Power transmission system key equipment identification method oriented to low-granularity time sequence attack

Abstract

The invention relates to the technical field of power system safety protection, and discloses a power transmission system key equipment identification method oriented to low-granularity time sequence attacks, which comprises the following steps: S1, constructing a modular topology model of a power transmission system, dividing equipment in the power transmission system into a plurality of equipment modules according to geographical aggregation, the module division is based on the electrical connection relation, the geographic position, the geographic aggregation characteristic and the function aggregation of the equipment; s2, establishing a fault propagation matrix, simulating a fault propagation path between modules, and analyzing the influence of module faults on other modules of the system; and S3, selecting an attack target area from an attacker perspective, setting load loss maximization in the target area as a target, and limiting the maximum proportion of additional load loss outside the area. Through modular modeling, a depth-first search algorithm and time sequence attack optimization, accurate identification and attack strategy optimization of key equipment of the power transmission system are realized, and the protection and recovery capability of the system under low-granularity time sequence attack is effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of power system security protection, and specifically provides a method for identifying key equipment of a power transmission system facing low-granularity timing attacks. Background Art

[0002] With the increasing complexity of power systems, the network security threats faced are also constantly increasing. Especially for timing attacks on power transmission systems, such attacks are often characterized by concealment and complexity, posing challenges to traditional protection mechanisms. In real life, electricity is the core of the country's infrastructure, and any systemic failure may lead to extensive social impacts. Therefore, enhancing the anti-attack ability of power transmission systems and improving the identification ability of key equipment have become urgent problems to be solved.

[0003] In the prior art, the security protection of power systems usually relies on holistic defense strategies, focusing on the holistic monitoring and protection of equipment and lines. Traditional power transmission system attack protection mainly conducts security defense through static topology models and protection level settings to ensure that the system can effectively defend against simple attacks. These technical solutions can usually respond to single-point failures and maintain the basic operation stability of the system. At the same time, the prior art also copes with attacks through certain resource allocation optimizations, mainly by regularly evaluating the performance and health status of key equipment to ensure the fault tolerance of the overall system.

[0004] However, the prior art has some deficiencies in dealing with low-granularity timing attacks. First of all, most of the existing methods rely on coarse-grained system models, ignoring the specific distribution and interrelationships of equipment, and it is difficult to accurately identify key modules after being attacked. For complex timing attacks, traditional models cannot track the attack path and its impact on other equipment in real time, and it is easy to miss the protection of key facilities. Secondly, most of the existing attack resource allocation schemes are static configurations and cannot dynamically adjust resources to cope with changes in multi-round attacks, resulting in poor protection effects. Finally, although the prior art already has certain solutions for single-point fault recovery, in the face of fault propagation between modules, there is a lack of sufficient refined analysis and cannot accurately predict the system state after the attack. Summary of the Invention

[0005] In view of the deficiencies of the prior art, the present invention provides a method for identifying key equipment of a power transmission system facing low-granularity timing attacks, which solves the problems in the prior art that key equipment of a power transmission system under low-granularity timing attacks cannot be accurately identified and lacks dynamic adjustment and recovery capabilities.

[0006] To achieve the above objectives, the present invention is realized through the following technical solutions: A method for identifying key equipment of a power transmission system facing low-granularity timing attacks, comprising the following steps:

[0007] S1. Construct a modular topological model of the power transmission system, divide the equipment in the power transmission system into multiple equipment modules according to geographical aggregation, and the module division is based on the electrical connection relationship, geographical location, geographical aggregation characteristics and functional aggregation of the equipment;

[0008] S2. Establish a fault propagation matrix, simulate the fault propagation path between modules, and analyze the impact of module faults on other modules in the system;

[0009] S3. Select the attack target area from the attacker's perspective, set the maximization of load loss within the target area as the goal, and limit the maximum proportion of additional load loss outside the area;

[0010] S4. Based on the depth-first search algorithm, expand outward from the load nodes in the target area, gradually search all possible power supply paths, record the modules and lines involved in the paths, and form an attack decision variable set;

[0011] S5. Define attack decision variables and recovery state variables to represent the attack state and recovery state of each module, and calculate their impact on the system fault propagation;

[0012] S6. Set the resource limit for each round of attack, control the number of modules attacked in each round, and ensure that the load loss outside the area does not exceed the preset threshold;

[0013] S7. Optimize the selection of attack target modules based on temporal analysis, calculate the cumulative impact of multiple rounds of attacks on load loss, and through temporal analysis and optimization algorithms, select the modules that can cause the most load loss in each round for attack, and adjust the attack order to maximize the load loss in the target area;

[0014] S8. Set the dispatching strategy of the defense side, simulate the load recovery process after the attack, and minimize the load loss of the system through an optimized dispatching plan;

[0015] S9. Optimize the module recovery time, combine the recovery time and repair status to adjust the selection of attack target modules, and ensure the stability of the modules after recovery;

[0016] S10. Identify the key equipment of the power transmission system according to the attack results, and determine the key modules through impact analysis.

[0017] The present invention provides a method for identifying key equipment of a power transmission system for low-granularity temporal attacks.

[0018] It has the following beneficial effects:

[0019] 1. The present invention conducts modular modeling of the power transmission system based on geographical clustering. By dividing the equipment into multiple modules, the connection relationship of the power system can be clearly presented. Different from the traditional overall network model, this modular division makes the identification of low-granularity attacks more efficient and improves the security of the system.

[0020] 2. Construct a fault propagation matrix to accurately analyze the mutual influence of each module in the system by simulating the fault propagation between modules. This method effectively makes up for the deficiency in the existing technology of insufficient consideration of fault interaction between modules, making the fault assessment more scientific and comprehensive.

[0021] 3. For multi-round time-series attacks, the present invention proposes an accurate attack target optimization strategy. By reasonably allocating attack resources and adjusting the attack order, the load loss in the target area can be maximized under the premise of restricting the external load loss. Compared with the existing methods, this strategy is more flexible and efficient, avoiding resource waste and optimizing the attack effect.

[0022] 4. The present invention adopts a two-layer optimization model to achieve dynamic coordination between the attacker and the defender. By simultaneously optimizing the attack and defense decisions, not only is the maximization of the attack effect enhanced, but also the efficiency of the defense response is improved. Different from the traditional methods that separately handle offense and defense, this integrated optimization framework ensures more comprehensive system protection. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a flowchart of the method of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0024] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the specification of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0025] Please refer to the attached Figure 1 , the embodiments of the present invention provide a method for identifying key equipment of a power transmission system facing low-granularity time-series attacks, including the following steps:

[0026] S1. Construct a modular topological model of the power transmission system, and divide the equipment in the power transmission system into multiple equipment modules according to geographical clustering. The module division is based on the electrical connection relationship, geographical location, geographical clustering characteristics, and functional aggregation of the equipment;

[0027] The purpose of step S1 is to construct a modular topological model of the power transmission system. Through this step, each device in the power transmission system is divided and organized into multiple functional modules based on geographical aggregation. The core idea of the modular topological model is to disassemble the complex structure in the power system into multiple relatively independent modules, facilitating subsequent fault propagation analysis, attack path optimization, and identification of critical devices.

[0028] In this step, each device module contains several devices, which are usually closely related in function. For example, devices such as busbars, circuit breakers, and transformers in a substation may be divided into different modules, and the devices within these modules work together through electrical connections. Therefore, the functional relationships between modules also determine their roles in the power system. This modular division helps to achieve fine control and identification of the system state and attack effects.

[0029] As an option, the module division method in the present invention can be based on a graph theory model, where each module is regarded as a node, and the edges between the nodes represent the electrical connection relationships between the modules. In this way, we can clearly represent the connection paths between modules, which provide a basis for fault propagation and attack path optimization in subsequent steps.

[0030] Specifically, the division of modules needs to consider the following factors:

[0031] Electrical connection relationship: The devices within each module jointly undertake certain functions through electrical connections such as transmission lines, busbars, and transformers. By analyzing the electrical connections of the devices in detail, it is determined which devices should be divided into the same module.

[0032] Functional aggregation: The functional characteristics of each module determine the importance of the module to the operation of the system.

[0033] Geographical aggregation: The proximity of devices in terms of geographical location and geographical aggregation characteristics is also an important factor considered in module division. Devices that are geographically adjacent and closely related in function should be divided into the same module as much as possible, which helps to improve the accuracy of system analysis and attack identification.

[0034] In a possible implementation, module division is performed on each substation, and the various devices within it (such as transformers, circuit breakers, busbars, etc.) are classified according to their electrical connection relationships and functions. The division of each module depends not only on the electrical characteristics of the devices but also on their geographical locations, geographical aggregation characteristics, and work tasks.

[0035] In this step, the electrical relationship between devices is expressed by constructing an association matrix between modules and lines. For each module M n, we define the set R of the power transmission paths it connects n , and this set contains all the power transmission paths related to module M n . The association matrix between the module and the line:

[0036]

[0037] where M i,j is the electrical connection state between module i and module j; N is the total number of modules in the system; i, j are the module numbers, representing different modules in the system.

[0038] This matrix is used to represent the electrical connection state of each module with other modules and provides a basis for subsequent attack path selection and fault propagation analysis. Module electrical transmission path set:

[0039] For each module M n , we define its electrical transmission path set R n :

[0040] R n = {R n1 , R n2 ,..., R nw};

[0041] where R n represents the set of all power transmission paths of module M n ; R nk represents the k-th power transmission path in module M n ; w represents the number of power transmission paths in module M n .

[0042] This set describes the connection relationship of all power transmission paths inside module M n and provides a path basis for subsequent fault propagation analysis.

[0043] For each module, a functional association matrix F is defined to represent the functional aggregation relationship of the devices within the module:

[0044]

[0045] where F i,j is the functional relationship between device i and device j; u is the total number of devices within the module; i, j are the device numbers, representing different devices within the module.

[0046] This matrix is used to express the functional relationship between the devices within the module, helps to identify those devices that have a close functional connection within the module, and thus provides a basis for subsequent attack identification and path optimization.

[0047] By constructing a modular topological model of the power transmission system, the electrical connection relationships, functional aggregation, geographical locations, and geographical aggregation characteristics of each module can be clearly described, which provides a solid foundation for subsequent fault propagation analysis, attack path optimization, and critical equipment identification.

[0048] S2. Establish a fault propagation matrix to simulate the fault propagation paths between modules and analyze the impact of module failures on other modules in the system;

[0049] The purpose of Step 2 is to analyze the vulnerability of the system by quantifying the impact of each module failure on other modules in the system, especially the fault conduction effect of critical equipment in the system when facing low-granularity timing attacks. The establishment of the fault propagation matrix helps to provide key data support for attack path identification, load loss calculation, etc. in subsequent steps.

[0050] In this step, the construction of the fault propagation matrix is based on the electrical connection relationships between modules. Each module can be regarded as a node in a network, and the nodes are connected by electrical connection lines to form edges. When a certain module fails, its fault state will affect the modules connected to it. By simulating the electrical relationships between these modules and constructing the fault propagation matrix, the paths of fault propagation from the source module to other modules can be accurately depicted.

[0051] As an option, the fault propagation matrix can be represented in a way similar to an adjacency matrix. The element D i,j in the matrix represents the propagation relationship of module i to the failure of module j. If D i,j = 1, it means that the failure of module i will directly affect module j. If D i,j = 0, it means that the failure of module i will not directly affect module j. These propagation relationships are directly calculated based on the electrical connections and equipment functions between modules.

[0052] Specifically, when constructing the fault propagation matrix, the electrical connections between modules should be considered first. Through the electrical transmission paths between modules, the fault propagation relationships between each module can be obtained. These paths include not only the directly connected lines but also the impacts indirectly transmitted through equipment such as transformers and circuit breakers. Each element in the matrix provides a basis for subsequent analysis by reflecting the dependencies between modules.

[0053] The fault propagation matrix D n is the core tool used to represent the fault propagation paths. The purpose of this matrix is to calculate and describe the possible direct or indirect impacts on other modules in the system after a module fails, including the fault propagation matrix:

[0054]

[0055] Among them, Dj,j is the fault propagation impact of module i on module j. If it is 1, it means that the fault of module i will cause the fault of module j; if it is 0, it means there is no direct impact; u is the total number of modules in the system, representing the dimension of the fault propagation matrix; i and j are the module numbers, representing different modules in the system; the fault propagation matrix D n provides a basis for subsequent attack path recognition and system vulnerability analysis, and can quantify the fault propagation effect between modules.

[0056] For each module M n , define its set of fault propagation paths R n , which contains all the paths that may be affected by the fault of module M n .

[0057] For each module M n , define a fault impact function f n , which is used to describe the impact of the fault of module M n on the fault propagation of the entire system. The form of this function is:

[0058]

[0059] where f n represents the impact of the fault of module M n on other modules in the system; D n,i is the degree of fault impact of module M n on module M i ; R n,i is the fault propagation path from module M n to module M i .

[0060] This function is used to quantify the system impact of module faults, providing a quantitative basis for subsequent attack path optimization and system vulnerability point identification.

[0061] Through the above formula and technical details, the fault propagation path between modules can be accurately described, and the impact of each module's fault on other modules can be quantified, not only providing data support for attack path selection and load loss calculation in subsequent steps, but also helping to identify potential vulnerable modules in system analysis.

[0062] S3. Select the attack target area from the attacker's perspective, set the maximization of load loss within the target area as the goal, and limit the maximum proportion of additional load loss outside the area;

[0063] S3 further determines the attack target area and sets the attack strategy to maximize the load loss within the target area, while limiting the additional load loss caused by the attack in other areas of the system to ensure the locality and accuracy of the attack.

[0064] In this step, the attacker's goal is to select one or more power plants and substations as the targets of attack, maximize the load loss within the target area, and ensure that the additional load loss outside the area is controlled within a reasonable range. This process involves multiple key parameters, including the selection of the target area, the calculation method of load loss, the allocation strategy of attack resources, and the constraint conditions of the additional load loss outside the area.

[0065] Generally, when selecting the target area, factors such as the location of the load center, the redundancy of power equipment, and the recovery ability after the attack need to be considered. In addition, the target area should not overlap with the core nodes of the overall system to avoid cascading failures beyond the controllable range.

[0066] In one possible implementation, a mathematical optimization model can be used to solve the selection of the target area and the attack strategy. Specifically, the optimization objective function for attacking the target area can be expressed as:

[0067] Objective function for maximizing the load loss in the target area:

[0068]

[0069] Where: represents the load lost by substation n after the t-th round of attack; V in represents the set of all substations within the selected target area; n ∈ V in represents the set of substations or load nodes in the target area, where V in is the set of all load nodes or substations within the target area, and n represents a specific node in this set; max represents the maximization objective function.

[0070] The significance of this objective function is to select the area that can cause the maximum load loss among all possible attack targets to optimize the attack effect. Constraint on additional load loss outside the area:

[0071]

[0072] Where: V out represents the set of all substations in the system that do not belong to the target area; ξ t is the maximum ratio of the additional load loss outside the area, usually set to be less than or equal to 0.2; is the total load of the system during the t-th round of the attack cycle.

[0073] The purpose of this constraint is to control the scale of the load loss outside the area, ensure the locality and accuracy of the attack, and avoid large-scale power outages caused by excessive attacks. Allocation of load loss in the target area:

[0074]

[0075] Where: B n represents the set of all bus nodes in substation n; represents the load loss of the i-th bus in substation n.

[0076] This formula is used to calculate the load loss of each substation in the target area and further refine it to the bus level to quantify the load impact of different buses.

[0077] To achieve the above goal, we need to define the attack decision variable

[0078]

[0079] Where: represents whether module i in substation n is attacked; when it means that the module is selected as the attack target in this round of attack; when it means that the module is not attacked.

[0080] This variable is used to control the target object of the attack and optimize the solution to select the optimal attack target. Attack resource constraint:

[0081]

[0082] Where: A t represents the maximum available attack resources of the attacker in the t-th round of attack; A represents the set of all optional attack targets; represents whether module i is selected as the attack target in the t-th round of attack; represents the total number of all modules selected as attack targets in the t-th round of attack.

[0083] This constraint is used to control the resource limit of each round of attack to ensure that the attacker conducts the optimal attack within the limited resource range.

[0084] Through the above formula and optimization strategy, this step can accurately select the attack target area, maximize the load loss in the target area through mathematical optimization methods, and keep the additional load loss outside the area within a controllable range. The introduction of the attack decision variable makes the selection of the attack target more flexible, and the constraint of the attack resources ensures that the attacker can execute the optimal strategy with limited resources.

[0085] The optimization solution process of this step can be calculated by methods such as mixed integer linear programming (MILP) or genetic algorithm (GA) to quickly obtain the optimal attack path and attack target combination. This strategy can not only improve the accuracy of the attack, but also ensure the effectiveness of the attack and avoid excessive damage to the overall stability of the system.

[0086] Through this strategy, attackers can effectively carry out low-granularity timing attacks, identify and attack critical power equipment, thus achieving the maximum disability of a local area and maintaining the concealment and controllability of the attack within a certain range.

[0087] S4. Expand outward from the load nodes in the target area based on the depth-first search algorithm, gradually search all possible power supply paths, record the modules and lines involved in the paths, and form an attack decision variable set.

[0088] S4 starts from the load nodes in the target area and expands outward using the depth-first search algorithm, gradually exploring all possible power supply paths, and recording the equipment modules and lines involved in the paths, finally forming an attack decision variable set.

[0089] This step starts from the load nodes in the target area, expands outward using the depth-first search algorithm, and gradually searches all possible power supply paths. In each path, the modules and lines involved will be recorded and used as the subsequent attack decision variable set. The definition of each power supply path not only helps the attacker lock in the key power supply paths in the system but also enables the attacker to make precise attack decisions based on the modules in the path.

[0090] Generally, searching all possible power supply paths starting from the load nodes can ensure that we can capture the most important power supply paths in the system. By using the depth-first search algorithm, the attacker can systematically traverse all paths to ensure that no modules and lines that may become attack targets are missed.

[0091] In a possible implementation, to improve the search efficiency, the search scope can be limited by setting the search depth and the maximum length of the path to avoid redundant calculations during the search process. For example, we can set a maximum search depth D max , and adjust the search strategy according to the topological structure and resource limitations of the power grid to ensure that the attacker can efficiently identify critical paths within an appropriate range.

[0092] In this step, the most crucial mathematical representation involves the search and recording of power supply paths. For this purpose, we define the path as the power supply path from the node n in the target area to the external power source node k. The path is gradually expanded through the depth-first search algorithm, and the path search:

[0093]

[0094] Where: represents the power supply path from the node n in the target area to the external power source node k; n represents the load node in the target area; l 1 , l2 ,..., l m are the power line nodes in the path; k 1 , k 2 ,..., k are the equipment nodes in the path.

[0095] This path representation helps us gradually expand the search and record all the power supply paths related to the target area.

[0096] Define P n as the set of all possible power supply paths for the load node n in the target area, which includes the lines and equipment modules directly or indirectly related to the target area:

[0097]

[0098] Where: P n represents the set of all power supply paths starting from the load node n in the target area; represents the power supply paths from the load node n in the target area to different external power source nodes k 1 , k 2 ,...,, k m of the power supply paths.

[0099] By recording the modules and lines involved in the path, the attacker can form a set of attack decision variables A n , which represents the attack status of the equipment modules in each path during the attack. Define the attack status of each module

[0100] To facilitate subsequent path selection and attack decision analysis, define the association matrix R of the path and the module n2 , representing the relevance of each module in each power supply path:

[0101]

[0102] Where: R n2 is the matrix representing the module recovery status; represents the recovery status of module u after the m-th round of attack; u is the total number of modules, representing the number of modules participating in the attack in the target area; m is the total number of attack rounds, representing the number of rounds in the attack process, which affects the recovery time and recovery process.

[0103] Through the depth-first search algorithm, it is possible to start from the load node in the target area and gradually expand the search for all possible power supply paths. In each path, the modules and lines involved will be recorded and form a set of attack decision variables.

[0104] S5. Define the attack decision variables and recovery status variables to represent the attack status and recovery status of each module, and calculate their impact on the system fault propagation;

[0105] The task of S5 is to define the attack decision variables and recovery status variables for each module, which provides important technical support for the subsequent attack process, resource allocation, and management of the recovery status.

[0106] In this step, we further define the attack decision variables and recovery status variables so that we can track the attack and recovery situations of the modules during the attack process and calculate and evaluate the overall impact of the system based on these statuses. Specifically, the attack decision variables and the recovery status variables continuously change throughout the attack process, affecting the efficiency of the attack and the system's recovery ability.

[0107] The definition of these variables is crucial for attack decision-making and resource optimization. The attack decision variables are used to determine whether module i in the target area will be selected as an attack object in a certain round of attack; while the recovery status variables are used to mark whether module i has returned to the normal state after being attacked. This mechanism not only supports the optimization of multi-round attacks but also can reasonably allocate attack resources and control the negative impacts during the attack process.

[0108] Generally, in order to accurately calculate the status of each module, the attack decision variables and recovery status variables need to be dynamically updated according to the different situations of each round of attack. During each round of attack, the recovery status of the module changes as the recovery process progresses, thus affecting the selection of subsequent attacks. Therefore, the design of these two variables is the key to ensuring the effective implementation of the attack strategy.

[0109] As an option, the update of the recovery status is closely related to the recovery time of the module. The recovery time is defined as the time required for the module to return to the normal state after being attacked, which is usually determined by the hardware repair of the module, system scheduling, and external factors. The recovery status of each module needs to be adjusted according to the recovery time to determine whether it is in the recovery process or the fully recovered state.

[0110] Specifically, define the attack decision variables and the recovery status variables as follows:

[0111] The recovery status variable indicates whether module i has returned to the normal state after the t-th round of attack. If it means that module i has returned to the normal state; if it means that module i has not recovered yet.

[0112]

[0113] Wherein: Indicates that module i has returned to the normal state; Indicates that module i has not yet recovered.

[0114] In a possible implementation, the recovery state is related to the recovery time of the module. The recovery time of the module refers to the time required for the module to return to the normal state from the start of the attack. The recovery time varies according to factors such as the type of module, the number of devices to be repaired, and the external environment.

[0115] The calculation formula for the recovery time is as follows:

[0116]

[0117] Where: t is the current attack time; tx is the time when module i is attacked; is the recovery time of module i.

[0118] Furthermore, if the recovery time of a module is long, then this module cannot be attacked again during the recovery period. Therefore, modules with longer recovery times may become more valuable attack targets. Through this strategy, the attacker can maximize the system loss within a limited time.

[0119] The attack decision variable and the recovery state variable can not only accurately describe the state of each module, but also optimize the attack strategy by calculating the mutual influence between modules, ensuring the maximum benefit of each round of attack.

[0120] S6. Set the resource limit for each round of attack, control the number of modules in each round of attack, and ensure that the off-region load loss does not exceed the preset threshold;

[0121] The main purpose of S6 is to set the resource limit for the attack, ensure that each round of attack is carried out within the controlled resource range, and avoid the off-region load loss caused by the attack exceeding the predetermined threshold. This step is closely linked to the foregoing step S5, ensuring the reasonable allocation of attack resources and the maximum attack effect. To achieve the goal, it is necessary to accurately control the resources for each round of attack and calculate the selection of attack targets and their impact on other regions.

[0122] Through step S6, we can ensure that in the case of multi-round attacks, the attack resources are not over-consumed, so that sufficient resources can be allocated in multiple attack rounds to strike the target area, and the system stability is guaranteed, avoiding excessive impact on other areas. In particular, controlling the loss of out-of-area load is one of the keys to ensuring that the system does not collapse. This strategy can optimize the attack effect while effectively reducing the risk of the system suffering a complete paralysis.

[0123] Restrict the resources for each round of attack through the formula of attack resource constraint in S3;

[0124] Generally, A t is set according to the size of the target area, the recovery state of the module, and the current attack strategy. For example, if the power load of the target area is large, the attacker may need to invest more resources in the attack, so A t may be large; while if the power load of the target area is small or the system recovery is good, then A t may be small.

[0125] In some embodiments, the setting of A t may depend on dynamic factors. Such as the current load level of the system, the recovery state of the module, or the degree of damage in the system, etc., can all affect the adjustment of A t For example, when the attacker selects to attack a module with a small impact range, A t can be appropriately reduced to avoid over-consumption of system resources.

[0126] In addition, represents the attack decision for each module within a specific round. By selecting the modules, the attacker can concentrate firepower on the most critical facilities to achieve the effect of quickly weakening the power transmission system. To avoid overly dispersed attacks, the number of modules attacked in each round is strictly controlled to ensure that the attack can maintain a high efficiency and reduce the negative impact on other irrelevant areas.

[0127] In step S6, the most important control mechanism is the restriction of the resources for each round of attack. This restriction not only relates to the attacker's decision-making but also affects the continuity of the entire attack process and the system's recovery ability. Through the formula the attack strategy can be flexibly adjusted to avoid the attacker overly relying on a single target module, thereby maximizing the comprehensive effect under multi-round attacks.

[0128] As a further illustration, in practical applications, when the attack decision of module i changes, A tIt can also be adjusted in real time according to the strategy to ensure that the attack not only has strategic significance but also can respond flexibly according to the actual situation. In this way, step S6 effectively combines the allocation of attack resources with the load control of the system, ensuring the accuracy of the attack and the stability of the system.

[0129] Specifically, if the attacker's goal is to ensure that the out-of-region load loss is controlled within a certain acceptable range, then the setting of A t must consider the load distribution. For example, when calculating A t , dynamic evaluation should be carried out according to the overall situation of the out-of-region load to ensure that each attack does not cause large-scale power outages. In this way, the attacker can precisely control the input of resources and minimize the negative impact on other parts of the system.

[0130] By restricting the number of attack modules in each round of attack and ensuring that the out-of-region load loss does not exceed the predetermined threshold, it is ensured that the attack can be carried out efficiently and orderly, so as to achieve the best effect in multiple rounds of attacks. At the same time, reasonable resource allocation also ensures that the attacker can continuously and effectively strike the target area without over-consuming the system's resources and avoiding the risk of causing the system to collapse excessively.

[0131] S7. Optimize the selection of attack target modules based on timing analysis, calculate the cumulative impact of multiple rounds of attacks on load loss, and through timing analysis and optimization algorithms, select the modules that can cause the most load loss in each round for attack, and adjust the attack order to maximize the load loss in the target area;

[0132] The goal of S7 is to optimize the selection of attack target modules based on timing analysis. Through the cumulative effect of multiple rounds of attacks, optimize the attack order to maximize the load loss in the target area. The key to this step is to make full use of the timing characteristics of the attack, comprehensively consider the load loss of each module, and adjust the order of attack target modules to achieve the optimization of the attack effect.

[0133] In this step, the goal of step S7 is to dynamically adjust the attack order according to the load loss situation of each round of attack, so that the total load loss of the system under multiple rounds of attacks reaches the maximum. Through timing analysis, the chain effect after each round of attack can be predicted, so as to reasonably select the attack order and target modules to maximize the damage to the load in the target area.

[0134] According to the effects of load loss and cascading failures, calculate the load loss caused to the system after each round of attack. The target modules of the attack will not only be directly affected by the attack, but also cause cascading failures of other modules and lines connected to them. Therefore, when selecting attack targets, the relevance between modules needs to be considered to predict the impact of the current attack on subsequent load loss.

[0135] According to the timing analysis, during multiple rounds of attacks, the results of the previous round of attack may affect the effect of the next round of attack. For example, some modules may remain in a failed state for a long time after being attacked, leading to an exacerbation of the effect of subsequent attacks. Therefore, step S7 needs to consider the cumulative impact of each round of attack and optimize the order of the target modules to be attacked, so that subsequent attacks can make the best use of the effect of the previous round of attack and increase the overall load loss.

[0136] Optimize the selection of attack targets under multiple rounds of attacks. By establishing a loss assessment model, analyze the load loss situation after each round of attack. This model will consider the system impact caused by different modules after being attacked, so as to optimize the selection of the target modules to be attacked. By dynamically adjusting the attack targets, ensure that each round of attack can cause the maximum load loss to the system.

[0137] Specifically, the adjustment of the attack order should be based on factors such as the load loss potential of the module, the possibility of cascading failures, and the recovery time. The failure of some modules may have a long-term impact on the system load, while other modules may recover in a short time. Therefore, when selecting the attack targets, it is necessary to comprehensively evaluate the influence and recovery cycle of each module to achieve the optimal attack strategy.

[0138] In a possible implementation, an optimal attack order can be determined by searching all possible attack orders in the system, so that under the given attack resource constraints, the load loss can be maximized. This strategy is based on a global understanding of the system and dynamically adjusts the attack strategy, enabling the attacker to achieve the maximum loss in the target area in multiple rounds.

[0139] The specific loss calculation model can be described by the following formula:

[0140]

[0141] Where: represents the load loss of substation n after the t-th round of attack; represents the load loss of module i in substation n after the t-th round of attack; B n represents the set of modules in substation n, including modules such as busbars, transformers, and circuit breakers.

[0142] This formula is used to calculate the total load loss of all modules in the substation after the t-th round of attack. The load loss of each module is determined by the characteristics of its module and is also affected by the states of other modules. Therefore, by calculating the load loss after each round of attack, it can provide a basis for optimizing the subsequent attack strategy.

[0143] S7 not only calculates the load loss of each round of attack, but also dynamically adjusts the attack order so that the effects of each round of attack can be superimposed, maximizing the load loss of the system. The implementation of step S7 ensures that the attacker can adjust the strategy according to the results of the previous round of attack, so as to achieve the optimal attack effect in multiple rounds of attack.

[0144] S8. Set the defense side scheduling strategy, simulate the load recovery process after the attack, and minimize the load loss of the system by optimizing the scheduling scheme;

[0145] The goal of S8 is to set the defense side scheduling strategy so that the power system can resume normal operation as soon as possible after multiple rounds of attack and minimize the load loss. This step needs to reasonably schedule the resources in the power grid based on the state information of the system after the attack, especially for the refined management of the allocation of power resources during the recovery process. By optimizing the scheduling scheme, the defense side can try to restore the power supply in key areas and avoid the situation of excessive load shedding.

[0146] First, according to the load loss situation after each round of attack, the system enters the recovery mode. The main task of the power system recovery is to allocate power from the available areas to the damaged areas and make each damaged module resume power supply as soon as possible through reasonable scheduling. Specifically, the simulation process of load recovery is based on the current state of the system. Assume that after the attack, some modules fail, and the task of the defense side is to restore the load of these modules by scheduling resources.

[0147] In this embodiment, the load loss of the system is minimized by optimizing the scheduling scheme. The goal of this optimization scheme is to ensure that as many load areas as possible can be restored while avoiding unnecessary load shedding. Among multiple possible recovery schemes, select the scheme that can restore the load fastest and with the least loss. To achieve this goal, the defense side simulates different scheduling strategies and evaluates their impacts on the system stability and load recovery speed.

[0148] The scheduling process is adjusted in real time based on the load state after each round of attack and the recovery time of the modules. Specifically, the following key factors need to be considered in the scheduling process:

[0149] Minimization of load loss: Ensure that as much load as possible is restored through scheduling and prevent large-scale power outages caused by untimely recovery.

[0150] Recovery time: The recovery time of the modules has a great impact on the scheduling scheme. Modules with longer recovery times need to be restored first to reduce the risk of system instability.

[0151] Power transmission paths between modules: During the recovery process, the power connection paths between modules need to be considered, and the power flow of these paths is optimized to ensure the recovery efficiency.

[0152] To achieve the optimization of load restoration, we need to introduce an optimization objective function that aims to minimize the total load loss and takes into account the restoration time and power flow constraints during this process.

[0153] The optimization problem can be described by the following formula:

[0154]

[0155] where: P d represents the load restoration status of the system; ΔPd i represents the load loss caused by module i during the restoration process after an attack, and B is the set of all affected modules in the system.

[0156] The purpose of this objective function is to minimize the sum of the load losses of all modules.

[0157] The load adjustment constraint is a crucial part to ensure that the adjustment of each load node conforms to the electrical characteristics and line transmission capacity, and is specifically expressed as:

[0158]

[0159] where: p i is the load of the i-th node, representing the electrical load borne by this node; v i is the voltage value of the i-th node; x i is the conductance of the line, representing the conductance capacity of the i-th line, which determines the current transmission effect; θ o(i) is the initial voltage angle of the i-th node; θ d(i) is the target voltage angle of the i-th node, that is, the target voltage angle after restoration.

[0160] This constraint controls the load adjustment through the relationship between voltage and voltage angle difference, ensuring that the load change of each node conforms to the system's electrical characteristics, thereby ensuring that the power transmission during the restoration process does not violate the system's electrical constraints.

[0161] To ensure that the load restoration does not exceed the power generation capacity, the defense side needs to ensure that the power output of each generator set is limited within its allowable range. The specific formula is:

[0162]

[0163] where: g j is the power generation of the j-th generator set; G j is the set of load nodes connected to the j-th generator set; p i is the load of the i-th node; ΔP di is the load change of the i-th load node.

[0164] This constraint ensures that the output of the generating unit does not exceed its maximum generating capacity, avoiding over-reliance on certain generating units and resulting in system overload or instability.

[0165] The load restoration process of the system is strictly restricted by the line flow to avoid system instability caused by overloading. The load restoration amount of each power line is restricted by its transmission capacity. The constraint is:

[0166] 0 ≤ ΔP di ≤ P max

[0167] ΔP di is the load change amount of the i-th node, representing the load adjustment of this node; P max is the maximum load limit of the i-th node.

[0168] This constraint ensures that during the restoration process, the load adjustment amount does not exceed the maximum capacity of the power grid, avoiding power outages or equipment damage caused by line overload.

[0169] During the load restoration process, it is necessary to prioritize the restoration of nodes that have a greater impact on system stability according to the restoration time and importance of each node. This constraint ensures that each node in the restoration process can be restored in a reasonable order, preventing the system from malfunctioning due to untimely restoration. The specific constraint is:

[0170]

[0171] where: ΔT i is the restoration time change amount of the i-th node, representing the time required for load restoration.

[0172] T max is the maximum restoration time allowed by the system.

[0173] This constraint ensures that the restoration time of each node in the system does not exceed the specified maximum restoration time, avoiding unnecessary delays or conflicts during the restoration process.

[0174] During the load restoration process, the control of voltage and phase angle is a key factor in ensuring the stability of the power grid, preventing power grid instability caused by excessive voltage angles or voltages outside the range. The voltage constraint and phase angle constraint can be expressed as follows:

[0175] Voltage constraint:

[0176] V min ≤ v i ≤ V max

[0177] where: v iis the voltage of the i-th node; V min is the minimum allowable value of the voltage of the i-th node; V max is the maximum allowable value of the voltage of the i-th node.

[0178] This constraint ensures that the voltage of each node does not exceed its maximum and minimum allowable values, avoiding equipment damage or system collapse caused by overvoltage or undervoltage conditions in the power grid.

[0179] Phase angle constraint:

[0180] θ o(i) -θ d(i) ≤Δθ max

[0181] where: θ o(i) is the initial voltage angle of the i-th node; θ d(i) is the target voltage angle of the i-th node; Δθ max represents the maximum allowable voltage angle difference.

[0182] This constraint ensures that the voltage angle difference between nodes in the power grid is not too large, preventing power grid instability or power grid collapse due to excessive phase angle differences.

[0183] The dispatching strategy of the defense side ensures the rapid recovery and stable operation of the system during the recovery process by introducing constraints on voltage, current, power generation capacity of generating units, line flow, and recovery time priority. Through these constraints, the defense side can not only minimize load losses but also control various key factors during the system recovery process, such as voltage, phase angle, generator output, etc., to ensure the stability and security of the power grid during recovery. At the same time, the phase angle and voltage constraints used during the recovery process further enhance the physical stability of the power grid, contributing to the effective recovery of the power system under multiple rounds of attacks.

[0184] S9. Optimize the module recovery time, adjust the selection of the attack target module by combining the recovery time and repair status, and ensure the stability of the module after recovery;

[0185] The core task of S9 is to reasonably select the attack target module by optimizing the module recovery time and combining the recovery status and repair cycle to ensure the stability of the module after recovery. In this process, not only the individual recovery situation of the module needs to be considered, but also based on the overall power transmission path analysis of the system, ensure that the recovered system can operate stably and avoid being affected by attacks again. The focus of this step is on how to utilize the recovery status of the module, repair time, and the power transmission dependence relationship between modules to formulate effective recovery and attack strategies for subsequent multiple rounds of attacks.

[0186] During multiple rounds of attacks, the recovery time and repair cycle of each module will directly affect the recovery speed and stability of the power system. The recovery time is usually determined by the repair time of the devices within the module, and the repair times of different devices vary. Therefore, in this step, the overall recovery time of the module is first evaluated based on the recovery times of the individual devices within the module. Modules with long recovery times are usually bottlenecks in the system recovery process, and these modules need to be recovered first; otherwise, it will affect the load recovery and power stability of the entire system.

[0187] The priority ranking and module selection of the recovery time rely on the following formula:

[0188]

[0189] Where: represents the recovery status of device i in module n at time t; M n is the set of devices included in module n; is the recovery status of device j in module n at time t; indicates that the recovery time of module n depends on the recovery status of all devices within the module, and the device with the longest recovery time is selected as the reference time for module recovery.

[0190] This formula obtains the recovery status of all devices within module n and finally arrives at the recovery status of this module, based on which the recovery strategy of the module is formulated.

[0191] During the actual recovery process, the recovery speeds of different modules will be affected by various factors, including their key roles in the power transmission path, possible reattacks during the recovery process, etc. Therefore, in order to improve the efficiency of system recovery, in this embodiment, the defender needs to dynamically adjust the selection of the attacked target modules, giving priority to those modules with longer recovery times and occupying important positions in the power transmission path. By analyzing the recovery status and repair progress of the modules in real time, the defender can select the modules with longer recovery times and greater impacts for protection in each round of attack.

[0192] When selecting modules, the following formula can be used to calculate the recovery priority of the modules:

[0193]

[0194] Where: is the recovery status of module i at time t; t x is module i at time point t x at the moment of being attacked; is the repair cycle of module i, starting from the moment of being attacked t x and after cycles the module recovery is completed; Indicates the status of module i after the end of the repair cycle. The recovery status is 1, indicating that the module has fully recovered.

[0195] This formula reflects how the defense side dynamically adjusts the selection of the attacked target module based on the repair cycle and recovery status of the module during multiple rounds of attacks, and ensures the stability of the system during the module recovery process.

[0196] The mutual influence between modules is a key factor determining the effectiveness of the recovery strategy. Some modules may have direct or indirect impacts on the recovery of other modules. For example, some modules may be key nodes on multiple power transmission paths. If these modules fail to recover in time, it will directly affect the power flow of other modules. Therefore, in this embodiment, when determining the module recovery priority, not only the recovery time of the module itself is considered, but also the status of the module in the power network and its interdependence with other modules need to be comprehensively considered.

[0197] To calculate the mutual influence between modules, the association matrix R of the defined paths and modules in S4 is used n2 , which represents the relevance of each module in each power supply path to simulate the dynamic changes of module recovery in the power transmission path.

[0198] This recovery path matrix describes the dynamic changes of the recovery paths between modules, which can help the defense side adjust the power transmission path in real time to ensure the rapid recovery of the power system.

[0199] By optimizing the dynamic adjustment of the module recovery time and repair status in S9, the defense side can timely adjust the selection of the attacked target module during multiple rounds of attacks, thereby reducing the negative impact on the system and ensuring the stability after module recovery. Combining the recovery status of the module, the repair cycle, and the dependency relationship of the power transmission path, the defense side can effectively optimize the recovery process and improve the recovery efficiency and stability of the system.

[0200] S10. Identify the key equipment of the power transmission system based on the attack results, and determine the key modules through impact analysis;

[0201] The purpose of S10 is to further identify the key equipment in the power transmission system by evaluating the attack results generated in the previous steps, and determine the key modules through fault propagation impact analysis. Through this process, the equipment and modules that have the greatest impact on the system stability when under attack can be identified. Its purpose is to ensure the identification of components that are crucial for the operation of the power system, and the failure of these components may lead to large-scale outages of the system, thereby providing a basis for subsequent defense and repair strategies.

[0202] The goal of impact analysis is to identify the most critical modules and devices based on the fault propagation and impact degree of each module. In this step, the fault propagation effect of a module is quantified by the impact degree. The larger the impact degree, the more extensive the impact of the module's failure on the system. By evaluating all modules and devices, the critical devices and modules that are crucial for the stability of the power system are finally determined.

[0203] In this embodiment, the calculation formula for the impact degree is as follows:

[0204]

[0205] Where: I n is the impact degree of module n on the entire system, reflecting the impact of the failure of module n on the system. The larger the impact degree, the more serious the fault propagation effect; is the recovery state of device i in module n on path j; f is the fault propagation coefficient of device i on path j, reflecting the impact of the device failure on path j. This formula calculates the impact degree I n of module n by calculating the recovery state and fault propagation coefficient of each device, helping the defense side identify which modules have a greater impact on the system operation.

[0206] Modules with larger impact degree values will be regarded as critical modules. Once these modules fail, it may lead to large-scale system failures.

[0207] During the implementation process, the formula for selecting critical modules is as follows:

[0208] M key ={m n |I n ≥α·max(I)};

[0209] Where: M key is the set of critical modules; m n represents module n; I n is the impact degree of module n; α is the impact degree threshold coefficient. This coefficient is used to determine which modules have a large enough impact degree to be regarded as critical modules. Usually, the value of α depends on the actual tolerance, and the value range is from 0 to 1; max(I) is the maximum value of the impact degrees of all modules, used to calculate the threshold.

[0210] Through this formula, the modules with an impact degree higher than the threshold can be screened out. These modules are regarded as critical modules and should be given priority protection or repair in the defense strategy.

[0211] The identification of critical devices not only depends on the impact degree of the modules, but also should consider the connectivity of the devices in the power network, and identify those devices that connect multiple modules and affect multiple paths.

[0212] The identification of critical devices is carried out using the following formula:

[0213] C key = {c i | f ci > β · max(f)};

[0214] Where: C key is the set of critical devices; c i is device i; f ci is the fault propagation coefficient of device c i , indicating the degree of influence of the device fault on the path or system; β is the fault propagation coefficient threshold coefficient. This coefficient is used to determine which device faults have a greater impact on the system; max(f) is the maximum value of the fault propagation coefficients of all devices.

[0215] Through the above-mentioned impact analysis and critical module identification process, the ultimate task is to comprehensively identify the critical modules and devices in the system. The faults of these modules and devices will directly affect the overall stability and load distribution of the system. Therefore, the identification process not only focuses on individual devices, but also comprehensively considers the interdependence between modules and the roles of devices in multiple paths.

[0216] S10 can determine the most vulnerable and important parts in the system through detailed impact analysis and fault propagation calculation. This analysis provides a scientific basis for subsequent defense and recovery measures, ensuring the effective protection of the critical parts of the system, thereby enhancing the recovery ability and risk resistance ability of the power system when facing attacks.

[0217] Although the embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for identifying key equipment in a power transmission system for low-granularity timing attacks, characterized in that: The following steps are involved: S1. Construct a modular topological model of the power transmission system, and divide the equipment in the power transmission system into multiple equipment modules according to geographical aggregation. The module division is based on the electrical connection relationship, geographical location, geographical aggregation characteristics and functional aggregation of the equipment; S2. Establish a fault propagation matrix, simulate the fault propagation path between modules, and analyze the impact of module failure on other modules of the system; S3, select the target area from the attacker's perspective, set the maximum load loss in the target area as the goal, and limit the maximum proportion of additional load loss outside the area; S4, based on the depth-first search algorithm, expand outward from the load nodes in the target area, gradually search all possible power supply paths, record the modules and lines involved in the path, and form an attack decision variable set; S5. Define attack decision variables and recovery state variables to represent the attack state and recovery state of each module, and calculate their impact on system fault propagation; S6. Set resource limits for each round of attack, control the number of modules for each round of attack, and ensure that the load loss outside the area does not exceed the preset threshold; S7. Optimize the selection of attack target modules based on timing analysis, calculate the cumulative impact of multiple rounds of attacks on load loss, select the module that can cause the most load loss in each round for attack through timing analysis and optimization algorithm, and adjust the attack sequence to maximize the load loss of the target area; S8. Set the defender’s scheduling strategy, simulate the load recovery process after the attack, and minimize the system’s load loss by optimizing the scheduling scheme; S9. Optimize module recovery time, adjust the selection of attack target modules based on recovery time and repair status, and ensure the stability of the module after recovery; S10. Identify key equipment of the power transmission system based on the attack results and determine key modules through impact analysis.

2. According to claim 1, a method for identifying key equipment in a power transmission system facing low-granularity timing attacks is characterized in that: The module division includes: Each module includes at least one or more of a busbar, a circuit breaker and a transformer; Divide equipment modules according to their geographical distribution and electrical functions and associate them in the system through module identifiers; The association matrix between modules and power lines is constructed to describe the connection relationship between modules and lines.

3. According to claim 1, a method for identifying key equipment in a power transmission system facing low-granularity timing attacks is characterized in that: The fault propagation matrix construction includes: Construct a fault propagation matrix between modules, where the matrix elements Indicates whether the failure of module i will directly or indirectly lead to the failure of module j; According to the fault propagation matrix, calculate the impact of each module failure on other modules in the system and determine the key equipment in the system; By analyzing the fault propagation path, vulnerable modules and possible attack impact ranges can be identified.

4. According to claim 1, a method for identifying key equipment in a power transmission system facing low-granularity timing attacks is characterized in that: The target area selection includes: Based on the attacker's analysis of the system, identify the critical areas in the system and select target areas with greater load loss; Set the maximum load loss in the target area as the attack target, and control the additional load loss outside the target area to ensure that it does not exceed the preset maximum ratio; Optimize the selection of attack areas through network analysis and determine the device modules that are attacked first.

5. According to claim 1, a method for identifying key equipment in a power transmission system facing low-granularity timing attacks is characterized in that: The path search algorithm includes: Starting from the load nodes in the target area, all power supply paths are gradually searched using the depth-first search algorithm; Record all modules and lines involved in the search path and remove paths that are not directly related to the target area; Construct an attack decision variable set and ensure that the power supply path within the attack area is effectively attacked by optimizing path selection.

6. The method for identifying key equipment in a power transmission system facing low-granularity timing attacks according to claim 1 is characterized in that: The definitions of the attack decision variables and recovery state variables include: Define attack decision variables for each module in It means that module i is attacked during the tth attack. It means that it has not been attacked; Define restore state variables for each module in represents the recovery state of module i after the tth attack, Indicates that it has not been restored; Based on the attack and recovery status of a module, its impact on other modules is calculated, and the attack decision is dynamically optimized.

7. The method for identifying key equipment of a power transmission system facing low-granularity timing attacks according to claim 1 is characterized in that: The attack resource restrictions include: Set the maximum attack resource amount A for each round of attack t , limit the number of modules in each round of attack to no more than A t ; By optimizing the attack decision variables, we can ensure the reasonable allocation of attack resources and reduce the attacks on modules outside the target area; Calculate and ensure that the load loss outside the area does not exceed the preset maximum acceptable ratio ξ t .

8. The method for identifying key equipment in a power transmission system facing low-granularity timing attacks according to claim 1 is characterized in that: The timing analysis includes: Optimize the selection of attack target modules based on module recovery time and attack sequence, giving priority to attacking modules with long recovery time and large load loss; Calculate the cumulative load loss through a multi-round attack model and adjust the attack sequence to ensure the maximum attack effect; By analyzing the impact of each round of attack, the attack plan and attack coverage can be optimized.

9. The method for identifying key equipment in a power transmission system facing low-granularity timing attacks according to claim 1, characterized in that: The defender scheduling optimization includes: The defender conducts emergency dispatch based on the state of the power transmission system after the attack to minimize load loss; By optimizing the dispatching strategy, the power supply of each node in the system is balanced to avoid excessive load shedding that may lead to system instability. Adjust the attack strategy according to the scheduling optimization results to ensure that the defense effect matches the dynamic adjustment of the attack target.

10. The method for identifying key equipment in a power transmission system facing low-granularity timing attacks according to claim 1, characterized in that: The module recovery time optimization includes: Define repair times for each module And adjust the attack decision according to the repair cycle and repair status of the device; Prioritize the restoration of modules that have a longer repair time and a greater impact on load loss to ensure stable power supply after the modules are restored; Avoid attacking the module again during the module recovery period to ensure system stability during the repair period.

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