AM, the total simulation time is 1 hour, and the time interval is set to 5 minutes. In this invention, the control of the R-SOP is achieved through relay switches, requiring only a control level input for rapid response, thus meeting the 5-minute control scale of this invention.

[0029] To fully demonstrate the effectiveness of the power supply restoration method for power distribution systems based on reconfigurable soft switches in response to cyber-physical threats, four schemes (Case 1, Case 2, Case 3, and Case 4) are set up for comparison in the case study section.

[0030] Case I: Multiplexed soft switch MOP is used for multi-stage recovery of power distribution system under cyber-physical combined threat, without considering false measurements caused by cyber attacks; Case II: Based on the multi-stage recovery method for power distribution systems, R-SOP is added to defend against cyber-physical collaborative threats, without considering false measurements caused by cyber attacks; Case III: A multi-stage recovery method for power distribution systems based on multiplexed soft switching MOPs under cyber-physical cooperative threats; Case IV: The method proposed in this invention.

[0031] All numerical simulations in the examples section were performed in MATLAB 2023a and solved using the YALMIP toolbox and Gurobi solver in a 64-bit Windows environment. The computing device was a computer configured with an Intel(R) Core(TM) i7-8700 @ 3.2GHz.

[0032] Figure 1This diagram illustrates the principle of load redistribution attacks and cyber-physical collaborative threats. Load redistribution attacks are a specific form of spoofed data injection attacks that have received extensive research in recent years. The primary target of load redistribution attacks is load demand measurements. In power distribution systems subjected to load redistribution attacks, the injection of spoofed data leads to a "redistribution" of loads within the system. Figure 1 As shown, node The load data decreased compared to the actual data, and the nodes... The load data increased. Load redistribution attacks created "high-load areas" in the distribution system. Dispatchers used the tampered load data to optimize scheduling, due to node... The increase in load data caused a drop from node 1 to node 2. The voltage drop is more pronounced. To make the node... Without exceeding the lower limit, the dispatchers then reduced the number of nodes. The load.

[0033] In this invention, a physical attack is used to disrupt power lines, while a network attack is used in conjunction with it. The attacker first disrupts the power lines, creating multiple power outage zones in the distribution system. Then, they selectively inject false data into specific load nodes. This false data bypasses malicious data monitoring mechanisms, and dispatchers execute load reduction plans based on the received false data. Because of the role of false data in the cyber-physical coordinated threat, the increase in load in the power outage zones and the significant spatiotemporal differences in load distribution make the recovery process more complex than with conventional faults.

[0034] exist Figure 2 In the IEEE 33-node test system shown, the four schemes described above, Case I to IV, are executed. Figure 3 To restore the topology of the power distribution system in multiple stages, Figure 4 This represents the load recovery rate of each node during each stage of the system's operation. Under network-physical combined threats, the system lines experience two types of faults, and the presence of false data leads to abnormal load distribution within the system (a surge in load at some feeder ends), making load recovery more difficult.

[0035] During the degradation phase, because the isolation action of the switch is not completed, most nodes of the power distribution system are in a fault state. During this phase, the power distribution system is most affected by network-physical collaborative threats.

[0036] During the isolation phase, the RCS on lines 5-6, 11-12, and 13-14 was disconnected, greatly reducing the fault area. However, since nodes 23-25 ​​had no power supply, the load on these nodes could not be restored.

[0037] During the power restoration phase, nodes 16 and 18 were affected by a network-physical coordination threat, causing a surge in load data. To restore the load in this area, R-SOP switched feeders 33 and 18 to "tethering switch mode," effectively restoring nodes 16-18. At the same time, tethering switches 25-29 and 8-21 were closed to connect the non-faulty areas (nodes 23-25) to the power supply, allowing the load in this area to be restored.

[0038] Based on the above analysis, under the influence of cyber-physical combined threats, the power distribution system underwent a multi-stage recovery process of degradation, isolation, and power restoration, with each stage affected by spurious measurements and physical faults. Through the coordinated operation of R-SOP and RCS, the system can reduce the scope of fault impact and enhance the recovery performance of the attacked area. Especially during the recovery phase, R-SOP significantly improves power transfer capabilities through mode switching, effectively alleviating the recovery difficulties caused by abnormal load distribution.

[0039] Figure 5 To compare the transmittable capacity of R-SOP with the total capacity of VSC, R-SOP achieves nearly double the transmittable capacity compared to the total capacity of VSC through mode switching. Meanwhile... Figure 5 The changes in feeder capacity over different time periods are demonstrated. R-SOP achieves time-varying port capacity through VSC reconfiguration, adapting to the characteristics of large spatiotemporal differences in load distribution in power distribution systems under network-physical collaborative threats.

[0040] The recovery rates of Case 1, Case 2, Case 3, and Case 4 are as follows: Figure 6 As shown. From Figure 6 The data shows that the recovery rate for Case III was higher than that for Case I, and the recovery rate for Case IV was higher than that for Case II. This is because Case I and Case II both ignored the impact of network attacks. In real-world scenarios, spurious measurements caused by network attacks would result in a greater load reduction.

[0041] From the recovery phase onwards, Case IV exhibits a better recovery rate than Case III. This is because, although the multiplexed soft-switching MOP has some port capacity adjustment capability, increasing the capacity of inter-feeder interconnection, it is always limited by the capacity of the VSC. The R-SOP, by switching operating modes at different ports, further enhances system flexibility and improves recovery capability. Meanwhile, from the recovery phase onwards, Case II shows a better recovery rate than Case I, further validating the superiority of the R-SOP.

[0042] In this specification, the illustrative descriptions of the invention are not necessarily directed at the same embodiments or examples. Those skilled in the art can combine and integrate the different embodiments or examples described in this specification. Furthermore, the embodiments in this specification are merely enumerations of implementation forms of the inventive concept, and the scope of protection of the invention should not be considered as limited to the specific forms stated in the embodiments. The scope of protection of the invention also includes equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.

Claims

1. A multi-stage power supply restoration method for a power distribution system containing a reconfigurable soft switch to cope with cyber-physical collaborative threats, characterized in that, Includes the following steps: Step 1: Construct the constraints of a multi-stage power supply recovery model for a power distribution system with reconfigurable soft switches to cope with cyber-physical threats; Step 2: Construct the objective function of a multi-stage power supply recovery model for a power distribution system with reconfigurable soft switches to address cyber-physical threats. ; Step 3: The multi-stage power supply recovery model of the power distribution system with reconfigurable soft switches to cope with cyber-physical collaborative threats is transformed into a mixed integer second-order cone programming constraint and then solved to obtain the operation scheme of the power distribution system including the action of the reconfigurable soft switch R-SOP and the actions of all switches.

2. The multi-stage power supply restoration method for a power distribution system containing a reconfigurable soft switch to cope with cyber-physical collaborative threats according to claim 1, characterized in that, Step 1 includes the following steps: Step 1.1: Obtain the quantitative constraints of network-physical cooperative threats from equations (1) to (7): (1) (2) (3) (4) (5) (6) (7) In equations (1)-(7), represent Time Node The amount of load tampering; This represents the extent of load tampering; The total number of moments; Represents the power transfer distribution factor matrix; Represents the attack vector for power flow measurement; Represents the attack vector for load measurement; Represents the set of all nodes in the power distribution system; for Time Node The active power consumed by the load; represent Time Node The 0-1 integer variables corresponding to the load nodes; represent Time Node With nodes Branch roads between The corresponding 0-1 integer variable; The set number of attackable resources; represent Time Branch Transmission power tampering amount; Representative branch road A 0-1 integer variable indicating whether the target has been subjected to a physical attack; Represents physical attack resources; represent Time Branch A 0-1 integer variable indicating whether the network is connected; Step 1.2: Obtain the constraints of the reconfigurable soft switch R-SOP from equations (8) to (17): (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) In equations (8)-(17), , These represent the set of nodes connected to the voltage source converter and the set of all tie switches, respectively. This refers to the number of voltage source converters; Indicates the first A voltage source converter in Whether a node is connected to the voltage source converter at any given time Connected; express Nodes that are always connected to the voltage source converter The status of all connected interconnecting switches; express Nodes that are always connected to the voltage source converter The status of all connected interconnecting switches; express Nodes that are always connected to the voltage source converter The status of all connected interconnecting switches; represent Nodes that are always connected to the voltage source converter The maximum apparent power transmitted across all connected feeders; For the first The capacity of the voltage source converter; , , Represent Time Node The active power, reactive power, and DC-side power transmitted by all connected voltage source converters; represent Time Node Active power losses on all connected voltage source converters; This is the loss coefficient; represent Time of the first Status of each contact switch; represent Nodes that are always connected to the voltage source converter The voltage; represent Nodes that are always connected to the voltage source converter The port open state of the reconfigurable intelligent soft switch R-SOP; The reference voltage for the power distribution system is M; M is a constant. Step 1.3: Construct the switching action constraints and fault state propagation constraints for the degradation stage using equations (18)-(20): (18) (19) (20) In equations (18)-(20), Represents the degeneration stage Time Node A 0-1 integer variable indicating whether it is in a fault state; Represents the degeneration stage Time Node A 0-1 integer variable indicating whether it is in a fault state; Represents the stage of degradation Timetable A 0-1 variable indicating whether the network is connected; Step 1.4: Construct the switching action constraints and fault state propagation constraints for the fault isolation stage using equations (21)-(24): (21) (22) (23) (24) In equations (21)-(24), Represents the fault isolation phase Time Node A 0-1 integer variable indicating whether it is in a fault state; Represents the fault isolation phase Time Node A 0-1 integer variable indicating whether it is in a fault state; Represents the fault isolation phase Timetable A 0-1 variable indicating whether the network is connected; Step 1.5: Construct the switching action constraints and fault state propagation constraints for the power supply restoration phase using equations (25) and (26): (25) (26) In equations (25)-(26), Represents the power restoration phase Time Node A 0-1 integer variable indicating whether it is in a fault state; Represents the power restoration phase Time Node A 0-1 integer variable indicating whether it is in a fault state; Represents the power restoration phase Timetable A 0-1 variable indicating whether the network is connected; Representative Line Whether to configure the 0-1 variable of the switch; Step 1.6: Construct the virtual power flow constraints for the power distribution system reconfiguration during the power supply restoration phase using equations (27)-(30): (27) (28) (29) (30) In equations (27)-(30), yes Time Branch The virtual trend; yes Time Node The current generated by the virtual power source; It is a node Virtual demand; The number of nodes in the power distribution system; Step 1.7: Construct multi-stage power flow constraints for a power distribution system with reconfigurable soft-switching R-SOP to cope with network-physical cooperative threats using equations (31)-(41): (31) (32) (33) (34) (35) (36) (37) (38) (39) (40) (41) (42) (43) (44) In equations (31)-(44), and They are respectively Phase 2 Timetable The active and reactive power transmitted upstream; and The lines are respectively Resistance and reactance; and They are respectively Phase 2 Time Node The injected active and reactive power; for Phase 2 Time Node Active load reduction for Phase 2 Time Node The amount of reactive load reduction; for Phase 2 Time Node voltage, for Phase 2 Time Line The current transmitted upwards; , They are respectively Time Node Photovoltaic active power output and The reduction in active power generation from photovoltaic power during the current phase; for Time Node Photovoltaic reactive power output; for Time Node The reactive power consumed by the load; and for Phase 2 Time Node The active and reactive power injected at R-SOP; for Phase 2 Time Node Active power injected by DG; and For the line The maximum transmitted active and reactive power; and These represent the maximum and minimum values ​​of the node voltage; This represents the upper limit of branch current in the power distribution system. and The maximum and minimum active power injected into DG; When c=1, The stage represents the degradation stage; when c=2, The stage represents the fault isolation stage; when c=3, The term "phase" indicates the power restoration phase.

3. The multi-stage power supply restoration method for a power distribution system containing a reconfigurable soft switch to cope with cyber-physical cooperative threats according to claim 2, characterized in that, In step 2, the objective function is constructed using equations (45) and (46). : (45) (46) In equations (45)-(46), Indicates the moment when the switch is activated to isolate a fault; Indicates the moment when the switch is activated to restore power; Indicates the moment when the maintenance personnel began the operation; This represents the amount of load reduced during the degradation phase; This represents the amount of workload reduced during the isolation phase; This represents the amount of load reduction during the recovery phase.

4. The multi-stage power supply restoration method for a power distribution system containing a reconfigurable soft switch to cope with cyber-physical co-threats according to claim 3, characterized in that, Step 3 includes the following steps: Step 3.1: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] and Replace them with two linear variables respectively and And the big-M method is used to relax equations (31)-(34) and (39)-(40), so that the transformed linear constraints can be obtained using equations (47)-(52): (47) (48) (49) (50) (51) (52) In equations (47)-(52), and respectively Phase 2 Time Node The square of the voltage at the point, Phase 2 Time Node To the node Branch road The square of the current; Step 3.2: Use equation (53) to transform equation (50) into a second-order cone constraint: (53) In equation (53), T represents transpose; Step 3.3: Use equation (54) to transform equation (12) into a rotating cone constraint: (54)。 5. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports the processor in executing the power restoration method according to any one of claims 1-4, and the processor is configured to execute the program stored in the memory.

6. A computer-readable storage medium storing a computer program thereon, characterized in that, The computer program is executed by the processor to perform the steps of the power restoration method according to any one of claims 1-4.

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