A power grid expansion planning method and device for blocking multiple fault propagation, equipment and medium

Abstract

The application discloses a power grid expansion planning method and device for blocking multiple fault propagation, equipment and medium, and belongs to the technical field of power grids. The method comprises the following steps: acquiring a target power topology corresponding to a target power system, determining a target power network ring structure with the largest influence range in the target power topology when multiple faults occur in the target power system, and creating a three-layer optimization model; the three-layer optimization model comprises: an upper-layer optimization model for simulating newly-built power transmission lines in the target power network ring structure, a middle-layer optimization model for simulating multiple faults occurring in the target power system, and a lower-layer optimization model for simulating a cascading propagation path when the multiple faults occurring in the target power system are blocked; the three-layer optimization model is solved by using a Benders decomposition algorithm, a target line set is obtained, and power transmission lines are newly built in the target power system according to the target line set. The method can further ensure the safe and stable operation of the power system.

Description

Technical Field

[0001] This invention relates to the field of power grid technology, and in particular to a power grid expansion planning method, apparatus, equipment and medium for blocking the propagation of multiple faults. Background Technology

[0002] When multiple components in a power system fail, it triggers a power flow shift, causing the fault to propagate rapidly throughout the entire system, resulting in a cascading failure and potentially a major blackout. A cascading failure in a power system can cause multiple lines within it to overload in a short period, making it difficult to implement effective emergency remedial measures.

[0003] Therefore, it is evident that how to construct new power transmission lines in the critical power network ring structure of a power system by considering the cascading propagation characteristics of multiple faults in the early stages of power system design, promptly interrupting cascading faults in the power system, and ensuring the safe and stable operation of the power system is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a power grid expansion planning method, apparatus, equipment, and medium for blocking the propagation of multiple faults, so as to further improve the safety of the power system during operation. The specific solution is as follows: To address the aforementioned technical problems, this invention provides a power grid expansion planning method for blocking the propagation of multiple faults, comprising: Obtain the power topology map corresponding to the target power system to obtain the target power topology map; In the target power topology map, determine the power network ring structure with the largest impact range when the target power system experiences multiple faults, and obtain the target power network ring structure; A three-layer optimization model is created based on the target power network ring structure. The three-layer optimization model includes: an upper-layer optimization model for simulating the construction of new power transmission lines in the target power network ring structure, a middle-layer optimization model for simulating multiple faults in the target power system, and a lower-layer optimization model for simulating the blocking of cascading propagation paths when multiple faults occur in the target power system. The Benders decomposition algorithm is used to solve the three-layer optimization model to obtain the target line set, and power transmission lines are newly built in the target power system according to the target line set.

[0005] Preferably, the step of determining the power network ring structure with the largest impact range when multiple faults occur in the target power system in the target power topology map, and obtaining the target power network ring structure, includes: The maximum matching result is obtained by performing maximum matching calculation on the target power system based on the minimum input theorem. The nodes that are not matched in the maximum matching result are determined as driving nodes, and the minimum set of driving nodes required to achieve structural controllability of the target power system is constructed from the driving nodes. Starting from the target node, the nodes and lines associated with the target node are divided into structurally controllable subsystems corresponding to the target node; the target node is any node in the set of minimum driving nodes. The structurally controllable subsystems corresponding to each driving node are equivalently reduced to generalized nodes, and a reduced-order power network is constructed based on the topological connection relationship between the generalized nodes. The target power network ring structure is obtained by using Fiedler eigenvalues ​​to find the power network ring structure with the largest eigenvalue in the reduced-order power network.

[0006] Preferably, the expression for the upper-level optimization model is: ; In the formula, Indicates load, Indicates load Load loss, Indicates the line Whether the variable corresponds to the construction of lines on the target power network ring structure. This represents the total load of the target power system; The constraints corresponding to the upper-level optimization model are: ; ; In the formula, Indicates whether the structure is controllable subsystem and structurally controllable subsystems The variables corresponding to adding edges, Represents a structurally controllable subsystem and structurally controllable subsystems The set of lines to be built between them Indicates the collection of lines to be built Total number of lines in Budget for adding borders; Indicates the route. Indicates the line Whether the variable corresponds to the construction of the line on the target power network ring structure; ; In the formula, For structurally controllable subsystems and structurally controllable subsystems The adjacency matrix between them.

[0007] Preferably, the expression for the mid-level optimization model is: ; In the formula, Indicates the line The variable corresponding to whether a fault occurs. Indicates load, This represents the total load of the target power system. Indicates load Load loss; The constraints of the mid-level optimization model are: ; In the formula, This represents the constraint conditions of the mid-level optimization model. Indicates the route. This represents the total number of lines in the target power system. Indicates the line The variable corresponding to whether a fault occurs. Indicates the line Whether the variable corresponds to the construction of lines on the target power network ring structure. This represents the number of faulty lines. For the existing line set, This is a collection of lines to be built.

[0008] Preferably, the expression for the lower-level optimization model is: ; In the formula, Indicates generator of efforts, Indicates load Load loss, Indicates load, This represents the total load of the target power system; The constraints of the lower-level optimization model include: Node power balance constraints: ; In the formula, Represents a node. Indicates the route. This represents the total number of lines in the target power system. Represents a node With the line The connection parameters between them Indicates the line The trend Indicates generator, This represents the total number of generators in the target power system. Represents a node With generator The connection parameters between them Indicates generator of efforts, Indicates load, This represents the total load of the target power system. Represents a node With load The connection parameters between them For load The initial load, Indicates load Load loss, This represents the set of all nodes in the target power system; Power flow constraints for the line: ; In the formula, Indicates the route. Indicates the line The trend Indicates the line Admittance, Represents a node. This represents the total number of nodes in the target power system. Represents a node With the line The connection parameters between them Represents a node phase angle, For nodes Maximum phase angle value, Indicates the line Whether the variable corresponds to the construction of lines on the target power network ring structure. Indicates the line The variable corresponding to whether a fault occurs. For the existing line set, For the collection of lines to be built; Line transmission capacity constraints: ; In the formula, Indicates the route. Indicates the line Whether the variable corresponds to the construction of lines on the target power network ring structure. Indicates the line The variable corresponding to whether a fault occurs. Indicates the line Maximum transmission capacity Indicates the line The trend For the existing line set, For the collection of lines to be built; Phase angle upper and lower limit constraints: ; In the formula, Represents a node. Represents a node phase angle, For nodes Maximum phase angle value, The set of all nodes in the target power system; Generator output upper and lower limit constraints: ; In the formula, Indicates generator, Indicates generator of efforts, Indicates generator Maximum output This represents the set of all generators in the target power system; Load loss upper and lower limit constraints: ; In the formula, Indicates load, Indicates load Load loss, For load The initial load, This represents the set of all loads in the target power system.

[0009] Preferably, the step of solving the three-layer optimization model using the Benders decomposition algorithm to obtain the target route set includes: The three-layer optimization model is decomposed into a main problem model and a sub-problem model using the Benders decomposition algorithm. The optimal solution of the three-layer optimization model is obtained by iterating between the main problem model and the sub-problem model, thus obtaining the target route set.

[0010] Preferably, the step of using the Benders decomposition algorithm to decompose the three-layer optimization model into a main problem model and sub-problem models, and obtaining the optimal solution of the three-layer optimization model through mutual iteration of the main problem model and the sub-problem models, to obtain the target route set, includes: The three-layer optimization model is decomposed into a sub-problem model and a main problem model using the Benders decomposition algorithm. The expression for the sub-problem model is: ; In the formula, Indicates the line The variable corresponding to whether a fault occurs. Indicates generator of efforts, Indicates load, Indicates load Load loss, This represents the total load of the target power system; The constraints of the intermediate-level optimization model and the constraints of the lower-level optimization model are determined as the constraints of the sub-problem model; The subproblem model is transformed into a single-layer optimization model using duality theory and the first duality constraint, and the single-layer optimization model is solved using the solver Gurobi to obtain the optimal solution of the subproblem model and the optimal Lagrange multiplier of the subproblem model. The expression for the single-layer optimization model is: ; In the formula, This represents the total number of nodes in the target power system. Represents a node. Indicates load, This represents the total load of the target power system. Represents a node With load The connection parameters between them For load The initial load, Indicates the route. This represents the total number of lines in the target power system. This represents the edge-adding path generated based on the optimal solution of the main problem model. Indicates the line The variable corresponding to whether a fault occurs. Indicates the line Maximum transmission capacity Indicates generator Maximum output For nodes Maximum phase angle value, Indicates the line Admittance, , , , , , , , , All of these are sub-problem models in the first... The optimal Lagrange multiplier under the nth iteration; The expression for the first dual constraint is: ; In the formula, Represents a node. This represents the total number of nodes in the target power system. Indicates the route. Represents a node With the line The connection parameters between them For the existing line set, For the collection of lines to be built, Represents a node With load The connection parameters between them Indicates generator, This represents the set of all generators in the target power system. Represents a node With load The connection parameters between them Indicates load, This represents the set of all loads in the target power system. Indicates the line Admittance, This represents the set of all nodes in the target power system. , , , , , , , , , , All of these are sub-problem models in the first... The optimal Lagrange multiplier under the nth iteration; The optimal Lagrange multipliers of the subproblem model are used to generate the dynamic optimal cut of the main problem model, and the constraints corresponding to the upper-level optimization model are determined as constraints of the main problem model to restrict the feasible region of the main problem model. The expression for the main problem model is: ; In the formula, Indicates the line Whether the variable corresponds to the construction of lines on the target power network ring structure. This is the optimal solution to the main problem model; The expression for the dynamic optimal cut is as follows: ; In the formula, This is the optimal solution to the main problem model. Represents a node. This represents the total number of nodes in the target power system. Indicates load, This represents the total load of the target power system. Represents a node With load The connection parameters between them For load The initial load, Indicates the route. This represents the total number of lines in the target power system. Indicates the line Whether the variable corresponds to the construction of lines on the target power network ring structure. Indicates the line The variable corresponding to whether a fault occurs. Indicates the line Maximum transmission capacity Indicates generator, This represents the total number of generators in the target power system. Indicates generator Maximum output This represents the total number of lines in the target power system. For load The initial load, For nodes Maximum phase angle value, Indicates the line Admittance, This represents the constraint conditions of the mid-level optimization model. , , , , , , , , , , All of these are sub-problem models in the first... The optimal Lagrange multiplier under the nth iteration; When the constraint coefficient matrix of the main problem model is a fully single-module matrix, the 0-1 variables in the main problem model will be... The equivalent relaxation is a continuous variable, and the main problem model is solved using duality theory and the second duality constraint to obtain the optimal solution of the main problem model; The expression for the second dual constraint is as follows: ; ; In the formula, This is the optimal solution to the main problem model. Indicates the route. This represents the total number of lines in the target power system. , , , For Lagrange multipliers, Indicates the line Whether the variable corresponds to the construction of lines on the target power network ring structure. This represents the number of faulty lines. Indicates generator, This represents the total number of generators in the target power system. Indicates generator Maximum output Indicates the line Admittance, For nodes Maximum phase angle value, Indicates load, This represents the total load of the target power system. For load The initial load, Represents a node. This represents the total number of nodes in the target power system. Represents a node With load The connection parameters between them For load The initial load, Indicates the line Maximum transmission capacity For the existing line set, , , , , , , , , , , All of these are sub-problem models in the first... The optimal Lagrange multiplier under the nth iteration; The sub-problem model and the main problem model are iteratively calculated. When the optimal solution of the sub-problem model and the optimal solution of the main problem model satisfy a preset condition, the edge-adding line corresponding to the optimal solution of the sub-problem model is determined as the target line set.

[0011] To address the aforementioned technical problems, this invention provides a power grid expansion planning device for blocking the propagation of multiple faults, comprising: The topology acquisition module is used to acquire the power topology map corresponding to the target power system, thereby obtaining the target power topology map. The ring structure acquisition module is used to determine the power network ring structure with the largest impact range when multiple faults occur in the target power system in the target power topology map, and obtain the target power network ring structure. The three-layer model creation module is used to create a three-layer optimization model based on the target power network ring structure. The three-layer optimization model includes: an upper-layer optimization model for simulating the construction of new power transmission lines in the target power network ring structure, a middle-layer optimization model for simulating multiple faults in the target power system, and a lower-layer optimization model for simulating the blocking of cascading propagation paths when multiple faults occur in the target power system. The line solving module is used to solve the three-layer optimization model using the Benders decomposition algorithm to obtain the target line set, and to build new power transmission lines in the target power system based on the target line set.

[0012] To address the aforementioned technical problems, this invention provides a power grid expansion planning device for blocking the propagation of multiple faults, comprising: Memory, used to store computer programs; A processor is configured to implement, when executing the computer program, the steps of a power grid expansion planning method for blocking the propagation of multiple faults as disclosed above.

[0013] To address the aforementioned technical problems, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of a power grid expansion planning method for blocking the propagation of multiple faults as disclosed above.

[0014] Beneficial effects: Compared with existing technologies, this invention first obtains a power topology map corresponding to the target power system, abstracting the network structure of the power system into a structured object that can be analyzed by algorithms; then, it identifies the target power network ring structure with the largest impact range when multiple faults occur in the target power topology map, thereby achieving accurate identification and location of critical protection positions; subsequently, it creates a three-layer optimization model based on the target power network ring structure, including an upper-layer optimization model, a middle-layer optimization model, and a lower-layer optimization model; wherein, the upper-layer optimization model can simulate the power transmission that needs to be newly built in the target power network ring structure. The three-layer optimization model simulates multiple faults in the target power system when a fault occurs, while the lower-layer optimization model simulates the cascading propagation paths when multiple faults in the target power system are blocked. This allows for analysis and adjustment of "line construction, fault occurrence, and fault blocking" within the unified framework of the three-layer optimization model. Finally, the Benders decomposition algorithm is used to solve the three-layer optimization model, yielding the target line set. Based on this set, new power transmission lines are constructed in the power network ring structure most prone to multiple cascading faults in the target power system. Therefore, this method can prevent cascading faults from the topological source of the power network during the initial design phase of the target power system. This effectively overcomes the technical shortcomings of existing technologies, such as the difficulty in remedying cascading faults after the fact and the lack of source control measures, thereby further improving the safety and reliability of the power system during operation.

[0015] Correspondingly, the power grid expansion planning device, equipment, and medium provided by the present invention for blocking the propagation of multiple faults also have the above-mentioned beneficial effects. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0017] Figure 1 A flowchart illustrating a power grid expansion planning method for blocking the propagation of multiple faults, provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of an optimal line deployment scheme on the critical ring structure of an IEEE 39-node system provided in an embodiment of the present invention. Figure 3 A comparative analysis of the propagation paths of high-risk faults in the IEEE 39-node system before and after the construction of new lines; Figure 4 A structural diagram of a power grid expansion planning device for blocking the propagation of multiple faults provided in an embodiment of the present invention; Figure 5 This is a structural diagram of a power grid expansion planning device for blocking the propagation of multiple faults, provided in an embodiment of the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] Please see Figure 1 , Figure 1 A flowchart of a power grid expansion planning method for blocking the propagation of multiple faults provided in an embodiment of the present invention is shown. The method includes: Step S11: Obtain the power topology map corresponding to the target power system to obtain the target power topology map; Step S12: Determine the power network ring structure with the largest impact range when multiple faults occur in the target power system from the target power topology map, and obtain the target power network ring structure; Step S13: Create a three-layer optimization model based on the target power network ring structure; the three-layer optimization model includes: an upper-layer optimization model for simulating the construction of new power transmission lines in the target power network ring structure, a middle-layer optimization model for simulating multiple faults in the target power system, and a lower-layer optimization model for simulating the cascading propagation path when multiple faults in the target power system are blocked; Step S14: Solve the three-layer optimization model using the Benders decomposition algorithm to obtain the target line set, and construct new power transmission lines in the target power system based on the target line set.

[0020] In this embodiment, to improve the safety and reliability of the target power system during operation, the first step is to obtain a power topology map corresponding to the target power system, thus obtaining the target power topology map. This operation aims to abstract the network structure of the target power system into a structural object that can be analyzed by subsequent algorithm models. Here, the target power system refers to the power system for which new power grid lines are to be constructed and optimized. Furthermore, when establishing the target power topology map, it can be based on the actual physical connection relationships between each node in the target power system and the power transmission path.

[0021] Since fault events in the target power system rely on cascading propagation through its internal power transmission lines, and the power network ring structure within the target power system can provide backup paths for power flow transfer, reducing the risk of cascading faults, after obtaining the target power topology map, it is also necessary to determine the power network ring structure with the largest impact range in the event of multiple faults within the target power topology map, thus obtaining the target power network ring structure. Determining the target power network ring structure is equivalent to identifying the most critical protection locations for precise maintenance of the target power system.

[0022] It should be noted that the power network ring structure with the largest impact range when multiple faults occur in the target power system refers to the power network ring structure with the largest fault cascading propagation range and the most severe load loss when multiple faults occur in the target power system.

[0023] Once the target power network ring structure is determined, a three-layer optimization model is created based on that structure. This three-layer model consists of an upper-layer optimization model, a middle-layer optimization model, and a lower-layer optimization model.

[0024] Specifically, the upper-level optimization model is used to simulate the construction of new power transmission lines in the target power network ring structure, thus enabling the fault prevention and control measures of the target power system to be implemented in advance during the design and planning stage of the target power system; the middle-level optimization model is used to simulate multiple faults in the target power system, thus enabling the cascading propagation characteristics of multiple faults to be proactively incorporated into the design and planning scheme of the target power system; the lower-level optimization model is used to simulate blocking the cascading propagation path of the target power system when multiple faults occur, thus enabling the transmission path of the faults to be cut off when a fault occurs in the target power system, and ensuring the safe and stable operation of the target power system.

[0025] After creating the three-layer optimization model, the Benders decomposition algorithm is used to solve the three-layer optimization model. The optimal solution obtained is the target line set. Then, based on the target line set, new power transmission lines can be built in the power network ring structure where cascading faults are most likely to occur in the target power system.

[0026] As can be seen from the above discussion, the method provided in this embodiment can prevent the occurrence of cascading failures from the structural source of the power network in the early stage of power system design. This can effectively overcome the technical defects of existing technologies, such as the difficulty in remedying cascading failures after the fact and the lack of source control measures, thereby further improving the safety and reliability of the power system during operation.

[0027] Based on the above embodiments, this embodiment further explains and optimizes the technical solution. As a preferred implementation, the above steps include: determining the power network ring structure with the largest impact range when multiple faults occur in the target power system in the target power topology diagram, thereby obtaining the target power network ring structure, including: The maximum matching result is obtained by performing maximum matching calculation on the target power system based on the minimum input theorem. The nodes that are not matched in the maximum matching result are identified as driving nodes, and the minimum set of driving nodes required to achieve structural controllability of the target power system is constructed from the driving nodes. Starting from the target node, the nodes and lines associated with the target node are divided into structurally controllable subsystems corresponding to the target node; the target node is any node in the set of minimum driving nodes. The structurally controllable subsystems corresponding to each driving node are equivalently reduced to generalized nodes, and a reduced-order power network is constructed based on the topological connection relationship between the generalized nodes. By using Fiedler eigenvalues, the power network ring structure with the largest eigenvalue in the reduced-order power network is found, and the target power network ring structure is obtained.

[0028] In this embodiment, in order to determine the target power network ring structure, the first step is to analyze the target power system based on the minimum input theorem. Perform maximum matching calculation to obtain the maximum matching result, then take the unmatched nodes in the maximum matching result as driving nodes, and use these driving nodes to construct the minimum set of driving nodes required to achieve structural controllability in the target power system.

[0029] The expression for the minimum set of driving nodes is as follows: Formula 1: ; In the formula, Represents the minimum set of driving nodes. This represents the total number of drive nodes in the target power system. This represents the maximum matching of a bipartite graph.

[0030] Secondly, starting from the target node, the nodes and lines associated with the target node are divided into structurally controllable subsystems corresponding to the target node. It should be noted that by applying external control signals to the drive nodes within the structurally controllable subsystem corresponding to the target node, the control signals can be transmitted to other nodes through the coupling relationships between nodes within the structurally controllable subsystem. This enables the structurally controllable subsystem to possess state regulation capabilities, thereby ensuring its stable operation during fault propagation.

[0031] Then, the structurally controllable subsystems corresponding to each driving node are equivalently reduced to generalized nodes, and a reduced-order power network is constructed based on the topological connections between the generalized nodes. The purpose of this operation is to reduce the complexity of subsequent calculations while preserving the main topological features of the target power system.

[0032] Then, the reduced-order power network is traversed again. All power network loop structures are analyzed, and the criticality of each power network loop structure is calculated using the contribution of Fiedler eigenvalues. The formula for calculating the criticality of a power network loop structure is as follows: Formula 2: ; In the formula, For power network ring structure edge set, and These are the eigenvectors corresponding to the eigenvalues ​​of Fiedler. The and the first Each component.

[0033] Finally, by ranking the criticality of each power network ring structure, the power network ring structure with the highest criticality can be obtained. This power network ring structure is the one with the largest impact range when multiple faults occur in the target power system, that is, the target power network ring structure.

[0034] As can be seen, the technical solution provided in this embodiment can accurately identify the target power network ring structure with the largest impact range in the target power system.

[0035] Based on the above embodiments, this embodiment further explains and optimizes the technical solution. As a preferred implementation method, the expression of the upper-level optimization model is: Formula 3: ; In the formula, Indicates load, Indicates load Load loss, Indicates the line Whether or not the line is constructed on the target power network ring structure is the corresponding variable. Indicates the total load of the target power system; The constraints corresponding to the upper-level optimization model are: Formula 4: ; Formula 5: ; In the formula, Indicates whether the structure is controllable subsystem and structurally controllable subsystems The variables corresponding to adding edges, Represents a structurally controllable subsystem and structurally controllable subsystems The set of lines to be built between them Indicates the collection of lines to be built Total number of lines in Budget for adding borders; Indicates the route. Indicates the line The variable corresponding to whether or not to construct lines on the target power network ring structure; Formula 6: ; In the formula, For structurally controllable subsystems and structurally controllable subsystems The adjacency matrix between them.

[0036] In this embodiment, the mathematical expression of the upper-level optimization model is explained in detail. Specifically, the number of controllable subsystems added to both sides of the line in the target power network ring structure needs to be less than the edge budget. At this point, the constraints corresponding to the upper-level optimization model can be obtained, namely, Formulas 4 and 5. Furthermore, the structurally controllable subsystems on both sides of the line in the target power network ring structure... and structurally controllable subsystems When adding edges, the controllable subsystem of the structure after adding edges should be guaranteed. and structurally controllable subsystems The adjacency matrix between them is 1, thus enabling controllable subsystems. and structurally controllable subsystems The interruption of fault transmission between them, that is, we get Formula 6.

[0037] It should be noted that, in this embodiment, Indicates the line Whether to construct lines on the target power network ring structure, and the corresponding variables, lines When constructing lines on the target power network ring structure ,line When there is no need to build lines on the target power network ring structure ; Indicates whether the structure is controllable subsystem and structurally controllable subsystems The variables corresponding to adding edges, when needed in a structurally controllable subsystem and structurally controllable subsystems China-Canada border time When it is not necessary to have a structurally controllable subsystem and structurally controllable subsystems China-Canada border time .

[0038] As can be seen, the technical solution provided in this embodiment enables the upper-level optimization model to perform line expansion operations on the structurally controllable subsystems on both sides of the line in the target power network ring structure under the constraint of edge budget, and to effectively block the propagation of faults between subsystems through the constraint of the rank of the adjacency matrix.

[0039] As a preferred implementation, the expression for the mid-level optimization model is: Formula 7: ; In the formula, Indicates the line The variable corresponding to whether a fault occurs. Indicates load, This represents the total load of the target power system. Indicates load Load loss; The constraints of the intermediate-level optimization model are: Formula 8: ; In the formula, This represents the constraints of the mid-level optimization model. Indicates the route. This represents the total number of lines in the target power system. Indicates the line The variable corresponding to whether a fault occurs. Indicates the line Whether or not the line is constructed on the target power network ring structure is the corresponding variable. This represents the number of faulty lines. For the existing line set, This is a collection of lines to be built.

[0040] In this embodiment, the objective function of the intermediate-level optimization model is to maximize the load loss of the target power system. Furthermore, in practical applications, in addition to the existing lines in the target power system potentially experiencing faults, newly constructed lines may also fail. Since the newly constructed lines vary depending on the upper-level planning and decision results, and the fault set exhibits decision-dependent characteristics, the constraints of the intermediate-level optimization model are as shown in Equation 8.

[0041] It should be noted that, Indicates the line Whether a fault occurs is the variable corresponding to the line. During normal operation When the line When malfunction .

[0042] As can be seen, the technical solution provided in this embodiment enables the mid-level optimization model to simulate the multiple fault occurrence process in the target power system.

[0043] As a preferred implementation, the expression for the lower-level optimization model is: Formula 9: ; In the formula, Indicates generator of efforts, Indicates load Load loss, Indicates load, Indicates the total load of the target power system; The constraints of the lower-level optimization model include: Node power balance constraints: Formula 10: ; In the formula, Represents a node. Indicates the route. This represents the total number of lines in the target power system. Represents a node With the line The connection parameters between them Indicates the line The trend Indicates generator, Indicates the number of generators in the target power system. Represents a node With generator The connection parameters between them Indicates generator of efforts, Indicates load, This represents the total load of the target power system. Represents a node With load The connection parameters between them For load The initial load, Indicates load Load loss, This represents the set of all nodes in the target power system; Power flow constraints for the line: Formula 11: ; In the formula, Indicates the route. Indicates the line The trend Indicates the line Admittance, Represents a node. This represents the total number of nodes in the target power system. Represents a node With the line The connection parameters between them Represents a node phase angle, For nodes Maximum phase angle value, Indicates the line Whether or not the line is constructed on the target power network ring structure is the corresponding variable. Indicates the line The variable corresponding to whether a fault occurs. For the existing line set, For the collection of lines to be built; Line transmission capacity constraints: Formula 12: ; In the formula, Indicates the route. Indicates the line Whether or not the line is constructed on the target power network ring structure is the corresponding variable. Indicates the line The variable corresponding to whether a fault occurs. Indicates the line Maximum transmission capacity Indicates the line The trend For the existing line set, For the collection of lines to be built; Phase angle upper and lower limit constraints: Formula 13: ; In the formula, Represents a node. Represents a node phase angle, For nodes Maximum phase angle value, The set of all nodes in the target power system; Generator output upper and lower limit constraints: Formula 14: ; In the formula, Indicates generator, Indicates generator of efforts, Indicates generator Maximum output This represents the set of all motors in the target power system; Load loss upper and lower limit constraints: Formula 15: ; In the formula, Indicates load, Indicates load Load loss, For load The initial load, This represents the load set.

[0044] This embodiment provides a detailed explanation of the mathematical expression of the lower-level optimization model and the various constraints within it. In practical applications, the lower-level optimization model can be used to simulate how, under the conditions of the line construction plan given by the upper-level optimization model and the line fault results given by the middle-level optimization model, the dispatch center can optimize and adjust generator output and load reduction to eliminate line power flow exceeding limits after a fault and prevent the cascading propagation of multiple faults.

[0045] It should be noted that, Represents a node With the line The connection parameters between nodes, if nodes With the line Connected nodes When it is the starting node If node With the line Connected nodes When it is a terminating node ,otherwise ; Represents a node With generator The connection parameters between nodes, if nodes With generator When connected ,otherwise ; Represents a node With load The connection parameters between nodes, if nodes With load When connected ,otherwise .

[0046] Clearly, the technical solution provided in this embodiment can be used to block the cascading propagation process of multiple faults in the target power system by utilizing the lower-level optimization model.

[0047] As a preferred implementation, the above steps include: solving the three-layer optimization model using the Benders decomposition algorithm to obtain the target route set, including: The Benders decomposition algorithm is used to decompose the three-level optimization model into a main problem model and a sub-problem model. The optimal solution of the three-level optimization model is obtained by iterating between the main problem model and the sub-problem model, thus obtaining the target route set.

[0048] Since the three-level optimization model contains three nested problem models, it is extremely difficult to calculate in practical applications. In this embodiment, in order to reduce the computational difficulty of the three-level optimization model, the Benders decomposition algorithm is first used to decompose the three-level optimization model into a main problem model and a sub-problem model, and the optimal solution of the three-level optimization model is obtained by iterating between the main problem model and the sub-problem model.

[0049] As a preferred implementation, the above steps involve: using the Benders decomposition algorithm to decompose the three-level optimization model into a main problem model and sub-problem models, and obtaining the optimal solution of the three-level optimization model through mutual iteration of the main problem model and sub-problem models, thus obtaining the target route set, including: The three-level optimization model is decomposed into sub-problem models and main problem models using the Benders decomposition algorithm; The expression for the subproblem model is: Formula 16: ; In the formula, Indicates the line The variable corresponding to whether a fault occurs. Indicates generator of efforts, Indicates load, Indicates load Load loss, Indicates the total load of the target power system; The constraints of the intermediate-level optimization model and the constraints of the lower-level optimization model are determined as the constraints of the sub-problem model. The subproblem model is transformed into a single-layer optimization model using duality theory and the first duality constraint. The single-layer optimization model is then solved using the solver Gurobi to obtain the optimal solution of the subproblem model and the optimal Lagrange multiplier of the subproblem model. The expression for the single-layer optimization model is: Formula 17: ; In the formula, This represents the total number of nodes in the target power system. Represents a node. Indicates load, This represents the total load of the target power system. Represents a node With load The connection parameters between them For load The initial load, Indicates the route. This represents the total number of lines in the target power system. This represents the edge-adding path generated based on the optimal solution of the main problem model. Indicates the line The variable corresponding to whether a fault occurs. Indicates the line Maximum transmission capacity Indicates generator Maximum output For nodes Maximum phase angle value, Indicates the line Admittance, , , , , , , , , All are sub-problem models in the first... The optimal Lagrange multiplier under the nth iteration; The expression for the first dual constraint is: Formula 18: ; In the formula, Represents a node. This represents the total number of nodes in the target power system. Indicates the route. Represents a node With the line The connection parameters between them For the existing line set, For the collection of lines to be built, Represents a node With load The connection parameters between them Indicates generator, This represents the set of all generators in the target power system. Represents a node With load The connection parameters between them Indicates load, Represents the load set, Indicates the line Admittance, This represents the set of all nodes in the target power system. , , , , , , , , , , All are sub-problem models in the first... The optimal Lagrange multiplier under the nth iteration; The optimal Lagrange multipliers of the subproblem model are used to generate the dynamic optimal cut of the main problem model, and the constraints corresponding to the upper-level optimization model are determined as constraints of the main problem model to restrict the feasible region of the main problem model. The expression for the main problem model is: Formula 19: ; In the formula, Indicates the line Whether the variable corresponds to the construction of lines on the target power network ring structure. This is the optimal solution to the main problem model; The expression for the dynamic optimal cut is as follows: Formula 20: ; In the formula, The optimal solution to the main problem model. Represents a node. This represents the total number of nodes in the target power system. Indicates load, This represents the total load of the target power system. Represents a node With load The connection parameters between them For load The initial load, Indicates the route. This represents the total number of lines in the target power system. Indicates the line The variable corresponding to whether a fault occurs. Indicates the line Maximum transmission capacity Indicates generator, This represents the total number of generators in the target power system. Indicates generator Maximum output This represents the total number of lines in the target power system. For load The initial load, For nodes Maximum phase angle value, Indicates the line Admittance, This represents the constraints of the mid-level optimization model. , , , , , , , , , , All are sub-problem models in the first... The optimal Lagrange multiplier under the nth iteration; When the constraint coefficient matrix of the main problem model is a fully single-module matrix, the 0-1 variables in the main problem model will be... The equivalent relaxation is a continuous variable, and the duality theory and the second duality constraint are used to solve the main problem model to obtain the optimal solution of the main problem model; The expression for the second dual constraint is as follows: Formula 21: ; Formula 22: ; In the formula, The optimal solution to the main problem model. Indicates the route. This represents the total number of lines in the target power system. , , , For Lagrange multipliers, Indicates the line Whether or not the line is constructed on the target power network ring structure is the corresponding variable. This represents the number of faulty lines. Indicates generator, This represents the total number of generators in the target power system. Indicates generator Maximum output Indicates the line Admittance, For nodes Maximum phase angle value, Indicates load, This represents the total load of the target power system. For load The initial load, Represents a node. This represents the total number of nodes in the target power system. Represents a node With load The connection parameters between them For load The initial load, Indicates the line Maximum transmission capacity Indicates the route. For the existing line set, , , , , , , , , , , All are sub-problem models in the first... The optimal Lagrange multiplier under the nth iteration; The sub-problem model and the main problem model are iteratively calculated. When the optimal solutions of the sub-problem model and the main problem model meet the preset conditions, the edge-adding lines corresponding to the optimal solutions of the sub-problem models are determined as the target line set.

[0050] In this embodiment, the sub-problem model is actually a two-level optimization problem. The objective function of the upper-level model is to maximize the load loss of the target power system, and the objective function of the lower-level model is to minimize the load loss of the target power system. The expression for the sub-problem model can be found in Equation 16. Then, Equation 8 is used as the constraint condition for the upper-level model, and Equations 10 to 15 are used as the constraint conditions for the lower-level model.

[0051] Then, using duality theory and the first duality constraint (Equation 18), the subproblem model (Equation 16) is transformed into a single-layer optimization model (Equation 17), and the single-layer optimization model is solved using the solver Gurobi to obtain the optimal solution of the subproblem model and the optimal Lagrange multiplier of the subproblem model.

[0052] Once the optimal Lagrange multipliers of the subproblem model are obtained, the dynamic optimal cut of the main problem model can be generated based on the optimal Lagrange multipliers of the subproblem model, and Equations 4 and 5 can be used as other constraints of the main problem model to limit the feasible region of the main problem model.

[0053] Since the constraint coefficient matrix corresponding to the main problem model (Equation 19) is a fully single-module matrix, the 0-1 variables in the main problem model can be... Equivalent relaxations are made into continuous variables, which does not change the optimality of the solution. Thus, the original non-convex problem with integer variables can be transformed into a convex optimization problem. Subsequently, by using duality theory and the second duality constraint (Equations 21 and 22) to solve the main problem model, the optimal solution of the main problem model can be obtained.

[0054] Specifically, the iterative solution process between the main problem model and the sub-problem models is as follows: Step 1: Input the target power network ring structure Initial fault set: Number of iterations The lower bound of the three-layer optimization model: The upper bound of the three-layer optimization model: Precision: .

[0055] Step 2: Solve the main problem model, which is transformed into a single-layer optimization problem, using the Gurobi solver to obtain the optimal solution. The optimal edge-adding scheme is obtained based on the edge-adding budget constraint of the target power network ring structure. Update the lower bound of the three-layer optimization model: .

[0056] Step 3: Solve the subproblem model using the Gurobi solver to obtain the optimal solution. Update the number of iterations between the main problem model and the sub-problem models: At the same time, update the upper bound of the three-layer optimization model: .

[0057] Step 4: If If yes, proceed to step 5; otherwise, proceed to step 2.

[0058] Step 5: Output the optimal power grid line construction plan for the target power system. And use it as the target route set.

[0059] As can be seen, the technical solution provided in this embodiment can efficiently and accurately solve for the target route set.

[0060] To enable those skilled in the art to more clearly understand the implementation principle of the present invention, a power grid expansion plan for blocking the propagation of multiple faults is described in detail here through the simulation results of a power system.

[0061] In this invention, the IEEE 39-node system is used for simulation analysis. Please refer to [link / reference]. Figure 2 , Figure 2This is a schematic diagram illustrating an optimal line deployment scheme for the critical ring structure of an IEEE 39-node system, provided by an embodiment of the present invention. The IEEE 39-node system has a total of 39 nodes and 46 lines. Assume the number of line faults... The upper limit is 3, which refers to the number of controllable subsystems on the critical ring structure that require improved connectivity on both sides of the line. The maximum is 2. Figure 2 The unmatched nodes (nodes 7, 11, 30-38) are identified as driving nodes, thus dividing the entire power system into 11 structurally controllable subsystems S1 to S11.

[0062] Calculations show that the criticality of the power network ring structure (S1, S3, S7, S6, S5, S4) is 1.047, which is the highest criticality among reduced-order networks. Therefore, this power network ring structure is the critical ring of the IEEE 39-node system.

[0063] The optimal edge addition scheme for the critical ring is as follows: On the critical ring (S1, S3, S7, S6, S5, S4), add new lines 30-24, 2-24, and 30-3 between structurally controllable subsystem 1 and structurally controllable subsystem 3, and add new lines 4-15 and 16-14 between structurally controllable subsystem 3 and structurally controllable subsystem 7.

[0064] To further verify the effectiveness of the proposed power grid expansion planning method for blocking the propagation of multiple faults, six high-risk multiple fault scenarios were selected to compare and analyze the changes in fault propagation paths and load losses before and after adding edges to critical loops. Please refer to [link / reference]. Figure 3 , Figure 3 A comparative analysis diagram of the propagation paths of high-risk faults in the IEEE 39-node system before and after the construction of new lines.

[0065] pass Figure 3 It can be seen that the maximum load loss suffered by the IEEE 39-node system before and after expansion under different combinations of multiple faults is different. According to the optimal power grid expansion scheme obtained by this invention, after constructing new lines 30-24, 2-24, and 30-3 between structurally controllable subsystems S1 and S3, and new lines 4-15 and 16-14 between structurally controllable subsystems S3 and S7, under the high-risk double fault scenario, lines 1 and 30, lines 35 and 38, and lines 26 and 42, after adding edges, did not trigger cascading faults, resulting in a load loss of 0 MW for the power system. This achieves complete blocking of cascading faults. Similarly, under the high-risk triple fault scenario, lines 1, 9, and 10, lines 10, 26, and 42, and lines 8, 9, and 42 also achieved complete blocking of cascading faults, resulting in a load loss of 0 MW for the power system, effectively reducing the scale of power outages.

[0066] The simulation results show that the method described in this invention can effectively improve the anti-interference capability of critical links, and can also effectively block the propagation of high-risk cascading faults without reducing the power system's transmission capacity.

[0067] Please see Figure 4 , Figure 4 This is a structural diagram of a power grid expansion planning device for blocking the propagation of multiple faults, provided in an embodiment of the present invention. The device includes: Topology acquisition module 21 is used to acquire the power topology map corresponding to the target power system to obtain the target power topology map; The ring structure acquisition module 22 is used to determine the power network ring structure with the largest impact range when the target power system experiences multiple faults in the target power topology map, and obtain the target power network ring structure. The three-layer model creation module 23 is used to create a three-layer optimization model based on the target power network ring structure. The three-layer optimization model includes: an upper-layer optimization model for simulating the construction of new power transmission lines in the target power network ring structure, a middle-layer optimization model for simulating multiple faults in the target power system, and a lower-layer optimization model for simulating the blocking of cascading propagation paths when multiple faults occur in the target power system. The line solving module 24 is used to solve the three-layer optimization model using the Benders decomposition algorithm to obtain the target line set, and to build new power transmission lines in the target power system according to the target line set.

[0068] The power grid expansion planning device for blocking the propagation of multiple faults provided in this embodiment of the invention has the beneficial effects of the power grid expansion planning method for blocking the propagation of multiple faults disclosed above.

[0069] Please see Figure 5 , Figure 5 This is a structural diagram of a power grid expansion planning device for blocking the propagation of multiple faults, provided in an embodiment of the present invention. The device includes: Memory 31 is used to store computer programs; The processor 32 is configured to implement, when executing the computer program, the steps of a power grid expansion planning method for blocking the propagation of multiple faults as disclosed above.

[0070] The power grid expansion planning device for blocking the propagation of multiple faults provided in this embodiment of the invention has the same effects as the power grid expansion planning method for blocking the propagation of multiple faults disclosed above.

[0071] Accordingly, embodiments of the present invention also provide a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of a power grid expansion planning method for blocking the propagation of multiple faults as disclosed above.

[0072] The computer-readable storage medium provided in this embodiment of the invention has the beneficial effects of the aforementioned power grid expansion planning method for blocking the propagation of multiple faults.

[0073] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to in the method section.

[0074] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0075] The above provides a detailed description of the power grid expansion planning method, apparatus, equipment, and medium for blocking the propagation of multiple faults provided by the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A power grid expansion planning method for blocking the propagation of multiple faults, characterized in that, include: Obtain the power topology map corresponding to the target power system to obtain the target power topology map; In the target power topology map, determine the power network ring structure with the largest impact range when the target power system experiences multiple faults, and obtain the target power network ring structure; A three-layer optimization model is created based on the target power network ring structure; The three-layer optimization model includes: an upper-layer optimization model for simulating the construction of new power transmission lines in the target power network ring structure, a middle-layer optimization model for simulating multiple faults in the target power system, and a lower-layer optimization model for simulating the blocking of cascading propagation paths when multiple faults occur in the target power system. The Benders decomposition algorithm is used to solve the three-layer optimization model to obtain the target line set, and power transmission lines are newly built in the target power system according to the target line set.

2. The power grid expansion planning method for blocking the propagation of multiple faults according to claim 1, characterized in that, The process of determining the power network ring structure with the largest impact range when multiple faults occur in the target power system in the target power topology map, and obtaining the target power network ring structure, includes: The maximum matching result is obtained by performing maximum matching calculation on the target power system based on the minimum input theorem. The nodes that are not matched in the maximum matching result are determined as driving nodes, and the minimum set of driving nodes required to achieve structural controllability of the target power system is constructed from the driving nodes. Starting from the target node, the nodes and lines associated with the target node are divided into structurally controllable subsystems corresponding to the target node; the target node is any node in the set of minimum driving nodes. The structurally controllable subsystems corresponding to each driving node are equivalently reduced to generalized nodes, and a reduced-order power network is constructed based on the topological connection relationship between the generalized nodes. The target power network ring structure is obtained by using Fiedler eigenvalues ​​to find the power network ring structure with the largest eigenvalue in the reduced-order power network.

3. The power grid expansion planning method for blocking the propagation of multiple faults according to claim 1, characterized in that, The expression for the upper-level optimization model is: ； In the formula, Indicates load, Indicates load Load loss, Indicates the line Whether the variable corresponds to the construction of lines on the target power network ring structure. This represents the total load of the target power system; The constraints corresponding to the upper-level optimization model are: ； ； In the formula, Indicates whether the structure is controllable subsystem and structurally controllable subsystems The variables corresponding to adding edges, Represents a structurally controllable subsystem and structurally controllable subsystems The set of lines to be built between them Indicates the collection of lines to be built Total number of lines in Budget for adding borders; Indicates the route. Indicates the line Whether the variable corresponds to the construction of the line on the target power network ring structure; ； In the formula, For structurally controllable subsystems and structurally controllable subsystems The adjacency matrix between them.

4. The power grid expansion planning method for blocking the propagation of multiple faults according to claim 3, characterized in that, The expression for the mid-level optimization model is: ； In the formula, Indicates the line The variable corresponding to whether a fault occurs. Indicates load, This represents the total load of the target power system. Indicates load Load loss; The constraints of the mid-level optimization model are: ； In the formula, This represents the constraint conditions of the mid-level optimization model. Indicates the route. This represents the total number of lines in the target power system. Indicates the line The variable corresponding to whether a fault occurs. Indicates the line Whether the variable corresponds to the construction of lines on the target power network ring structure. This represents the number of faulty lines. For the existing line set, This is a collection of lines to be built.

5. The power grid expansion planning method for blocking the propagation of multiple faults according to claim 4, characterized in that, The expression for the lower-level optimization model is: ； In the formula, Indicates generator of efforts, Indicates load Load loss, Indicates load, This represents the total load of the target power system; The constraints of the lower-level optimization model include: Node power balance constraints: ; In the formula, Represents a node. Indicates the route. This represents the total number of lines in the target power system. Represents a node With the line The connection parameters between them Indicates the line The trend Indicates generator, This represents the total number of generators in the target power system. Represents a node With generator The connection parameters between them Indicates generator of efforts, Indicates load, This represents the total load of the target power system. Represents a node With load The connection parameters between them For load The initial load, Indicates load Load loss, This represents the set of all nodes in the target power system; Power flow constraints for the line: ; In the formula, Indicates the route. Indicates the line The trend Indicates the line Admittance, Represents a node. This represents the total number of nodes in the target power system. Represents a node With the line The connection parameters between them Represents a node phase angle, For nodes Maximum phase angle value, Indicates the line Whether the variable corresponds to the construction of lines on the target power network ring structure. Indicates the line The variable corresponding to whether a fault occurs. For the existing line set, For the collection of lines to be built; Line transmission capacity constraints: ; In the formula, Indicates the route. Indicates the line Whether the variable corresponds to the construction of lines on the target power network ring structure. Indicates the line The variable corresponding to whether a fault occurs. Indicates the line Maximum transmission capacity Indicates the line The trend For the existing line set, For the collection of lines to be built; Phase angle upper and lower limit constraints: ; In the formula, Represents a node. Represents a node phase angle, For nodes Maximum phase angle value, The set of all nodes in the target power system; Generator output upper and lower limit constraints: ; In the formula, Indicates generator, Indicates generator of efforts, Indicates generator Maximum output This represents the set of all generators in the target power system; Load loss upper and lower limit constraints: ; In the formula, Indicates load, Indicates load Load loss, For load The initial load, This represents the set of all loads in the target power system.

6. The power grid expansion planning method for blocking the propagation of multiple faults according to claim 5, characterized in that, The Benders decomposition algorithm is used to solve the three-layer optimization model to obtain the target route set, including: The three-layer optimization model is decomposed into a main problem model and a sub-problem model using the Benders decomposition algorithm. The optimal solution of the three-layer optimization model is obtained by iterating between the main problem model and the sub-problem model, thus obtaining the target route set.

7. The power grid expansion planning method for blocking the propagation of multiple faults according to claim 6, characterized in that, The Benders decomposition algorithm is used to decompose the three-layer optimization model into a main problem model and sub-problem models. The optimal solution of the three-layer optimization model is obtained through iterative processing of the main problem model and the sub-problem models, resulting in the target route set, including: The three-layer optimization model is decomposed into a sub-problem model and a main problem model using the Benders decomposition algorithm. The expression for the sub-problem model is: ； In the formula, Indicates the line The variable corresponding to whether a fault occurs. Indicates generator of efforts, Indicates load, Indicates load Load loss, This represents the total load of the target power system; The constraints of the intermediate-level optimization model and the constraints of the lower-level optimization model are determined as the constraints of the sub-problem model; The subproblem model is transformed into a single-layer optimization model using duality theory and the first duality constraint, and the single-layer optimization model is solved using the solver Gurobi to obtain the optimal solution of the subproblem model and the optimal Lagrange multiplier of the subproblem model. The expression for the single-layer optimization model is: ； In the formula, This represents the total number of nodes in the target power system. Represents a node. Indicates load, This represents the total load of the target power system. Represents a node With load The connection parameters between them For load The initial load, Indicates the route. This represents the total number of lines in the target power system. This represents the edge-adding path generated based on the optimal solution of the main problem model. Indicates the line The variable corresponding to whether a fault occurs. Indicates the line Maximum transmission capacity Indicates generator Maximum output For nodes Maximum phase angle value, Indicates the line Admittance, , , , , , , , , All of these are sub-problem models in the first... The optimal Lagrange multiplier under the nth iteration; The expression for the first dual constraint is: ； In the formula, Represents a node. This represents the total number of nodes in the target power system. Indicates the route. Represents a node With the line The connection parameters between them For the existing line set, For the collection of lines to be built, Represents a node With load The connection parameters between them Indicates generator, This represents the set of all generators in the target power system. Represents a node With load The connection parameters between them Indicates load, This represents the set of all loads in the target power system. Indicates the line Admittance, This represents the set of all nodes in the target power system. , , , , , , , , , , All of these are sub-problem models in the first... The optimal Lagrange multiplier under the nth iteration; The optimal Lagrange multipliers of the subproblem model are used to generate the dynamic optimal cut of the main problem model, and the constraints corresponding to the upper-level optimization model are determined as constraints of the main problem model to restrict the feasible region of the main problem model. The expression for the main problem model is: ； In the formula, Indicates the line Whether the variable corresponds to the construction of lines on the target power network ring structure. This is the optimal solution to the main problem model; The expression for the dynamic optimal cut is as follows: ； In the formula, This is the optimal solution to the main problem model. Represents a node. This represents the total number of nodes in the target power system. Indicates load, This represents the total load of the target power system. Represents a node With load The connection parameters between them For load The initial load, Indicates the route. This represents the total number of lines in the target power system. Indicates the line Whether the variable corresponds to the construction of lines on the target power network ring structure. Indicates the line The variable corresponding to whether a fault occurs. Indicates the line Maximum transmission capacity Indicates generator, This represents the total number of generators in the target power system. Indicates generator Maximum output This represents the total number of lines in the target power system. For load The initial load, For nodes Maximum phase angle value, Indicates the line Admittance, This represents the constraint conditions of the mid-level optimization model. , , , , , , , , , , All of these are sub-problem models in the first... The optimal Lagrange multiplier under the nth iteration; When the constraint coefficient matrix of the main problem model is a fully single-module matrix, the 0-1 variables in the main problem model will be... The equivalent relaxation is a continuous variable, and the main problem model is solved using duality theory and the second duality constraint to obtain the optimal solution of the main problem model; The expression for the second dual constraint is as follows: ； ； In the formula, This is the optimal solution to the main problem model. Indicates the route. This represents the total number of lines in the target power system. , , , For Lagrange multipliers, Indicates the line Whether the variable corresponds to the construction of lines on the target power network ring structure. This represents the number of faulty lines. Indicates generator, This represents the total number of generators in the target power system. Indicates generator Maximum output Indicates the line Admittance, For nodes Maximum phase angle value, Indicates load, This represents the total load of the target power system. For load The initial load, Represents a node. This represents the total number of nodes in the target power system. Represents a node With load The connection parameters between them For load The initial load, Indicates the line Maximum transmission capacity For the existing line set, , , , , , , , , , , All of these are sub-problem models in the first... The optimal Lagrange multiplier under the nth iteration; The sub-problem model and the main problem model are iteratively calculated. When the optimal solution of the sub-problem model and the optimal solution of the main problem model satisfy a preset condition, the edge-adding line corresponding to the optimal solution of the sub-problem model is determined as the target line set.

8. A power grid expansion planning device for blocking the propagation of multiple faults, characterized in that, include: The topology acquisition module is used to acquire the power topology map corresponding to the target power system, thereby obtaining the target power topology map. The ring structure acquisition module is used to determine the power network ring structure with the largest impact range when multiple faults occur in the target power system in the target power topology map, and obtain the target power network ring structure. The three-layer model creation module is used to create a three-layer optimization model based on the target power network ring structure. The three-layer optimization model includes: an upper-layer optimization model for simulating the construction of new power transmission lines in the target power network ring structure, a middle-layer optimization model for simulating multiple faults in the target power system, and a lower-layer optimization model for simulating the blocking of cascading propagation paths when multiple faults occur in the target power system. The line solving module is used to solve the three-layer optimization model using the Benders decomposition algorithm to obtain the target line set, and to build new power transmission lines in the target power system based on the target line set.

9. A power grid expansion planning device for blocking the propagation of multiple faults, characterized in that, include: Memory, used to store computer programs; A processor, configured to implement the steps of a power grid expansion planning method for blocking the propagation of multiple faults as described in any one of claims 1 to 7 when executing the computer program.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of a power grid expansion planning method for blocking the propagation of multiple faults as described in any one of claims 1 to 7.

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